---
title: "Forcing Technologies: Why Firms Adopt and Who Profits"
author: Ren (Electric Capital), GPT 6 Astra and Claude 5.1 Fable
date: 2026-10-20
updated: 2026-10-20
description: How competitive pressure makes technologies necessary, and why
  urgent adoption does not guarantee durable supplier profits. A model and
  investment framework, with proofs and case studies.
url: https://rencryptofish.com/posts/forcing-technologies
---

# Forcing Technologies: Why Firms Adopt and Who Profits

*Working draft, October 20, 2026.*

## The argument in one page

In June 2010, Spread Networks and Infinera announced a New York–Chicago fiber route below 13.33 milliseconds round trip. By February 2013, McKay Brothers reported 8.27 milliseconds on its Illinois–New Jersey microwave route (Infinera, [2010](https://rencryptofish.com/posts/forcing-technologies#bib.bib634); McKay Brothers, [2013](https://rencryptofish.com/posts/forcing-technologies#bib.bib108)). Traders competing to arrive first faced a choice: buy speed or lose position. Their suppliers faced the next generation of the same race. Zayo agreed to buy Spread for \$127 million in November 2017 (Zayo Group Holdings, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib635)). An urgent purchase had not guaranteed its first supplier a durable advantage.

*Technology becomes economically forcing when its spread makes the old way of operating less viable for holdouts. That pressure creates urgency; market structure determines who captures the spending, and for how long.* Rivals change prices, service expectations and access to customers. Attacks make defenses inadequate. Regulatory and private requirements supply another mechanism, with distinct enforcement risks.

The two-curve model separates the incentive to adopt from the buyer’s gain or loss and the supplier’s price ceiling. A tool can pay its first user and become necessary as rivals change the market. The paper follows that transition through competition, fulfillment costs, networks and defenses; prices, deployment and supplier profits require additional assumptions. Its test is an observable mechanism, an exposed buyer and a credible timing window: a margin crossing or deployment schedule can establish one without an announced deadline.

AI and crypto show how adoption pressure and supplier returns can differ across applications, platforms and infrastructure. NVIDIA earned \$193.7 billion of Data Center revenue in fiscal 2026; Ethereum’s 2022 Merge removed mining from its network while Bitcoin’s hardware race continued (NVIDIA Corporation, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib166); Ethereum.org Contributors, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib604)). Section [4](https://rencryptofish.com/posts/forcing-technologies#S4) compares four crypto networks and five foundation-model strategies, separating useful services, platform advantages and repeated infrastructure spending.

The investment screen asks which companies can retain revenue after adoption becomes common. A comparison of sixteen investment opportunities identifies the following priorities (Section [6](https://rencryptofish.com/posts/forcing-technologies#S6)); these are conditional diligence judgments, not completed investment decisions:

1. **AI-operated specialist services.** Own accepted work and recurring customer contracts; prove that automation reduces cash cost after review and repricing.

2. **Repeatable industrial cells.** Own an application, reliable field service and financeable equipment; deployment capital and guarantees determine the return.

3. **Flexible power access, subject to enforceable contracts.** Accepted load flexibility can change usable capacity; a scheduler must possess enforceable operating and payment rights.

4. **Cross-border payout operations, subject to access to customers and local partners.** Stablecoin rails can improve a difficult endpoint; all-in costs, local liquidity and retained fees constrain the entrant.

5. **Fraud signals and seller negotiation, as options.** These opportunities require evidence of additional fraud prevented in live use and higher seller profit after costs. Complex certificate operations remain a requirement-led benchmark.

**What would prove us wrong**

The economic thesis fails in a proposed market if holdouts retain their margins, customers and access as adoption spreads. The investment thesis fails if an equivalent substitute captures the spending, delivery costs consume the gain or financing outlasts the useful window. Public deployments show that these technologies can work. The scenarios examine the adoption, pricing and cash requirements a new supplier would face. Neither a useful technology nor an urgent purchase guarantees an attractive company.

## 1 The model

Take a fixed field of rivals: the merchants selling into a state, the trading firms on an exchange, the swimmers in a final. Let $x$ be the share of them that has adopted a technology, from none to all. Each rival is small enough that its own choice leaves $x$ where it is. Two payoffs describe its position, both measured against the world before the technology existed: $U_{A}(x)$ if it adopts and $U_{N}(x)$ if it holds out. Zero means nothing has changed. Both curves can sit below zero at once, which is what an arms race looks like from the inside. The cost of adopting, $c$, is a flow per period: the subscription, the hardware amortized, the staff who run it.

Economic forcing is the deterioration of the holdout’s position as the technology spreads: rivals take its customers, lower the price it can charge, raise the service customers expect, or leave it outside a useful network. A positive return to adoption is insufficient evidence of that mechanism. A tool can pay its first user before it changes anyone else’s circumstances, then become necessary as competitors pass its benefits through to customers. Requirements imposed by a platform, a buyer or a regulator can produce similar urgency, but their enforcement is a separate source of pressure. We first identify the mechanism and the exposed buyer, then ask what a supplier can capture.

### 1.1 Four channels

Four sources of value or pressure determine the payoff gap.

**Direct value, $\gamma$.**

The technology does something for the adopter whether or not anyone else has it. An AI assistant increased issues resolved per hour by 15% in a study of 5,172 support agents, without requiring rival firms to adopt (Brynjolfsson et al., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib29)). Net value also depends on its cost.

**Network value, $\beta x$.**

The technology is worth more as counterparties join. A bank connection is worth nothing until both the bank and the app are on it; Plaid’s product got better with every bank it added and every app that integrated it.

**Competitive edge, $\alpha$ and $r$.**

The adopter takes something from rivals that have not adopted: business, a ranking, the next trade. The prize is fixed, so one side’s gain is the other’s loss, and the edge erodes as rivals catch up. Spread Networks’ fiber gave its customers a speed advantage that competing routes could erode. The strength ratio $r$ determines how the edge changes with adoption; it does not set the speed of diffusion.

**Exclusion, $\varepsilon\Phi(x)$.**

A gatekeeper penalizes holdouts, and nobody in the field collects the penalty. After *Wayfair*, a remote seller that did not collect sales tax answered to the state rather than to a rival. The gatekeeper can as easily be a browser, a card network, a dominant customer or an insurer, and Section [2](https://rencryptofish.com/posts/forcing-technologies#S2) says what changes when it is. The pressure curve $\Phi$ rises from zero to one; $\theta$ locates its rise in adoption share and $k$ controls its steepness. A calendar deadline requires a separate time-dependent enforcement path.

Let $p$ be the shared belief that the technology works. Subtracting the holdout’s payoff from the adopter’s gives the gain from adopting,

$$
\underbrace{\Delta(x)}_{\text{adopt minus hold out}}=\underbrace{p\gamma}_{\text{direct}}+\underbrace{p\beta x}_{\text{network}}+\underbrace{\frac{p\alpha}{1+(r-1)x}}_{\text{contest}}+\underbrace{\varepsilon\Phi(x)}_{\text{exclusion}}-c.
$$

Beliefs scale the three technology channels and leave the penalty alone, which is why a company can doubt a technology and still buy it before a deadline. A rival acts when the gain exceeds the value of waiting, $W$, and once it has acted it cannot undo the decision. The four channels are the model’s accounting; the economics that fill them, rivals, counterparties, cost curves, customers and gatekeepers, are the subject of Section [2](https://rencryptofish.com/posts/forcing-technologies#S2). Appendix [A](https://rencryptofish.com/posts/forcing-technologies#A1) derives the two curves, adds an outside option, and walks through each parameter one at a time.

The field and the supplier must be named separately. An application developer choosing a chain or model, a miner replacing machines and a laboratory buying compute face different payoff comparisons (Section [4](https://rencryptofish.com/posts/forcing-technologies#S4)). Network value means that other participants or complements improve the adopter’s service. Spreading a fixed training bill over more customers is instead an economy of scale; migration and re-evaluation costs can retain customers without a network effect. Those distinctions determine what evidence can support $\beta$, and which business might charge for it.

### 1.2 Three tests and four patterns

With the technology proven ($p=1$), three numbers summarize a technology for a rival of average cost:

$\displaystyle\Delta(0)$

$\displaystyle=\gamma+\alpha-c$

Does adopting first pay?

(1)

$\displaystyle\Delta(1)$

$\displaystyle=\gamma+\beta+\alpha/r+\varepsilon-c$

Would dropping it hurt once everyone has it?

$\displaystyle y_{R}$

$\displaystyle=\gamma+\beta-c$

Is the field better off with everyone in?

The third line adds up everyone’s payoff, so the contest cancels and the penalty disappears from the total: at full adoption there are no holdouts left to pay it, although a defector would still face it. The formal taxonomy calls a technology *forced* when $\Delta(1)>0$, *competitively compelled* when $\Delta(0)\leq 0$, and *wasteful for the field* when $y_{R}<0$. These are endpoint labels, not causal findings: a useful standalone product can satisfy the full-adoption test with no harm to holdouts. Economic forcing additionally requires evidence about how the holdout’s position changes. Table [1](https://rencryptofish.com/posts/forcing-technologies#S1.T1) combines the first two tests with the third, and Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) draws one technology of each kind.

Table 1: Four endpoint patterns. The sign of $y_{R}$ gives the labels in the last two columns.

| Pattern | Adopt first / stay at full adoption | $y_{R}>0$: full adoption pays | $y_{R}\leq 0$: no net gain at full adoption |
| --- | --- | --- | --- |
| Dominant | yes / yes | productive | arms race |
| Tipping | no / yes | coordination | wasteful bandwagon |
| Selective | yes / no | selective | wasteful selective |
| Never | no / no | suppressed | inert |

![Figure 1: One technology of each kind, with its parameters above each panel. The vertical gap between the curves is the incentive to adopt; the height of each curve relative to zero is the change from the world before the technology. In the arms race, everyone adopts and everyone ends below zero. In the coordination case, nobody moves until half the field has, and then everyone gains. Under selective forcing the edge wears away and adoption stops at 42%, where adopters and holdouts are equally badly off. Under the mandate, the adopter’s curve never rises above −0.2; the penalty on holdouts does all the work, and the field as a whole ends worse off than it started.](https://rencryptofish.com/images/forcing-technologies/two_curves.png)

Figure 1: One technology of each kind, with its parameters above each panel. The vertical gap between the curves is the incentive to adopt; the height of each curve relative to zero is the change from the world before the technology. In the arms race, everyone adopts and everyone ends below zero. In the coordination case, nobody moves until half the field has, and then everyone gains. Under selective forcing the edge wears away and adoption stops at 42%, where adopters and holdouts are equally badly off. Under the mandate, the adopter’s curve never rises above $-0.2$; the penalty on holdouts does all the work, and the field as a whole ends worse off than it started.

Figure [2](https://rencryptofish.com/posts/forcing-technologies#S1.F2) places 14 historical cases on the last two tests. To the right of zero, staying adopted pays when everyone else has adopted; above zero, full adoption leaves the rival group better off than no adoption. In the fitted estimates, hybrid corn and containers have positive group payoffs across their displayed intervals. Dreadnoughts and clap skates sit in the lower-right area: *privately worth keeping, collectively costly*. Frequent-flyer programs and LZR suits lie near the welfare boundary, where the intervals matter more than the point estimates. These are comparisons at full adoption, including cases whose observed adoption remains partial; their interpretation depends on the model and its priors.

The welfare columns and historical map are the buyers’ accounting; nothing in them says what a company earns.

![Figure 2: Historical cases on the adoption-pressure and welfare map. Dots pair posterior medians of Δ⁢(1) and yR; bars show separate 5th–95th percentile intervals, not joint regions. Estimates are conditional on priors and observation assumptions, use units normalized within each case, and exclude outside options, counters and wider spillovers. They describe full-adoption incentives and rival-group payoffs, not causal holdout losses or dollar comparisons across industries. Data and estimation: Appendices J and K.](https://rencryptofish.com/images/forcing-technologies/calibration_scatter.png)

Figure 2: Historical cases on the adoption-pressure and welfare map. Dots pair posterior medians of $\Delta(1)$ and $y_{R}$; bars show separate 5th–95th percentile intervals, not joint regions. Estimates are conditional on priors and observation assumptions, use units normalized within each case, and exclude outside options, counters and wider spillovers. They describe full-adoption incentives and rival-group payoffs, not causal holdout losses or dollar comparisons across industries. Data and estimation: Appendices [J](https://rencryptofish.com/posts/forcing-technologies#A10) and [K](https://rencryptofish.com/posts/forcing-technologies#A11).

### 1.3 Productivity can change the market around the buyer

The fixed-prize contest is one source of that deterioration, not a general model of price competition. Suppose automation saves a firm $\gamma$ per period and competitors pass some of those savings through in lower market prices. Let $h(x)$ be the resulting revenue loss at a fixed output, common to adopters and holdouts, with $h(0)=0$. Their changes from the old operating profit are

$$
U_{A}^{\mathrm{prod}}(x)=\gamma-c-h(x),\qquad U_{N}^{\mathrm{prod}}(x)=-h(x).
$$

The switching gain remains $\gamma-c$, yet the holdout’s operating profit, its original profit less $h(x)$, can cross zero. Adoption was profitable at the start and can become necessary to keep operating later. That crossing supplies a timing window even when no rule supplies a date; installation time must be subtracted from the window.

This common downward shift is an explicit extension to the base model’s payoff levels. It leaves the direct-value adoption gap unchanged but changes producer welfare and viability: at full adoption the field’s change is $\gamma-c-h(1)$, and consumers receive the price reduction. It is not a zero-sum transfer among the firms, and the base model’s outside-option and welfare results cannot simply be applied to it. The case in Section [7.2](https://rencryptofish.com/posts/forcing-technologies#S7.SS2) works through the extension with stated assumptions. In a network, likewise, a rising adoption gain alone establishes attraction; an exclusion or lost-demand mechanism must be observed before claiming that holdouts are being harmed.

### 1.4 The price ceiling moves with adoption

A buyer facing exposed rivals will pay at most its gross benefit from adopting,

$$
B(x,p)=p\left[\gamma+\beta x+\frac{\alpha}{1+(r-1)x}\right]+\varepsilon\Phi(x),
$$

(2)

less its own implementation cost $\kappa$ and the value of waiting $W$. The company’s price $q$ has to fit inside $B-\kappa-W$, and the slope of $B$ in $x$ says what happens to that room as the market fills:

$$
\frac{\partial B}{\partial x}=p\left[\beta-\frac{\alpha(r-1)}{(1+(r-1)x)^{2}}\right]+\varepsilon\Phi^{\prime}(x).
$$

Under a contest the ceiling falls: the tenth buyer of a speed advantage gets less of it than the first, and the company either cuts price or ships the next generation. Under network value and exclusion the ceiling rises: holdouts face a larger exclusion penalty, and new participants gain access to more counterparties. Under direct value alone the incremental ceiling is flat. Price competition can still make the purchase urgent while reducing the buyer’s ability to pay; the productivity case therefore checks continued operation and competing suppliers as well as the incremental ceiling. The 14 historical fits in Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) show both slopes: the fitted budget for a dreadnought falls from about $1.9$ to $1.0$ as navies catch up, and the budget for a container berth rises from $0.5$ to $1.0$ as ports join.

### 1.5 Two exits that bound the pressure

Holdouts have two ways out, and each caps what a company can charge. One is to leave the contested segment: ally, specialize, or exit, for a payoff $Q\leq 0$. Once holdouts take the outside option, adopters lose their competitive edge. The adoption gain falls by the same amount and can stop further adoption, under the shakeout conditions of Proposition [3](https://rencryptofish.com/posts/forcing-technologies#Thmproposition3). The other is a counter, a defense that shields a share $\varphi$ of a holdout’s stake at cost $c_{K}$. In this model, demand for a counter develops as the technology it defends against spreads (Appendix [F](https://rencryptofish.com/posts/forcing-technologies#A6)). The two exits disarm different things. An exit can end pressure from a contest or a gatekeeper; a counter can end pressure from a contest only. Neither disarms a technology whose direct and network gains alone cover its cost (Corollaries [1](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary1) and [4](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary4)). For a company, an exit is a lost customer and a counter may be a second product line.

### 1.6 What each channel means for a company

Table [2](https://rencryptofish.com/posts/forcing-technologies#S1.T2) sets the five channels side by side as company business models.

Table 2: Supplier business models associated with each channel. “Ceiling” is the buyer’s maximum price $B-\kappa-W$ as adoption spreads.

| Channel | Who pays | Why now | Ceiling as $x$ rises | Durability | Main commercial risk |
| --- | --- | --- | --- | --- | --- |
| Direct value $\gamma$ | The adopter, from its own P&L | ROI first; a margin or service threshold can later make delay costly | Incremental ceiling flat; viability and substitutes can cap it | While savings persist and the company retains a cost or workflow advantage | The incumbent bundles; competitors pass the saving to customers |
| Network $\beta x$ | Adopters, once counterparties are on | After a threshold, if standalone value is insufficient | Rises; supplier capture depends on control of access | Strong where the operator retains the network | The standard opens; a gatekeeper reprices access |
| Contest $\alpha,r$ | Exposed rivals whose gains cover costs | Early buyers have the largest edge | Falls as the edge erodes, unless the company sells the next generation | Through re-buys, while the race runs | A ban; a counter; the venue sells the race itself |
| Exclusion $\varepsilon\Phi$ | Holdouts, on the gatekeeper’s clock | Expected enforcement; often a deadline | Rises with expected penalty; need not fall after compliance | Recurring service or a temporary migration wave | Installed demand saturates; the capability is bundled; enforcement changes |
| Counter $\varphi,c_{K}$ | The exposed side of someone else’s race | Only once the attack has spread | Rises with the attack | While the attack keeps evolving | The platform defends natively; the attack is banned |

For investment, the rows answer two separate questions: what makes waiting costly for the buyer, and what lets a company retain part of the resulting budget? A contest can renew the purchase with each generation; productivity gains can make the old cost structure unviable; a network can make disconnection costly; a mandate can announce an enforcement date. None guarantees supplier profit. The next section traces these pressures before the paper applies a narrower screen for a new company’s entry, capture and timing.

## 2 Where the pressure comes from

The question is what happens to a firm that keeps operating as before while others adopt. It may lose customers to a faster rival, face lower market prices, fall short of a service expectation, or lose access to counterparties. Those are economic mechanisms. A procurement requirement, platform policy or statute can also make holding out costly, through an imposed condition rather than the market response alone. Both kinds can operate together: fraud creates a loss, for example, while a liability rule changes who bears it. The examples below establish mechanisms, not their frequency across the economy. For each, an investor needs evidence of the buyer’s exposure and a timing window, followed by a separate account of how a supplier can retain the budget.

### 2.1 Rivals force each other when the prize is fixed

The simplest forcing has no gatekeeper in it. When customers, rankings or fills are allocated by relative position, a technology that improves position is worth having only because rivals lack it, and a rival that lacks it loses ground whether or not it ever buys. Hirsch called the goods positional; Lazear and Rosen showed that when pay depends on rank, the effort each contestant puts in is set by the spread between the prizes rather than by what the effort produces; Frank and Cook described the markets in which small differences in position carry most of the reward, and why the spending they induce is wasted from the group’s point of view (Hirsch, [1976](https://rencryptofish.com/posts/forcing-technologies#bib.bib9); Lazear and Rosen, [1981](https://rencryptofish.com/posts/forcing-technologies#bib.bib420); Frank and Cook, [1995](https://rencryptofish.com/posts/forcing-technologies#bib.bib429)). In the model this is the contest term, $\alpha/(1+(r-1)x)$: a lone adopter takes ground from every holdout, each later adopter has less ground to take, and a holdout’s loss, $\alpha x/(1+(r-1)x)$, grows with every rival that moves. Adoption here is a strategic substitute in the sense of Bulow, Geanakoplos and Klemperer: rivals’ adoption lowers the gain from adopting while raising the cost of abstaining (Bulow et al., [1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib4)). Two things follow. There is no tipping point, so adoption can begin without a critical mass of users; and a static equilibrium can lie well short of everyone, with the holdouts worse off than before the race began. Irreversible adoption can overshoot that equilibrium; the simulated field in Case 1, Section [7.1](https://rencryptofish.com/posts/forcing-technologies#S7.SS1), reaches 72% at month 48. The field as a whole ends poorer whenever the direct value is below the cost: the arms race of Table [1](https://rencryptofish.com/posts/forcing-technologies#S1.T1), and the Red Queen of Barnett and Hansen, in which rivals’ improvements offset one another while their costs remain (Barnett and Hansen, [1996](https://rencryptofish.com/posts/forcing-technologies#bib.bib25)).

Markets with this structure are easy to list, because a venue ranks, matches or fills. Trading (Spread Networks), search and AI answers (Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px4)), applicant screening and programmatic advertising all allocate by position. Retail media shows how the venue can profit from competition for placement. A retailer’s shelf, search box and app are positional: placement can move business between brands, giving exposed brands a reason to buy while the gain covers their costs. Retailers have turned that competition into a product line. Amazon’s advertising revenue went from \$37.7 billion in 2022 to \$56.2 billion in 2024 and about \$68.6 billion in 2025; Walmart’s grew 46% to nearly \$6.4 billion in its fiscal 2026; Instacart’s reached \$1.07 billion, and it sells the capability on to more than 310 other grocers (Amazon.com, Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib438), [2026d](https://rencryptofish.com/posts/forcing-technologies#bib.bib440); Marketing Dive, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib439); Walmart Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib475); Maplebear Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib457)). More than 200 retailers ran a network by the end of 2024, up from 150 a year earlier, because, as one company put it, “pretty much every retailer feels like they need to be doing this” (Mewborn et al., [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib445); Modern Retail, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib462)), and 36% of the consumer-goods companies surveyed in late 2023 were buying from ten or more networks, against 6% in 2022 (Path to Purchase Institute, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib463)). The software intermediary grew more slowly: Criteo’s retail-media revenue rose 2% in 2025 and fell 17% in the fourth quarter, which the company attributed partly to scope changes at two clients (Criteo S.A., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib451)). The contrast illustrates different revenue paths; it does not measure how much profit each layer captured. Exposed rivals buy while the competitive edge covers their costs. Early adopters value it most, and new generations can sustain demand. Venues can also sell the advantage directly, as exchanges do with colocation and search engines with advertising. Regulation can end this demand. A contest that imposes costs on the field may attract a ban (Section [3.1](https://rencryptofish.com/posts/forcing-technologies#S3.SS1)).

### 2.2 Network adoption can accelerate without an announced deadline

The opposite structure is the strategic complement: a rival’s adoption raises your gain from adopting. Katz and Shapiro and Farrell and Saloner worked out what follows when a technology is worth more the more others use it: an installed base nobody wants to be first to leave, inertia below a threshold and a bandwagon above it, and a winner chosen by expectations as much as by quality (Katz and Shapiro, [1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib6), [1986](https://rencryptofish.com/posts/forcing-technologies#bib.bib430); Farrell and Saloner, [1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib7), [1986](https://rencryptofish.com/posts/forcing-technologies#bib.bib431); Arthur, [1989](https://rencryptofish.com/posts/forcing-technologies#bib.bib8)). Under their strategic-complementarity conditions, Milgrom and Roberts established largest and smallest equilibria that bound adaptive play; convergence to one of those extremes is not a general result (Milgrom and Roberts, [1990](https://rencryptofish.com/posts/forcing-technologies#bib.bib427)). In the model this is $\beta x$. With identical costs, known effectiveness and no waiting value, a network-led tipping point occurs where $\Delta(x_{T})=0$ crosses from negative to positive. Below it no unassisted actor adopts; above it the gain from connecting grows. A falling holdout payoff additionally requires that unconnected firms lose access or business; the network term alone does not establish that loss. Someone has to pay for the crossing, because the pioneers adopt at a loss. Sometimes a regulator pays with a mandate. A large actor can instead fund the crossing: by subsidizing one side, which is Rochet and Tirole’s platform, pricing the two sides so as to internalize the externality between them (Rochet and Tirole, [2003](https://rencryptofish.com/posts/forcing-technologies#bib.bib421)); by switching the default on for an installed base it already owns, as Stripe and Shopify did with stablecoin acceptance (Section [4](https://rencryptofish.com/posts/forcing-technologies#S4)); or by being large enough that its own adoption is the tip. Switching costs then hold the field where it tipped (Klemperer, [1987](https://rencryptofish.com/posts/forcing-technologies#bib.bib426); Farrell and Klemperer, [2007](https://rencryptofish.com/posts/forcing-technologies#bib.bib433)).

When the participants are competitors, these incentives can support coordinated pricing. The Justice Department’s complaint against RealPage, filed on August 23, 2024, alleges that rivals encouraged one another to use a tool: the software set prices for about three million apartments on data from sixteen million, with about 80% of its market, and the complaint alleges that landlords “know that others are using the same software,” asked whether competitors nearby were already on it before licensing it themselves, and said they would rather their competitors used it too, since widespread use would benefit them all (U.S. Department of Justice, Antitrust Division, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib464); U.S. Department of Justice, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib465)). Those allegations describe a possible complementarity among landlords, with renters bearing the cost; they do not establish a measured $\beta$ or a causal adoption path. Thoma Bravo paid \$10.2 billion for RealPage in April 2021 (RealPage, Inc., [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib472)). The Justice Department’s proposed settlement of November 24, 2025 would restrict competitors’ nonpublic data in pricing, require changes to price-alignment features and impose a monitor (U.S. Department of Justice, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib684)). It was proposed without a trial or admission of wrongdoing. This is evidence of legal risk to a coordination mechanism, not evidence that RealPage retained its customers or lost all the reasons they bought.

Section [3.3](https://rencryptofish.com/posts/forcing-technologies#S3.SS3) examines the commercial consequence: ownership of access can matter more than having funded the network’s growth. Shapiro and Varian’s advice to give the technology away until the field tips and charge for the lock-in afterwards works only if the pioneer owns the lock-in (Shapiro and Varian, [1999](https://rencryptofish.com/posts/forcing-technologies#bib.bib422)). Plaid built the connection layer but remained dependent on banks for data access; Sea-Land pioneered containerization without owning the resulting standard. The investor should ask whether the startup will control an asset that remains valuable after the network has formed.

### 2.3 A falling cost curve can make the old cost structure unviable

Wright found in 1936 that the labor cost of an airframe fell by a fixed fraction with every doubling of cumulative output, and Arrow built the economics of learning by doing on the same regularity (Wright, [1936](https://rencryptofish.com/posts/forcing-technologies#bib.bib423); Arrow, [1962](https://rencryptofish.com/posts/forcing-technologies#bib.bib424)). A learning curve can make adoption profitable for a class of buyers in a similar period. Griliches showed that the timing and spread of hybrid corn tracked its profitability in different regions (Griliches, [1957](https://rencryptofish.com/posts/forcing-technologies#bib.bib14)). That first crossing establishes an adoption incentive. Economic forcing requires the next step: lower costs change the prices or service levels rivals can sustain, and the firms that keep the old process lose margin or demand.

The two steps need separate measurements. A pilot can establish a saving; price quotes, contract renewals, conversion rates and holdout margins show whether the saving is changing competition. Amazon’s description of its next-generation fulfillment center makes the proposed connection explicit: it targeted a 25% improvement in cost to serve during peak seasons and identified savings it could pass to customers (Amazon, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib636)). That is a company target, not a measured industry effect. The fulfillment case in Section [7.2](https://rencryptofish.com/posts/forcing-technologies#S7.SS2) assumes a pass-through path and shows exactly when it would exhaust a holdout’s margin, and how lower pass-through would remove that crossing. Its point is that useful automation and competitive pressure can coexist; neither a saving nor a deployment count establishes the second on its own. Published price and adoption data show how quickly these economics can change. BloombergNEF’s survey put the average lithium-ion pack at \$115 a kilowatt-hour in 2024, down 20% in a year, and at \$108 in 2025, with packs for battery-electric cars below \$100 and Chinese packs at \$84 (BloombergNEF, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib448), [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib447)); new-energy vehicles were 47.9% of China’s vehicle sales in 2025, 16.5 million of them (CnEVPost, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib449)). IRENA put the global levelized generation cost of utility-scale solar at 4.3 cents a kilowatt-hour in 2024, about 90% below 2010, against 7.3 cents for coal and 8.5 for gas, and 91% of the renewable capacity commissioned that year was cheaper than the cheapest new fossil plant (International Renewable Energy Agency (IRENA), [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib458)); renewables were 85.6% of the generating capacity the world added in 2025 (TaiyangNews, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib459)). A 60-watt-equivalent LED bulb that cost more than \$50 in 2007 cost \$5.90 in 2017, and LEDs went from 8% of installed US lighting in 2015 to about 48% in 2020 (U.S. Department of Energy, Solid-State Lighting Program, [2020](https://rencryptofish.com/posts/forcing-technologies#bib.bib453); inside.lighting, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib460)). These price and adoption series establish changing economics; they do not by themselves identify damage to comparable holdouts. The question for companies is who owns the curve and how much of its saving customers and competing suppliers take. Sutton’s argument about endogenous sunk costs supplies one route to concentration when maintaining quality requires continuing fixed investment (Sutton, [1991](https://rencryptofish.com/posts/forcing-technologies#bib.bib419)). When many producers drive a commodity’s curve together, margins can instead migrate to installation, finance and integration. In either case, an urgent purchase can coexist with a flat or falling supplier price ceiling.

### 2.4 Expectations ratchet to what most rivals offer

A fourth source of pressure is the customer. Kano separated features that delight when present from features that are expected and punish when absent, and features move from the first group to the second as rivals supply them (Kano et al., [1984](https://rencryptofish.com/posts/forcing-technologies#bib.bib26)); Kahneman and Tversky’s reference dependence is the mechanism, since customers judge an offer against the reference the market has set and weigh losses against it more than gains (Kahneman and Tversky, [1979](https://rencryptofish.com/posts/forcing-technologies#bib.bib432)). Appendix [H.3](https://rencryptofish.com/posts/forcing-technologies#A8.SS3) adds an expectation that follows adoption upward and can persist if adoption recedes. Business transferred to rivals belongs in the contest channel; demand lost to the whole field requires a separate loss term. Neither is established by the base network term alone. If matching the expectation adds cost without enough producer surplus, full adoption can leave firms worse off even though dropping the feature hurts. A wasteful bandwagon additionally requires that adopting alone did not pay; an initially profitable feature can instead produce the arms-race pattern. Customers may gain in either case. Delivery speed is the running example. Amazon reported more than 13 billion Prime items delivered the same or next day worldwide in 2025; its US volume grew 30% from 2024 (Amazon.com, Inc., [2026c](https://rencryptofish.com/posts/forcing-technologies#bib.bib441)); Walmart’s chief executive promised in April 2025 to reach 95% of the US population in under three hours by the end of the year, and its February 2026 results reported sales through its expedited delivery channels up more than 50% (TheStreet, via AOL, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib477); Walmart Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib475)); Target extended next-day delivery from 20% to 54% of the population in September 2025, an effort, in the wire report’s words, to “narrow gap with rivals” (D’Innocenzio, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib471)). The surveys discussed in Section [3.2](https://rencryptofish.com/posts/forcing-technologies#S3.SS2) support the role of delivery expectations, although they do not identify the causal loss suffered by slower retailers. Another rapid response took three months. Lyft let its drivers cash out daily in December 2015; Uber announced the same in March 2016, “a little behind the times” in Fortune’s words, and had paid out \$1.3 billion that way within a year (Reisinger, [2016](https://rencryptofish.com/posts/forcing-technologies#bib.bib473); Yeung, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib474)). For companies, the consequences are timing and price. A discretionary budget can become difficult to defer when the feature becomes expected, often after platforms have begun to bundle it. The relevant window is the interval before lost conversion, retention or renewals exhausts the buyer’s tolerance; a calendar announcement is unnecessary. An adoption wave can also reflect an informational cascade. Bikhchandani, Hirshleifer and Welch showed that rational actors who watch each other’s choices can adopt in a wave that carries no information about payoffs, and such waves end as abruptly as they start (Bikhchandani et al., [1992](https://rencryptofish.com/posts/forcing-technologies#bib.bib425)); evidence for an economic ratchet requires holdout losses attributable to the changed expectation, which is the row of Table [10](https://rencryptofish.com/posts/forcing-technologies#S5.T10) on holdouts losing share.

### 2.5 Gatekeepers are not only regulators

Private requirements remain requirements: changing the identity of the gatekeeper does not establish competitive forcing. Their distinct evidence is enforcement and the gatekeeper’s incentive to continue it, rather than a measured market-price or demand response.

Exclusion, $\varepsilon\Phi(x)$, is a penalty on holdouts that no rival collects, and nothing in the term says the penalty comes from the state. A browser (Chrome 68), a card network (the EMV liability shift), a dominant customer (Walmart’s supplier mandates), a platform (Apple’s tracking prompt), an insurer (controls required at renewal), a standards body (the CA/Browser Forum’s certificate lifetimes) and the customers who send security questionnaires (SOC 2) each set a penalty, a date and a steepness, and more than half the mandates in Section [3](https://rencryptofish.com/posts/forcing-technologies#S3) are of this kind. Walmart’s two tag mandates provide a useful comparison. On June 11, 2003 it told its 100 largest suppliers to put radio tags on every pallet and case by January 1, 2005, with the rest to follow by 2006; a tag cost 40 cents to a dollar, the supplier paid for it, and the expected savings, which Bernstein put at \$8.4 billion a year, would accrue to Walmart (Violino, [2003](https://rencryptofish.com/posts/forcing-technologies#bib.bib467); Roberti, [2003](https://rencryptofish.com/posts/forcing-technologies#bib.bib454)). The January 2006 deadline passed with few suppliers compliant, the program was “fizzling” by 2007, and the penalty Walmart eventually set, \$2 a pallet at Sam’s Club from February 2008, was cut to 12 cents within a year (Supply Chain Digest, [2009](https://rencryptofish.com/posts/forcing-technologies#bib.bib470)). The January 2022 expansion of the item-level program, already used for apparel, required tags on additional home, electronics and toy categories arriving in stores by September 2, 2022, and on nine more categories by February 1, 2024; by then a tag cost three to five cents, and the inventory accuracy it bought, from about 60% to 99% by SKU in Auburn University’s measurements, was the supplier’s gain as well as Walmart’s (Swedberg, [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib476); CYBRA Corporation, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib452); R.R. Donnelley & Sons, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib469)). The later mandate coincided with substantial growth for tag suppliers. The industry shipped 52.9 billion tag chips in 2024, 77% of them for apparel; Impinj’s revenue went from \$190 million in 2021 to \$366 million in 2024; Avery Dennison’s label business reached about \$850 million growing 18% a year, and the two companies announced a fresh-food expansion in October 2025 (Taylor, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib434); Impinj, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib456); edgar.tools, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib455); Avery Dennison Corporation, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib444); Hickey, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib468)). Apple’s prompt is the platform version. From April 26, 2021 every iOS app had to ask permission to track; Meta told investors the change would cost it about \$10 billion in 2022, and AppLovin had agreed to pay about \$1 billion for Adjust, a measurement company, in the February before the rule took effect (9to5Mac, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib443); Meta Platforms, Inc., [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib461); AppLovin Corporation, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib442)). The gatekeeper paid nothing, its rivals paid a great deal, and fines of €150 million in France and €98.6 million in Italy have since been levied without the rule changing (Autorité de la concurrence, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib435); PPC Land, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib437)). A private gatekeeper’s incentive to enforce matters for timing. Its own gain from compliance can strengthen the credibility of a penalty, although implementation costs, contracts and legal constraints also matter. The 2003 mandate asked suppliers to pay for a benefit that was Walmart’s, and Walmart did not enforce it; the 2022 mandate came with cheap tags, a measured gain on both sides and enforcement. The signal to read is the gatekeeper’s own gain from compliance, and the risk to price is the one the platform row of Table [11](https://rencryptofish.com/posts/forcing-technologies#S5.T11) names: a gatekeeper that supplies the capability itself can displace vendors unless they offer additional value.

### 2.6 Who keeps the budget: appropriability

Teece’s theory of appropriability explains why the innovator may not capture the returns. An innovator profits when imitation is hard, or when it owns the complementary assets the innovation needs to reach the customer: distribution, the workflow, the installed base, the venue (Teece, [1986](https://rencryptofish.com/posts/forcing-technologies#bib.bib418)). When a specified capability is easy to imitate or supplied through an open standard, the complementary asset may retain more value: the accounting suite above the free exchange (TeamSystem), the operating system above the age check, the rails above the stablecoin, the exchange above the fiber, the bank above the data connection. Sutton identifies a further route to concentration: continuing fixed investment in quality can prevent a growing market from fragmenting among small suppliers (Sutton, [1991](https://rencryptofish.com/posts/forcing-technologies#bib.bib419)). That mechanism is consistent with some consolidation in defense and certificate operations, but does not establish its cause. The opportunities in Section [6](https://rencryptofish.com/posts/forcing-technologies#S6) therefore require either a capability that remains difficult to copy or complementary assets the entrant can retain: customer contracts, distribution, data, field service or financing capacity. Without either advantage, a startup risks selling a capability that competitors or platforms will provide at no additional charge.

Table 3: Six sources of pressure. Each requires its own evidence about exposure, timing and capture; the productivity row uses the explicit extension in Section [1.3](https://rencryptofish.com/posts/forcing-technologies#S1.SS3).

| Source | In the model | Timing evidence | Possible capture | Running examples |
| --- | --- | --- | --- | --- |
| Rivals, over a fixed prize | $\alpha/(1+(r-1)x)$; holdouts’ loss grows with $x$ | The first rival’s move; renewed by each generation; ended by a ban | The venue that hosts the race; the company selling the next increment | Spread Networks and the exchanges; LZR; AI answers |
| Counterparties, through a network | $\beta x$; a threshold if early gains do not cover costs | Whoever crosses the tipping point: a subsidized side, a switched default, a large joiner | The operator that retains control of access | Plaid; containers; stablecoin rails; rent-setting software |
| A cost curve and price response | $\gamma-c$ pays; common loss $h(x)$ erodes operating profit | Saving, observed pass-through and the holdout’s margin crossing, less installation time | The curve’s owner, complementary suppliers or customers through lower prices | Fulfillment automation; hybrid corn; batteries; solar; LEDs |
| Customers’ expectations | History-dependent expectations; transfers and lost demand must be separated | The share of rivals already offering the feature | The platform that bundles it for many sellers at once | Free and same-day delivery; pay-later at checkout; mobile deposit |
| A private gatekeeper (platform, dominant customer, card network, insurer, standards body) | $\varepsilon\Phi(x)$; credibility depends on enforcement incentives | The policy’s date, credible when compliance pays the gatekeeper | The gatekeeper, if it can supply the capability; otherwise the companies it tolerates | Chrome 68 and Let’s Encrypt; EMV and Verifone; SOC 2 and Vanta; Walmart’s tags; Apple’s prompt |
| A regulator or court | $\varepsilon\Phi(x)$ is a proxy; a calendar rule needs time-dependent enforcement | The final text and enforcement; distinguish migration from recurring work | Required service providers; bundles can limit commodity fees | *Wayfair* and Avalara; SdI and TeamSystem; age assurance and the OS age signals |

## 3 Economic pressure and the company’s business

The cases begin with rivals competing over position, then follow productive tools into changing customer expectations, networks and defenses. They ask what happens to the holdout and who retains the spending. Private requirements and public mandates supply comparisons with a more explicit enforcement mechanism. None of these channels establishes an attractive entry point for a new supplier on its own. Table [4](https://rencryptofish.com/posts/forcing-technologies#S3.T4), at the end of the section, records the company outcomes.

### 3.1 Arms races create repeated demand for an edge

In a pure positional contest, rivals spend to protect a relative advantage that disappears from the field’s total payoff. Purchases can recur with each generation, but supplier profit depends on who controls the next improvement and whether buyers can exit or defend. Bitcoin mining and frontier AI combine this pressure with security or productive demand; Section [4](https://rencryptofish.com/posts/forcing-technologies#S4) separates those channels. A positional supplier faces four hazards: the edge erodes with $x$, the company selling the edge is itself in a race, the venue that hosts the contest can sell the race directly, and a regulator can end it.

Spread Networks lit a private fiber route from Chicago to the New Jersey data centers in June 2010, 825 miles at a round trip of 13.33 milliseconds, at a cost Forbes estimated at \$300 million (Matsumoto, [2010](https://rencryptofish.com/posts/forcing-technologies#bib.bib106); Steiner, [2010](https://rencryptofish.com/posts/forcing-technologies#bib.bib107)). Trading firms paid because three milliseconds was the difference between the fill and the miss; the edge was pure $\alpha$. McKay Brothers reported 8.27 milliseconds on its microwave route in February 2013 (McKay Brothers, [2013](https://rencryptofish.com/posts/forcing-technologies#bib.bib108)); when Zayo agreed to buy Spread in November 2017 for \$127 million fewer than a quarter of its 432 fibers were lit (Zayo Group Holdings, Inc., [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib76); Hardy, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib109)). Those disclosures do not establish customer migration or Spread’s lifetime return. They show competing generations of speed alongside a different position in the market: exchanges sell colocation and proprietary data to both sides of the race, revenue that Budish, Lee and Shim put at \$675 to 790 million in 2015 and projected at \$1.3 to 1.5 billion for 2022 (Budish et al., [2019](https://rencryptofish.com/posts/forcing-technologies#bib.bib110)); ICE’s exchange data and connectivity line alone was \$1.03 billion in 2025 (Intercontinental Exchange, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib111)). IEX’s speed bump, approved by the SEC in June 2016, is the counter to this race, and it illustrates the limit of counters: it protected IEX’s own customers and left the race running everywhere else (U.S. Securities and Exchange Commission, [2016](https://rencryptofish.com/posts/forcing-technologies#bib.bib112)).

The LZR Racer shows how a regulator ends one. Speedo launched the suit in February 2008 at \$550; swimmers wearing it set 62 world records by the Beijing Games, and 108 fell in 2008 (Sports Illustrated, [2008](https://rencryptofish.com/posts/forcing-technologies#bib.bib113); Associated Press, [2009](https://rencryptofish.com/posts/forcing-technologies#bib.bib114)). Arena’s polyurethane X-Glide beat it at the 2009 world championships, and on July 31, 2009 FINA’s Bureau confirmed January 1, 2010 as the date for the new textile-only requirements (FINA, [2009](https://rencryptofish.com/posts/forcing-technologies#bib.bib64)). Speedo’s parent, Pentland, is private, so the company’s revenue through the episode is not public; TYR’s antitrust suit against Speedo was dismissed in 2010, and the non-textile category ended by rule less than two years after the launch (Katten Muchin Rosenman LLP, [2010](https://rencryptofish.com/posts/forcing-technologies#bib.bib115)). An investment in this market depends on the supplier’s ability to keep improving, its relationship with the venue and the risk of a ban.

Some suppliers sustain revenue by combining a competitive advantage with services that are costly to replace. The Bloomberg terminal reached the market in December 1982 with twenty units at Merrill Lynch (McCracken, [2015](https://rencryptofish.com/posts/forcing-technologies#bib.bib527)); its combination of data, tools and communication has sustained paid demand for more than forty years. Subscribers passed 325,000 in 2015 and Bloomberg now says more than 350,000 (McCracken, [2015](https://rencryptofish.com/posts/forcing-technologies#bib.bib527); BlueGamma, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib528)); Burton-Taylor put Bloomberg’s share of a \$27.5 billion market-data industry at 33% in 2016, and the industry’s revenue at a record \$49.2 billion in 2025 (Burton-Taylor International Consulting, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib529), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib530)); and the reported single-terminal price rose to \$31,980 a year from January 2025 (NeuGroup, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib531)), with the customers saying in 2000 what they say now: “We are upset about the increase, but what can we do about it?” (WatersTechnology, [2000](https://rencryptofish.com/posts/forcing-technologies#bib.bib532)). The terminal’s communication network and embedded workflows help explain its persistence: a departing desk must replace more than a faster data feed. That is a capture mechanism to test, not proof that customers cannot switch. Semrush kept the search-placement race for seventeen years. Its revenue grew from \$92 million in 2019 to \$444 million in 2025 and Adobe paid \$1.9 billion for it in April 2026, four times ARR (SEMrush Holdings, Inc., [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib533); Semrush Holdings, Inc., [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib534); Adobe Inc. and Semrush Holdings, Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib535); Adobe, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib229)); net revenue retention had fallen from 120% to 104% over the same years, indicating slower expansion within the customer base without identifying its cause, and the race itself was moving to AI answers, the opportunity discussed in Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px4). The Trade Desk kept the programmatic bidding race for a decade, with customer retention above 95% every year and \$2.9 billion of revenue on \$13.4 billion of spend in 2025, in a market where programmatic is now more than 90% of US display advertising (The Trade Desk, Inc., [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib536), [b](https://rencryptofish.com/posts/forcing-technologies#bib.bib537); eMarketer, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib538)), while competing with venues that also sell buying tools: its filing names Google and Amazon among its competitors. Revenue growth fell from 26% in 2024 to 3% in the second quarter of 2026, and the shares are down about 80% from their August 2025 level (The Trade Desk, Inc., [2026c](https://rencryptofish.com/posts/forcing-technologies#bib.bib539); 24/7 Wall St., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib540)). Those outcomes do not isolate the effect of venue competition. Retail media, in Section [2.1](https://rencryptofish.com/posts/forcing-technologies#S2.SS1), provides another example of venues selling placement directly.

The dreadnought race, whose falling ceiling Section [1](https://rencryptofish.com/posts/forcing-technologies#S1) uses, brought orders to the shipyards without insulating them from the later contraction. Britain’s annual naval expenditure rose from £31.5 million to £50 million, and the yards sold the race abroad as well: Armstrong Whitworth sold the dreadnought it was building for Brazil to the Ottoman navy for £2.75 million in December 1913 (Cartwright, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib541); Wikipedia contributors, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib542)). After the Armistice Vickers reported losses of more than £1.25 million, Armstrong lost £626,000 in the first eleven months of 1926, and the two merged their armaments businesses in 1927 (Wikipedia contributors, [2026c](https://rencryptofish.com/posts/forcing-technologies#bib.bib543); Grace’s Guide to British Industrial History, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib544)). Major League Baseball centralized the purchase of tracking systems for all thirty clubs (TrackMan’s radar in 2015 and Hawk-Eye’s cameras in 2020) and distributes the data to every club, so the sensor companies sold one contract each and the edge moved to the analysts (Major League Baseball, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib545); Ballpark Digest, [2020](https://rencryptofish.com/posts/forcing-technologies#bib.bib546)). What separates Bloomberg from Spread Networks is what the company owns besides the edge: the network, the workflow, or an exit to an incumbent before the venue moves.

### 3.2 A productive tool can become necessary as the market changes

When standalone value exceeds adoption cost and the value of waiting, the gain from adopting is already positive at $x=0$. With direct value alone, that gain stays positive: the dominant pattern of Table [1](https://rencryptofish.com/posts/forcing-technologies#S1.T1). Diffusion then depends on budgets, information and installation capacity rather than a tipping point. Customer-support AI illustrates the direct benefit. In the staggered-rollout field study cited in Section [1](https://rencryptofish.com/posts/forcing-technologies#S1), 5,172 agents at one software firm resolved 15% more issues per hour with an assistant, the least experienced gaining most (Brynjolfsson et al., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib29)), and the gain needed no other firm to adopt. Economic forcing requires a further link: rivals’ lower prices, improved service or faster delivery must damage the firms that keep the old process. The fulfillment case in Section [7.2](https://rencryptofish.com/posts/forcing-technologies#S7.SS2) makes the price channel explicit.

Broad demand for a useful product does not establish an advantage for any particular supplier. The budget that direct value creates is contestable by every company with access to the same models, and by the incumbent that already owns the workflow. Intercom’s Fin charges \$0.99 per resolution (Intercom, [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib70)); Google folded Gemini into Workspace in January 2025 and Microsoft put Copilot into consumer Microsoft 365 the same week (Google Workspace, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib167); Rognier, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib168)); and the standalone leaders are priced as if the market were already theirs: Sierra reported more than \$150 million of ARR entering its third year, and Decagon raised \$250 million at a \$4.5 billion valuation in January 2026, triple its price of six months earlier (Sierra, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib208); Decagon, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib209)). A differentiated product, distribution or installed workflow may protect it. The additional forcing question is whether adopters change prices, response times or service levels enough to damage comparable holdouts. Section [6](https://rencryptofish.com/posts/forcing-technologies#S6) sets aside the broad support category on entry and capture grounds, while retaining that economic test for narrower markets.

Customer expectations supply a second route: rivals raise what customers expect, and a holdout loses demand to a standard it did not set. Section [2.4](https://rencryptofish.com/posts/forcing-technologies#S2.SS4) gives the mechanism and Appendix [H.3](https://rencryptofish.com/posts/forcing-technologies#A8.SS3) models it as a ratchet, an expectation that follows adoption upward and stays there if adoption recedes. Amazon Prime is the case, and it has run for twenty years. It launched on February 2, 2005 at \$79 a year for unlimited two-day shipping (Amazon.com, Inc., [2005](https://rencryptofish.com/posts/forcing-technologies#bib.bib478)); in April 2019 Amazon put about \$800 million into a single quarter to make one-day delivery the default (The Motley Fool, [2019a](https://rencryptofish.com/posts/forcing-technologies#bib.bib479)); the same-day volumes of Section [2.4](https://rencryptofish.com/posts/forcing-technologies#S2.SS4) are where that has reached, with 30-minute delivery following in May 2026 (Amazon.com, Inc., [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib480), [a](https://rencryptofish.com/posts/forcing-technologies#bib.bib481)). The customers moved with it: 62% of US holiday shoppers defined fast shipping as two days or less in 2018, up from 54% a year earlier (Chain Store Age, [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib482)), and in 2025 62% said faster shipping decides between retailers at the same price (Radial, Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib483)). Retailers serving customers with those expectations faced pressure to improve fulfillment; existing logistics networks supplied one way to respond. Walmart’s own fulfillment service handled more than 40% of its marketplace sales by late 2024 and had 52% of its sellers by February 2026 (Walmart Inc., [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib484); Investing.com, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib485)); Target bought Shipt for \$550 million in December 2017 (Target Corporation, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib486)); and Shopify, which paid \$2.1 billion for Deliverr in May 2022 because fast shipping was “now table stakes,” sold the business to Flexport thirteen months later for a 13% stake and booked \$1.7 billion of one-time charges (Shopify Inc., [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib487), [2023a](https://rencryptofish.com/posts/forcing-technologies#bib.bib488), [2023b](https://rencryptofish.com/posts/forcing-technologies#bib.bib489)). The independents that sell Prime-like fulfillment to everyone else raised at \$1 billion (ShipBob, 2021) and \$3 billion (Stord, May 2026) (ShipBob, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib490); TechCrunch, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib491)): a real company market, made by a rival’s service level rather than by a rule.

AI features in SaaS provide a possible parallel, with less evidence yet of a common customer requirement. Bessemer found AI features on the roadmaps of 96% of its portfolio companies in 2023 and wrote in August 2025 that “there is no cloud without AI anymore” (Crunchbase News, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib492); Bessemer Venture Partners, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib493)); the bundling above is what meeting the expectation cost the incumbents; and some existing businesses reported weaker demand as customers turned to AI tools. Chegg told investors on May 1, 2023 that students’ interest in ChatGPT was cutting its new-customer growth, and lost 48% of its value the next day (Chegg, Inc., [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib494); Associated Press, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib495)); new questions on Stack Overflow fell from 1.34 million in 2022 to 109,000 in 2025 (PPC Land, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib496)). These observations show changing offers and demand, but do not establish that every SaaS buyer must purchase an AI feature. Even where a requirement develops, suppliers of the capability remain in competition. What the ratchet adds is a signal, in the customer surveys and holdout revenues of Section [5](https://rencryptofish.com/posts/forcing-technologies#S5), that a budget has become compulsory without any gatekeeper saying so.

### 3.3 Coordination goods can pay the operator

A network good with little standalone value can be worth little to the first adopter and much more to later ones, leaving early adopters below the profitability threshold shown in Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1): below the tipping point nobody moves, and whoever funds the crossing does so at a loss. A tipping point establishes a growing gain from connection. Economic pressure on holdouts additionally requires lost access or demand, such as customers leaving a merchant that cannot accept the standard. The question for companies is who owns the network and who can reprice its access.

Plaid built the connection layer between US banks and the apps that read their data, a business with network effects represented by $\beta x$: each bank added made every app more valuable and each app made every bank connection more worth having. Visa agreed to buy it for \$5.3 billion in January 2020, the Justice Department sued, and the deal was abandoned in January 2021; Plaid then raised at \$13.4 billion in April 2021 and at \$6.1 billion in April 2025 (Visa Inc., [2020](https://rencryptofish.com/posts/forcing-technologies#bib.bib125); U.S. Department of Justice, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib126); Beltran, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib127)). That valuation decline preceded the bank-fee announcements below and cannot be attributed to them. JPMorgan told aggregators in July 2025 that they would pay for access to customer data, fees it said would total hundreds of millions of dollars, and the companies announced a renewed access agreement that September, without disclosing its financial terms (Bloomberg Law, [2025a](https://rencryptofish.com/posts/forcing-technologies#bib.bib83); JPMorganChase, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib128)); the Consumer Financial Protection Bureau’s 2024 open-banking rule, which would have made that access a right, was enjoined in October 2025 while the Bureau reconsidered it (ABA Banking Journal, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib129)). Demand for bank connections did not give Plaid control over access fees. The banks’ ability to set terms creates a capture risk; the cited announcements do not quantify its effect on Plaid’s margins.

Containerization tells the same story over sixty years. Malcom McLean’s container service began with the *Ideal X* voyage on April 26, 1956 and sold out to R.J. Reynolds in 1969; the box became an ISO standard from 1968; and the lines that adopted it destroyed more than \$100 billion of shareholder value over the twenty years to 2017, earning less than their cost of capital in most of them (Rodrigue, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib130); Wackett, [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib131)). The standard created benefits beyond the pioneering shipping line, including lower transport costs for shippers. Those gains need not appear as durable profits for carriers. For a supplier, the investment case depends on control over access to the network or a credible acquisition route.

### 3.4 Counters are the arms race’s second market

Some competitive technologies create losses that make protection valuable. The model treats a counter as a third choice within a defined rival field (Appendix [F](https://rencryptofish.com/posts/forcing-technologies#A6)); external threats require a separate exposure model. Greater loss can raise the willingness-to-pay ceiling for effective protection, but does not guarantee a higher realized price. It also has a failure mode the attack side lacks: the venue can defend natively, and then the counter is a feature of the platform rather than a company.

Distributed denial-of-service protection is the historical case. Attack sizes reset their record almost every year, to 31.4 terabits per second in late 2025 (Cloudflare, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib134)); Akamai bought Prolexic, the largest standalone defender, for about \$370 million in February 2014, and Cloudflare, with mitigation at its core, grew from \$287 million of revenue in 2019 to \$2.17 billion in 2025 (Akamai Technologies, [2014](https://rencryptofish.com/posts/forcing-technologies#bib.bib132); Cloudflare, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib133)). E-commerce fraud prevention followed the same path: Riskified listed in July 2021 at \$21 a share, and five years later reports \$345 million of revenue and names generative AI and agentic commerce as the next things changing fraud (Riskified Ltd., [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib135), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib136)). Cybersecurity as a whole is the largest counter market in the taxonomy. Gartner expects \$244 billion of information-security spending in 2026 (Gartner, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib547)), and CrowdStrike, which sells endpoint defense, grew its recurring revenue from \$313 million in January 2019 to \$5.84 billion in July 2026 (CrowdStrike Holdings, Inc., [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib548), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib549)). Its July 2024 update crashed about 8.5 million Windows machines (TechCrunch, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib550)), and the year still ended with recurring revenue up 23% and gross retention of 97% (CrowdStrike Holdings, Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib551)): persistent threat exposure can sustain demand through a service failure. Customers can still switch suppliers, and retention alone does not identify pricing power.

Identity verification remains a live benchmark in Section [6](https://rencryptofish.com/posts/forcing-technologies#S6): attacks can create renewed demand for defense, while requirements sustain some of the verification flows. Attackers have industrialized the deepfake: in Entrust’s 2026 Identity Fraud Report, published in November 2025 on more than a billion verification events, deepfakes were one in five biometric fraud attempts, deepfaked selfies rose 58% in a year and injection attacks 40% (Entrust, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib145)). At the same time regulators mandate the check: the United Kingdom’s age-assurance rules took effect on July 25, 2025 and produced 69 million age checks in the second half of the year across a 32-service sample, 23 times the prior six months (Ofcom, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib139)); Australia’s under-16 ban took effect on December 10, 2025 and 4.7 million accounts were removed within days (The Register, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib140)); and Texas’s app-store law came into force after the Supreme Court declined to block it in July 2026 (Wiley Rein LLP, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib142)). A counter that leaves the compliance requirement unmet cannot disarm it (Corollary [4](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary4)): a platform that would rather not verify anyone still has to run a check, and the check is the flow a detection company sells into. Operating-system signals and platforms’ own estimation can reduce demand for paid checks. An evolving attack can preserve a separate detection budget where those controls remain inadequate. Socure reported \$364 million of recurring revenue growing 63% and raised at \$5.2 billion in August 2026; Persona raised \$200 million at \$2 billion in April 2025; Yoti’s revenue grew 62% to £29 million in 2025 (Biometric Update, [2026d](https://rencryptofish.com/posts/forcing-technologies#bib.bib147), [c](https://rencryptofish.com/posts/forcing-technologies#bib.bib148); Persona, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib138); Borak, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib149)). The risk is the one every counter carries: Apple and Google now ship age signals at the operating-system level, and Discord said at its September 2026 rollout that more than 90% of its users would never face an active check (Apple Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib143); Biometric Update, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib144)).

### 3.5 Low supply costs can eliminate revenue from the required capability

A mandate can achieve widespread adoption without creating substantial revenue for suppliers. HTTPS is the case (Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) fits it as a mix of dominant and tipping adoption). Google made encryption a ranking signal in August 2014 and announced on February 8, 2018 that Chrome 68 would mark every HTTP page “Not secure” from July; by then 68% of Chrome traffic on Android and Windows was already encrypted (Bahajji and Illyes, [2014](https://rencryptofish.com/posts/forcing-technologies#bib.bib116); Schechter, [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib67)). Chrome 68 shipped on July 24, 2018 (Google, [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib117)): a gatekeeper’s penalty with a date, applied to every website.

Free certificates limited the revenue available from basic issuance. Let’s Encrypt opened its public beta on December 3, 2015 and issued domain-validated certificates free, automatically, to anyone; by 2025 it served 762 million websites and had issued more than seven billion certificates in its first decade (Aas, [2015](https://rencryptofish.com/posts/forcing-technologies#bib.bib118); Internet Security Research Group, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib119)). Free issuance constrained prices for basic certificates; it did not eliminate every paid certificate service. Symantec agreed on August 2, 2017 to sell its certificate authority to DigiCert for \$950 million in cash and a 30% stake, as Chrome prepared to stop trusting Symantec’s certificates altogether (Symantec Corporation, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib120); O’Brien et al., [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib121)). A distinct paid market developed above basic issuance. Enterprises with more than 100,000 certificates pay for inventory, rotation and outage prevention: 86% of 450 organizations surveyed in 2025 had suffered a certificate-related outage in the past year, one in ten every week (Keyfactor, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib122)). CyberArk bought Venafi, the largest certificate-lifecycle company, for \$1.54 billion in 2024 on about \$150 million of recurring revenue, and Palo Alto Networks announced its \$25 billion CyberArk deal in July 2025 citing machine identities (CyberArk Software Ltd., [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib123); Palo Alto Networks, Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib124)). When a nonprofit or platform supplies an equivalent capability free, exclusion need not create a separately chargeable budget for it. Complex certificate operations can still support paid services. Shorter browser certificate lifetimes increase demand for that work (Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px1)).

### 3.6 Mandates create migration waves and recurring work

A mandate often supplies an announced enforcement date, making its purchase window easier to observe than a competitive threshold. Expected enforcement can raise a holdout’s willingness to pay and compress the sales window. Once most firms comply, new-installation demand can fall even though the penalty for dropping compliance remains. The base model captures that continuing incentive; a migration sales wave additionally depends on the installed base and replacement cycle. Recurring filings, monitoring or new transactions can sustain paid work after the initial deadline.

Sales tax recurs every month. *Wayfair* let states require collection from sellers with no physical presence, and 33 states and the District of Columbia had adopted economic-nexus rules within eight months (The Motley Fool, [2019b](https://rencryptofish.com/posts/forcing-technologies#bib.bib92)). Avalara’s revenue grew from \$213.2 million in 2017 to \$272.1 million in 2018, \$382.4 million in 2019, \$500.6 million in 2020 and \$699.0 million in 2021 (Avalara, Inc., [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib87), [2020](https://rencryptofish.com/posts/forcing-technologies#bib.bib88), [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib89)); Vista agreed to pay \$8.4 billion for it in August 2022, and the company filed confidentially for a second listing in July 2025 (Vista Equity Partners, [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib90); Srivastava, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib91)). Its chief executive was careful about the cause: “We filed for our IPO before the ruling, and we never counted on it. However, it has given us a tailwind” (Prete and Baltz, [2019](https://rencryptofish.com/posts/forcing-technologies#bib.bib93)). SOC 2 recurs every year, and it is enforced by customers rather than by a regulator: a security questionnaire that asks for the report is a gatekeeper with a budget attached. Vanta, founded in 2018, crossed \$100 million of recurring revenue in the fiscal year to January 2024 and \$300 million by April 2026, with 16,000 customers and a last valuation of \$4.15 billion (Vanta, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib94); Lazarus, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib73); Bloomberg Law, [2025b](https://rencryptofish.com/posts/forcing-technologies#bib.bib95)). Drata, founded in 2020, passed \$100 million in February 2025 (Drata, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib96)).

EMV illustrates a migration wave under a continuing liability rule. From October 1, 2015, US merchants accepting chip cards without chip-capable terminals could bear counterfeit-fraud losses. Upgrading avoided that exposure; it did not require every merchant to buy a new terminal, nor did the liability incentive expire after the upgrade (Visa, [2016](https://rencryptofish.com/posts/forcing-technologies#bib.bib685)). Verifone’s North American revenue rose from \$526 million in fiscal 2014 to \$792 million in 2015 and \$804 million in 2016, then fell to \$630 million in 2017 (VeriFone Systems, Inc., [2015](https://rencryptofish.com/posts/forcing-technologies#bib.bib97), [2016](https://rencryptofish.com/posts/forcing-technologies#bib.bib98), [2017b](https://rencryptofish.com/posts/forcing-technologies#bib.bib99)). Its 2017 annual report says why: “revenue increases due to the adoption of standards such as EMV in the United States have in the past slowed and declined” (VeriFone Systems, Inc., [2017a](https://rencryptofish.com/posts/forcing-technologies#bib.bib77)). Francisco Partners took the company private in April 2018 for \$23.04 a share, about \$3.4 billion with debt, a 54% premium to a stock that had fallen to \$15 (VeriFone Systems, Inc., [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib100)). Y2K is the same shape at a larger scale. Gartner put worldwide remediation spending at \$300 to \$600 billion (Edward W. Kelley, [1998](https://rencryptofish.com/posts/forcing-technologies#bib.bib101)); Keane’s Y2K revenue went from \$369.5 million in 1998 to \$206.1 million in 1999 to \$5.4 million in 2000, and Cognizant’s from 44% of revenue to 0.4% over the same three years (Keane, Inc., [2001](https://rencryptofish.com/posts/forcing-technologies#bib.bib102); Cognizant Technology Solutions Corp., [2001](https://rencryptofish.com/posts/forcing-technologies#bib.bib103)). Post-quantum migration (Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px1)) also creates migration work, but its deadlines are less uniform.

Private requirements also depend on the gatekeeper’s enforcement incentives. Walmart’s two RFID programs and Apple’s tracking prompt, discussed in Section [2.5](https://rencryptofish.com/posts/forcing-technologies#S2.SS5), show why an announced policy, its enforcement and its effect on supplier revenue need separate evidence.

Italy is the precedent for the e-invoicing case in Section [7](https://rencryptofish.com/posts/forcing-technologies#S7), and its warning is about bundling rather than dates. Italy introduced mandatory business-to-business e-invoicing for in-scope firms through the state’s own exchange, the Sistema di Interscambio, from January 1, 2019 (European Commission, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib104)). The exchange is free. Free public transmission limited that fee opportunity; accounting software above the exchange remained a paid market. TeamSystem, the largest Italian company selling that software, reported €1.06 billion of revenue, €476 million of adjusted EBITDA and a €37.7 million consolidated net loss in 2025 (TeamSystem Holdco S.p.A., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib105)). A September 2026 press report put the valuation in minority-stake transactions with Francisco Partners and KKR at €8 to 10 billion (Private Equity Wire, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib75)). A French transmission startup would compete with the free and bundled offers described in Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px5).

Table 4: Who kept the budget. One row per running example, with a demand mechanism and a reported company outcome. Receipts and transaction values are not estimates of profits caused by the mechanism.

| Example | Channel | Demand mechanism | Who paid | Who kept the budget, and what ended it |
| --- | --- | --- | --- | --- |
| AI support assistants | Direct | ChatGPT demonstration, Nov. 2022 | Support operations, from their own labor line | Model providers and workflow incumbents; bundling |
| HTTPS certificates | Exclusion | Chrome 68 “Not secure,” July 2018 | Website operators | Free issuance constrains basic certificate fees; lifecycle companies a layer up (Venafi, \$1.54bn) |
| Bank data connections | Network | App demand; the 2024 open-banking rule, enjoined in 2025 | Fintech apps | Plaid as operator; banks can charge for access, but its Sept. 2025 JPMorgan agreement’s financial terms were undisclosed |
| Sales-tax compliance | Exclusion, recurring | *Wayfair*, June 2018 | Remote sellers | Avalara (\$8.4bn take-private, 2022); recurring compliance demand continues |
| SOC 2 | Exclusion, recurring | Customer questionnaires | SaaS companies | Vanta (\$300m ARR, 2026), Drata; the risk is a free tier |
| EMV terminals | Exclusion; migration wave | Liability shift, Oct. 2015 | US merchants | Verifone, during the upgrade wave (\$3.4bn take-private, 2018) |
| Italian e-invoicing | Exclusion | SdI mandate, Jan. 2019 | In-scope VAT-registered firms | The accounting suite (TeamSystem, reported €8–10bn valuation), above the free public exchange |
| Low-latency fiber | Contest | Spread Networks, 2010 | Trading firms | The next company (microwave), then the venue (exchange colocation); Spread sold for \$127m |
| Polyurethane suits | Contest | LZR Racer, Feb. 2008 | Elite swimmers | Speedo for one season, rivals the next; FINA’s ban ended it, Jan. 2010 |
| Market-data terminals | Contest and network | Bloomberg terminal, Dec. 1982; periodic price increases | Subscribing trading desks | Bloomberg, for forty years (more than 350,000 seats at about \$32,000); the terminal is also the network |
| Search placement | Contest | Google’s rankings; AI answers from 2024 | Sites competing for organic traffic | Semrush (\$444m revenue, 2025; sold to Adobe for \$1.9bn, 2026), Ahrefs; the race moved to AI answers |
| Programmatic ad bidding | Contest | Real-time bidding; 90% of US display by 2025 | Programmatic advertisers | The Trade Desk for a decade (\$2.9bn revenue, 2025), facing venue competitors Google and Amazon; later growth slowed |
| Dreadnoughts | Contest | HMS *Dreadnought*, 1906; the 1909 eight-ship programme | Navies, from estimates rising from £31.5m to £50m | Vickers and Armstrong while the race ran; losses after the Armistice and a merger in 1927 |
| AI compute | Productive demand and contest | Repeated model and hardware generations | Labs, clouds and application providers | NVIDIA: \$193.7bn Data Center revenue in FY2026; corporate gross margin 71.1%, not a segment margin. Utilization and replacement risk remain downstream (Section [4](https://rencryptofish.com/posts/forcing-technologies#S4)) |
| Bitcoin mining | Reward contest and security | Relative hashpower and equipment efficiency | Miners, through hardware and power bills | Suppliers receive spending; difficulty, energy costs and the dollar reward determine miners’ returns. Ethereum’s Merge ended a different network’s mining market (Section [4](https://rencryptofish.com/posts/forcing-technologies#S4)) |
| Endpoint security | Counter | Ransomware and breaches; Gartner forecasts \$244bn spending in 2026 | Enterprises buying protection | CrowdStrike (\$5.8bn ARR, July 2026; 97% gross retention in FY2025); the risk is the platform’s own defense |
| Identity verification | Counter and mandate | Deepfakes; age laws 2025–26 | Platforms, from fines and fraud avoided | Socure, Persona, Yoti; the risk is OS-level age signals |
| RFID tags at Walmart’s suppliers | Exclusion, customer as gatekeeper | Walmart’s letters: pallets by Jan. 2005 (lapsed); items by Sept. 2, 2022 | Suppliers in the named categories | Impinj (\$366m revenue, 2024), Avery Dennison; the 2003 mandate failed to achieve broad compliance |
| Mobile ad tracking | Exclusion, platform as gatekeeper | Apple’s prompt, April 26, 2021 | Advertisers and ad networks (Meta: about \$10bn in 2022) | The platform; measurement re-tooled (AppLovin bought Adjust, \$1bn); EU fines have not reversed the tracking rule |
| Rent-setting software | Coordination among rivals | DOJ alleges shared pricing data; suit Aug. 23, 2024 | Landlords, then renters | RealPage (\$10.2bn, 2021) faced restrictions on its pricing mechanism in the proposed Nov. 2025 settlement; customer retention is unverified |
| Retail media | Contest; the venue sells the race | Amazon’s ad line; more than 200 networks by 2024 | Consumer brands | The retailers (Amazon \$56bn, 2024; Walmart \$6.4bn, FY2026); Criteo’s 2025 retail-media revenue grew 2% |
| Battery packs and solar | Cost curve | Packs at \$115/kWh (2024) and \$108 (2025); solar at 4.3 cents/kWh | Automakers, utilities | Low-cost producers and customers may capture the saving; holdout losses require evidence of substitution and price response |
| Delivery speed | Expectations | Prime, Feb. 2005; one-day by default, 2019; 13bn same- or next-day items, 2025 | Rival retailers (Walmart, Target), from fulfillment capex | Amazon and Walmart as operators; Shopify paid \$2.1bn for Deliverr and sold for a 13% stake; Stord and ShipBob sell to the rest |

## 4 AI and crypto: useful products, competing platforms, expensive races

AI and crypto can create substantial value while competition reduces suppliers’ returns. A support worker using an assistant, a trader using Hyperliquid, a developer choosing Ethereum and a laboratory buying another GPU cluster are making different investments. Their gains cannot be inferred from one industry’s adoption curve. The comparison has to follow the buyer’s alternative, the source of pressure and the recipient of the payment.

The strongest common mechanism is competition to supply a base on which others build. Bitcoin, Ethereum, Solana and Hyperliquid offer different combinations of settlement, execution and liquidity; OpenAI, Anthropic, Google, Meta and DeepSeek offer models, distribution and tools. Applications can strengthen those bases while also acquiring the customers and retaining the margin. Meanwhile, miners and model developers buy infrastructure whose suppliers can earn before the ultimate economics are settled. The cases below test those mechanisms rather than treating either sector as a single regime.

### 4.1 Payoffs for users, platforms and infrastructure buyers

For a user, $\gamma$ is the value of completing a task or accessing a service relative to the existing alternative, after holding other users’ adoption fixed. A network term belongs where additional counterparties or complementary applications improve that service. For a platform, the question is whether another application attracts users who then attract other applications, and whether the platform can charge for that connection. For an infrastructure buyer, the question is whether more capacity serves paying demand, protects a competitive position, or does both. Table [5](https://rencryptofish.com/posts/forcing-technologies#S4.T5) keeps these decisions separate.

Table 5: The paired comparison. Channels describe a specified decision, not an entire industry.

| Decision | AI | Crypto | Evidence that identifies the mechanism |
| --- | --- | --- | --- |
| Use a service | Worker or firm buys a better task outcome; rivalry can later lower prices or raise expectations | Holder, trader, merchant or recipient buys asset exposure, execution, settlement or dollar access | Task quality and total cost against the actual alternative; losses incurred by comparable holdouts |
| Build on a base | Developer chooses a model, API, host and distribution channel | Developer chooses a chain, liquidity pool, settlement layer and distribution channel | Retained paid activity after credits or incentives end; complement use; cost of switching or using several bases |
| Supply capacity | Lab trains models; cloud serves training and inference | Miner competes for rewards; validator supplies consensus and execution | Realized utilization, replacement spending and returns after capital costs; changes in competitors’ outcomes |

A larger training run is not automatically a network effect: spreading its cost over more customers is an economy of scale. Nor is a larger validator set interchangeable with more paying applications. The adoption share $x$ must refer to a defined field making a comparable choice. Dollars of capital expenditure, hashrate and model benchmark scores are useful observations, but none is $x$. Months of technical leadership do not directly measure the model’s erosion parameter $r$.

### 4.2 Adoption: direct value can precede competitive pressure

The evidence for useful AI is strongest where the outcome is specified. The staggered introduction studied by Brynjolfsson et al. ([2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib29)) covered 5,172 support agents and raised issues resolved per hour by 15% on average, with larger gains for less experienced workers. This is evidence of a productive channel in that workplace, not a universal return on an AI subscription. Verification, integration, error correction and organizational change still enter the adopting firm’s cost. A public demonstration can raise belief $p$ without proving a particular production workflow.

Results differ across tasks and users. METR’s early-2025 randomized study found experienced open-source developers took 19% longer with the available AI tools. Its February 2026 update reported apparent improvements in a later study but warned that developers and tasks were selecting out of the no-AI condition, making the new estimate unreliable (Becker et al., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib619)). Neither result licenses a claim about all software work. Together with the support study, they make task-level testing necessary and show why self-reported enthusiasm, benchmark gains and realized productivity must remain separate.

Productivity can nevertheless become pressure. Once rivals pass savings to customers, a firm can lose margin while the technology continues to create value; Section [1.3](https://rencryptofish.com/posts/forcing-technologies#S1.SS3) models that distinction. Competition for a fixed position in search or an AI answer is a different mechanism, closer to $\alpha$. AI-generated attacks create a third: the buyer pays to prevent losses imposed by attackers. Section [7.3](https://rencryptofish.com/posts/forcing-technologies#S7.SS3) evaluates that defense at the verification workflow, where catching an additional fraud attempt matters more than general model capability.

Crypto demand needs equally specific treatment. In the Federal Reserve’s October 2025 household survey, 9% of US adults reported buying or holding cryptocurrency as an investment during the prior year, while 2% reported transactional use (Board of Governors of the Federal Reserve System, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib623)). Those overlapping categories measure different purposes, not the success and failure of one payment product. A holder’s demand for an asset, a trader’s demand for liquidity and a merchant’s demand for acceptance have different alternatives and network requirements.

Dollar access and cross-border payouts can have direct value before general merchant acceptance. In Stripe’s customer account, Remote’s payments executive estimates that optional USDC payouts reach contractors two to three days faster and avoid currency-conversion costs exceeding 1% of payout value (Stripe, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib625)). These are company-published estimates, not a controlled comparison or a complete cost calculation: later redemption, local spending, custody and compliance can reduce the gain. But they identify a buyer and a plausible saving that a blanket coordination story misses. Conversely, Visa’s filtering of stablecoin transfers removes substantial automated and other non-economic activity; even its adjusted series is not a census of purchases (Sheffield, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib624)). Repeat use after all costs is the demand test.

### 4.3 Four Layer 1 cases

Bitcoin: monetary coordination and a separate mining contest.

Bitcoin’s original design combines peer-to-peer transfer with proof-of-work to establish a transaction history (Nakamoto, [2008](https://rencryptofish.com/posts/forcing-technologies#bib.bib602)). Its potential network advantage comes from other holders, counterparties, liquidity and infrastructure accepting the same asset and history. That differs from attracting developers to a general-purpose application runtime. Holding bitcoin does not entitle its owner to a corporate revenue stream. Users pay transaction fees; miners receive those fees and protocol issuance in exchange for block production. Custodians, exchanges, hardware makers and power suppliers have separate businesses. The monetary network may retain demand while competition erodes an individual miner’s return. That separation is the central Bitcoin lesson for the model-provider comparison.

Ethereum: shared applications, with value divided across layers.

Ethereum makes applications and assets available within a shared execution environment. Contracts can call other contracts, allowing a new application to use existing services rather than recruit every complement afresh (Ethereum.org Contributors, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib605)). That is a concrete network mechanism; developer counts alone are only a proxy. It does not ensure that all value accrues to ETH holders. Under EIP-1559 the base transaction fee is burned, while the priority fee goes to the block producer; issuance and other validator receipts require separate accounting (Buterin et al., [2019](https://rencryptofish.com/posts/forcing-technologies#bib.bib606)). Rollups can retain their own execution relationships while buying settlement and data availability from Ethereum. EIP-4844 introduced a separate blob transaction and fee mechanism intended to lower rollup data costs (Buterin and others, [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib607)). Greater ecosystem use can therefore coexist with a lower fee per operation at the base. The empirical question is whether demand growth and settlement dependence compensate for that compression.

Solana: execution quality must turn into retained demand.

Solana’s case is a shared execution platform competing on the cost and performance of using applications. Its fee rules distinguish base fees, split between burning and the validator, from prioritization fees paid to the validator (Solana Documentation, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib608)). Cheap execution can make new activities viable, but low fees and high transaction counts do not by themselves establish pricing power. Reliability is part of the product: the February 6, 2024 halt lasted approximately five hours, according to the developers’ incident report (Anza, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib609)). The outage illustrates the importance of reliability, although it does not establish the network’s current performance. The durable-advantage test is whether applications and users remain after incentives fall and competing chains improve, paying enough to support the relevant suppliers. A trading boom, validator votes and repeated automated transactions cannot be treated as interchangeable measures of customer demand.

Hyperliquid: an application can build the base around itself.

Hyperliquid reverses the assumption that a broad developer ecosystem must come first. HyperCore includes the order books and matching engine; HyperEVM supplies general-purpose execution under the same HyperBFT consensus and can connect applications to that trading state (Hyperliquid, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib610), [c](https://rencryptofish.com/posts/forcing-technologies#bib.bib611)). The proposed network loop is specific: trading liquidity attracts traders, and applications can reuse that liquidity. Fee routing gives a closer connection to monetization than token market capitalization does. The documentation directs trading fees among HLP, deployers and an assistance fund that converts fees into HYPE; its current description says that fund’s HYPE is burned (Hyperliquid, [2026d](https://rencryptofish.com/posts/forcing-technologies#bib.bib612)). These are protocol rules, not audited company earnings. The unresolved question is how much independent application demand persists beyond the core trading venue. Liquidity concentration, dependence on the venue’s risk controls and changing fee rules limit the inference from one successful application to a defensible general platform.

### 4.4 Five foundation-model strategies

A foundation model is a reusable model adapted to many downstream tasks (Bommasani and others, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib617)). Reuse can support a platform, but the economics depend on what the provider controls besides the model. Table [6](https://rencryptofish.com/posts/forcing-technologies#S4.T6) summarizes the comparison; the following examples are dated demonstrations of different strategies, not a ranking of today’s model quality.

OpenAI: model access plus a direct customer relationship.

OpenAI supplies models through an API and through ChatGPT, so a developer can buy a component from a firm that also serves end users. Its July 2024 GPT-4o mini release priced input tokens at \$0.15 and output tokens at \$0.60 per million, over 60% below GPT-3.5 Turbo (OpenAI, [2024a](https://rencryptofish.com/posts/forcing-technologies#bib.bib507)). This is evidence of price competition and product segmentation, not a quality-adjusted industry price index. Distribution, integrations and accumulated workflow context may retain users when a capability lead narrows. Automatic learning from every customer is a weaker claim: OpenAI’s business and API policy excludes training on customer data by default, subject to explicit opt-in (OpenAI, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib620)). A data advantage needs lawful access and evidence of improvement, not just a usage count.

Anthropic: enterprise distribution and a first-party application.

The February 2025 Claude 3.7 release offered access through Anthropic, Amazon Bedrock and Google’s Vertex AI, alongside the introduction of Claude Code (Anthropic, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib621)). The dated release illustrates two routes to customers: distribution through several clouds and a direct application built on the model. Neither requires all developers to assemble around one exclusive host. Cloud relationships can expand reach while giving the distributor bargaining power; a first-party coding product can retain workflow value while competing with developers that buy the underlying model. Renewals and paid use after a competing release are better evidence of durability than a launch benchmark.

Google: integration changes where the return is earned.

Google included Gemini capabilities in Workspace Business and Enterprise plans in January 2025, removing the need for a separate AI add-on (Google Workspace, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib167)). That gives the model an existing route to users and changes the price a standalone application must beat. Bundling does not make development or inference costless. It means the return may be earned through suite retention, cloud demand or other products, rather than a separately reported Gemini margin. Comparing a standalone model company’s revenue with the whole of Google’s business would obscure that distinction.

Meta’s Llama: access to weights changes the supplier.

Llama 3.1 permits deployment and modification under its community license, including a special permission requirement for licensees above its 700-million-monthly-user threshold (Meta, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib622)). The license makes the weights available subject to these restrictions. A user can purchase hosting, adaptation and operations from another supplier rather than pay the model originator for every call. That can shift the budget toward infrastructure and applications. It leaves inference, evaluation, support and subsequent upgrades to fund. Downloads reveal distribution; they do not establish Meta’s model revenue or the profitability of a third-party host. Zuckerberg’s stated rationale links model release to Meta’s own products and reduced dependence on closed suppliers (Zuckerberg, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib630)); that is a strategy for earning elsewhere in the business, whose incremental return still needs evidence.

DeepSeek: efficiency can reset the cost of competing.

DeepSeek-V3’s technical report describes 2.788 million H800 GPU-hours for its training and an estimated \$5.576 million at an assumed \$2 per GPU-hour, explicitly excluding prior research and ablation experiments (DeepSeek-AI, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib599)). The reported result challenges a simple equation between spending and capability. It does not measure the cost of building the company, reproducing its research or serving customers. More efficient training may reduce entry costs; cheaper inference may also expand demand enough to increase total compute purchases. Which effect dominates is an empirical question, and neither follows from the training bill alone.

Table 6: Layer 1s and foundation models: where the platform analogy holds and breaks. Interpretations follow the case evidence above.

| Economic question | Layer 1 networks | Foundation-model providers |
| --- | --- | --- |
| What do users share? | An asset and transaction history; on application chains, state, contracts and liquidity | A reusable capability; tools and distribution may be shared, but customer workflows need not share state |
| Where can the network effect arise? | Counterparties, liquidity and composable applications; the mix differs across the four cases | Complementary tools and distribution; a data feedback loop requires access rights and useful learning |
| What makes moving costly? | Moving assets and liquidity, bridging risk, contract dependencies and counterparty coordination | Re-evaluation, integrations, model-specific behavior, data policies and committed cloud spend |
| Who receives the payment? | Miners or validators, application operators and intermediaries; burns change supply without creating corporate profit | Model API, application or hosting company; bundled returns may appear elsewhere in the provider’s business |
| What weakens capture? | Competing chains, cheaper blockspace, applications retaining fees and developers using several chains | Competing models, available weights, routing, cheaper inference and incumbent bundles |

Both types of platform can subsidize entry and attract complements without retaining their eventual value. Electric Capital’s 2024 analysis found one in three crypto developers working across multiple chains; its current methodology counts such developers in individual ecosystem totals and covers open-source repositories (Electric Capital, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib615), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib614)). Those totals cannot be added as exclusive market shares. In AI, availability through several hosts similarly creates options, although moving a workflow still requires testing. Neither multi-chain development nor model routing implies frictionless switching.

The “fat protocols” thesis proposed that shared state and tokens would concentrate value at the protocol layer (Monegro, [2016](https://rencryptofish.com/posts/forcing-technologies#bib.bib616)). Here it is a hypothesis to test. Ethereum’s rollups and Hyperliquid’s integration show why the application/base boundary matters; model providers moving into applications pose the same capture question. A rollup may still purchase Ethereum settlement, whereas a self-hosted model need not buy an inference call from its originator. They are different ways of changing the supplier, with different residual dependencies.

### 4.5 The arms race: mining supplies the mechanism, AI changes the prize

Bitcoin mining makes relative investment unusually visible. A miner’s expected share of rewards depends on its share of network hashpower. Difficulty adjusts, and issuance follows a protocol schedule, so adding machines does not proportionately expand the long-run number of blocks. The dollar value of the prize still changes with bitcoin’s price and fees (Bitcoin Developer Documentation, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib603)). More efficient equipment can benefit its buyer while inducing rivals to replace equipment too. Budish’s model links this rent competition to the cost of deterring attacks (Budish, [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib37)). The security service prevents a conclusion that all mining expenditure is socially wasted merely because miners compete for rewards.

MARA’s reported results expose the pressure without requiring a welfare estimate. Year-end energized hashrate rose from 53.2 to 66.4 EH/s in 2025, yet fourth-quarter blocks won fell from 703 to 595 compared with the prior-year quarter. The company attributed higher purchased energy cost per bitcoin partly to network difficulty outrunning its hashrate growth (MARA Holdings, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib627)). Energized capacity is a point-in-time capability, while blocks are a period outcome; uptime, fees and chance also matter. The evidence is consistent with a race and does not isolate the causal return to each machine. Its reported net loss also included large asset revaluations, which cannot be read as mining’s operating loss.

AI laboratories face an analogous incentive when an improvement wins customers, developers or distribution and rivals respond with another training run, release or price cut. But AI can expand the prize by enabling work that was previously uneconomic. It also involves learning about uncertain demand. Compute-optimal training research demonstrates that how compute is allocated across model size and data matters to performance (Hoffmann and others, [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib618)). Capital expenditure alone cannot distinguish productive expansion, experimentation and defensive investment. Evidence of competition requires a sequence connecting rivals’ advances to purchases and to losses experienced by those that fall behind.

NVIDIA’s sales show the scale of spending on AI infrastructure: its fiscal-2026 Data Center revenue was \$193.7 billion. The 71.1% GAAP gross margin reported for that year belongs to the entire company, not specifically to Data Center (NVIDIA Corporation, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib166)). Those sales combine several workloads and do not identify the fraction attributable to a positional contest. Nor do they establish that every infrastructure supplier earns equally durable returns. Financed capacity carries utilization, replacement and customer-credit risks after the equipment seller books revenue.

The two races also meet in physical infrastructure. Core Scientific’s 2025 filing reports \$65.4 million of colocation revenue, against \$24.4 million in 2024, as it adapted capacity for high-density computing (Core Scientific, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib626)). Power and sites can have alternative uses; bitcoin ASICs cannot simply become AI accelerators. Conversion requires investment and a customer. The distinction separates an asset owner’s option from a claim that every miner can escape deteriorating economics by switching to AI.

### 4.6 A worked race and six possible outcomes

Consider one round of the model with $p=1$, $r=2$, $c=0.4$ and $\beta=\varepsilon=0$, in normalized payoff units. If $\gamma=0.2$ and $\alpha=1$, adopting first pays $0.8$ and adopting when everyone else has pays $0.3$, but the field’s saturated payoff is $y_{R}=-0.2$. Set $\gamma=0.6$ and $\alpha=0.2$ instead: the saturated adoption gain is still $0.3$, while $y_{R}=+0.2$. Both can sustain adoption; one destroys value for the modeled field and the other creates it. This is an illustration, not a calibration to mining or AI, and the two examples need not have the same adoption path.

A sequence of new generations can restart the contest: a useful advance gives an early lead, rivals match it, prices or rankings adjust, and the next purchase restores an advantage. That sequence is an extension in interpretation; the base model makes a single irreversible adoption decision. It does not prove perpetual expenditure. Table [7](https://rencryptofish.com/posts/forcing-technologies#S4.T7) states conditional branches that may overlap, with no assigned probabilities.

Table 7: Conditional arms-race outcomes and observations that would distinguish them.

| Outcome | Evidence supporting it | Contrary evidence; who bears the downside |
| --- | --- | --- |
| Productive expansion | Paid demand and task quality grow enough to cover inference, development and replacement costs | Idle capacity and weak renewals undermine it; capacity owners and financiers bear excess investment |
| Returns consumed by competition | Shorter-lived leads, matching expenditure and falling returns after capital costs despite continued adoption | Durable differentiation or expanding surplus weakens it; exposed producers absorb the replacement bill |
| Consolidation or specialization | Exits from the frontier, durable niche customers or outsourcing at acceptable margins | Continued profitable entry weakens it; exiting firms bear stranded assets and creditors may lose |
| Several bases remain viable | Customers use multiple chains or models, switch after price changes and retain portable complements | Persistent exclusive retention weakens it; platforms fund recruitment without corresponding pricing power |
| A technical or protocol change | Comparable service delivered with less resource use, or consensus changes remove a hardware requirement | Rebound demand or new bottlenecks sustain spending; owners of obsolete equipment bear write-downs |
| Rules partition the market | Export restrictions, access rules or customer procurement divide suppliers and demand | Substitution and continued trade weaken the partition; excluded suppliers lose sales and restricted buyers pay more |

These markets can change when their underlying technical or regulatory rules change. Ethereum’s September 15, 2022 Merge ended proof-of-work on that network while preserving its transaction history and applications; it did not end Bitcoin mining (Ethereum.org Contributors, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib604)). Cambridge’s October 2021 account of China’s mining restrictions reports geographic displacement and a partial recovery in global hashrate by August (Rauchs, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib629)). The race continued elsewhere. Available model weights and efficient inference can lower the cost of participating without shielding a rival from competitive loss. A counter in the formal model does the latter; a cheaper input need not.

### 4.7 Forecasts for 2031 and 2036

Our five-year forecast is that AI creates the broadest pressure through competition in repeatable services, with intense defensive spending in businesses exposed to automated attacks. Compute replacement creates a more concentrated race. In crypto, the strongest candidate beyond trading is settlement in costly payment corridors; within trading, liquidity can create stronger local dependence. By 2036, the leading additional candidates are agent-compatible customer access, shared collateral and physical automation. Their wider reach requires operational milestones that have not yet been demonstrated across the relevant populations.

These are conditional judgments from October 20, 2026, for October 20, 2031 and October 20, 2036. “Leading” identifies the strongest supported mechanism within a stated field; “narrow” separates intensity from breadth; “conditional” identifies a necessary milestone; “weak” means the proposed holdout-loss channel lacks support. The tiers are not estimated probabilities. The public evidence identifies useful capabilities and some operating outcomes, but does not identify comparable losses among holdouts, exits and adopters across these fields.

We distinguish pressure already present from additional deterioration, and an event reached *by* a horizon from one still active *at* it. Our provisional materiality test is a loss of at least 10% of positive baseline annual operating profit for at least half a defined commercial field, lasting two years after feasible alternatives, with adoption able to improve the actor’s position. The threshold is a research convention. Appendix [O.6](https://rencryptofish.com/posts/forcing-technologies#A15.SS6) specifies sensitivity tests and identifies outcomes for which probabilities remain unestimated.

Table 8: Conditional forcing forecasts from October 20, 2026. Tiers compare mechanisms within the stated fields; they are not probability bins.

| **Capability / field** | **2031** | **2036** |
| --- | --- | --- |
| Specialist workflows | Leading: pressure in measurable, repeatable services. | Leading: pressure on staffing and service delivery if complete workflows become reliable. |
| Compute and power | Narrow but intense: capacity and replacement pressure. | Conditional: specialization and efficiency may relocate or reduce the bottleneck. |
| Agent interfaces | Conditional: important customer channels require compatibility. | Leading conditional candidate: machine-readable access becomes routine procurement. |
| Attack defenses | Leading within exposed workflows: repeated defense purchases. | Leading within exposed workflows if attacks keep adapting. |
| Physical automation | Narrow: repeatable tasks and favorable sites. | Conditional expansion: deployment and maintenance become repeatable across sites. |
| Stablecoin operations | Leading crypto candidate outside trading, in high-friction corridors. | Leading capability candidate; particular coins and chains remain substitutable. |
| Shared collateral | Conditional: specialist financial networks. | Conditional expansion: collateral mobility and integration become economically important. |
| Trading liquidity | Narrow but intense where execution quality concentrates. | Narrow and persistent if liquidity survives adverse cycles. |
| Bitcoin mining | Narrow and intense among continuing miners. | Conditional persistence after reward, energy and exit changes. |
| Bitcoin monetary use | Weak general forcing; possible specialist niches. | Conditional niches; no forecast of universal business dependence. |
| Agent payments | Conditional: selected production commerce. | Conditional expansion: authorization and settlement become access requirements. |

AI: cost competition first, wider coordination later.

For support, coding and back-office suppliers selling comparable output, the 2031 mechanism is verified savings becoming lower prices or lost orders for holdouts. The support study’s 15% productivity improvement establishes a task benefit, not that competitive transmission. METR’s later measurement difficulties and Anthropic’s conversation-based estimates also caution against equating apparent speed with accepted output or firm returns (Brynjolfsson et al., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib29); Becker et al., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib619); Anthropic, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib637)). Census measured AI use in any business function at 19.8% in early May 2026, following a broadened question; that is not the adoption share for a particular production workflow (U.S. Census Bureau, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib161)). We would downgrade this leading forecast if comparable holdouts retain prices, orders and margins despite sustained rival savings.

By 2036, reliable performance across complete workflows could extend pressure from individual tasks to staffing, service speed and the organization of firms. The likely recipients are operators selling accepted outcomes and companies controlling customer distribution. A specialist must retain value after model charges, review and integration. Physical automation could transmit similar pressure to logistics and factory operators, but its ranking remains below software workflows until multisite deployment and maintenance become repeatable. Existing industrial robot counts do not isolate AI capability or establish those returns (International Federation of Robotics, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib641)). Downtime or supervision that erases the cost advantage reverses the forecast.

Frontier laboratories and AI hosts face a different five-year problem: delivering competitive capacity and replacing it. NVIDIA’s realized sales and the IEA’s electricity analysis support the scale of infrastructure demand; neither separates productive expansion from positional expenditure. The IEA’s 2030 electricity figure is itself a projection (NVIDIA, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib639); International Energy Agency, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib638)). Delivered power, differentiated compute and infrastructure can receive this spending. Ten-year capture is less secure because efficiency, custom hardware, outsourcing and exits can move the bottleneck. Buyers that defer upgrades without losing capability or customers would weaken the forcing thesis; supplier revenue alone would not establish competitive pressure on buyers.

For financial verification and enterprise security, the forecast concerns additional expected losses after existing controls. Selected documented misuse supports the mechanism, without measuring its population incidence (Anthropic, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib640)). Through 2031, effective defenses can attract repeated spending in exposed workflows; through 2036, adaptation can sustain it. Owners of identity, payment and security signals have an advantage, while specialists need measured protection beyond bundled controls. If incremental losses stop rising or existing defenses absorb them, the independent budget shrinks. Attackers and defenders are separate populations here.

Crypto: particular financial relationships, with competing rails.

For payout and treasury providers, begin with a named corridor, such as US-to-Mexico contractor payments. Remote’s reported USDC payout gains make this a concrete candidate, but complete redemption costs and competitor losses remain unmeasured (Stripe, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib625)). By 2031, sustained delivered savings could force competing providers to match cost and availability. Distribution, redemption and local liquidity are plausible recipients. By 2036, continuous settlement could become ordinary service infrastructure, while the coin and chain remain replaceable. Project Agora’s tokenized bank-deposit prototype provides a plausible alternative to stablecoin settlement, although a prototype does not establish realized savings (Bank for International Settlements, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib642)). Bank services matching the full economics would reverse the crypto-specific forecast.

Shared collateral ranks below corridor operations for 2031. The exposed actors are institutions and applications financing the same assets: useful composability becomes forcing only if outsiders suffer worse financing or lose counterparties. By 2036, usable rights, liquidity and integration could widen that dependence, benefiting custody, financing and application providers. Equivalent financing outside the network would defeat the stronger claim. Ethereum settlement, L2 execution and bank-led infrastructure therefore remain competing or complementary implementations, rather than a single adoption decision (Ethereum.org Contributors, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib605); Buterin and others, [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib607); Bank for International Settlements, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib642)).

Trading venues can generate intense pressure on traders and market makers in particular instruments by 2031. For 2036, retained liquidity through adverse conditions matters more than current activity. Venues and order-flow distributors can charge only while execution or customer access remains difficult to replace. Cheap migration after incentives end would reverse the persistence forecast. Bitcoin mining supplies an existing replacement-pressure benchmark, with rewards, energy and exit determining its continuation; it does not establish a new economy-wide forcing event. General business dependence on holding bitcoin remains a weak forecast unless refusing it causes durable commercial losses despite alternatives.

The intersection: access can become necessary while implementations compete.

MCP connects applications to tools and context; A2A coordinates agent systems. AP2 addresses payment authority, while x402 supplies a payment interface with multiple possible rails (Model Context Protocol Contributors, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib644); A2A Project, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib645); Parikh and Surapaneni, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib68); x402, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib646)). These layers do not imply that agent commerce requires cryptocurrency. A priced x402 API endpoint establishes an offer, not repeat paid demand (Coinbase, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib647)). For 2031, software suppliers and merchants face conditional pressure where customers actually delegate purchases. For 2036, interoperable access, authority and recourse could become procurement requirements. Workflow distributors and trusted payment operations are stronger capture candidates than generic connectors. Existing channels preserving orders cheaply would defeat the forcing claim; interchangeable connectors would defeat a supplier’s margin claim.

Table 9: The nine existing cases under the two horizons. These are conditional strategy judgments, not provider rankings or asset-return forecasts.

| **Case** | **2031 dependence** | **2036 structural change** | **Capture and challenge** |
| --- | --- | --- | --- |
| OpenAI | Paid workflows and distribution can make the capability important; provider dependence remains unproved. | Renewal depends on workflow ownership, reliability and customers’ ability to route elsewhere. | Distribution and accepted outcomes could support returns; cheap switching and weak paid retention would undermine them. |
| Anthropic | Enterprise workflows can support demand where measured reliability pays for review and integration. | Interoperability can widen use while moving bargaining power toward workflow owners. | Reliable paid workloads could support returns; equivalent alternatives and cheap switching would weaken the case. |
| Google | Existing workspace and cloud distribution can bundle AI into ordinary purchases. | Capture depends on retained customer access and infrastructure returns as model supply changes. | Distribution and infrastructure could support returns; unprofitable bundling or customers bypassing those channels would weaken the case. |
| Meta / Llama | Available weights can reduce dependence on a single API and complement existing distribution. | Cheaper substitutes can spread capability while shifting revenue to hosts and applications. | Complementary businesses and deployment services; licenses and hosting still matter. |
| DeepSeek | Efficient models challenge the cost of matching frontier capability; full costs remain unobserved. | Efficiency may lower entry costs or expand demand; neither guarantees a lasting model margin. | Efficient operation with retained customers; a training-run estimate cannot establish profit. |
| Bitcoin | Strong existing replacement pressure for miners; weak general business need to hold the asset. | Mining depends on rewards, costs and exit; monetary forcing still needs counterparty loss evidence. | Power, equipment and paid services; token appreciation is a separate outcome. |
| Ethereum / L2s | Shared assets and collateral can create dependence within connected financial applications. | Wider collateral use is conditional; execution may move while base settlement persists or changes. | Liquidity and application access; base fees require separately measured settlement dependence. |
| Solana | Local dependence can form around retained applications, liquidity and execution quality. | Durability requires paid use through competing improvements and adverse cycles. | Applications, distribution and validation could support returns; cheap migration of useful activity would weaken the case. |
| Hyperliquid | The strongest case is concentrated trading liquidity; broader application dependence is conditional. | A wider platform requires external applications that retain paying users through stress. | Trading and application receipts; fee routing and burns alone do not establish holder profit. |

Who can retain the spending.

Table [9](https://rencryptofish.com/posts/forcing-technologies#S4.T9) carries the nine existing cases into both horizons without assuming today’s suppliers remain dominant. For incumbents, distribution, scarce delivered capacity and control of useful financial relationships offer the strongest capture mechanisms. For new specialists, the better candidates sell verified outcomes, incremental protection or difficult settlement operations across platforms. A new base needs retained customers and complements after subsidies; a protocol participant needs separately specified economic rights. Neither widespread use nor token appreciation establishes company profit.

Circle illustrates the payment boundary: its second-quarter 2026 distribution, transaction and other costs were \$412 million against \$701 million of revenue and reserve income, approximately 58.8%; the remainder is before operating expenses (Circle Internet Group, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib643)). A strong settlement forecast therefore does not locate all the value at the issuer. We would revisit these rankings as independent cohorts establish accepted-output savings, changed competing offers and retained paid demand during 2027–2029. The stronger ten-year forecasts depend on those observations and on the specified deployment or interoperability milestones.

### 4.8 What would justify a new supplier

For another base platform, the burden is to identify demand that persists after recruitment subsidies and technical novelty fade, then show a defensible way to charge for it. For a supplier serving several bases, the test is whether portability, reliability or a specialized workflow saves customers enough to support a margin after infrastructure and support. Multi-platform demand is useful only if the platforms cannot cheaply absorb the function.

The stablecoin investment case also depends on the source of demand: issuer rules can create compliance budgets, but settlement can also earn through direct savings and counterparty demand. A new company needs corridor-level retention and net savings, not merely aggregate stablecoin supply. Likewise, useful AI does not guarantee a profitable model provider, and model-provider losses do not establish negative social value. Appendix [O](https://rencryptofish.com/posts/forcing-technologies#A15) records the accounting boundaries and remaining evidence gaps. Section [5](https://rencryptofish.com/posts/forcing-technologies#S5) turns these cases into observable signals; the investment memos then ask which of those signals leaves room for a new company.

## 5 Spotting a forcing event early

The useful signal is a change in the buyer’s economics that makes delay costly. Establish the mechanism first: a rival’s cost or performance improvement, a change in customer demand, a network access loss, a rising attack, or an enforced requirement. Then identify the exposed buyer and estimate the interval before the loss exceeds its tolerance, allowing for installation time. The market signals in Table [10](https://rencryptofish.com/posts/forcing-technologies#S5.T10) come first; Table [11](https://rencryptofish.com/posts/forcing-technologies#S5.T11) records the distinct evidence left by gatekeepers. Published enforcement dates can make timing easier to document.

A cost-saving pilot establishes what adoption can earn. Comparable holdouts’ prices, margins, win rates and retention show what abstention costs as adoption spreads. Use observations before and after a rival’s rollout and an unexposed comparison where possible; control for input prices, customer mix and the exit of weak firms. A capital budget, benchmark or expectation survey is an early hypothesis about pressure, not proof of it. The identification argument of Appendix [I](https://rencryptofish.com/posts/forcing-technologies#A9) becomes practical here: adoption counts alone cannot separate productive value from competitive transfer.

A timing window can be expressed as a threshold and a range rather than a date. In the illustrative fulfillment case, an assumed rival deployment path reaches the holdout’s zero-profit threshold in about sixteen months; a nine-month installation leaves about seven months to begin. Lower pass-through removes the crossing entirely (Section [7.2](https://rencryptofish.com/posts/forcing-technologies#S7.SS2)). A buyer’s tolerance may bind before zero profit, but it has to be stated. The equivalent evidence in other channels is a renewal cohort losing customers, counterparties moving transactions, or expected attack losses overtaking the cost of defense.

Table 10: Leading indicators from the market, by channel. Lead times are illustrative diligence windows, not estimated predictive lags. Dated examples establish chronology, not causation.

| Signal | Channel | Lead | What it looked like | False positive |
| --- | --- | --- | --- | --- |
| Replacement spending rising while realized returns fall | Contest hypothesis | Observe each equipment or model generation | Compare mining efficiency with rewards per unit; AI capacity with paid utilization and replacement costs (Section [4](https://rencryptofish.com/posts/forcing-technologies#S4)) | Demand growth, experimentation or input-price shocks can explain spending; capacity is not an adoption share |
| Paid cohorts retained after incentives or a rival release | Platform durability | Cohort renewals; no universal lead | Measure fee-paying applications and paid model workloads, switching and use of several platforms (Appendix [O](https://rencryptofish.com/posts/forcing-technologies#A15)) | Overlapping developers, airdrop activity, credits and account counts mistaken for exclusive retained customers |
| Capacity delivery, cash receipts and financing tracked separately | Supplier capture | Contract and delivery milestones | Distinguish orders, energized capacity, use and payment; trace supplier-funded purchases and residual asset risk | Backlog or a letter of intent counted as current sales; one dollar counted at several layers |
| A rival’s capital-expenditure or procurement guidance | Contest | Concurrent; 1–3 quarters before the company’s revenue | Meta raised its 2024 capex guidance on April 24, 2024 “to support our AI roadmap,” then guided \$60–65bn for 2025 and \$115–135bn for 2026; Alphabet guided \$175–185bn and Amazon about \$200bn for 2026 (Meta Platforms, Inc., [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib497), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib498); Alphabet Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib499); GeekWire, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib500)); Nvidia’s data-center quarter went from \$22.6bn to \$62.3bn behind them (NVIDIA Corporation, [2024a](https://rencryptofish.com/posts/forcing-technologies#bib.bib501), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib166)) | A capacity signal read as demand: TD Cowen’s February 2025 report of Microsoft lease cancellations, and CoreWeave’s November 2025 capex cut for a late developer, while the company’s revenue kept rising (Fortune, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib502); TIKR, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib503)) |
| A company’s generation cadence or price list | Contest | About 3 quarters to the company’s revenue | Blackwell announced March 18, 2024, samples in August, “in full production” in November, a \$35.6bn data-center quarter in February 2025; a “one-year rhythm” dated through 2028 (NVIDIA Corporation, [2024b](https://rencryptofish.com/posts/forcing-technologies#bib.bib504), [c](https://rencryptofish.com/posts/forcing-technologies#bib.bib505), [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib506)); OpenAI’s price per token down 99% from 2022 to July 2024 (OpenAI, [2024a](https://rencryptofish.com/posts/forcing-technologies#bib.bib507)) | A slipped generation the last one covers (the August 2024 Blackwell delay report; Hopper filled the gap and revenue rose 16% a quarter (SiliconANGLE, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib508))); a price list falling because the capability is commoditizing, the last row of this table |
| A public benchmark or leaderboard result | Capability signal; can revise $p$ | Weeks when the benchmark is a product; 5–15 months when a company can sell against it; years for a new industry | ImageNet 2012: 15.3% error against 26.2% (ImageNet, [2012](https://rencryptofish.com/posts/forcing-technologies#bib.bib509)); ChatGPT to Microsoft’s multibillion-dollar investment in 54 days (OpenAI, [2022](https://rencryptofish.com/posts/forcing-technologies#bib.bib510); Microsoft, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib511)); SWE-bench Verified (August 2024) to Cursor’s \$100m of ARR in five months and \$1bn in fifteen (OpenAI, [2024b](https://rencryptofish.com/posts/forcing-technologies#bib.bib512); Anysphere, Inc., [2025a](https://rencryptofish.com/posts/forcing-technologies#bib.bib513), [b](https://rencryptofish.com/posts/forcing-technologies#bib.bib514)) | A result with no buyer behind it: Inflection-2, “the second most capable LLM in the world,” November 2023, and the team hired away four months later (Inflection AI, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib515)); a leaderboard that is gamed (27 private Llama-4 variants tested on Chatbot Arena) (Singh et al., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib516)) |
| Competitors passing cost savings into prices or service, with holdout margins or retention falling | Cost and price response | The buyer’s tolerance threshold, less installation time | Fulfillment case: monitor realized cost per order, comparable contract quotes and rival deployment; the numerical path in Section [7.2](https://rencryptofish.com/posts/forcing-technologies#S7.SS2) is illustrative | Savings retained as profit; unrelated price cuts; changing customer mix; holdouts able to specialize or exit cheaply |
| A learning curve on course to cross the incumbent’s cost for a class of buyers | Direct value, synchronized | 12–36 months; computable from the curve | Battery packs at \$115 then \$108 a kilowatt-hour (BNEF, 2024–25) with Chinese EVs at parity; solar at 4.3 cents against coal at 7.3 (IRENA) | A curve that flattens before the crossing; a crossing in a segment too small to matter; a commodity whose producers’ margins go to zero as it crosses |
| Rivals naming the technology on earnings calls, or a CEO memo making it a condition of headcount | Contest or direct value | 0–6 months (late) | Shopify’s April 2025 memo requiring teams to show AI could not do a job before hiring for it | Talk without a budget line; the mention is itself the competitive signal and the capability is bundled |
| Holdouts losing measurable share, fills, traffic or applicants, or saying so in a filing | Contest | Concurrent; the filing 1–2 quarters later | Pew’s observed 8% click-through with an AI summary against 15% without one, before establishing causation; slower trading firms losing fills in the latency race; Chegg’s May 2023 call, with ChatGPT “having an impact on our new customer growth” and the shares down 48% (Chegg, Inc., [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib494); Associated Press, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib495)); Nokia’s smartphone share from 50.9% to 40.8% in the year after the iPhone (Fierce Wireless, [2009](https://rencryptofish.com/posts/forcing-technologies#bib.bib517)) | Share lost for unrelated reasons, or an adoption share rising because holdouts exited (Appendix [H.2](https://rencryptofish.com/posts/forcing-technologies#A8.SS2)); a holdout’s price hit with no share loss (Pearson fell 15% in sympathy with Chegg and called itself ChatGPT-proof (The Motley Fool, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib518))); an analyst’s forecast of holdout loss (Gartner’s projected 25% fall in search volume by 2026 (Gartner, Inc., [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib519)); revenue growth is not a direct test of a volume forecast) |
| A service level that most rivals match within a few quarters | Expectations | 0–12 months | Same-day delivery (Amazon, Walmart and Target in 2025); daily driver payouts (Lyft to Uber in three months, 2015–16) | A cascade with no measured customer loss; a platform that bundles the feature before any company budget forms |
| Customer-expectation surveys | Expectations | 2–5 years, once the supply side moves | PwC, 2018: 32% of customers would leave a brand after one bad experience (PwC, [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib521)); Salesforce, 2023: 77% expect to interact with someone immediately (Salesforce, Inc., [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib522)); the delivery surveys of Section [3.2](https://rencryptofish.com/posts/forcing-technologies#S3.SS2); the support-AI budgets of 2023–26 followed (Fin, Sierra, Decagon) | A stated preference without a budget: openness to AI fell in the 2023 survey while support-AI budgets rose fastest |
| Attack statistics rising faster than defenses | Counter | 6–18 months | Deepfakes in one of five biometric fraud attempts; DDoS record sizes reset yearly | The platform absorbs the defense (mail providers against AI-written outbound; job boards against AI-written applications) |
| A counter company appearing, or a venue adding a native defense | Counter | 3–7 years from founding to an enterprise budget; its statistics lead by 2–3 years | DDoS: the attacks on Yahoo and eBay in February 2000, Prolexic founded in 2003, bought by Akamai for \$370m in 2014 (Wikipedia contributors, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib523)); deepfakes: Deeptrace’s 2019 census, Sumsub’s tenfold rise in 2023, a Gartner designation and a KPMG stake for Reality Defender in 2026 (Deeptrace, [2019](https://rencryptofish.com/posts/forcing-technologies#bib.bib524); Sumsub, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib525); Reality Defender, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib526)) | A counter founded before the attack is commercial (96% of the deepfakes Deeptrace counted in 2019 were pornography); the venue absorbs the defense, and the counter becomes a feature |
| The venue launching its own product for the race | Contest | Negative signal | Ads in ChatGPT and in Google’s AI Mode (2026); retailers’ own media networks, more than 200 by 2024, with Criteo’s retail-media line flat | Possible exception: customers retain independent tools that improve on the venue’s product |
| The price of the forced capability falling toward zero | Any | Negative signal | Let’s Encrypt, December 2015; a free e-invoicing tier inside an accounting suite | Possible exception: customers still pay for complementary integration or management services |

Table 11: Leading indicators from a gatekeeper. Lead times are illustrative windows from the signal to the first budget, not estimated predictive lags.

| Signal | Channel | Lead | What it looked like | False positive |
| --- | --- | --- | --- | --- |
| A final rule with a dated obligation, in the Federal Register, the EU Official Journal or a ministry circular | Exclusion | 12–36 months | CMMC’s acquisition rule, published September 10, 2025, with Level 2 certification required in solicitations from November 10, 2026; France’s September 1, 2026 and 2027 e-invoicing phases | A proposed rule; a rule with no enforcement (France levies no sanctions in 2026); a date that slips (the EU AI Act’s Annex III moved 16 months in July 2026) or is suspended (CMMC’s second phase, July 13, 2026) |
| A platform policy post with a version number and a date | Exclusion, steep $\Phi$ | 3–18 months | Chrome’s February 8, 2018 announcement that version 68 would mark HTTP “Not secure”; the CA/Browser Forum’s 2025 ballot cutting certificate lifetimes; Apple’s age-range API | The platform supplies the capability itself, free, and the company market never forms |
| A new line item in security questionnaires, RFPs or subcontract flow-downs | Exclusion, buyer as gatekeeper | 6–24 months | SOC 2 reports as a condition of enterprise sales, which built Vanta; CMMC clauses flowing down to subcontractors; AI-governance questions appearing in company reviews | Boilerplate questions nobody scores; a requirement an existing supplier satisfies by default |
| An insurer or lender condition | Exclusion | 6–12 months | Cyber insurers tightening underwriting and stipulating controls such as multi-factor authentication and endpoint detection in the 2021 hard market, when US pricing rose 96% in a year (Marsh, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib262)) | Conditions waived at renewal once the market softens |
| A dominant customer’s supplier letter with a tagging, labelling or data requirement and a date | Exclusion, customer as gatekeeper | 6–24 months | Walmart’s January 2022 letter (tags in the specified additional categories by September 2, 2022) and its February 2024 expansion; Impinj’s revenue up 93% over 2021–24 | A mandate the customer does not enforce, or whose gain it keeps for itself: Walmart’s 2003 pallet mandate had fizzled by 2007 |

Three signals warrant closer examination: announced deadlines, platform competition and pilot results. The first is the deadline that moves. The model separates belief in technical effectiveness from expected enforcement. A rule’s legal status does not remove uncertainty about enforcement or timing; $\varepsilon$ must reflect the expected loss. Regulation 2026/1744 moved the AI Act’s Annex III high-risk requirements from August 2026 to December 2, 2027, with a separate August 2028 date for product-related high-risk systems (European Parliament and Council of the European Union, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib260)). France’s e-invoicing mandate was postponed from 2024 before it started in 2026. The SEC ended its defense of the stayed climate-disclosure rules in March 2025 and proposed rescission in May 2026; neither action was itself a completed repeal (U.S. Securities and Exchange Commission, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib261), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib686)). A supplier planning around the original date could incur sales costs before delayed or cancelled demand. For a thesis that depends on a mandate, the strongest timing evidence is final text with credible enforcement. A proposal requires a probability and delay allowance; economic losses already borne by the buyer should be assessed separately.

The second is the platform that owns both sides of a race. AI-written outbound against inbox filtering is a real arms race, and Google and Microsoft include the defense in their mailbox products, limiting demand for a separate supplier. AI-written job applications against screening has the same shape, with LinkedIn, Workday and Greenhouse holding the defense. An independent supplier needs protection or information beyond the bundled controls. Identity verification is one such possibility, which is why these races inform that memo rather than establish separate investable markets here.

The third is the pilot. Its result may include a temporary positional advantage and omit the network value of later adoption. Appendix [E.2](https://rencryptofish.com/posts/forcing-technologies#A5.SS2)’s $\alpha-\beta$ comparison is between the first adopter’s payoff and the field’s payoff at full adoption; it is not a general formula for a company’s price ceiling. The memos therefore estimate the buyer’s incremental ceiling $B(x,p)-\kappa-W$ along an adoption path, test continued operation and alternatives, and record what observable evidence would change that path. In a productive market, urgency can increase while the incremental ceiling stays flat.

## 6 Where we would invest now

We would prioritize companies that can operate at the new cost structure and suppliers of scarce complements that make adoption useful. The strongest new research priorities are narrowly operated AI services and repeatable industrial automation, followed by contract-backed power flexibility and corridor-specific payment operations. Security and compliance provide useful comparisons. Productive operators also merit consideration when they can demonstrate a customer advantage.

The distinction is between an attractive direction and an investable company. Public sources establish deployments, competing products and some company outcomes. They do not establish private unit economics, an entry valuation or a causal estimate of holdout losses in the proposed fields. The decisions below allocate diligence, not capital. A software-only seed investor should treat equipment financing, acquisitions and power contracts as separate capabilities to acquire or partner for, rather than hide them inside a software revenue multiple.

The analysis compares sixteen opportunities across crypto, AI, fintech and other markets, with detailed assessments of four and two-year operating scenarios for six. Appendix [N](https://rencryptofish.com/posts/forcing-technologies#A14) gives their parameters and the full decision map. The repository note paper/investment\_directions\_findings.md contains the source ledger, public organization map, competing alternatives and calculations. The assessment uses public sources; interviews and paid experiments remain to be conducted.

Table 12: Investment research priorities as of October 20, 2026. “Advance” means investigate an identifiable paid position; it is not a completed investment decision.

|  | Direction | Position worth owning | Decision and binding condition |
| --- | --- | --- | --- |
| 1 | AI-operated specialist services | Recurring delivery contracts and dependable exception handling | Advance a narrow workflow; cash labor reduction and retained contribution must survive repricing. |
| 2 | Repeatable industrial cells | Application expertise, field service and financeable equipment | Advance one job family; uptime, changeovers and debt service must fit the fee. |
| 3 | Flexible power access | Accepted operating obligations and access/payment rights | Requires enforceable operating and payment rights. |
| 4 | Corridor payout operations | Embedded distribution and a difficult local endpoint | Conditional; a matched all-in saving and attainable retained flow are required. |
| 5 | Shared fraud signals | Useful receiving-account labels and operational access | Requires a data partner and evidence of losses prevented in live use. |
| 6 | Seller negotiation | Authority over a vertical commercial workflow | Run a small experiment; the scenario assumes no bargaining advantage until one is measured. |

### 6.1 Own the delivered service, then test the competitive pressure

For AI-operated specialist services, start with a defined document-completion or exception-resolution service in logistics. The investee sells accepted work and owns delivery quality; it is not merely selling seats in an assistant. C.H. Robinson reports deployed agents contributing to productivity, while its H1 2026 disclosure shows headcount declining alongside higher personnel expense, including restructuring (C.H. Robinson, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib648), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib649)). That combination supports feasibility and warns against turning time saved directly into cash saved. It does not isolate an AI effect or identify non-adopting rivals.

The constructed mature operator has \$20m revenue and \$12m of addressable labor. A realizable 20% saving gives $\gamma=\$2.4m$; \$400k upstream capability purchases and \$600k other costs leave $F=\$1.4m$. If competition passes through 80% of the saving, $h(1)=\$1.92m$ and the producer payoff change is $-\$520k$. With \$1.2m initial profit, the saturated adopter still earns \$680k while the holdout loses \$720k. The forcing mechanism is a change in market prices or service, not a mandate. The pass-through rate and adoption trajectory remain assumptions.

Value can persist in distribution, contracts and reliable completion as models improve. It need not persist in the first tool used. The investee pays models, staff and working capital before retaining the residual. The illustrative new-business funnel reaches \$3.27m annualized service receipts at month 24 and needs about \$4.06m of equity including a 25% contingency, before any acquisition. It remains cash-consuming at that point. The established operator used in the payoff calculation is much larger than the startup projected at month 24.

Convoy illustrates the risk that a logistics platform may change owners without delivering durable returns to its original investors: Flexport describes buying Convoy’s platform and later selling it to DAT (Flexport, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib650)). That is not a controlled failure of AI. It is a reminder that distribution, finance and operating execution are part of the product.

### 6.2 Make the industrial application repeatable and financeable

For industrial automation, the initial product is a machine-tending or packaging cell designed for a consistent set of tasks. Formic’s 3D Machine case reports operating hours and a capacity gain under a service arrangement, without disclosing the price or cash saving (Formic, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib651)). Greater capacity counts in $\gamma$ only when it eliminates expense or earns contribution on sold output. The performance guarantee transfers some risk from buyer to operator.

The scenario assumes a \$150k reduction in labor expenditure and \$50k of scrap/rework savings, with a \$100k annual fee and \$60k of other buyer cost. Thus $F=\$40k$. With the assumed effectiveness haircut and waiting value, the current margin is $-\$30k$: an application with slightly worse economics should wait or fail. The \$100k fee is an assumed \$25 per paid hour at 4,000 annual hours, not Formic’s quoted price.

Supplier economics are a separate calculation. A \$180k installed asset depreciated over five years, \$35k annual cash delivery expense and \$100k fee produce \$29k economic gross profit before overhead. At half the fee, that becomes a \$21k loss. The assumed equipment loan does not eliminate capital need: the 24-month path reaches about 29 active cells, requires \$3.93m peak equity before contingency, and carries \$3.51m equipment debt at month 24. Without that facility, peak cash need is \$7.10m before contingency.

The industry comparison reinforces the distinction. Symbotic disclosed non-billable deployment overruns in its FY2024 reporting and a net loss alongside substantial FY2025 revenue (Symbotic / SEC, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib683); Symbotic / SEC Exhibit 99.1, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib654)). Its warehouse systems are not retrofit cells, but backlog growth does not establish that contract prices cover installation and maintenance risks. The attractive asset is a repeatable application with local service density and financing, rather than a generic robotics label.

### 6.3 Own a scarce complement: usable power or a payout endpoint

Flexible power access.

The hypothesis is that accepted load flexibility lets a site obtain usable power sooner or on better terms. A Phoenix field study demonstrated a 25% power reduction on a 256-GPU cluster for three hours under its selected workload commitments; Google announced utility agreements; Indiana’s case index lists a Google capacity and demand-response arrangement as pending (Coskun et al., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib660); Google, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib659); Indiana Office of Utility Consumer Counselor, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib662)). None is a disclosed startup fee or a general right to connect a new site.

For a 20MW site, assume 5MW becomes usable earlier and contributes \$200k per MW-year after ordinary compute, power and workload opportunity costs, before the separately listed flexibility costs. Then $\gamma=\$1m$; a \$250k fee and \$350k other cost leave $F=\$400k$. The current haircut and waiting value require about 5.83MW to clear the purchase hurdle, so the assumed 5MW does not yet do so. If the utility recognizes no incremental capacity or access, set that benefit to zero.

The investee must control useful workload flexibility and possess enforceable payment/access rights. A cloud, site owner, utility or incumbent aggregator may own them instead. Duke’s modeled system headroom is not a site inventory or a software market (Norris et al., Duke University, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib661)). The coordination-only funnel reaches four active sites and \$1m annualized receipts at month 24, requiring roughly \$7m equity with contingency. Generation, storage, buildings and transmission are excluded and require separate project finance.

Corridor payout operations.

For payments, the scarce complement can be local redemption, liquidity and distribution. Stripe’s Remote case supports practical stablecoin use, while Wise’s falling aggregate take rate and fast transfers show that the competing rails are improving too (Stripe, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib625); Wise, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib656)). Compare completed recipient value in a named corridor, including conversion, failures, support and prefunding; blockchain speed alone is not the advantage.

The payout scenario assumes \$200m annual eligible flow, a 20bp operational saving, a 6bp fee and 6bp other cost, with no unmeasured network premium. It gives $F=\$160k$ and a current decision margin of zero. At 80% pass-through, producer payoff falls \$160k despite the positive adoption incentive. These are required economics to test, not a disclosed corridor quote.

The scale check is restrictive. McKinsey and Artemis estimate \$226bn of annualized B2B stablecoin payment activity from December 2025, not total on-chain transfers or a full-year forecast (McKinsey and Artemis Analytics, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib655)). At an assumed retained 6bp, that is \$135.6m of global category receipts; 10% share gives \$13.56m before corridor restrictions. \$100m would require about \$167bn flow, 74% of the dated global run rate. A narrow independent entrant needs exceptional distribution, a more valuable endpoint or additional paid services.

Reserve-income distribution is a different pool: Circle’s Q2 2026 filing records substantial Coinbase-related distribution expense (Circle / SEC, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib658)). It illustrates the value of a distribution relationship, not a fee available to any payment startup. The 24-month customer acquisition scenario for payouts produces only \$0.55m annualized receipts against a \$4.69m equity envelope including contingency, even with a hypothetical liquidity facility. An existing operator improving its rail can be a better investment than building a low-fee corridor company from zero.

### 6.4 Negotiation and fraud services require further evidence

Seller negotiation.

Automated procurement may create demand for seller-side negotiation tools. Buyers and rival suppliers must be modeled as separate groups. Rival suppliers can compete over contribution; buyer automation is an external state. Pactum documents procurement deployments and supplier satisfaction, while Vendavo already supplies seller pricing and commercial workflows (Pactum, [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib58); Vendavo, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib668)). These establish activity and substitutes, not the seller’s incremental bargaining gain.

With no measured bargaining advantage, the scenario counts only \$100k in administrative savings against \$200k in annual costs, giving $F=-\$100k$. At $r=2$, at least \$200k of lone-adopter contest edge would be needed merely to restore $F=0$, with no added cost. That edge must be measured in contribution after volume, payment timing and concessions. The interesting product may be a system that prices terms, finances a concession or refuses an unprofitable agreement. Conversational skill alone is not the investment.

Shared fraud signals.

Retain the bank’s residual-loss problem but narrow the product to receiving-account information an entrant can legally and operationally use. Pay.UK’s reported detection uplift came from historical transaction data; Mastercard describes live customer deployments; BIS Hertha used synthetic data (Pay.UK, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib664); Mastercard, [2023](https://rencryptofish.com/posts/forcing-technologies#bib.bib665); Bank for International Settlements, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib666)). Those are three different evidence levels. None directly estimates an entrant’s incremental net prevented loss.

The fraud scenario assumes 15% prevention of \$5m residual annual loss and no separately counted network benefit: $\gamma=\$750k$, $c=\$600k$, $F=\$150k$. With the current haircut and waiting value, the buyer needs 25% net prevention to buy now. Network operators and established suppliers already have access, so a new company needs a specific data right, useful incremental signal and paying counterparties. A rising expected loss can raise a willingness-to-pay ceiling; competition and false positives still determine the realized price. The fraudsters and banks are not interchangeable shares in the paper’s same-field counter theorem.

### 6.5 Other investment opportunities and benchmarks

Certificate lifecycle and cryptographic agility.

This remains the clearest requirement-led benchmark for heterogeneous machine estates. The adopted public-certificate schedule moves to 200-day validity in March 2026, 100 days in March 2027 and 47 days in March 2029 (CA/Browser Forum, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib682)). Inventory, rotation and outage prevention can remain valuable above a cheap credential. Free automation and incumbent integration constrain the independent company’s fee. Five hundred customers at \$50–200k means \$25–100m revenue, reaching the top only at the highest fee and, in a 2,000-account pool, 25% share. Post-quantum migration and recurring certificate operation have different renewal economics.

Deepfake identity and age verification.

Retain incremental defense inside an existing paid workflow. Separate the requirement to check age from fraud prevention. Counts of checks and requests from different platforms are not automatically deduplicated, independently payable events. Require incremental prevented loss or improved acceptance after false rejects, review expense and a credible bundled substitute. The counter model does not predict that realized per-check prices must rise.

Civil counterdrone.

Keep it for an investor with the appropriate hardware, installation and customer channel. Legal authority and a funding line can open a market without forcing a recurring purchase. A grant, procurement order or site count is not software ARR. Recurring maintenance, detection quality and the platform’s ownership of the customer determine the paid position.

Placement in AI answers.

Keep the contest as a model benchmark; downgrade a new horizontal measurement entrant. The venue controls access and can sell the optimization workflow. A transaction feed, regulated workflow or proprietary outcome measurement may justify a narrower company. The category spending estimate and the worked supplier revenue scenario measure different things. Neither establishes that a new entrant can reach \$100m in revenue.

Invoice exceptions.

Retain a vertical exception-resolution opportunity only where it beats an already compliant system. A mandate for the base platform does not make the add-on compulsory. The worked example in Section [7](https://rencryptofish.com/posts/forcing-technologies#S7) compares it against suite capabilities. Five country opportunities of €18m yield €90m before proving comparability, adoption and share; an eventual category pool is not the startup’s sales plan.

Horizontal compliance and CMMC.

Monitor enforcement dates before prioritizing an investment. Underwrite the current enforceable condition, who owns the workflow, recurring paid effort and alternatives. A multiyear assessment contract is not annual recurring revenue. A deadline can synchronize shopping while most spending remains with suites, auditors and established service firms.

**What would reverse this ranking**

Lower the priority of AI-operated services if delivery savings disappear after all costs or accrue entirely to customers. Lower the priority of industrial cells if failures, changeovers or financing eliminate the operator’s margin. Do not advance flexible power access without accepted rights, or payout operations without matched corridor economics and distribution. Seller negotiation rises in priority only with measured seller contribution; shared fraud signals rise only with live incremental prevention and usable data rights. Across all sixteen, persistent profitable holdouts or a compatible lower-priced incumbent can invalidate the forcing or capture thesis. Absence of public AI claims is not evidence that a firm is a holdout.

## 7 Four worked cases

The cases begin with two economic mechanisms: brands competing for answer placement, then fulfillment operators whose productivity gains change market prices. They are followed by a hybrid defense sold into existing verification flows and an invoice add-on sold above a compliant platform. The first case’s field path uses the contest model; the second is the explicit price-response extension in Section [1.3](https://rencryptofish.com/posts/forcing-technologies#S1.SS3), with its deployment path assumed rather than estimated. The final two compare the startup with an alternative that already satisfies the mandate, so the penalty cancels. Detection earns avoided fraud losses; invoice exceptions earn labor savings. Three cases trace monthly company revenue paths, while fulfillment isolates the timing and capture consequences of a changing cost structure. Inputs and generation commands are recorded in Appendix [S](https://rencryptofish.com/posts/forcing-technologies#A19); planning assumptions are not forecasts of named companies.

### 7.1 Case 1: answer placement for a consumer brand

No imposed adoption requirement drives this case; brands compete for placement on the answer platforms. The buyer is a consumer brand with \$10 million of digital marketing spend, of which search takes 22.8%, the share Gartner reports for SEM and SEO (Semrush, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib224)): \$2.28 million a year. Pew observed clicks on conventional results in 8% of visits with an AI summary, against 15% without one (Chapekis and Lieb, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib222)). That comparison motivates exposure to changing search behavior; it does not show that named brands receive all the lost traffic. This case assumes a fixed prize. A category’s answers name a handful of brands, so a brand that optimizes while its rivals do not takes placement from them, and gives it back as they catch up. We assume answer placement decides \$100,000 a year of the brand’s gross profit, about 4% of its search budget, and that an optimizing brand is named five times as often as one that is not ($r=5$); together those put the lone adopter’s edge at $\alpha=\$400{,}000$ a year, the number a pilot would show while no rival had the tool. With every rival on it the edge is $\alpha/r=\$80{,}000$, plus \$20,000 of measurement value that does not depend on rivals. Against a \$60,000 price, just under Semrush’s \$64,000 enterprise average (Semrush Holdings, Inc., [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib226)), \$60,000 of the brand’s own content and feed work and \$10,000 of waiting value, the margin to buy first is \$290,000 and the margin at full adoption is minus \$30,000 (Table [13](https://rencryptofish.com/posts/forcing-technologies#S7.T13)). The launch price clears until 66% of the brand’s rivals have a tool (Figure [4](https://rencryptofish.com/posts/forcing-technologies#S7.F4)). These are purchase margins at the launch price, not price ceilings. The full-adoption ceiling is $B(1,1)-\kappa-W=\$30{,}000$; leaving the buyer a further \$20,000 of margin reduces the supplier price to \$10,000.

Table 13: Case 1 scenarios: an answer-placement tool sold to a consumer brand whose rivals are buying the same thing. Monetary amounts are USD thousands, annual except acquisition, onboarding and cumulative cash. Peak ARR is measured over the first 24 months. The field’s adoption share is simulated from the same parameters with the model’s dynamics; “launch price held” means customers whose margin turns negative do not renew.

<table><tbody><tr><td>Input or result (USD thousands per year unless stated)</td> <td>Downside</td> <td>Central</td> <td>Upside</td></tr> <tr><td></td> <td></td> <td></td> <td></td></tr> <tr><td>Direct value, $\gamma$</td> <td>10</td> <td>20</td> <td>40</td></tr> <tr><td>Lone adopter’s edge, $\alpha$</td> <td>280</td> <td>400</td> <td>500</td></tr> <tr><td>Strength ratio, $r$</td> <td>5.0</td> <td>5.0</td> <td>3.0</td></tr> <tr><td>Gross buyer benefit $B$ with no rivals on the tool ($x=0$)</td> <td>290</td> <td>420</td> <td>540</td></tr> <tr><td>Gross buyer benefit $B$ with every rival on it ($x=1$)</td> <td>66</td> <td>100</td> <td>207</td></tr> <tr><td>Launch price, $q$</td> <td>60</td> <td>60</td> <td>60</td></tr> <tr><td>Other annual buyer cost, $\kappa$</td> <td>60</td> <td>60</td> <td>60</td></tr> <tr><td>Waiting value, $W$</td> <td>20</td> <td>10</td> <td>0</td></tr> <tr><td>Margin to buy first, $M(0)$</td> <td>150</td> <td>290</td> <td>420</td></tr> <tr><td>Margin at full adoption, $M(1)$</td> <td>-74</td> <td>-30</td> <td>87</td></tr> <tr><td>Share of rivals on the tool at which the launch price stops clearing</td> <td>28.8%</td> <td>65.9%</td> <td>100%</td></tr> <tr><td>Month the field reaches that share</td> <td>9</td> <td>34</td> <td>never</td></tr> <tr><td>Field adoption at month 18, 24 and 48</td> <td>40 / 44 / 52%</td> <td>50 / 58 / 72%</td> <td>50 / 60 / 82%</td></tr> <tr><td>Qualified accounts over 24 months</td> <td>300</td> <td>600</td> <td>1,000</td></tr> <tr><td>Win fraction</td> <td>10%</td> <td>15%</td> <td>20%</td></tr> <tr><td>Installations per month after ramp</td> <td>2</td> <td>4</td> <td>6</td></tr> <tr><td>Annual churn while the price clears</td> <td>15%</td> <td>10%</td> <td>8%</td></tr> <tr><td>Second generation: launch month</td> <td>never</td> <td>20</td> <td>16</td></tr> <tr><td>Active customers at month 24, launch price held</td> <td>2</td> <td>74</td> <td>120</td></tr> <tr><td>Peak ARR in first 24 months, launch price held (month)</td> <td>545 (9)</td> <td>6,897 (24)</td> <td>12,196 (24)</td></tr> <tr><td>ARR at month 24, launch price held</td> <td>118</td> <td>6,897</td> <td>12,196</td></tr> <tr><td>ARR at month 24, price cut to the ceiling</td> <td>272</td> <td>6,231</td> <td>12,196</td></tr> <tr><td>Gross margin at the launch price</td> <td>90%</td> <td>90%</td> <td>90%</td></tr> <tr><td>CAC payback (months)</td> <td>7.8</td> <td>7.8</td> <td>7.8</td></tr> <tr><td>ARR at month 18 (Series A), launch price held</td> <td>218</td> <td>3,305</td> <td>7,405</td></tr> <tr><td>Burn multiple, trailing 12 months</td> <td>n/a</td> <td>1.0</td> <td>0.5</td></tr> <tr><td>Cumulative cash low point</td> <td>-5,853</td> <td>-4,701</td> <td>-5,130</td></tr></tbody></table>

The field’s own path says when that happens. Simulating the brand’s category from the same parameters (costs dispersed with $\sigma=0.3$ around the mean, 3% of brands on a tool at launch, eligible non-adopters each having a 4.5% monthly adoption probability; Appendix [S](https://rencryptofish.com/posts/forcing-technologies#A19)) puts the field at 50% after 18 months, 58% after 24 and 72% after 48; it passes 66% after 34. This is an irreversible path, not the static equilibrium: adoption continues beyond month 48 and can strand brands that bought while the edge was larger. Holdouts lose ground even though full adoption does not pay the mean-cost brand. Under these assumptions, the supplier can sustain its launch price for 34 months.

The supplier’s early revenue and acquisition costs appear attractive. Six hundred qualified brands over 24 months, a 15% win rate against Profound, Peec, Adobe’s Brand Visibility and the enterprise SEO platforms, four installations a month, \$6,000 of variable cost a customer (a 90% gross margin), \$35,000 of acquisition and onboarding (a 7.8-month payback) and \$250,000 a month of fixed cost give \$2.1 million of ARR at month 12 and \$3.3 million at month 18, with \$2.5 million of net new ARR in the trailing year and a burn multiple of 1.0 (Table [14](https://rencryptofish.com/posts/forcing-technologies#S7.T14)). Those early results could support a Series A, but the launch price becomes unsustainable in month 34, within the financing period considered here. The path table compares two policies against the same simulated field at the launch price. It does not solve the feedback from this supplier’s repricing to industry adoption; customers can leave the supplier while retaining the capability elsewhere. Hold the price, and from month 35 customers do not renew: ARR peaks at \$11.3 million in month 34 and is \$3.5 million at month 48, and the second generation, placement in agent-driven purchases launched at month 20 with a smaller edge at the same price, is past its own break-even by month 39, because its edge erodes on the same timetable. Cut the price to the ceiling, keeping \$20,000 of margin for the buyer, and the customers stay: ARR is \$8.2 million at month 48, with the first generation at \$33,000 a year by month 48. Revenue depends on successive product generations. The two-generation illustration does not establish a sustainable release cadence. Both the next product’s value and its timing must be tested against the platform-controlled contest described in Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px4).

Table 14: Case 1 central path under two price policies, and the ceiling at three prices.

<table><tbody><tr><td>Central case (USD thousands)</td> <td>Launch price held</td> <td>Price cut to the ceiling</td></tr> <tr><td></td> <td></td> <td></td></tr> <tr><td>Field adoption at month 12</td> <td colspan="2">39%</td></tr> <tr><td>Field adoption at month 24</td> <td colspan="2">58%</td></tr> <tr><td>Field adoption at month 36</td> <td colspan="2">67%</td></tr> <tr><td>Field adoption at month 48</td> <td colspan="2">72%</td></tr> <tr><td>ARR at month 12</td> <td>2,092</td> <td>2,092</td></tr> <tr><td>ARR at month 24</td> <td>6,897</td> <td>6,231</td></tr> <tr><td>ARR at month 36</td> <td>10,186</td> <td>8,244</td></tr> <tr><td>ARR at month 48</td> <td>3,499</td> <td>8,192</td></tr> <tr><td>of which the second generation, month 48</td> <td>1,884</td> <td>3,453</td></tr> <tr><td>Price at month 48 (gen. 1, USD thousands)</td> <td>60</td> <td>33</td></tr> <tr><td>Series A snapshot, month 18: ARR</td> <td>3,305</td> <td>3,305</td></tr> <tr><td>Net new ARR, prior 12 months</td> <td>2,493</td> <td>2,493</td></tr> <tr><td>Burn multiple</td> <td>1.0</td> <td>1.0</td></tr> <tr><td>Gross margin at the launch price</td> <td colspan="2">90%</td></tr> <tr><td>Eligible accounts</td> <td colspan="2">5,000</td></tr> <tr><td>Achievable share</td> <td colspan="2">10%</td></tr> <tr><td>Ceiling ARR at the launch price (60)</td> <td colspan="2">30,000</td></tr> <tr><td>Ceiling ARR at the price the field at month 48 supports (33)</td> <td colspan="2">16,727</td></tr> <tr><td>Ceiling ARR at the price full adoption supports (10)</td> <td colspan="2">5,000</td></tr></tbody></table>

The size of the prize and the rate at which rivals adopt limit attainable revenue. Five thousand enterprise brands at a 10% share is \$30 million of ARR at the launch price, \$16.7 million at the price the field supports at month 48 and \$5 million at the price full adoption supports; a category leader at a 40% share clears \$100 million at the launch price and not at the month-48 price. The downside is the small prize: at \$70,000 the launch price clears for nine months, ARR peaks at \$545,000 and the company has spent \$5.9 million. The upside is the large one: at \$250,000, with a holdout one third as likely to be named, the price clears at any adoption and ARR reaches \$12.2 million at month 24 on a burn multiple of 0.5, which is the category leader’s case. What separates the three is the prize and the strength ratio, and a pilot measures neither. The two numbers a seed memo in a contest has to carry are the ceiling at full adoption and the share of rivals already on a tool.

### 7.2 Case 2: fulfillment savings become competitive pressure

An illustrative fulfillment operator processes one million orders a year. Automation lowers its operating cost; as rivals adopt, competition passes part of the saving to customers through lower prices. The mechanism has observable precursors: Amazon has described cost savings it aims to pass to customers, and Symbotic’s January 2025 agreement envisaged systems at 400 Walmart pickup and delivery centers, subject to performance criteria (Amazon, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib636); Symbotic Inc., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib374)). Neither source establishes the price response or holdout losses assumed here. Every numerical input below is a planning assumption, recorded in data/investor/productivity.json; none estimates a named company.

At the initial price of \$5 an order, the operator’s \$4.50 of operating cost leaves \$0.50, or \$500,000 a year. Costs include the allocated operating costs of the site at this volume. Automation saves \$1.20 per order before a supplier charge of \$0.35 and the buyer’s own \$0.15 of integration and operating costs. The supplier charge includes annualized equipment and support. At unchanged prices the adopter earns \$1.20 per order, or \$1.2 million a year. Adoption already pays: the \$700,000 improvement exceeds the assumed \$50,000 annual equivalent of waiting value. Economic pressure arrives when rivals change the price the old process must earn.

Let $s=\$1.20$ be the gross saving and let $\rho=0.8$ be the assumed share of that saving passed through when the rival field is fully automated. At rival adoption share $x$, suppose the market price is

$$
P(x)=P_{0}-\rho sx=5-0.96x.
$$

With annual volume $N$, incumbent cost $C_{0}$, supplier price $q$ and other buyer cost $\kappa$, annual operating profits are

$$
\pi_{N}(x)=N[P(x)-C_{0}],\qquad\pi_{A}(x)=N[P(x)-(C_{0}-s)-q-\kappa].
$$

These are operating profits, not the changes from the old world used in the base model. Subtracting the original \$500,000 from both yields the extension in Section [1.3](https://rencryptofish.com/posts/forcing-technologies#S1.SS3): $\gamma=Ns$, $c=N(q+\kappa)$ and the common loss $h(x)=N\rho sx$. A price reduction is received by customers; it is not a fixed prize redistributed among the operators.

Table 15: Illustrative fulfillment economics at fixed annual volume. Supplier price is \$0.35 per order throughout. The combined ceiling is the lower of the incremental-return and continued-operation bounds, before competing suppliers. All values follow from stated assumptions.

<table><tbody><tr><td>Rivals automated</td> <td>0%</td> <td>50%</td> <td>75%</td> <td>100%</td></tr> <tr><td>Market price per order (USD)</td> <td>5.00</td> <td>4.52</td> <td>4.28</td> <td>4.04</td></tr> <tr><td>Holdout operating profit (USD thousands)</td> <td>500</td> <td>20</td> <td>-220</td> <td>-460</td></tr> <tr><td>Adopter operating profit (USD thousands)</td> <td>1,200</td> <td>720</td> <td>480</td> <td>240</td></tr> <tr><td>Incremental margin after waiting value (USD thousands)</td> <td>650</td> <td>650</td> <td>650</td> <td>650</td></tr> <tr><td>Incremental price ceiling per order (USD)</td> <td>1.00</td> <td>1.00</td> <td>1.00</td> <td>1.00</td></tr> <tr><td>Viability price ceiling per order (USD)</td> <td>1.55</td> <td>1.07</td> <td>0.83</td> <td>0.59</td></tr> <tr><td>Combined price ceiling per order (USD)</td> <td>1.00</td> <td>1.00</td> <td>0.83</td> <td>0.59</td></tr></tbody></table>

The holdout breaks even at $x^{*}=(P_{0}-C_{0})/(\rho s)=52.1\%$. At full adoption it loses \$460,000 a year; the adopter still earns \$240,000. The old process has become unviable even though the incremental gain from switching remains \$700,000, or \$650,000 after waiting value, at every adoption share in Table [15](https://rencryptofish.com/posts/forcing-technologies#S7.T15). This is why a positive-ROI product can also become forcing, and why urgency alone does not imply a rising supplier price.

The threshold gives a conditional sales window. Suppose rival adoption is currently 20% and rises by two percentage points a month. Zero holdout profit is then about sixteen months away. With nine months to install, implementation must start within roughly seven months to finish before that crossing. This is an assumed deployment path across firms with different constraints, not a simulated equilibrium or a forecast. At 40% pass-through, even full adoption leaves the holdout \$20,000 of annual profit and this particular deadline disappears; at 100%, the installation window shrinks to about two months. The records to collect are realized cost per order, matched contract prices, rival deployments and the buyer’s installation lead time. Lost volume or a minimum acceptable margin would move the deadline earlier; customer differentiation or an inexpensive exit could weaken the pressure.

The supplier faces two buyer-side bounds. Incremental return permits at most $s-\kappa-w=\$1.00$ per order, with $w=\$0.05$ of waiting value. Continued operation also requires $q\leq P(x)-(C_{0}-s)-\kappa$, assuming exit yields zero and no extra financing buffer is needed. The combined ceiling therefore falls from \$1.00 at launch to \$0.59 at full adoption. At the assumed \$0.35 price, the supplier earns \$350,000 of annual revenue per site. An assumed \$0.18 per order of delivery cost, including annualized equipment, maintenance and support, leaves \$170,000 of gross profit, a 49% gross margin before acquisition costs and central overhead. An equivalent competing offer at \$0.28 would cap the price below either buyer-side bound.

For scale, assume 1,000 technically suitable sites and a 10% attainable share: annual supplier revenue is \$35 million, or \$28 million at that competing price. These are illustrative site counts, not a market estimate or an acquisition forecast. Reaching \$100 million at the original price needs at least 286 sites with the same volume and economics. The investment question is whether a supplier can win and service that many sites while retaining a cost, deployment or integration advantage. Economic pressure establishes the buyer’s urgency; it does not establish that advantage. A seed test would measure both the saving and the price response on comparable contracts, and a subsequent financing would need repeat deployments with retained gross margin.

### 7.3 Case 3: a detection layer sold into verification flows

This is the attack–defense branch of Section [4](https://rencryptofish.com/posts/forcing-technologies#S4): more capable generative tools can raise losses at an existing verification flow, creating demand for a counter. The calculation values incremental fraud prevented after the base check; a general model benchmark cannot establish the detector’s catch rate or the buyer’s avoided loss.

The hypothetical buyer is a consumer platform that already runs a compliant age/identity check and considers a separate detection layer. Its requirement is unchanged, so $\varepsilon=0$. For the numerical illustration, assume external expected loss $L=\alpha x/(1-\varphi y)$ and incremental avoided loss $z_{K}=\varphi L$. Here $x$ is the deepfake share of fraud attempts, $y$ is the defended share of platforms, and $\alpha$ is a loss normalizer. These are different populations: this is a stipulated exposure/displacement scenario, not an application of the common-population equilibrium in Appendix [F](https://rencryptofish.com/posts/forcing-technologies#A6), and $\alpha$ is not an identified contest stake $V(r-1)$. Holding $L$ fixed would instead give a simple defense-ROI case.

Entrust’s one-in-five share of biometric fraud attempts and Pindrop’s reported deployment statistic provide context, not a matched estimate for this hypothetical platform (Entrust, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib145); Biometric Update, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib146)). The central scenario sets $x=0.2$, $y=0.1$, $\varphi=0.8$ and $\alpha=\$3.45m$, which produces \$600k avoided loss by construction. At two million checks per year, an assumed \$0.15 price per check, \$150k other cost and \$50k waiting value, the margin is \$100k and the price ceiling is \$0.20 per check. These are annual scenarios, not a disclosed detection quote or measured prevention effect. False rejects, review, displaced attacks and residual losses must be reconciled to the customer’s actual records. The downside scenario’s smaller attack share and catch rate make adoption fail (Table [16](https://rencryptofish.com/posts/forcing-technologies#S7.T16)).

Table 16: Case 3 scenarios: a detection layer sold into a platform’s verification flow. Monetary amounts are USD thousands per year except prices per check and the one-time acquisition and onboarding costs; run rates are at the stated month. The burn multiple is net cash consumed over net new ARR in the twelve months to month 18; “n/a” where no ARR was added, “cash positive” where the business funds itself.

<table><tbody><tr><td>Input or result (USD thousands per year unless stated)</td> <td>Downside</td> <td>Central</td> <td>Upside</td></tr> <tr><td>Verifications per year</td> <td>1,000,000</td> <td>2,000,000</td> <td>3,000,000</td></tr> <tr><td>Price per verification (USD)</td> <td>0.10</td> <td>0.15</td> <td>0.20</td></tr> <tr><td>Deepfake share of fraud attempts, $x$</td> <td>10%</td> <td>20%</td> <td>30%</td></tr> <tr><td>Platforms already running detection, $y$</td> <td>10%</td> <td>10%</td> <td>10%</td></tr> <tr><td>Catch rate of the layer, $\varphi$</td> <td>50%</td> <td>80%</td> <td>90%</td></tr> <tr><td>Assumed annual loss normalizer, $\alpha$</td> <td>3,450</td> <td>3,450</td> <td>3,450</td></tr> <tr><td>Fraud avoided by the layer, $z_{K}=\varphi\alpha\tilde{x}$</td> <td>182</td> <td>600</td> <td>1,024</td></tr> <tr><td>Mandate penalty avoided beyond the existing check, $\varepsilon$</td> <td>0</td> <td>0</td> <td>0</td></tr> <tr><td>Annual contract value, $q$</td> <td>100</td> <td>300</td> <td>600</td></tr> <tr><td>Other annual buyer cost, $\kappa$</td> <td>150</td> <td>150</td> <td>150</td></tr> <tr><td>Waiting value, $W$</td> <td>100</td> <td>50</td> <td>0</td></tr> <tr><td>Buyer’s margin to purchase now, $M$</td> <td>-168</td> <td>100</td> <td>274</td></tr> <tr><td>Qualified accounts over 24 months</td> <td>60</td> <td>100</td> <td>150</td></tr> <tr><td>Win fraction</td> <td>8%</td> <td>15%</td> <td>20%</td></tr> <tr><td>Installations per month after ramp</td> <td>1</td> <td>1</td> <td>2</td></tr> <tr><td>Annual churn</td> <td>20%</td> <td>10%</td> <td>8%</td></tr> <tr><td>Active customers at month 24</td> <td>0</td> <td>13</td> <td>26</td></tr> <tr><td>ARR at month 24</td> <td>0</td> <td>3,860</td> <td>15,738</td></tr> <tr><td>Gross margin</td> <td>50%</td> <td>73.3%</td> <td>85%</td></tr> <tr><td>CAC payback (months)</td> <td>45.6</td> <td>8.2</td> <td>3.4</td></tr> <tr><td>ARR at month 18 (Series A)</td> <td>0</td> <td>2,908</td> <td>11,797</td></tr> <tr><td>Burn multiple, trailing 12 months</td> <td>n/a</td> <td>1.9</td> <td>cash positive</td></tr> <tr><td>Cumulative cash low point</td> <td>-8,400</td> <td>-7,641</td> <td>-3,497</td></tr></tbody></table>

The company sells the layer at a 73% gross margin, after \$0.04 of inference and review cost per check (\$0.05 and \$0.03 in the downside and upside). The funnel is deliberately slow: 100 qualified accounts over 24 months, a 15% win rate because Socure, Persona, Incode, Entrust and Veriff sell or build detection and are in every deal, one installation a month after a six-month ramp, 10% annual churn. At the flat price that produces 13 active customers and \$3.9 million of ARR at month 24, \$2.9 million at month 18 with \$2.1 million of net new ARR in the trailing year and a burn multiple of 1.9, and a cumulative cash need of \$7.6 million through month 24 at \$350,000 a month of fixed cost. The financing case depends heavily on the assumed win rate against established providers that could build the same capability.

The flat price is one policy; pricing at a fixed fraction of a changing ceiling is another explicit assumption. Entrust reported 58% growth in the count of deepfaked selfies (Entrust, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib145)). Applying that growth rate to the share of attempts is a sensitivity exercise, not a valid inference about the denominator. Under that assumed share path, fixed catch rate and displacement rule, avoided loss rises from \$600k to \$948k and \$1.5m, and the price ceiling rises from \$0.20 to \$0.37 and \$0.65 per check. The calculation does not imply a company can charge those amounts.

A company that could retain 75% of the ceiling would charge about \$0.49 at month 24 and reach the higher revenue path in Table [17](https://rencryptofish.com/posts/forcing-technologies#S7.T17). The \$12.5m ARR and 92% gross margin in that path additionally assume unchanged per-check inference/review costs, no competitive fee response and successful repricing. The flat-price path remains valid even if expected loss rises. Likewise, the higher avoided loss when more platforms defend is a stipulated displacement stress, not a measured network effect. Incremental prevented loss, operational costs, supplier alternatives and renewal prices decide which path is attainable. A rising ceiling alone cannot establish pricing power.

Table 17: Case 3 under the stipulated external-exposure scenario: the attack, the exposure, the ceiling, and the company’s path if the price tracks it. Central sensitivity: the deepfake share of fraud attempts starts at one in five and is assumed to rise 58% a year, the layer catches 80% of the loss, and 10% of platforms are already defended. USD thousands unless stated.

<table><tbody><tr><td>Central case</td> <td>Month 0</td> <td>Month 12</td> <td>Month 24</td></tr> <tr><td></td> <td></td> <td></td> <td></td></tr> <tr><td>Deepfake share of fraud attempts, $x$ (growing 58% a year)</td> <td>20%</td> <td>31.6%</td> <td>49.9%</td></tr> <tr><td>Exposure of an undefended platform, $\tilde{x}=x/(1-\varphi y)$</td> <td>0.22</td> <td>0.34</td> <td>0.54</td></tr> <tr><td>Fraud cost exposed, $\alpha\tilde{x}$ (USD thousands)</td> <td>750</td> <td>1,185</td> <td>1,872</td></tr> <tr><td>Fraud avoided by the layer, $z_{K}=\varphi\alpha\tilde{x}$ (USD thousands)</td> <td>600</td> <td>948</td> <td>1,498</td></tr> <tr><td>Buyer’s margin at the flat price of 0.15 a check (USD thousands)</td> <td>100</td> <td>448</td> <td>998</td></tr> <tr><td>Price ceiling per check, $(z_{K}-\kappa-W)/\text{checks}$ (USD)</td> <td>0.20</td> <td>0.37</td> <td>0.65</td></tr> <tr><td>Price per check if the company keeps its month-0 share of the ceiling (USD)</td> <td>0.15</td> <td>0.28</td> <td>0.49</td></tr> <tr><td>Fraud avoided at month 0 if half of platforms run detection ($y=0.5$)</td> <td>920</td> <td></td> <td></td></tr> <tr><td>Deepfake share at which the flat price stops paying the buyer</td> <td>16.7%</td> <td></td> <td></td></tr> <tr><td>Company ARR (USD thousands)</td> <td>Month 12</td> <td>Month 24</td> <td>Month 48</td></tr> <tr><td>Price tracks the ceiling</td> <td>3,563</td> <td>12,523</td> <td>46,091</td></tr> <tr><td>Flat price</td> <td>1,905</td> <td>3,860</td> <td>7,202</td></tr> <tr><td colspan="4"><em>Indexed-price operating measures (USD thousands unless stated)</em></td></tr> <tr><td>Series A ARR, month 18</td> <td colspan="3">7,210</td></tr> <tr><td>Net new ARR, prior 12 months</td> <td colspan="3">6,035</td></tr> <tr><td>Burn multiple, prior 12 months</td> <td colspan="3">0.3</td></tr> <tr><td>Gross margin at month 24</td> <td colspan="3">91.8%</td></tr> <tr><td>Cumulative cash low point, first 24 months</td> <td colspan="3">-4,274</td></tr></tbody></table>

![Figure 3: Case 3 under the stipulated external-exposure scenario: the price ceiling per check against the deepfake share of fraud attempts, with the central scenario’s other inputs fixed. The ceiling is (zK−κ−W) per check, where zK=φ⁢α⁢x~ is the loss the layer shields; the dots mark Entrust’s one in five and where a 58% annual rise takes it by months 12 and 24, and the dashed line is the price of a company that keeps the share of the ceiling it held at signing. Run with p=1, r=1, φ=0.8, y=0.1, β=0, σ=0 and no sheltering; the formula is printed on the figure.](https://rencryptofish.com/images/forcing-technologies/investor_idv_counter.png)

Figure 3: Case 3 under the stipulated external-exposure scenario: the price ceiling per check against the deepfake share of fraud attempts, with the central scenario’s other inputs fixed. The ceiling is $(z_{K}-\kappa-W)$ per check, where $z_{K}=\varphi\alpha\tilde{x}$ is the loss the layer shields; the dots mark Entrust’s one in five and where a 58% annual rise takes it by months 12 and 24, and the dashed line is the price of a company that keeps the share of the ceiling it held at signing. Run with $p=1$, $r=1$, $\varphi=0.8$, $y=0.1$, $\beta=0$, $\sigma=0$ and no sheltering; the formula is printed on the figure.

Table 18: Case 3 central company path and unverified market arithmetic. The final four rows reproduce an unreconciled check/request sum; they do not estimate an eligible market.

<table><tbody><tr><th>Central case (USD thousands)</th> <td></td></tr> <tr><td>ARR at month 12</td> <td>1,905</td></tr> <tr><td>ARR at month 24</td> <td>3,860</td></tr> <tr><td>ARR at month 36</td> <td>5,619</td></tr> <tr><td>ARR at month 48</td> <td>7,202</td></tr> <tr><td>Series A snapshot, month 18: ARR</td> <td>2,908</td></tr> <tr><td>Net new ARR, prior 12 months</td> <td>2,060</td></tr> <tr><td>Burn multiple</td> <td>1.9</td></tr> <tr><td>Gross margin</td> <td>73%</td></tr> <tr><td>Unverified raw sum of checks and requests (millions)</td> <td>6,800</td></tr> <tr><td>Assumed fraction of that raw count</td> <td>10%</td></tr> <tr><td>Illustrative unit price (USD)</td> <td>0.15</td></tr> <tr><td>Revenue arithmetic, not an estimated market</td> <td>102,000</td></tr></tbody></table>

A simple scale calculation would add Incode’s 4.1 billion checks and Socure’s 2.7 billion requests (Burt, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib152); Biometric Update, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib215)). Multiplying 10% of that sum by \$0.15 gives \$102m arithmetically, but does not establish an addressable independent detection market. The units, overlap, eligibility and suppliers’ rights to attach another paid layer have not been reconciled. A higher assumed price leaves the uncertainty about eligible transaction volume unresolved. A qualified flow inventory and the revenue the incumbent leaves to an independent company are required before using this as venture-scale evidence.

### 7.4 Case 4: invoice exceptions for a French mid-sized firm

The buyer is a French mid-sized firm with several finance systems, no invoice-automation tool today, and 12,000 invoice exceptions a year, which at 20 minutes each and €60 a loaded hour (Eurostat puts France’s average at €44.30 and its finance sector at €70.50 (Eurostat, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib197), [b](https://rencryptofish.com/posts/forcing-technologies#bib.bib198))) cost it €240,000 of staff time; Billentis’s benchmarks put exceptions at 20 to 30% of paper invoices (Koch, [2017](https://rencryptofish.com/posts/forcing-technologies#bib.bib196)). It already has a compliant platform for the September 2026 mandate, because the accounting suites include one (Section [6.5](https://rencryptofish.com/posts/forcing-technologies#S6.SS5.SSS0.Px5)). The startup sells an add-on that removes exceptions. The mandate’s penalty therefore cancels in the comparison, as it did in Italy, and the add-on is worth only $\gamma$: 40% of the exception work removed is valued at €96,000 a year. This assumes the released staff capacity can be used or converted to cash savings; it is not a measured payroll reduction. At €48,000 of price, €18,000 of other cost and €6,000 of waiting value, the margin to buy is €24,000, and the product must remove more than 30% of the work to be bought at all (Figure [4](https://rencryptofish.com/posts/forcing-technologies#S7.F4)); a ten-point miss on the 40% ends the purchase. If the suite’s next release, or the AP-automation companies already selling exception workflows (Basware, Esker, Yooz, Medius, Coupa, SAP), halves the exceptions first, the add-on’s 40% is worth €48,000 and the margin is minus €24,000: the mandate goes on driving compliance while the startup’s product stops paying.

Table 19: Case 4 scenarios: invoice exceptions relative to a compliant bundle. Monetary amounts are EUR thousands per year except the one-time acquisition and onboarding costs.

<table><tbody><tr><td>Input or result (EUR thousands per year unless stated)</td> <td>Downside</td> <td>Central</td> <td>Upside</td></tr> <tr><td>Exception work removed, $e$</td> <td>20%</td> <td>40%</td> <td>60%</td></tr> <tr><td>Gross annual benefit, $\gamma$</td> <td>48</td> <td>96</td> <td>144</td></tr> <tr><td>Annual contract value, $q$</td> <td>36</td> <td>48</td> <td>60</td></tr> <tr><td>Other annual buyer cost, $\kappa$</td> <td>24</td> <td>18</td> <td>12</td></tr> <tr><td>Waiting value, $W$</td> <td>12</td> <td>6</td> <td>0</td></tr> <tr><td>Buyer’s margin to purchase now, $M$</td> <td>-24</td> <td>24</td> <td>72</td></tr> <tr><td>Qualified accounts over 24 months</td> <td>100</td> <td>300</td> <td>500</td></tr> <tr><td>Win fraction</td> <td>10%</td> <td>20%</td> <td>20%</td></tr> <tr><td>Installations per month after ramp</td> <td>1</td> <td>4</td> <td>6</td></tr> <tr><td>Annual churn</td> <td>20%</td> <td>10%</td> <td>8%</td></tr> <tr><td>Active customers at month 24</td> <td>0</td> <td>51</td> <td>87</td></tr> <tr><td>ARR at month 24</td> <td>0</td> <td>2,470</td> <td>5,203</td></tr> <tr><td>Gross margin</td> <td>66.7%</td> <td>75%</td> <td>75%</td></tr> <tr><td>CAC payback (months)</td> <td>15.0</td> <td>9.3</td> <td>8.3</td></tr> <tr><td>ARR at month 18 (Series A)</td> <td>0</td> <td>1,861</td> <td>3,887</td></tr> <tr><td>Burn multiple, trailing 12 months</td> <td>n/a</td> <td>0.8</td> <td>0.4</td></tr> <tr><td>Cumulative cash low point</td> <td>-2,400</td> <td>-2,099</td> <td>-2,116</td></tr></tbody></table>

The scenario produces attractive unit economics but limited revenue scale. A 75% gross margin, a nine-month payback on €28,000 of acquisition and onboarding, and a lean fixed base of €100,000 a month give a burn multiple of 0.8 at month 18 on €1.9 million of ARR, with €2.1 million of cumulative cash needed. The €28,000 assumes distribution through the accounting firms that Pennylane and Cegid already sell through; a field sales motion into mid-sized firms costs about twice that and doubles the payback. ARR reaches €2.5 million at month 24 and €4.6 million at month 48. Assume 2,500 eligible French firms have the multi-system exception problem, an unverified customer count. Then a 15% share against the suites at €48,000 is €18 million of ARR, and at the five-times-revenue multiple Vertex paid for ecosio in 2024 (Vertex, Inc., [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib188)), a €90 million exit. The upside scenario reaches €5.2 million at month 24, but does not establish a larger eligible market. Under the central scale assumptions, five comparable countries yield €90 million of ARR; at least six would be needed to exceed €100 million. Comparable demand, localization costs and achievable share must be established country by country.

Table 20: Case 4 central path and ceiling.

<table><tbody><tr><td>Central case (EUR thousands)</td> <td></td></tr> <tr><td>ARR at month 12</td> <td>1,219</td></tr> <tr><td>ARR at month 24</td> <td>2,470</td></tr> <tr><td>ARR at month 36</td> <td>3,596</td></tr> <tr><td>ARR at month 48</td> <td>4,609</td></tr> <tr><td>Series A snapshot, month 18: ARR</td> <td>1,861</td></tr> <tr><td>Net new ARR, prior 12 months</td> <td>1,318</td></tr> <tr><td>Burn multiple</td> <td>0.8</td></tr> <tr><td>Gross margin</td> <td>75%</td></tr> <tr><td>Eligible accounts</td> <td>2,500</td></tr> <tr><td>Achievable share</td> <td>15%</td></tr> <tr><td>Mature ACV</td> <td>48</td></tr> <tr><td>Ceiling ARR</td> <td>18,000</td></tr></tbody></table>

What would change the answer is the sequence of mandates. Domestic B2B requirements began in Belgium in January 2026 and were phased in across Poland in February and April 2026. Germany’s issuance transition generally ends in January 2027 for firms above €800,000 of prior-year turnover and in January 2028 for the remaining in-scope firms, with an EDI transition through 2027. ViDA’s cross-border B2B reporting starts in July 2030 (Belgian Federal Government, [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib689); Polish Ministry of Finance, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib688); German Federal Ministry of Finance, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib687); European Commission, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib194)). These are different populations and requirements; they offer possible expansion windows rather than interchangeable copies of France, and established providers such as Pagero and Sovos already serve multiple jurisdictions. We would advance a French exceptions startup as a venture case only if it has paying customers in a second mandate country before that country’s deadline, an expansion milestone that should be tested before further financing. Italy’s precedent holds either way: in the mandate’s first year 3.9 million Italian firms sent 2.09 billion invoices through the state’s exchange (Osservatori Politecnico di Milano, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib195)); TeamSystem sold the suite above that exchange, and the exchange itself was free to use.

![Figure 4: One input at a time, with the central scenario’s other inputs fixed. The vertical value is the buyer’s margin to buy now, M=B−q−κ−W, in local currency; dots mark the central case and the break-even. Case 3 varies the price per check, with assumed avoided loss at today’s attack share as the benefit (Figure 3 varies the attack); Case 4 varies the share of exception work removed. In the two add-on cases the mandate penalty cancels against the compliant alternative, with p=1, β=0, r=1 and σ=0. Case 3’s α is the stipulated external-loss normalizer, not the contest stake of the common-population counter theorem; Case 4 sets α=0. Case 1 varies rival adoption, which moves the contest’s ceiling; the orange dot is the simulated share at the Series A. The settings and formulas are printed on the figure. The productivity case uses Table 15 to separate switching gains from operating profits.](https://rencryptofish.com/images/forcing-technologies/investor_sensitivities.png)

Figure 4: One input at a time, with the central scenario’s other inputs fixed. The vertical value is the buyer’s margin to buy now, $M=B-q-\kappa-W$, in local currency; dots mark the central case and the break-even. Case 3 varies the price per check, with assumed avoided loss at today’s attack share as the benefit (Figure [3](https://rencryptofish.com/posts/forcing-technologies#S7.F3) varies the attack); Case 4 varies the share of exception work removed. In the two add-on cases the mandate penalty cancels against the compliant alternative, with $p=1$, $\beta=0$, $r=1$ and $\sigma=0$. Case 3’s $\alpha$ is the stipulated external-loss normalizer, not the contest stake of the common-population counter theorem; Case 4 sets $\alpha=0$. Case 1 varies rival adoption, which moves the contest’s ceiling; the orange dot is the simulated share at the Series A. The settings and formulas are printed on the figure. The productivity case uses Table [15](https://rencryptofish.com/posts/forcing-technologies#S7.T15) to separate switching gains from operating profits.

## 8 Where the framework misleads

The model organizes the reasons firms adopt, but adoption curves alone cannot identify those reasons. We fitted it to 14 historical adoption series, from hybrid corn to generative AI, with every observation traced to a source (Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10)). The fits describe the paths well and say almost nothing about where the value came from. In every case the split between productive value and competitive transfer stays close to its prior. In the linear restriction with no outside option and no waiting value, a direct benefit of $0.3$ with an edge of $0.2$ traces the same curve as a benefit of $0.1$ with an edge of $0.4$ (Proposition [12](https://rencryptofish.com/posts/forcing-technologies#Thmproposition12)); that exact equivalence does not hold for every nonlinear specification. With adoption data alone, the classification remains sensitive to prior assumptions. The classification has to come from holdout outcomes, bans, beliefs and buyer records, which is why every memo in Section [6](https://rencryptofish.com/posts/forcing-technologies#S6) needs a buyer, an observable mechanism and a timing window; an S-curve alone supplies none of them.

The base model holds the market environment fixed except for its specified contest, network and exclusion terms. It does not solve for output prices, demand or firms’ deployment schedules. The common revenue loss in Section [1.3](https://rencryptofish.com/posts/forcing-technologies#S1.SS3) is an explicit extension, and the fulfillment case’s price response and adoption path are assumptions. They establish a conditional threshold, not an estimated competitive effect or forecast. Volume, financing constraints, specialization and exit can move that threshold. Stronger evidence would connect a measured cost advantage to a market response and then to comparable holdouts’ outcomes.

The investment screen adds another limitation. Its emphasis on identifiable buyers and accessible sales windows favors some requirement-led opportunities. That is a preference in underwriting, not evidence that economic forcing is rare or that useful products cannot create it. A supplier’s weak capture can justify passing on an investment while leaving the forcing mechanism intact.

The model has four further limitations. It treats a private gatekeeper’s penalty like a statute’s, though enforcement depends on the gatekeeper’s incentives and constraints; Walmart’s failed 2003 tag mandate illustrates the risk (Section [2.5](https://rencryptofish.com/posts/forcing-technologies#S2.SS5)). It treats a ban as outside the game, although FINA’s ban eliminated the polyurethane-suit market. It treats a deadline as fixed, although Section [5](https://rencryptofish.com/posts/forcing-technologies#S5) lists three that moved. And it bounds the company’s price by the buyer’s gain without determining how many companies share that gain. The certificate case shows that a mandate can induce adoption without generating supplier profits. Assessing those profits requires a separate analysis of supply and competition.

The AI and crypto comparison adds a boundary on the unit of analysis. Repeated hardware replacement, new model generations, changing token prices, multi-platform use and entry change the field and the prize; a single irreversible adoption decision cannot determine their long-run equilibrium. A miner’s security service and a model’s benefits to downstream users also lie outside the profits of competing producers. Private-company losses, token burns, supplier revenue and capital expenditure measure different objects. Section [4.7](https://rencryptofish.com/posts/forcing-technologies#S4.SS7) adds conditional 2031 and 2036 forecasts with separate judgments about capability pressure and company capture. Appendix [O.6](https://rencryptofish.com/posts/forcing-technologies#A15.SS6) distinguishes those qualitative tiers from constructed stress tests: neither supplies fitted event probabilities, validated long-horizon accuracy or a ranking by estimated social welfare.

Finally, the historical refits in Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) are hindsight. They use today’s priors on cases chosen because they mattered, and the early-window estimates would not have been available on the day an investor needed them. We do not claim the framework would have picked historical winners. The investment implication is to pair evidence of a deteriorating holdout position with an asset the supplier can retain: accepted work, customer access, effective protection or difficult operating capacity. The former establishes urgency; the latter must survive competition, delivery costs and financing.

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- Amazon.com, Inc. (2026c) Amazon sets new Prime delivery speed record in 2025 with over 13 billion items arriving the same or next day around the world. Note: About AmazonFebruary 3, 2026. Accessed 2026-10-20 External Links: [Link](https://aboutamazon.com/news/retail/amazon-prime-same-day-next-day-delivery-2025) Cited by: [§2.4](https://rencryptofish.com/posts/forcing-technologies#S2.SS4.p1).

- Amazon.com, Inc. (2026d) Amazon.com Announces Fourth Quarter Results (Exhibit 99.1 to Form 8-K). Note: February 5, 2026. Accessed 2026-10-20 External Links: [Link](https://www.sec.gov/Archives/edgar/data/1018724/000101872426000002/amzn-20251231xex991.htm) Cited by: [§2.1](https://rencryptofish.com/posts/forcing-technologies#S2.SS1.p2).

- Amazon.com, Inc. (2026e) Amazon.com Announces Fourth Quarter Results. Note: February 5; year ended December 31, 2025; accessed 2026-10-20 External Links: [Link](https://ir.aboutamazon.com/news-release/news-release-details/2026/Amazon-com-Announces-Fourth-Quarter-Results/default.aspx) Cited by: [Table 28](https://rencryptofish.com/posts/forcing-technologies#A15.T28).

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- Anysphere, Inc. (2025b) Series d, november 13, 2025. Note: Cursor BlogAccessed 2026-10-20 External Links: [Link](https://cursor.com/blog/series-d) Cited by: [Table 10](https://rencryptofish.com/posts/forcing-technologies#S5.T10).

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- Apple Inc. (2025) Declared age range. Note: Apple Developer Documentation; developer news item of December 23, 2025Accessed 2026-10-19 External Links: [Link](https://developer.apple.com/documentation/declaredagerange) Cited by: [§3.4](https://rencryptofish.com/posts/forcing-technologies#S3.SS4.p3).

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- Bank for International Settlements (2025) Project Hertha. Note: Accessed October 20, 2026. External Links: [Link](https://www.bis.org/project/hertha) Cited by: [§6.4](https://rencryptofish.com/posts/forcing-technologies#S6.SS4.SSS0.Px2.p1).

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- Biometric Update (2026b) Discord launches age-adaptive design, says 90% of users won’t need active checks. Note: Biometric Update, September 23, 2026Accessed 2026-10-19 External Links: [Link](https://www.biometricupdate.com/202609/discord-launches-age-adaptive-design-says-90-of-users-wont-need-active-checks) Cited by: [§3.4](https://rencryptofish.com/posts/forcing-technologies#S3.SS4.p3).

- Biometric Update (2026c) Socure acquires Fravity, raises \$156m to bring agentic AI to fraud investigations. Note: Biometric Update, August 27, 2026Accessed 2026-10-19 External Links: [Link](https://www.biometricupdate.com/202608/socure-acquires-fravity-raises-156m-to-bring-agentic-ai-to-fraud-investigations) Cited by: [§3.4](https://rencryptofish.com/posts/forcing-technologies#S3.SS4.p3).

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## Appendix A The model in full

This appendix derives the two payoff curves of Section [1](https://rencryptofish.com/posts/forcing-technologies#S1), adds the outside option, and works through the four patterns of Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) with numbers.

### A.1 Whose decision is modeled

Take a fixed group of rivals and let $x$ be the share that has adopted: $x=0$ means none and $x=1$ means all. Each actor is small enough that its own choice does not materially change that share. In a firm-level application, $x$ should reflect the competitors or partners that actually affect the firm’s business. Appendix [E.10](https://rencryptofish.com/posts/forcing-technologies#A5.SS10) allows their influence to differ.

Let $U_{A}(x)$ be the payoff from adopting and $U_{N}(x)$ the payoff from holding out. Both are measured relative to the world without this technology. Zero means no change from that baseline, not zero revenue or profit. A negative number means the actor is worse off than before.

Use a common period for all amounts. The cost $c$ includes annualized acquisition cost and the cost of operating the technology. For now, consider an actor with the average cost. An individual actor’s calculation replaces $c$ with its own $c_{i}$. The model later allows those costs to differ across the population.

The illustrative figures use a common payoff unit per period. If one unit represents a pre-technology annual stake of \$1 million, a benefit of $0.1$ means \$100,000 per year and a cost of $0.3$ means \$300,000 per year. These are amounts relative to that chosen unit, not adoption percentages. The adoption share $x$ and strength ratio $r$ have no monetary units. Multiplying all payoff amounts by the same positive factor changes the vertical scale, not which choice pays more. The numerical examples are chosen to expose mechanisms; they are not estimates of a particular technology.

### A.2 Four sources of value or pressure

The model distinguishes four sources of value or pressure.

**Direct benefit, $\gamma$.**

The technology improves your work even if no rival adopts. Lower handling costs from better equipment belong here.

**Network benefit, $\beta x$.**

The technology becomes more useful when others have compatible equipment or practices. More container-ready ports make a container system more useful.

**Competitive edge, $\alpha$ and $r$.**

The technology helps you capture a share of something rivals would otherwise receive. The prize might be business, a ranking or a strategic position. An adopter’s gain has a matching loss elsewhere in the rival group.

**Exclusion, $\varepsilon\Phi(x)$.**

A holdout loses access or faces a penalty that no rival receives as a gain. A platform warning or a procurement requirement can work this way. If the lost business goes to another rival, that transferred portion belongs in the contest instead.

These channels can operate together. A productive tool can also redistribute business; a useful standard can also be enforced by a gatekeeper. Keeping the channels separate prevents the same gain or loss from being counted twice.

### A.3 The two curves and their gap

First suppose holdouts remain exposed to competition and exclusion. Let $p\in[0,1]$ be the common belief that the technology works. The denominator

$$
D(x)=1+(r-1)x
$$

tracks how much competitive strength is already in the field. Here $r$ is an adopter’s strength relative to a holdout’s, and $\alpha$ is the positional edge available to a lone adopter. The two payoffs are

$\displaystyle U_{A}^{\mathrm{exposed}}(x)$

$\displaystyle=p\left[\gamma+\beta x+\frac{\alpha(1-x)}{D(x)}\right]-c,$

(3)

$\displaystyle U_{N}^{\mathrm{exposed}}(x)$

$\displaystyle=-p\frac{\alpha x}{D(x)}-\varepsilon\Phi(x).$

(4)

Read the adopter’s curve from left to right: direct benefit, compatibility benefit, an edge over the remaining holdouts, then cost. Read the holdout’s curve as two losses: ground taken by adopters and an exclusion penalty. The pressure curve $\Phi$ rises from zero to one; its location $\theta$ is an adoption share and $k$ controls its steepness. Calendar enforcement requires an explicit time path rather than interpreting $\theta$ as a date.

Beliefs scale the technology’s direct, network and competitive effects. They do not scale the cost or the gatekeeper’s penalty. A firm can face a real compliance requirement while remaining doubtful about the underlying technology.

Subtracting the holdout’s payoff from the adopter’s payoff gives the *gain from adopting*:

$$
\underbrace{\Delta(x)}_{\text{adopt minus hold out}}=\underbrace{p\gamma}_{\text{direct}}+\underbrace{p\beta x}_{\text{network}}+\underbrace{\frac{p\alpha}{D(x)}}_{\text{contest}}+\underbrace{\varepsilon\Phi(x)}_{\text{exclusion}}-c.
$$

A positive gap means adopting pays better than holding out. It does not mean the adopter is better off than before the technology existed: both curves can lie below zero.

The practical decision also includes the value of waiting, $W$. A holdout acts when $\Delta(x)-W>0$, subject to adjustment delays. Waiting may allow another trial to finish or avoid committing to a generation that will soon be replaced. It affects the decision date; it is not an additional resource cost in the welfare calculation.

### A.4 A credible alternative to staying exposed

A holdout may be able to ally, specialize or leave the contested segment. Let $Q\leq 0$ be the payoff from that alternative. A value of $Q=-0.1$ means accepting a loss of $0.1$ per period relative to the original baseline in exchange for shelter. A better alternative has a $Q$ closer to zero.

The loss from remaining exposed is

$$
L(x)=p\frac{\alpha x}{D(x)}+\varepsilon\Phi(x).
$$

(5)

The holdout shelters once that loss reaches $-Q$. Call the first such adoption share $x_{Q}$; set $x_{Q}=\infty$ if the loss never gets that large. The notation $Q=-\infty$ means no outside option.

This version assumes a common outside option and that holdouts shelter together. Once they leave, their stakes are no longer available for adopters to capture. The full payoff curves are therefore

$\displaystyle U_{A}(x)$

$\displaystyle=p\left[\gamma+\beta x+\frac{\alpha(1-x)}{D(x)}\,\mathbf{1}\{x<x_{Q}\}\right]-c,$

(6)

$\displaystyle U_{N}(x)$

$\displaystyle=\max\{-L(x),Q\}.$

(7)

The indicator switches the competitive edge off after sheltering. The full adoption gain becomes

$$
\Delta(x)=\begin{cases}p[\gamma+\beta x+\alpha/D(x)]+\varepsilon\Phi(x)-c,&x<x_{Q},\\[3.0pt] p[\gamma+\beta x]-Q-c,&x\geq x_{Q}.\end{cases}
$$

(8)

At the sheltering boundary the gap drops because the adopter loses its edge over the departed rivals. A worked example in Appendix [B](https://rencryptofish.com/posts/forcing-technologies#A2) shows how this can stop further adoption.

The common-$Q$ assumption makes that response abrupt. It selects sheltering only when remaining exposed has become individually worse, given that others have not sheltered yet. Different outside options would spread the exits over time. A rival implementation that preserves compatibility is also a different alternative from leaving the segment; Appendix [H.4](https://rencryptofish.com/posts/forcing-technologies#A8.SS4) discusses that case.

### A.5 Why a competitive advantage wears away

The contest divides a fixed prize worth $V$ per rival in proportion to strength. Adopters have strength $r$, holdouts strength one, so the average strength is $D(x)$. Their shares relative to the original equal split are $r/D(x)$ and $1/D(x)$. Subtract the original prize $V$ and the two competitive payoffs become

$$
V\left(\frac{r}{D(x)}-1\right)=\frac{\alpha(1-x)}{D(x)},\qquad V\left(\frac{1}{D(x)}-1\right)=-\frac{\alpha x}{D(x)},\quad\alpha=V(r-1).
$$

One side’s gain is the other side’s loss. Across the population, the terms cancel:

$$
x\frac{\alpha(1-x)}{D(x)}+(1-x)\left(-\frac{\alpha x}{D(x)}\right)=0.
$$

This is what a zero-sum contest means here. Adopting still costs resources; those costs remain after the transfer cancels.

With $V>0$ and $r>1$, a lone adopter has many holdouts to take ground from. As rivals catch up, the opportunity shrinks. The contest’s contribution to the adoption gap, $\alpha/D(x)$, falls with $x$. The paper also uses a linear limit, written $r=1$ with $\alpha$ fixed. In that limit the gap stays constant even though the adopter’s payoff falls. This specification is a limit with a fixed positional edge; it does not describe equal-strength players competing for a finite prize.

### A.6 Irreversibility and cost dispersion

The static comparison asks what each actor would choose at a given exposure. The diffusion model adds irreversible commitment: an actor that has adopted cannot undo the decision. The forcing test still asks whether dropping the technology and saving its cost would pay. If acquisition costs are already sunk, dropping saves less; that makes continued use easier to justify.

Cost differences matter too. The model uses a log-logistic distribution with mean $c$ and dispersion $\sigma$. At $\sigma=0$ everyone has the same cost; a larger $\sigma$ creates both cheap early adopters and costly holdouts. Its exact formula and the full parameter guide are in Appendix [L](https://rencryptofish.com/posts/forcing-technologies#A12). The distinction between cheap early adopters and actors stranded by an eroding edge will matter for the diffusion results.

## Appendix B Three tests, worked with numbers

Once the technology is known to work, set $p=1$ and ask the three questions of Section [1](https://rencryptofish.com/posts/forcing-technologies#S1). With no outside option, the answers for a mean-cost actor are

$\displaystyle\Delta(0)$

$\displaystyle=\gamma+\alpha-c$

Would adopting first pay?

(9)

$\displaystyle\Delta(1)$

$\displaystyle=\gamma+\beta+\alpha/r+\varepsilon-c$

Would dropping out hurt?

$\displaystyle y_{R}$

$\displaystyle=W_{R}(1)-W_{R}(0)=\gamma+\beta-c$

Does full adoption benefit rivals?

The third line adds everyone’s payoff, so the competitive transfer disappears. Exclusion also disappears at full adoption because no holdouts remain to bear it. The outsider-adjusted comparison is $y_{S}=y_{R}+\eta$, where $\eta$ is the benefit per adopter to customers or other outsiders.

A technology is *forced* when $\Delta(1)>0$: a mean-cost actor would lose by dropping it once everyone else uses it. It is *competitively compelled* when $\Delta(0)\leq 0$: that actor would not strictly gain by adopting alone. It is *wasteful for rivals* when $y_{R}<0$. These are separate tests. Other cost types can get different answers, and a worthwhile outside option can change the first two.

A yes means a strictly positive private gain. The labels summarize endpoints, not every point between them: a curved gap may cross zero more than once. The dominant label is the endpoint label used by the implementation, not a guarantee that adoption pays at every intermediate share. At $y_{R}=0$ the welfare comparison is neutral; strict waste requires $y_{R}<0$.

### B.1 An arms race: everyone follows, everyone loses

Consider the linear-limit example in Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1), with direct benefit $\gamma=0.1$, competitive edge $\alpha=0.9$ and cost $c=0.3$. There is no network benefit, exclusion or outside option. These are illustrative payoff units per period, not estimated historical returns. The curves are

$$
U_{A}(x)=0.7-0.9x,\qquad U_{N}(x)=-0.9x,\qquad\Delta(x)=0.7.
$$

A first adopter gains $0.7$. When half the field has adopted, an adopter earns $0.25$ and a holdout loses $0.45$. At full adoption, every adopter loses $0.2$ relative to the original world; a lone actor dropping out would lose $0.9$. At every stage, adopting beats holding out by $0.7$.

Individually, keeping the technology is the right choice. Collectively, abandoning it would save each rival $0.2$. The technology is forced and wasteful, even though nobody needed to wait for rivals before adopting. That is the arms-race pattern.

### B.2 Critical mass: adoption becomes more useful as others join

Now remove the contest and use a direct benefit of $\gamma=0.2$, a network benefit of $\beta=0.8$ and cost $c=0.6$. Holdouts lose nothing:

$$
U_{A}(x)=-0.4+0.8x,\qquad U_{N}(x)=0,\qquad\Delta(x)=-0.4+0.8x.
$$

A lone adopter loses $0.4$. At $x=0.5$ the two choices pay equally. Above that share, adoption pays and each new adopter makes joining more useful. At full adoption everyone gains $0.4$.

This is a coordination problem. A sponsor needs enough compatible use to make adoption self-sustaining. With identical actors and no shocks, a seed below half does not trigger the rest. Cost differences smooth this picture, but the distinction from an arms race remains: compatibility creates value that survives when everyone joins.

### B.3 Partial adoption: the edge stops covering its cost

Return to a pure contest, now with a prize $V=0.3$, relative strength $r=4$, cost $c=0.4$ and no direct benefit. The lone adopter’s edge is $\alpha=V(r-1)=0.9$. Its adoption gap is

$$
\Delta(x)=\frac{0.9}{1+3x}-0.4.
$$

Adopting first pays: $\Delta(0)=0.5$. Keeping the technology at full adoption does not: $\Delta(1)=-0.175$. The gap reaches zero at

$$
x^{\circ}=\frac{0.9/0.4-1}{3}=\frac{5}{12}\approx 42\%.
$$

Below that point the edge still covers the cost; above it, too many rivals have caught up. At the static equilibrium, adopters and holdouts both earn $-1/6$, approximately $-0.167$. The advantage has been competed away, leaving the field worse off.

For the same pure contest with a direct benefit $\gamma$, the general interior solution is

$$
x^{\circ}=\frac{\alpha/(c-\gamma)-1}{r-1},\qquad\frac{\alpha}{r}<c-\gamma<\alpha,\quad r>1.
$$

This is *selective adoption*. It can force a response from the whole field without making universal copying attractive. It is a static reference point; irreversible decisions can carry actual adoption beyond it, as Appendix [E.8](https://rencryptofish.com/posts/forcing-technologies#A5.SS8) shows.

### B.4 Pressure on holdouts need not create a cascade

In the pure contest, holdouts lose more as adoption spreads, yet the gap between adopting and holding out gets smaller. A late adopter avoids a loss but no longer gets the large first-mover advantage. The derivative makes the distinction explicit:

$$
\Delta^{\prime}(x)=p\beta-\frac{p\alpha(r-1)}{D(x)^{2}}+\varepsilon\Phi^{\prime}(x)\quad(x<x_{Q}).
$$

The network and exclusion terms push the incentive upward; a positive-prize contest pushes it downward. Economists call the latter *strategic substitutes*: others’ adoption reduces your incremental gain from adopting. With only that contest, an upward tipping threshold cannot arise. Network benefits or exclusion are needed to make adoption self-reinforcing. Figure [5](https://rencryptofish.com/posts/forcing-technologies#A2.F5) shows the resulting patterns.

![Figure 5: How cost and competitive strength change the endpoint pattern. The curves mark whether adopting first pays (blue), whether remaining adopted at full use pays (orange), and whether full adoption benefits rivals (dashed). Held fixed: V=0.5, γ=0.1, β=0.3, p=1, ε=σ=W=0, Q=−∞. Both c and r vary along the axes, and α=0.5⁢(r−1) changes with r: this holds the prize fixed, not the first adopter’s edge. A decisive edge opens a region of selective adoption; tipping requires the network benefit to outweigh the erosion of the competitive gap.](https://rencryptofish.com/images/forcing-technologies/pattern_map.png)

Figure 5: How cost and competitive strength change the endpoint pattern. The curves mark whether adopting first pays (blue), whether remaining adopted at full use pays (orange), and whether full adoption benefits rivals (dashed). Held fixed: $V=0.5$, $\gamma=0.1$, $\beta=0.3$, $p=1$, $\varepsilon=\sigma=W=0$, $Q=-\infty$. Both $c$ and $r$ vary along the axes, and $\alpha=0.5(r-1)$ changes with $r$: this holds the prize fixed, not the first adopter’s edge. A decisive edge opens a region of selective adoption; tipping requires the network benefit to outweigh the erosion of the competitive gap.

### B.5 An alternative can stop the race before the field catches up

Give the selective-adoption example an outside option $Q=-0.1$. Holdouts now accept a loss of $0.1$ to shelter rather than remain exposed. They reach that point when

$$
\frac{0.9x}{1+3x}=0.1\quad\Longrightarrow\quad x_{Q}=\frac{1}{6}\approx 17\%.
$$

Once they shelter, adopters have no remaining holdout stake to capture. An adopter earns $-0.4$, a sheltered holdout earns $-0.1$, and the gap drops to $-0.3$. New adoption no longer pays.

Under irreversible adoption, this is a stopping boundary: a discrete round of commitments can carry adoption past it, leaving existing adopters with continuing costs after their competitive advantage has disappeared. It is not an indifference equilibrium at which those adopters would willingly remain if they could switch. The lesson for an investment decision is to evaluate rivals’ alternatives before projecting an early competitive return.

At full adoption, a credible outside option caps the private cost of dropping out:

$$
\Delta(1)=\gamma+\beta-c+\min\{\alpha/r+\varepsilon,-Q\}.
$$

A costly exit reduces pressure but leaves a cost to avoiding the technology. Only a costless alternative, $Q=0$, removes that extra term entirely. No such option can disarm forcing if direct and network gains already strictly exceed the cost.

### B.6 A gatekeeper can make adoption necessary without adding value

Exclusion raises the payoff gap by lowering the holdout curve. While holdouts remain exposed, increasing $\varepsilon$ raises the full-adoption forcing margin but leaves $y_{R}$ unchanged. The penalty is paid during the transition, when some holdouts remain; it vanishes when everyone complies.

The reach of the gatekeeper matters. A supplier may escape a retailer’s mandate by leaving that supply chain, at the cost of its business there. If the penalty follows the actor into every feasible alternative, leaving does not provide the modeled shelter. Assess that reach, the transition burden and any benefit to users separately. A faster transition reduces the time penalties are paid, but the model does not include every installation cost of accelerating it.

### B.7 What each parameter changes

Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) shows four possible technologies, with a different set of assumptions in each panel. It does not isolate the effect of any one assumption. Figure [6](https://rencryptofish.com/posts/forcing-technologies#A2.F6) does: every panel starts from the same selective-forcing example, then changes just the parameter named in its title. The plotted quantity is now the gap $\Delta=U_{A}-U_{N}$. Above zero, adopting pays more; below zero, holding out pays more.

Table [21](https://rencryptofish.com/posts/forcing-technologies#A2.T21) connects each change to the original two curves. The last column asks a separate question: does that change make *full adoption* more valuable for the rival group? All comparisons hold the other parameters fixed, assume known effectiveness ($p=1$), and leave holdouts exposed ($Q=-\infty$).

Table 21: How changing one parameter moves the payoffs. Here $d>0$ is an increase in payoff units per period, $D=1+(r-1)x$, and $y_{R}=\gamma+\beta-c$. The $r$ row assumes a positive competitive edge.

| Change | What moves in the two-curve picture? | Full-adoption payoff $y_{R}$ |
| --- | --- | --- |
| Direct benefit $\gamma+d$ | Adopter curve rises by $d$ at every share. The gap widens equally everywhere. | Rises by $d$ |
| Network benefit $\beta+d$ | Adopter curve rises by $dx$: unchanged at zero adoption, larger gains as use spreads. | Rises by $d$ |
| Competitive edge $\alpha+d$, fixed $r$ | Adopter curve rises by $d(1-x)/D$; holdout curve falls by $dx/D$. The gap widens by $d/D$. | Unchanged |
| Faster edge erosion: higher $r$, fixed $\alpha$ | Once $x>0$, the gap narrows. The first adopter’s gain is unchanged; later adopters recover less of it. | Unchanged |
| Exclusion penalty $\varepsilon+d$ | Holdout curve falls by $d\Phi(x)$. Adoption becomes harder to avoid without improving the adopter’s payoff. | Unchanged |
| Adoption cost $c+d$ | Adopter curve falls by $d$ at every share. The gap narrows equally everywhere. | Falls by $d$ |

The numerical comparison shows why adoption and value need separate answers. Raising either the direct benefit or the network benefit from zero to $0.5$ makes full adoption privately sustainable and raises its collective payoff from $-0.4$ to $+0.1$. Doubling the competitive edge from $0.9$ to $1.8$, or adding an exclusion penalty of $0.3$, also makes full adoption privately sustainable. In those cases its collective payoff stays at $-0.4$: the stronger incentive comes from transfers or pressure on holdouts.

Each panel reports both the stable static adoption share and $y_{R}$. These are different comparisons. For the unchanged selective example, the stable share is $42\%$ and welfare there is approximately $-0.167$ per rival. The displayed $y_{R}=-0.4$ is what rivals would receive *if everyone adopted*. A negative $y_{R}$ does not say that the static outcome is full adoption, and a static share does not predict how far irreversible investment will go.

![Figure 6: One parameter changes; the others stay fixed. The baseline is selective forcing with γ=β=ε=0, α=0.9, r=4 and c=0.4 (V=0.3 initially). All panels use p=1, σ=W=0 and Q=−∞; exclusion, when added, uses θ=0.5, k=8. Gray dashed curves repeat the baseline; blue solid curves apply the change in the panel title. Dots mark stable static adoption shares. The numbers below each panel separate adoption from the payoff to the rival group at full adoption. In the r panel, α is held fixed, so V changes. These are illustrative scenarios, not fitted estimates.](https://rencryptofish.com/images/forcing-technologies/parameter_effects.png)

Figure 6: One parameter changes; the others stay fixed. The baseline is selective forcing with $\gamma=\beta=\varepsilon=0$, $\alpha=0.9$, $r=4$ and $c=0.4$ ($V=0.3$ initially). All panels use $p=1$, $\sigma=W=0$ and $Q=-\infty$; exclusion, when added, uses $\theta=0.5$, $k=8$. Gray dashed curves repeat the baseline; blue solid curves apply the change in the panel title. Dots mark stable static adoption shares. The numbers below each panel separate adoption from the payoff to the rival group at full adoption. In the $r$ panel, $\alpha$ is held fixed, so $V$ changes. These are illustrative scenarios, not fitted estimates.

Changing $r$ requires saying what stays fixed.

In Figure [6](https://rencryptofish.com/posts/forcing-technologies#A2.F6), raising $r$ from $4$ to $8$ keeps the lone adopter’s edge at $\alpha=0.9$. That edge wears away faster, so stable adoption falls from $42\%$ to $18\%$. The implied prize $V=\alpha/(r-1)$ falls from $0.3$ to about $0.129$. If instead the prize stays at $V=0.3$, the same increase in $r$ raises $\alpha$ from $0.9$ to $2.1$ and stable adoption rises to $61\%$. At fixed $V$, a stronger technology captures more of the same prize; at fixed $\alpha$, the experiment changes how quickly the same initial advantage disappears. Figure [5](https://rencryptofish.com/posts/forcing-technologies#A2.F5) holds $V$ fixed; the $r$ panels of Figures [6](https://rencryptofish.com/posts/forcing-technologies#A2.F6) and [11](https://rencryptofish.com/posts/forcing-technologies#A5.F11) hold $\alpha$ fixed.

The remaining parameters answer different questions.

The exclusion location $\theta$ and steepness $k$ change where and how abruptly pressure arrives, with $\Phi(0)=0$ and $\Phi(1)=1$ unchanged. They do nothing when $\varepsilon=0$. A better outside option $Q$ can cap holdouts’ loss and remove the adopter’s contest return when sheltering begins. Cost dispersion $\sigma$ changes how many actors lie above or below the mean-cost calculation; it does not move that actor’s payoff curves or the total cost of full adoption. The outsider benefit $\eta$ changes social value, $y_{S}=y_{R}+\eta$, without changing either private curve.

Belief $p$ scales direct, network and competitive effects, while leaving adoption cost and exclusion unchanged. The later diffusion parameters describe the starting share ($x_{0}$), the evidence needed to establish effectiveness ($p_{0},x_{v}$), the speed of action ($\lambda_{0},\lambda$), temporary shocks ($\tau$) and the value of waiting ($W$). They help determine the path taken through the incentives. Figures [11](https://rencryptofish.com/posts/forcing-technologies#A5.F11) and [12](https://rencryptofish.com/posts/forcing-technologies#A5.F12) show those path comparisons with their complete baseline settings; Appendix [L](https://rencryptofish.com/posts/forcing-technologies#A12) provides the full reference.

## Appendix C Formal statements

This appendix collects the assumptions and results behind the walkthrough. The main text explains their use; the next appendix gives the proofs. Static indifference equilibria, sheltering boundaries and rest points under irreversible adoption are distinguished explicitly.

Unless stated otherwise, the economic applications use nonnegative contest and exclusion pressure, $r\geq 1$, and fixed beliefs. A stable static reference means that the gain crosses zero downward (or $g(x)-x$ does so with dispersed costs). This is stability under continuous adjustment toward the best response, not a guarantee that the discrete map $x_{t+1}=g(x_{t})$ converges or that irreversible adoption returns after an overshoot.

###### **Lemma 1** (Zero sum)**.**

For all $x<x_{Q}$, $x\cdot\alpha(1-x)/D(x)+(1-x)\cdot\big{(}{-\alpha x}/D(x)\big{)}=0$, and for $x\geq x_{Q}$ both terms are zero. The contest never enters the aggregate payoff of the rivals in it.

###### **Lemma 2** (Shape of the contest)**.**

The contest’s contribution to the switching gain is $\alpha/D(x)$, with slope $-\alpha(r-1)/D(x)^{2}=-V(r-1)^{2}/D(x)^{2}$.

1. (a)

   For a positive prize ($V>0$) it is strictly decreasing in $x$ whenever $r\neq 1$, and constant when $r=1$.

2. (b)

   As $r\to 1$ with $\alpha$ fixed, the payoffs converge uniformly to the linear forms $\alpha(1-x)$ and $-\alpha x$.

3. (c)

   As $r\to\infty$ with $V$ fixed, the holdout’s positional payoff converges to $-V$ for every $x>0$, a step at zero, while the adopter’s converges to $V(1-x)/x$.

###### **Definition 1****.**

Evaluate $\Delta$ at $p=1$ for the mean-cost rival, and let $y_{R}=W_{R}(1)-W_{R}(0)$ and $y_{S}=W_{S}(1)-W_{S}(0)$.

1. (i)

   The technology is *forced* if $\Delta(1)>0$: at full adoption, holding it beats the best non-adopting response in realized flow payoff, so a mean-cost adopter would not drop it. Each other cost type has its own test, obtained by replacing $c$ with $c_{i}$. Waiting value is excluded because this is a flow-payoff classification, not a solution of the timing decision.

2. (ii)

   It is *competitively compelled* if $\Delta(0)\leq 0$: a mean-cost rival would not strictly gain by adopting alone.

3. (iii)

   It is *wasteful for rivals* if $y_{R}<0$ and *socially wasteful* if $y_{S}<0$.

###### **Proposition 1** (Contests are strategic substitutes)**.**

The slope of the payoff gap is

$$
\Delta^{\prime}(x)=p\beta-\frac{p\,\alpha(r-1)}{D(x)^{2}}+\varepsilon\,\Phi^{\prime}(x)\quad\text{for }x<x_{Q},\qquad\Delta^{\prime}(x)=p\beta\quad\text{for }x>x_{Q},
$$

and at $x_{Q}$ the gap jumps down by the adopter’s edge $p\alpha(1-x_{Q})/D(x_{Q})$. If $\beta=\varepsilon=0$, $\alpha\geq 0$ and $r\geq 1$, then $\Delta$ is non-increasing, jump included. The tipping pattern is then impossible, the homogeneous game has no unstable interior equilibrium, and with $\sigma>0$ a continuous best-response map has a unique stable fixed point in the sense defined above. A downward sheltering jump can skip the fixed point; it then gives a stopping boundary for one-way adoption rather than an indifference equilibrium. Within these restrictions, tipping requires a network gain ($\beta>0$) or exclusion ($\varepsilon>0$).

###### **Proposition 2** (Selective forcing)**.**

Let $\beta=\varepsilon=0$, $\sigma=0$, $p=1$, $V>0$, $r>1$, let holdouts have no outside option, and write $\kappa\equiv c-\gamma$. If $\alpha/r<\kappa<\alpha$, then $\Delta(0)>0>\Delta(1)$, and the unique equilibrium is

$$
x^{\circ}=\frac{\alpha/\kappa-1}{r-1}\in(0,1),
$$

which is stable. At $x^{\circ}$ holdouts receive $U_{N}(x^{\circ})=-\kappa x^{\circ}$, and so do adopters net of their cost: rivalry dissipates the edge.

###### **Proposition 3** (Shakeout)**.**

Under the conditions of Proposition [2](https://rencryptofish.com/posts/forcing-technologies#Thmproposition2), give holdouts an outside option with $-\kappa x^{\circ}<Q<0$. They shelter at

$$
x_{Q}=\frac{-Q}{\alpha+(r-1)Q}\in(0,x^{\circ}),
$$

which is the boundary at which the switching gain changes from positive to negative. At $x_{Q}$ every holdout has taken the outside option, no adopter holds an edge, and $\Delta(x_{Q}^{+})=-Q-\kappa<0$. Under irreversible, noiseless adoption, new adoption stops at or beyond this boundary. This is not an interior Nash equilibrium of the reversible payoff game: committed adopters would prefer to shelter if they could switch.

###### **Proposition 4** (Exclusion forces without changing full-adoption welfare)**.**

Raising $\varepsilon$ raises $\Delta(1)$ one for one as long as the full-adoption pressure stays below $-Q$, but leaves $y_{R}$ and $y_{S}$ unchanged. Its welfare cost, $(1-x)\,\varepsilon\,\Phi(x)$, is borne by exposed holdouts during the transition and vanishes at $x\in\{0,1\}$.

###### **Corollary 1** (What an outside option can disarm)**.**

For nonnegative contest and exclusion pressure, $\Delta(1)\geq p(\gamma+\beta)-c$. When the outside option binds, $\Delta(1)=p(\gamma+\beta)-Q-c$; the lower bound is attained by a costless outside option $Q=0$. An outside option can disarm forcing that comes from the contest or from exclusion, never forcing that comes from standalone or network gains.

###### **Proposition 5** (Private–social wedge)**.**

Let $p=1$, $\sigma>0$, and let the cheapest share $x$ adopt. For $x\neq x_{Q}$,

$$
W_{S}^{\prime}(x)-\Delta\big{(}x;c(x)\big{)}=\beta x+\eta-\Big{[}\frac{\alpha}{D(x)}+(1-x)\,\varepsilon\,\Phi^{\prime}(x)\Big{]}\mathbf{1}\{x<x_{Q}\},
$$

where $\Delta(x;c(x))$ is the marginal adopter’s private gain. At an interior allocation where the marginal adopter is indifferent, the wedge itself determines whether adoption is socially excessive ($W_{S}^{\prime}<0$). If $\beta x+\eta\geq 0$, this occurs if and only if holdouts are exposed and

$$
\frac{\alpha}{D(x)}+(1-x)\,\varepsilon\,\Phi^{\prime}(x)>\beta x+\eta.
$$

###### **Corollary 2** (Rivalry as a Pigouvian subsidy)**.**

At an interior private equilibrium in the linear model ($r=1$, $\varepsilon=\eta=0$) with exposed holdouts, adoption is excessive if and only if $\alpha>\beta x$. The marginal private–social wedge is zero when $\alpha=\beta x$; that equality alone does not establish a global welfare optimum.

###### **Corollary 3** (Pure exclusion over-forces)**.**

With only exclusion pressure ($\alpha=\beta=\eta=0$, $\Phi^{\prime}>0$ and holdouts exposed), every interior private equilibrium has excessive adoption. This is a marginal statement. Whether adoption raises welfare relative to the status quo also depends on standalone gains, real costs and the burden placed on laggards.

###### **Proposition 6** (A sufficient condition against a complete ban)**.**

Let $p=1$, $c>0$, $0<\sigma<1$, and let holdouts have no outside option. Then

$$
W_{S}^{\prime}(0^{+})=\gamma+\eta-\varepsilon\Phi^{\prime}(0).
$$

If this is positive, a complete ban is not welfare-maximizing. If also $W_{S}(1)=\gamma+\beta+\eta-c<0$, a welfare-maximizing allocation exists strictly between zero and full adoption.

###### **Proposition 7** (An interior maximum of contest waste)**.**

Consider the linear pure contest: $r=1$, $\alpha>0$, $\gamma=\beta=\varepsilon=\eta=W=0$, no outside option and known effectiveness. Let costs be $c_{i}=cR_{i}$, where $R_{i}$ has the mean-one log-logistic distribution with $0<\sigma<1$. At the static equilibrium,

$$
x(c)=\Pr(R_{i}<\alpha/c),\qquad\mathcal{L}(c)=-W_{R}(x(c))=c\int_{0}^{\alpha/c}uf_{R}(u)\,du.
$$

The loss is positive for every finite $c>0$ and tends to zero as either $c\downarrow 0$ or $c\uparrow\infty$. It therefore attains a maximum at an interior cost level.

###### **Proposition 8** (Aggregation)**.**

In the continuum limit:

1. (a)

   *Persistent heterogeneity only* ($\tau=0$). If the initial adopters are the cheapest $x_{0}$ and $z_{t}$ is non-decreasing in $t$, then

   $$
   x_{t+1}=x_{t}+\lambda_{t}\max\{0,\,F_{c}(z_{t})-x_{t}\},
   $$

   where $F_{c}$ is the cost distribution function.

2. (b)

   *Transitory heterogeneity only* ($\sigma=0$). Then $x_{t+1}=x_{t}+(1-x_{t})\,\lambda_{t}\,\Lambda\big{(}(z_{t}-c)/\tau\big{)}$, which with $\lambda_{t}=1$ is the discrete-time logit hazard of panel adoption models.

###### **Proposition 9** (Dormancy)**.**

Let $\sigma>0$, $\tau=0$ and $\lambda_{0}\in(0,1)$. Let the cheapest $x_{0}<x_{v}$ be seeded, let there be no exogenous demonstration, and let the waiting value $W$ be constant before the demonstration. Suppose $z(x,p_{0})$ is non-decreasing in $x$, as it is whenever $r=1$, $\beta,\varepsilon\geq 0$ and no outside option binds below $x_{L}$. Let $x_{L}$ be the smallest $x\geq x_{0}$ with $g_{p_{0}}(x)\leq x$. Before the demonstration, adoption rises monotonically toward $x_{L}$ and stays strictly below it, unless $x_{L}=x_{0}$, in which case no one adopts. An endogenous demonstration therefore occurs if and only if $x_{v}<x_{L}$, and its date grows without bound as $x_{v}\uparrow x_{L}$.

###### **Observation 1** (Overshoot under an eroding edge)**.**

Take $V=0.5$, $r=6$, $c=0.6$ and $\sigma=0.4$, for which the static stable equilibrium is $x^{\circ}\approx 0.65$. The exact continuum path ends at $0.85$ with $\lambda=0.6$ and at $0.77$ with $\lambda=0.1$. The closed recursion ends at the static equilibrium (Figure [10](https://rencryptofish.com/posts/forcing-technologies#A5.F10)). Realized rival welfare is $-0.41$ on the fast path against $-0.22$ at the static equilibrium. The overshoot is a property of myopic, irreversible adoption with cost-independent frictions. Whether it survives forward-looking timing in the sense of Fudenberg and Tirole ([1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib12)) remains open.

###### **Proposition 10** (Counters)**.**

Let $p=1$, $\alpha>0$, $r\geq 1$ and $Q=-\infty$, with $x,y\geq 0$ and $x+y\leq 1$. For $r>1$ this is a positive-prize contest; $r=1$ denotes the fixed-$\alpha$ linear limit. Set $\tilde{x}=0$ at the no-adopter corner $x=0,y=\varphi=1$, as in the implementation. Then:

1. (a)

   *Nesting.* With $y=0$ or $\varphi=0$, the payoffs ([13](https://rencryptofish.com/posts/forcing-technologies#A6.E13)) are ([6](https://rencryptofish.com/posts/forcing-technologies#A1.E6))–([7](https://rencryptofish.com/posts/forcing-technologies#A1.E7)).

2. (b)

   *Zero sum.* The contest terms sum to zero over adopters, counterers and plain holdouts. Rivals’ welfare is therefore $W_{R}(x,y)=\gamma x+\beta x^{2}-(1-x)\varepsilon\Phi(x)$ minus the costs paid by adopters and counterers.

3. (c)

   *Counters complement adoption and each other.* $z_{K}(0,y)=0$. For $x>0$ and $\varphi>0$, $z_{K}$ is increasing in $x$ and in $y$.

4. (d)

   *Counters substitute for adoption.* For $x>0$ and $\varphi>0$, $z_{A}-z_{K}$ is decreasing in $y$. $z_{A}$ itself is decreasing in $y$ if $r>1$ and constant if $r=1$.

5. (e)

   *A full counter restores the split.* With $\varphi=1$, $x>0$ and $x+y=1$, adopters and counterers both receive the no-technology share of the prize.

###### **Corollary 4** (What a counter can disarm)**.**

Under Proposition [10](https://rencryptofish.com/posts/forcing-technologies#Thmproposition10)’s assumptions, with $c_{K}\geq 0$, $\Delta_{K}(1)\geq\Delta(1)-\alpha/r=\gamma+\beta+\varepsilon-c$. A technology whose standalone, network and exclusion gains alone exceed its cost cannot be disarmed by this counter. The counter removes positional pressure; it does not supply compatibility or satisfy the gatekeeper’s requirement.

###### **Proposition 11** (Nesting)**.**

1. (i)

   *Threshold model.* With $\alpha=\beta=0$, $r=1$, $\gamma=B$, $c=C+Q$, $W=W$, $\varepsilon=S$ and no outside option, the switching gain is $\tilde{\Delta}(x)\equiv\Delta(x)-W=S\,\Phi(x)-G$ with $G=C+W+Q-B$. The threshold model’s $Q$ is a constant opportunity cost of adopting, which the unified model folds into $c$; it is not the outside option of ([7](https://rencryptofish.com/posts/forcing-technologies#A1.E7)), which caps a holdout’s loss instead of shifting every gain. Its four statuses (independent, forced, latent, not forceable) are $\tilde{\Delta}(0)>0$; $\tilde{\Delta}(0)\leq 0<\tilde{\Delta}(x)$; $\tilde{\Delta}(x)\leq 0<\max\tilde{\Delta}$; and $\max\tilde{\Delta}\leq 0$.

2. (ii)

   *Linear model.* With $r=1$, $\varepsilon=W=\eta=0$ and no outside option, payoffs, welfare, the two tests $F=\Delta(1)$ and $y=y_{R}$, and the critical mass $x^{*}=(c-\gamma-\alpha)/\beta$ all coincide with the linear model. Its diffusion recursion is Proposition [8](https://rencryptofish.com/posts/forcing-technologies#Thmproposition8)(a), which is exact because $z_{t}$ is non-decreasing when $\beta\geq 0$ and $\gamma+\alpha\geq 0$.

###### **Proposition 12** (Observational equivalence)**.**

Adoption paths, at any level of aggregation, depend on the payoff parameters through the gross gain $(x,p)\mapsto z(x,p)$ of Appendix [E](https://rencryptofish.com/posts/forcing-technologies#A5), together with $F_{c}$, the waiting-value process, and the diffusion parameters $(p_{0},x_{v},\lambda_{0},\lambda,\tau)$. Holding the initial state, cost distribution, waiting-value process and diffusion rules fixed, parameter vectors that induce the same gain map produce the same adoption paths but in general different welfare. For example, with $r=1$, no outside option and $W=0$, moving $\delta$ from $\gamma$ to $\alpha$ leaves every path unchanged and lowers $W_{R}(x)$ by $\delta x$. The result need not hold if that change also alters the edge-dependent waiting value.

## Appendix D Proofs

Lemma [1](https://rencryptofish.com/posts/forcing-technologies#Thmlemma1).

For $x<x_{Q}$, $x\alpha(1-x)/D-(1-x)\alpha x/D=0$. For $x\geq x_{Q}$ the adopter’s edge is switched off in ([6](https://rencryptofish.com/posts/forcing-technologies#A1.E6)) and the holdout’s contest loss is replaced by $Q$ in ([7](https://rencryptofish.com/posts/forcing-technologies#A1.E7)), so both contest terms are zero.

Lemma [2](https://rencryptofish.com/posts/forcing-technologies#Thmlemma2).

The switching gain’s contest term is $\alpha(1-x)/D+\alpha x/D=\alpha/D$. Differentiating gives $-\alpha(r-1)/D^{2}$, and $\alpha(r-1)=V(r-1)^{2}$, which gives (a). For (b), $|\alpha(1-x)/D-\alpha(1-x)|=|\alpha|(1-x)x|r-1|/D\leq|\alpha||r-1|/\min_{x}D$, and similarly for the holdout term; both vanish as $r\to 1$. For (c), $-V(r-1)x/(1+(r-1)x)\to-V$ for $x>0$, and $V(r-1)(1-x)/(1+(r-1)x)\to V(1-x)/x$.

Proposition [1](https://rencryptofish.com/posts/forcing-technologies#Thmproposition1).

Differentiate each branch of ([8](https://rencryptofish.com/posts/forcing-technologies#A1.E8)). The jump at $x_{Q}$ follows from $L(x_{Q})=-Q$, which gives $\Delta(x_{Q}^{+})-\Delta(x_{Q}^{-})=-p\alpha(1-x_{Q})/D(x_{Q})$. With $\beta=\varepsilon=0$, $\alpha\geq 0$ and $r\geq 1$, $\Delta^{\prime}=-p\alpha(r-1)/D^{2}\leq 0$ below $x_{Q}$ and zero above it, and the jump is downward, so $\Delta(1)\leq\Delta(0)$ and the tipping pattern ($\Delta(0)\leq 0<\Delta(1)$) is impossible. An unstable interior equilibrium of the homogeneous game needs $\Delta$ to cross zero from below, which a non-increasing $\Delta$ cannot do. With $\sigma>0$, a continuous non-increasing best-response map $x\mapsto F_{c}(z(x))$ crosses the diagonal exactly once, from above. At a downward discontinuity the sign can change without equality; this defines a sheltering boundary rather than a fixed point.

Proposition [2](https://rencryptofish.com/posts/forcing-technologies#Thmproposition2).

Here $\Delta(x)=\alpha/D(x)-\kappa$, which is strictly decreasing since $r>1$. $\Delta(0)=\alpha-\kappa>0$ and $\Delta(1)=\alpha/r-\kappa<0$, so there is a unique root, solving $D(x^{\circ})=\alpha/\kappa$. It lies in $(0,1)$ because $1<\alpha/\kappa<r$. It is stable because $\Delta>0$ below it and $\Delta<0$ above it, and neither corner is an equilibrium. Finally, $U_{N}(x^{\circ})=-\alpha x^{\circ}/D(x^{\circ})=-\kappa x^{\circ}$, and $U_{A}(x^{\circ})=U_{N}(x^{\circ})$ because $\Delta(x^{\circ})=0$.

Proposition [3](https://rencryptofish.com/posts/forcing-technologies#Thmproposition3).

The exposed loss $\alpha x/D(x)$ is increasing in $x$ and equals $\kappa x^{\circ}$ at $x^{\circ}$ (Proposition [2](https://rencryptofish.com/posts/forcing-technologies#Thmproposition2)), so $-\kappa x^{\circ}<Q<0$ puts $x_{Q}$, the root of $\alpha x/D(x)=-Q$, in $(0,x^{\circ})$. Solving gives $x_{Q}=-Q/(\alpha+(r-1)Q)$, whose denominator is positive because $-Q<\alpha/(r-1)$, the supremum of the exposed loss. For $x<x_{Q}<x^{\circ}$, $\Delta(x)=\alpha/D(x)-\kappa>\alpha/D(x^{\circ})-\kappa=0$. For $x\geq x_{Q}$ holdouts have sheltered, so $\Delta(x)=\gamma-c-Q=-Q-\kappa$, which is negative because $-Q<\kappa x^{\circ}<\kappa$. Hence the sign changes at $x_{Q}$. Under irreversible, noiseless adoption, new commitments cease once the path reaches or passes it. Since $\Delta(x_{Q})<0$, it is not an interior indifference equilibrium of the reversible game. At $x_{Q}$ the adopter’s edge is switched off by ([6](https://rencryptofish.com/posts/forcing-technologies#A1.E6)).

Proposition [4](https://rencryptofish.com/posts/forcing-technologies#Thmproposition4).

By ([9](https://rencryptofish.com/posts/forcing-technologies#A2.E9)), $\Phi(1)=1$ gives $\partial\Delta(1)/\partial\varepsilon=1$ while $p\alpha/r+\varepsilon<-Q$. $\Phi(0)=0$ and $1-x=0$ at $x=1$ remove $\varepsilon$ from $W_{R}(0)$ and $W_{R}(1)$.

Proposition [5](https://rencryptofish.com/posts/forcing-technologies#Thmproposition5).

$C^{\prime}(x)=c(x)$. For $x<x_{Q}$, differentiating ([15](https://rencryptofish.com/posts/forcing-technologies#A7.E15)) gives $W_{S}^{\prime}(x)=\gamma+2\beta x+\varepsilon\Phi-(1-x)\varepsilon\Phi^{\prime}-c(x)+\eta$, and subtracting $\Delta(x;c(x))=\gamma+\beta x+\alpha/D+\varepsilon\Phi-c(x)$ gives the bracketed wedge. For $x>x_{Q}$, $W_{S}^{\prime}(x)=\gamma+2\beta x-Q-c(x)+\eta$ and $\Delta(x;c(x))=\gamma+\beta x-Q-c(x)$, whose difference is $\beta x+\eta$. At indifference $\Delta(x;c(x))=0$, so $W_{S}^{\prime}(x)$ equals the wedge.

Corollary [1](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary1).

At $x=1$ a lone deviator faces $D=r$ and the pressure $p\alpha/r+\varepsilon$; its best non-adopting payoff is $\max\{-(p\alpha/r+\varepsilon),Q\}$. Thus $\Delta(1)=p(\gamma+\beta)-c+\min\{p\alpha/r+\varepsilon,-Q\}$. With nonnegative pressure and $Q\leq 0$ the minimum is nonnegative. If the outside option binds it equals $-Q$, which reaches zero at $Q=0$.

Proposition [6](https://rencryptofish.com/posts/forcing-technologies#Thmproposition6).

With no outside option, ([15](https://rencryptofish.com/posts/forcing-technologies#A7.E15)) is continuous on $[0,1]$. The log-logistic quantile satisfies $c(0)=0$, and $\Phi(0)=0$. Differentiating from the right gives $W_{S}^{\prime}(0^{+})=\gamma+\eta-\varepsilon\Phi^{\prime}(0)$. A positive derivative gives $W_{S}(x)>W_{S}(0)=0$ for sufficiently small positive $x$. Continuity on the compact interval gives a maximizer. When also $W_{S}(1)<0$, neither endpoint can maximize welfare, so every maximizer is interior.

Proposition [7](https://rencryptofish.com/posts/forcing-technologies#Thmproposition7).

The private gain is $\alpha-cR_{i}$, so the stated cutoff defines the unique static adopted share. Contest payoffs cancel, leaving the integral of adopted resource costs. The density is positive on $(0,\infty)$, so the loss is positive and continuous for $c>0$. Since $\operatorname{E}[R_{i}]=1$, $\mathcal{L}(c)\leq c\to 0$ as $c\downarrow 0$. Also $\mathcal{L}(c)\leq\alpha\Pr(R_{i}<\alpha/c)\to 0$ as $c\uparrow\infty$, since there is no atom at zero. A positive value at any finite $c$ and these two limits restrict the global maximum to a compact subinterval of $(0,\infty)$, where continuity guarantees attainment.

Proposition [8](https://rencryptofish.com/posts/forcing-technologies#Thmproposition8).

(a) Let $E_{t}=\{q:c(q)<z_{t}\}$, the cheapest $F_{c}(z_{t})$. Because $z_{t}$ is non-decreasing, $E_{t}$ is increasing, and every adopter is either a seed (the cheapest $x_{0}$) or entered from some $E_{s}\subseteq E_{t}$. If $F_{c}(z_{t})\geq x_{0}$, all adopters lie in $E_{t}$, so the eligible non-adopters have mass $F_{c}(z_{t})-x_{t}\geq 0$, and a share $\lambda_{t}$ of them adopts. If $F_{c}(z_{t})<x_{0}$, no non-seed has yet been eligible, so $x_{t}=x_{0}$ and no one adopts. (b) With a common cost, every non-adopter faces the same hazard.

Proposition [9](https://rencryptofish.com/posts/forcing-technologies#Thmproposition9).

Write $g\equiv g_{p_{0}}$, which is continuous and non-decreasing because $F_{c}$ is continuous and increasing for $\sigma>0$. Before the demonstration $p_{t}=p_{0}$, so if $x_{0},\dots,x_{t}$ are non-decreasing then so are $z_{0},\dots,z_{t}$. Proposition [8](https://rencryptofish.com/posts/forcing-technologies#Thmproposition8)(a) then gives $x_{t+1}=x_{t}+\lambda_{0}\max\{0,g(x_{t})-x_{t}\}\geq x_{t}$, and by induction the recursion holds throughout. By continuity $g(x_{L})\leq x_{L}$. If $x_{L}=x_{0}$, then $g(x_{0})\leq x_{0}$ and $x_{t}=x_{0}$ for all $t$. Otherwise $g(x)>x$ on $[x_{0},x_{L})$. For $x_{t}$ in that interval, $x_{t+1}=(1-\lambda_{0})x_{t}+\lambda_{0}g(x_{t})$ is greater than $x_{t}$, and less than $x_{L}$ because $g(x_{t})\leq g(x_{L})\leq x_{L}$ and $\lambda_{0}<1$. The path is increasing and bounded by $x_{L}$, so it converges. Its limit $\bar{x}\geq x_{0}$ satisfies $g(\bar{x})\leq\bar{x}$, so $\bar{x}\geq x_{L}$ by the definition of $x_{L}$, and hence $\bar{x}=x_{L}$. If $x_{v}<x_{L}$ the path crosses $x_{v}$ in finite time. If $x_{v}\geq x_{L}$ it never does, because $x_{t}<x_{L}$ for all $t$ (or $x_{t}=x_{0}<x_{v}$). Finally, for any horizon $\bar{T}$, $\max_{t\leq\bar{T}}x_{t}<x_{L}$, so every $x_{v}$ between that maximum and $x_{L}$ has a demonstration date later than $\bar{T}$.

Proposition [10](https://rencryptofish.com/posts/forcing-technologies#Thmproposition10).

(a) $y=0$ or $\varphi=0$ gives $\tilde{x}=x$. (b) The contest terms sum to $(\alpha/D)\big{[}x(1-\tilde{x})-(1-\varphi)y\tilde{x}-(1-x-y)\tilde{x}\big{]}=(\alpha/D)\big{[}x-\tilde{x}(1-\varphi y)\big{]}=0$. Welfare is then the mean of ([13](https://rencryptofish.com/posts/forcing-technologies#A6.E13)) without the contest terms. (c) $z_{K}=p\varphi\,h(\tilde{x})$ with $h(u)=\alpha u/(1+(r-1)u)$, $h(0)=0$ and $h^{\prime}(u)=\alpha/D(u)^{2}>0$. Further, $\partial\tilde{x}/\partial x=1/(1-\varphi y)>0$ and $\partial\tilde{x}/\partial y=\varphi x/(1-\varphi y)^{2}>0$. (d) $z_{A}-z_{K}=p[\gamma+\beta x+\alpha(1-\varphi\tilde{x})/D(\tilde{x})]+\varepsilon\Phi(x)$, whose derivative in $\tilde{x}$ is $-p\alpha(\varphi+r-1)/D(\tilde{x})^{2}<0$. The derivative of $\alpha/D(\tilde{x})$ in $\tilde{x}$ is $-\alpha(r-1)/D^{2}$, which is negative for $r>1$ and zero for $r=1$. (e) $\tilde{x}=x/(1-y)=1$, so $\alpha(1-\tilde{x})/D=0$, and $1-\varphi=0$.

Corollary [4](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary4) and ([14](https://rencryptofish.com/posts/forcing-technologies#A6.E14)).

A single deviator leaves $y=0$, so $\tilde{x}=1$ and $D=r$. Then $U_{A}-U_{N}=\Delta(1)$ and $U_{K}-U_{N}=\varphi\alpha/r-c_{K}$, so $U_{A}-\max\{U_{N},U_{K}\}=\Delta(1)-\max\{0,\varphi\alpha/r-c_{K}\}$. Since $c_{K}\geq 0$ and $\varphi\leq 1$, the maximum is at most $\alpha/r$, and $\Delta(1)-\alpha/r=\gamma+\beta+\varepsilon-c$.

Proposition [11](https://rencryptofish.com/posts/forcing-technologies#Thmproposition11).

Substitute the restrictions into ([6](https://rencryptofish.com/posts/forcing-technologies#A1.E6))–([15](https://rencryptofish.com/posts/forcing-technologies#A7.E15)). For (i), $\Phi$ is increasing, so $\max\tilde{\Delta}=\tilde{\Delta}(1)=S-G$, and the statuses reduce to the threshold model’s ($G<0$; $0\leq G<S$ and $S\Phi(x)>G$; $0\leq G<S$ and $S\Phi(x)\leq G$; $G\geq S$). For (ii), $D\equiv 1$, and the stated conditions make $z_{t}=p_{t}(\gamma+\alpha+\beta x_{t})$ non-decreasing.

Proposition [12](https://rencryptofish.com/posts/forcing-technologies#Thmproposition12).

With the waiting-value process held fixed, the hazard ([11](https://rencryptofish.com/posts/forcing-technologies#A5.E11)) depends on payoffs only through $z-W_{t}$. Identical initial states and diffusion rules then produce identical paths by induction, including identical demonstration dates. Welfare ([15](https://rencryptofish.com/posts/forcing-technologies#A7.E15)) depends on $\gamma$ separately. The edge-dependent specification of $W_{t}$ must be held fixed or disabled for this argument to apply.

## Appendix E When adoption starts and where it stops

The endpoint tests and static crossings describe incentives at a given adoption share. They do not determine the share ultimately reached, the time required or whether adoption stops at a static equilibrium. Three ingredients settle those questions: when rivals learn that the technology works, how fast they act on a positive gain, and the fact that adoption cannot be undone. This section adds them in turn. The main tool is the best-response map of Appendix [E.5](https://rencryptofish.com/posts/forcing-technologies#A5.SS5), which turns the payoff curves of Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) into a picture of motion. For an investor, three results here matter most: a working technology can stay dormant until something demonstrates it (Appendix [E.6](https://rencryptofish.com/posts/forcing-technologies#A5.SS6)), a gatekeeper has to apply pressure before adoption is widespread or it never bites (Appendix [E.9](https://rencryptofish.com/posts/forcing-technologies#A5.SS9)), and a field can over-invest in an eroding edge and leave late buyers stranded (Appendix [E.8](https://rencryptofish.com/posts/forcing-technologies#A5.SS8)).

### E.1 What starts adoption

Before a demonstration event, rivals hold belief $p_{0}$. The demonstration happens either when usage reaches a visibility threshold ($x_{t}\geq x_{v}$) or at an exogenous date. After it, $p=1$. Cost differences or a sponsor’s initial adoption can bring usage to the visibility threshold, triggering a common revision in beliefs. A war can supply such evidence. A deadline or mandate may instead change exclusion or expected demand; representing it as a belief jump is a reduced-form approximation. Appendices [E.2](https://rencryptofish.com/posts/forcing-technologies#A5.SS2) and [E.3](https://rencryptofish.com/posts/forcing-technologies#A5.SS3) distinguish these interpretations. A global-games refinement of the learning process (Carlsson and van Damme, [1993](https://rencryptofish.com/posts/forcing-technologies#bib.bib19); Morris and Shin, [1998](https://rencryptofish.com/posts/forcing-technologies#bib.bib20)) remains outside the baseline.

### E.2 A pilot’s return mixes edge and network

A good pilot answers whether the first user gains. It does not by itself answer what happens after competitors catch up. At $p=1$, with a common cost and no outside option, the first adopter earns $U_{A}(0)=\gamma+\alpha-c$, whereas each rival at full adoption earns $U_{A}(1)=y_{R}=\gamma+\beta-c$. Thus

$$
U_{A}(0)-y_{R}=\alpha-\beta.
$$

(10)

In the arms-race walkthrough, the first adopter earns $0.7$ while full adoption leaves each rival at $-0.2$: the pilot-to-saturation gap is the $0.9$ competitive edge. In the coordination walkthrough, the pilot earns $-0.4$ while full adoption earns $0.4$: the missing network is worth $0.8$.

The pilot includes the whole first mover’s positional edge and none of the eventual network gain. It overstates the full-adoption payoff when $\alpha>\beta$ and understates it when $\beta>\alpha$. Relative to the standalone payoff $\gamma-c$, its positional component is exactly $\alpha$. These are different comparisons. Nor is the pilot necessarily representative: if its cost is $c_{L}<c$, its advantage over the mean rival’s full-adoption payoff is $\alpha-\beta+c-c_{L}$.

This is an interpretation of the two curves, not a claim that rational rivals must be deceived. A rival that knows the decomposition can anticipate the edge’s erosion. The empirical problem arises when the decomposition is unknown and a pilot’s private return is treated as evidence of persistent productivity. A useful demonstration should therefore measure output and costs, outcomes for exposed holdouts, and the adopter’s return as competitors catch up. A large private return with offsetting holdout losses supports the contest channel; a gain that persists when rivals catch up supports the standalone or network channels. A successful demonstration and a wasteful arms race can coexist.

### E.3 Mistaken beliefs and early preparation

The baseline demonstration rule is deliberately one-sided: it reveals a technology that works. It cannot describe a disappointing trial or a mistaken belief about the competitive stakes. For that extension, distinguish a perceived switching gain $\widehat{d}_{it}$ from the switching gain $d_{it}^{\mathrm{true}}$ evaluated using the realized payoff primitives. An adoption episode is *belief-driven false forcing* when $\widehat{d}_{it}>0$ but $d_{it}^{\mathrm{true}}\leq 0$ at the same exposure and costs. This differs from a wasteful bandwagon: a wasteful technology can confer a real private advantage and be adopted under correct beliefs. An unfavorable realization also does not by itself show that an ex ante decision was irrational.

A more general learning model would let beliefs rise after a good trial and fall after a bad one. It would also account for the pilot’s cost and its advantage over unprepared rivals. A downward revision can stop new adoption while leaving earlier commitments stranded. Exclusion may persist after a disappointing trial because the gatekeeper’s penalty is not scaled by confidence in the technology.

Firms may also act before rivals deploy. A future deadline can bring orders forward when installation takes time or capacity must be reserved. If installation is instantaneous and freely available, a future penalty alone need not justify today’s operating cost. Record order, installation and productive-use dates separately before treating early purchases as evidence against competitive pressure.

Appendix [R](https://rencryptofish.com/posts/forcing-technologies#A18) retains a Bayesian update and a forward-looking timing formulation. The baseline simulations instead use current incentives and a reduced-form waiting value. Whether anticipation removes their overshoot is an open question.

### E.4 How a favorable decision becomes an actual adoption

A positive gain does not mean every firm installs the technology immediately. Budgets, build times and implementation capacity delay action. The model represents those delays with $\lambda_{t}$, which controls the speed of adjustment. Temporary shocks can also move a decision around its threshold; their scale is $\tau$. Persistent differences in cost remain attached to the same actor.

The *adoption hazard* is simply the probability that an actor adopts this period, conditional on not having adopted yet. Let $z_{t}\equiv z(x_{t},p_{t})-W_{t}$ be the gross switching gain, where $z(x,p)$ is the payoff gap ([8](https://rencryptofish.com/posts/forcing-technologies#A1.E8)) before the cost at belief $p$: $p[\gamma+\beta x+\alpha/D(x)]+\varepsilon\Phi(x)$ while holdouts are exposed and $p[\gamma+\beta x]-Q$ once they have sheltered. A rival with cost $c_{i}$ that has not yet adopted does so in period $t$ with probability

$$
h_{t}(c_{i})=\lambda_{t}\,\Lambda\!\Big{(}\frac{z_{t}-c_{i}}{\tau}\Big{)},\qquad\lambda_{t}=\begin{cases}\lambda_{0}&\text{before the demonstration,}\\ \lambda&\text{after,}\end{cases}
$$

(11)

where $\Lambda$ is the logistic function and $\tau\geq 0$ scales a transitory shock. As $\tau\to 0$ the logistic becomes the indicator $\mathbf{1}\{c_{i}<z_{t}\}$. Adoption is irreversible. The split between $\lambda_{0}$ and $\lambda$ is the model’s version of the innovation–imitation distinction in Bass ([1969](https://rencryptofish.com/posts/forcing-technologies#bib.bib15)).

The same decision rule can generate an aggregate adoption curve or individual adoption dates. With only persistent cost differences and a non-decreasing gain, the simple update counts eligible actors who have not yet adopted. With identical costs and temporary shocks, every remaining actor faces the same adoption probability. The exact conditions and both formulas are in Proposition [8](https://rencryptofish.com/posts/forcing-technologies#Thmproposition8).

The two limits leave different fingerprints even when payoffs are identical. Figure [7](https://rencryptofish.com/posts/forcing-technologies#A5.F7) holds the switching gain fixed at $z=0.5$, below the mean cost of $0.6$, so that no rival’s incentive ever changes. With persistent heterogeneity only, the rivals for whom adopting pays adopt first and the rest never do. Adoption plateaus at $F_{c}(z)=56\%$, and the hazard among rivals yet to adopt falls from $0.17$ to zero. With transitory heterogeneity only, every non-adopter faces the same odds in every period. The hazard is flat at $0.08$ and adoption creeps toward saturation. A falling aggregate hazard is therefore not evidence of a weakening incentive, because sorting on persistent costs produces one by itself. Aggregate series can tell the two apart only through the plateau. Panels tell them apart directly, because they follow the same rival over time.

![Figure 7: Persistent versus transitory heterogeneity with identical, constant payoffs (γ=0.3, α=0.2, r=1, c=0.6, λ=0.3, so z=0.5 throughout). Left: persistent cost differences produce a plateau at the share for whom adopting pays, and transitory shocks produce slow saturation. Right: the hazard falls under persistent heterogeneity only because the rivals who remain are the costly ones. Shared settings: β=ε=0, p=1, x0=0, Q=−∞ and W=0; each legend entry gives its σ and τ.](https://rencryptofish.com/images/forcing-technologies/heterogeneity.png)

Figure 7: Persistent versus transitory heterogeneity with identical, constant payoffs ($\gamma=0.3$, $\alpha=0.2$, $r=1$, $c=0.6$, $\lambda=0.3$, so $z=0.5$ throughout). Left: persistent cost differences produce a plateau at the share for whom adopting pays, and transitory shocks produce slow saturation. Right: the hazard falls under persistent heterogeneity only because the rivals who remain are the costly ones. Shared settings: $\beta=\varepsilon=0$, $p=1$, $x_{0}=0$, $Q=-\infty$ and $W=0$; each legend entry gives its $\sigma$ and $\tau$.

### E.5 The best-response map

Let $F_{c}(z)$ be the fraction of actors whose cost is below $z$. The *best-response map* counts the share for whom adoption would pay at the current exposure:

$$
g_{p}(x)\equiv F_{c}\big{(}z(x,p)-W\big{)},
$$

(12)

Here $z(x,p)$ is the gain before paying the actor’s cost or subtracting the value of waiting. With fixed beliefs, no temporary shocks, the cheapest actors seeded first and a non-decreasing switching gain, the next share is

$$
x_{t+1}=x_{t}+\lambda\max\{0,\,g_{p}(x_{t})-x_{t}\}.
$$

For example, if $30\%$ have adopted, the gain currently covers the costs of $50\%$, and $\lambda=0.25$, the next period adds a quarter of the twenty-point gap: adoption reaches $35\%$. If the eligible share is already below the adopted share, this irreversible update adds nobody. Proposition [8](https://rencryptofish.com/posts/forcing-technologies#Thmproposition8) gives the exact conditions under which that counting rule works.

Where the map lies above the diagonal, adoption moves a fraction $\lambda$ of the way up to it. Where the map lies below the diagonal, adoption does not move. Figure [8](https://rencryptofish.com/posts/forcing-technologies#A5.F8) draws the map for a network good with dispersed costs, which is the coordination archetype of Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) with heterogeneous costs. Four features of the picture hold in general.

- *Crossings identify the static reference points.* With $W=0$, a fixed point is a static payoff equilibrium. A positive constant waiting value instead gives a switching threshold. A downward crossing gives the usual stable static reference; an upward crossing gives a tipping threshold. Here the stable equilibria are at $0.6\%$ and $93\%$, and the tipping point is at $39\%$.

- *Irreversibility freezes failed seeds.* In the static game the low equilibrium attracts every state below the tipping point. In the dynamic model nothing pulls adoption down. A seed of $38\%$ stays at $38\%$: the cheapest $38\%$ have adopted, the next-cheapest rival still does not gain, and no adopter leaves. Every seed at which the map lies on or below the diagonal is a rest point. Two seeds two points apart, on either side of the tipping point, end at $38\%$ and $93\%$.

- *The S-curve comes from the shape of the map.* Just above the tipping point the map barely clears the diagonal, so each period adds few adopters. The gap widens as adoption grows and closes again near the high equilibrium. The seed of $40\%$ takes five periods to reach $50\%$ and four more to reach $90\%$. The S-shape of diffusion curves needs no separate imitation term here: it comes from the network gain, which makes the map rise, and from the dispersion of costs, which makes it smooth.

- *The map has the slope of the switching gain.* $F_{c}$ is increasing, so $g_{p}$ rises where $\Delta$ rises and falls where $\Delta$ falls. Network and exclusion channels bend the map upward, the contest bends it down, and an outside option, where it binds, drops it by the adopters’ edge. A continuous falling map crosses the diagonal once (Proposition [1](https://rencryptofish.com/posts/forcing-technologies#Thmproposition1)), so a pure contest has no tipping point. Appendix [E.8](https://rencryptofish.com/posts/forcing-technologies#A5.SS8) shows that a falling map also no longer describes the state completely.

![Figure 8: The best-response map g⁢(x)=Fc⁢(z⁢(x)) for a network good with dispersed costs (γ=0.2, β=0.8, c=0.6, σ=0.2, λ=1). (a) Adoption grows where the map lies above the 45° line (blue) and stops where it lies below (gray). With λ=1 the path is the staircase xt+1=g⁢(xt). Filled circles are stable equilibria and the open circle is the tipping point. (b) Paths from different seeds. Seeds below the tipping point freeze, because adoption is irreversible. Seeds above it trace an S-curve to the high equilibrium. Other settings: α=ε=0, r=p=1, Q=−∞, W=τ=0; seed shares are labeled in the figure.](https://rencryptofish.com/images/forcing-technologies/best_response.png)

Figure 8: The best-response map $g(x)=F_{c}(z(x))$ for a network good with dispersed costs ($\gamma=0.2$, $\beta=0.8$, $c=0.6$, $\sigma=0.2$, $\lambda=1$). (a) Adoption grows where the map lies above the 45° line (blue) and stops where it lies below (gray). With $\lambda=1$ the path is the staircase $x_{t+1}=g(x_{t})$. Filled circles are stable equilibria and the open circle is the tipping point. (b) Paths from different seeds. Seeds below the tipping point freeze, because adoption is irreversible. Seeds above it trace an S-curve to the high equilibrium. Other settings: $\alpha=\varepsilon=0$, $r=p=1$, $Q=-\infty$, $W=\tau=0$; seed shares are labeled in the figure.

### E.6 Why a working technology can remain dormant

Beliefs scale the technology channels, so before the demonstration rivals act on a lower map, $g_{p_{0}}$, than after it, $g_{1}$ (Figure [9](https://rencryptofish.com/posts/forcing-technologies#A5.F9)a). The path therefore has two phases. A seed $x_{0}$ first creeps at the slow pre-demonstration speed $\lambda_{0}$ toward the first rest point of the pre-demonstration map, the *ceiling* $x_{L}$. If usage crosses the visibility threshold $x_{v}$ on the way, beliefs jump, the map shifts up to $g_{1}$, and adoption takes off at speed $\lambda$. If it does not, adoption approaches $x_{L}$ and stays there. The technology works, but it never reaches the usage needed to show that it works.

Figure [9](https://rencryptofish.com/posts/forcing-technologies#A5.F9)(b) shows both outcomes with identical payoffs. With $x_{v}=15\%$, below the ceiling $x_{L}=17.4\%$, the demonstration comes at $t=19$ and adoption rises to $81\%$. With $x_{v}=18\%$ it never comes, and adoption stalls at $17\%$ until an external demonstration supplies the missing evidence. A mandate could instead change the payoffs; that is a different intervention. Panel (c) traces the demonstration date as $x_{v}$ rises. The date grows slowly at first, then without bound as $x_{v}$ approaches the ceiling, because the path approaches $x_{L}$ only geometrically. Near the ceiling, a small change in $x_{v}$ moves the demonstration by many periods or removes it altogether. The inherited nuclear-weapons fit in Appendix [Q](https://rencryptofish.com/posts/forcing-technologies#A17) sits at this sensitive boundary.

A sponsor has several ways to get past that barrier. It can seed usage past $x_{v}$ directly. It can lower $x_{v}$ with a public trial, or replace it with an exogenous demonstration. Or it can raise the prior $p_{0}$, which lifts the pre-demonstration map and with it the ceiling. A seed that stops short of $x_{v}$ helps only if it clears a tipping point of the pre-demonstration map. In Figure [9](https://rencryptofish.com/posts/forcing-technologies#A5.F9), where that map crosses the diagonal once, a seed between $17.4\%$ and $18\%$ simply stays where it is.

![Figure 9: Demonstration and dormancy (γ=0.2, β=0.5, α=0.2, r=1, c=0.6, σ=0.4; p0=0.5, x0=2%, λ0=0.15, λ=0.5). (a) The best-response map before the demonstration (dashed) and after it (solid). (b) Paths with identical payoffs. A visibility threshold below the ceiling xL is crossed and adoption takes off (blue). One above the ceiling is never crossed (orange) unless an exogenous event demonstrates the technology (aqua). Open circles mark demonstrations. (c) The demonstration date diverges as xv approaches xL. (d) With an exogenous demonstration at t=12, a waiting value (ω=0.8) silences adoption beforehand. Exclusion and transitory shocks are off (ε=τ=0), Q=−∞, and W0=κW=0; ω=0 except for the waiting comparison in (d).](https://rencryptofish.com/images/forcing-technologies/demonstration.png)

Figure 9: Demonstration and dormancy ($\gamma=0.2$, $\beta=0.5$, $\alpha=0.2$, $r=1$, $c=0.6$, $\sigma=0.4$; $p_{0}=0.5$, $x_{0}=2\%$, $\lambda_{0}=0.15$, $\lambda=0.5$). (a) The best-response map before the demonstration (dashed) and after it (solid). (b) Paths with identical payoffs. A visibility threshold below the ceiling $x_{L}$ is crossed and adoption takes off (blue). One above the ceiling is never crossed (orange) unless an exogenous event demonstrates the technology (aqua). Open circles mark demonstrations. (c) The demonstration date diverges as $x_{v}$ approaches $x_{L}$. (d) With an exogenous demonstration at $t=12$, a waiting value ($\omega=0.8$) silences adoption beforehand. Exclusion and transitory shocks are off ($\varepsilon=\tau=0$), $Q=-\infty$, and $W_{0}=\kappa_{W}=0$; $\omega=0$ except for the waiting comparison in (d).

### E.7 When waiting is valuable

In reduced form, $W_{t}=(W_{0}+\omega\,p_{t}(1-p_{t}))/(1+\kappa_{W}\max\{0,p_{t}\alpha/D(x_{t})\})$. Waiting is valuable while beliefs are uncertain, and the value is eroded by the positional ground lost to rivals in the meantime. A constant $W_{0}$ shifts every switching gain by the same amount and so moves the rest points of the dynamics, but it never enters the payoff gap or the classification. A demonstration then does two things at once: it raises the expected gain and removes the reason to wait. Figure [9](https://rencryptofish.com/posts/forcing-technologies#A5.F9)(d) shows both effects with an exogenous demonstration date. With $\omega=0.8$, no one beyond the seed adopts before the demonstration ($2\%$, against $13\%$ without a waiting value). The jump at the demonstration is also larger (21 points against 19). Waiting suppresses adoption before the demonstration and produces a larger jump afterward. The optimal-stopping formulation in Appendix [E.3](https://rencryptofish.com/posts/forcing-technologies#A5.SS3) makes this structural problem explicit. Deriving the reduced-form $W_{t}$ from equilibrium in a timing game remains open (Reinganum, [1981](https://rencryptofish.com/posts/forcing-technologies#bib.bib11); Fudenberg and Tirole, [1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib12); Dixit and Pindyck, [1994](https://rencryptofish.com/posts/forcing-technologies#bib.bib13)).

### E.8 Why the field can invest too much before the edge disappears

The simple update works only while the gross switching gain does not fall. Under strategic substitutes (Proposition [1](https://rencryptofish.com/posts/forcing-technologies#Thmproposition1)), the map falls and $z_{t}$ falls as $x_{t}$ rises. Some rivals then adopt while their cost is below $z_{t}$ and stay adopted after it is not. The closed recursion subtracts all past adopters from the currently eligible pool. When some past adopters are no longer eligible, that subtraction is too large and it understates the remaining pool. The share $x_{t}$ then no longer describes the state. It matters which rivals have adopted, not just how many.

For the example in Figure [10](https://rencryptofish.com/posts/forcing-technologies#A5.F10), the static equilibrium is about $65\%$. The exact adoption path reaches $85\%$ with fast adjustment ($\lambda=0.6$) and $77\%$ with slower adjustment ($\lambda=0.1$). Rival welfare on the fast path is $-0.41$, compared with $-0.22$ at the static allocation. The example uses $V=0.5$, $r=6$, $c=0.6$ and cost dispersion $\sigma=0.4$.

Figure [10](https://rencryptofish.com/posts/forcing-technologies#A5.F10)(b) shows the mechanism. In the first period the edge is at its largest, $z_{0}=\alpha=2.5$, and adopting pays for $99\%$ of rivals. Sixty percent of them adopt, at every cost level. Their adoption shrinks the edge, so in the second period adopting pays only for the cheapest $70\%$, and $60\%$ of those not yet in adopt. By the end, the edge pays only the cheapest $53\%$, fewer than at the static equilibrium, yet $85\%$ have adopted. The $32\%$ of rivals to the right of the final threshold are stranded. They would not adopt today, but they adopted while the edge was large and cannot undo it. Each of them pays $c_{i}>\alpha/D(x_{T})$ every period for an edge that no longer covers it. With avoidable flow costs they would drop the technology if they could, so the overshoot and its welfare cost are the price of commitment, and with reversible adoption the path would be free to unwind toward the static equilibrium. With sunk acquisition costs they would stay, because an adopter’s contest payoff $\alpha(1-x)/D(x)$ exceeds a holdout’s $-\alpha x/D(x)$ at every $x$, and the waste is the acquisition cost rather than a perpetual flow. Which reading applies is a fact about the technology, not the model; Section [1](https://rencryptofish.com/posts/forcing-technologies#S1) fixes the flow reading throughout. Slower adjustment overshoots less: fewer rivals commit in each period, so the edge has shrunk further by the time most of them decide. The closed recursion loses track of those stranded early adopters and therefore misses the overshoot in this example.

![Figure 10: Selective forcing with an eroding edge (V=0.5, r=6, c=0.6, σ=0.4). (a) The exact paths overshoot the static stable equilibrium, and faster adjustment overshoots more. The closed recursion of Proposition 8(a) misses this. (b) Who has adopted by period 30 on the fast path, by cost and by the period in which they adopted. Adopting pays only to the left of the dotted line, given the final edge. The rivals to its right adopted while the edge was large and cannot undo it. Here α=V⁢(r−1)=2.5, γ=β=ε=0, p=1, Q=−∞, W=τ=0, x0=0; adjustment speeds are λ=0.6 and 0.1.](https://rencryptofish.com/images/forcing-technologies/overshoot.png)

Figure 10: Selective forcing with an eroding edge ($V=0.5$, $r=6$, $c=0.6$, $\sigma=0.4$). (a) The exact paths overshoot the static stable equilibrium, and faster adjustment overshoots more. The closed recursion of Proposition [8](https://rencryptofish.com/posts/forcing-technologies#Thmproposition8)(a) misses this. (b) Who has adopted by period 30 on the fast path, by cost and by the period in which they adopted. Adopting pays only to the left of the dotted line, given the final edge. The rivals to its right adopted while the edge was large and cannot undo it. Here $\alpha=V(r-1)=2.5$, $\gamma=\beta=\varepsilon=0$, $p=1$, $Q=-\infty$, $W=\tau=0$, $x_{0}=0$; adjustment speeds are $\lambda=0.6$ and $0.1$.

### E.9 Comparative dynamics, one parameter at a time

Figures [11](https://rencryptofish.com/posts/forcing-technologies#A5.F11) and [12](https://rencryptofish.com/posts/forcing-technologies#A5.F12) vary one parameter at a time around a common baseline technology in which all four channels are active and holdouts have no outside option: $\gamma=0.05$, $\beta=0.4$, $\alpha=0.3$, $r=2$, $\varepsilon=0.2$ ($\theta=0.5$, $k=8$), $c=0.6$ and $\sigma=0.3$. A seed of $2\%$ adopts first and $\lambda=0.3$. The baseline’s best-response map lies above the diagonal all the way to its rest point at $72\%$, but comes within five points of it at $38\%$ adoption. Early on, the erosion of the contest’s edge cancels most of the network gain, so the map rises slowly while the diagonal rises at slope one. Exclusion pressure, centered at $50\%$, steepens the map only later. Adoption crawls through this bottleneck and reaches $50\%$ only in period 22. The bottleneck is why so many panels in Figure [11](https://rencryptofish.com/posts/forcing-technologies#A5.F11) show the same pattern. A modest change in one direction closes the gap, and adoption stalls below it. The same change in the other direction widens the gap, and adoption sweeps through. The response is lopsided: lowering $\gamma$ from $0.05$ to $0$ cuts final adoption from $70\%$ to $21\%$, while raising it to $0.15$ lifts it only to $84\%$, although half the field then adopts three times as fast (by period 7 rather than 22).

![Figure 11: Comparative dynamics of the payoff parameters. Each panel varies one parameter around the baseline (γ=0.05, β=0.4, α=0.3, r=2, ε=0.2, θ=0.5, k=8, c=0.6, σ=0.3, no outside option; the technology is known to work, x0=2%, λ=0.3). Darker lines are higher values; the solid, thicker line is the baseline, repeated in every panel. Waiting and transitory shocks are off (W=τ=0). In the r panel, α=0.3 stays fixed, so the implied prize changes.](https://rencryptofish.com/images/forcing-technologies/sweep_payoffs.png)

Figure 11: Comparative dynamics of the payoff parameters. Each panel varies one parameter around the baseline ($\gamma=0.05$, $\beta=0.4$, $\alpha=0.3$, $r=2$, $\varepsilon=0.2$, $\theta=0.5$, $k=8$, $c=0.6$, $\sigma=0.3$, no outside option; the technology is known to work, $x_{0}=2\%$, $\lambda=0.3$). Darker lines are higher values; the solid, thicker line is the baseline, repeated in every panel. Waiting and transitory shocks are off ($W=\tau=0$). In the $r$ panel, $\alpha=0.3$ stays fixed, so the implied prize changes.

The panels sort the parameters by *when* in the path they act.

- *The edge acts at the start.* The contest’s $\alpha/D(x)$ is largest when adopters are few, so $\alpha$ decides whether adoption gets going. With $\alpha=0.1$ no one beyond the seed adopts. With $\alpha=0.5$ half the field has adopted by period 5. The decisiveness $r$, holding $\alpha$ fixed, decides whether the edge lasts. With $r=1$ the edge never erodes, and adoption climbs to $86\%$. With $r=6$ the same initial edge erodes so quickly that adoption stalls at $15\%$, slightly above its static rest point of $13\%$, which is the overshoot of Appendix [E.8](https://rencryptofish.com/posts/forcing-technologies#A5.SS8) on a small scale. In this example, rapid erosion prevents the initial competitive edge from sustaining widespread adoption.

- *Network and exclusion channels act later.* In the $\beta$ and $\varepsilon$ panels, the low-value paths track the baseline for the first few periods and only then fall away, stalling at $23\%$ and $30\%$. These channels do not start adoption. They decide whether it keeps going once a share of rivals has adopted. With $\beta=0.6$ or $\varepsilon=0.4$, adoption sweeps through the bottleneck to $88\%$ or $89\%$.

- *The timing of exclusion matters as much as its strength.* Pressure centered early ($\theta=0.2$) lifts the map before the bottleneck, and half the field adopts by period 8. Pressure centered late ($\theta=0.8$) arrives only after a point that adoption never reaches, and adoption stalls at $32\%$. In this specification, exclusion must affect incentives before adoption reaches the point at which it would otherwise stall.

- *Level shifters act everywhere.* The cost $c$ shifts the whole map, like $\gamma$ in the opposite direction. Raising $c$ from $0.6$ to $0.7$ stalls adoption at $19\%$.

- *An outside option acts at its shelter point.* With $Q=-0.35$ nothing changes, because holdouts’ loss never reaches $0.35$ and no one shelters. With $Q=-0.15$ holdouts shelter once $41\%$ have adopted, in period 16. The adopters’ edge vanishes, the map drops below the diagonal, and adoption stops at $42\%$ instead of $70\%$. Rivals are worse off, at $-0.136$ against $-0.116$: adopters keep paying for an edge over no one, and holdouts pay $0.15$ a period to shelter from it. This is the shakeout of Proposition [3](https://rencryptofish.com/posts/forcing-technologies#Thmproposition3) with every channel on.

- *Cost dispersion can encourage early adoption while limiting its eventual extent.* At low adoption the mean-cost rival does not gain, so someone has to be cheaper than average for adoption to start. With $\sigma=0.1$ almost no one is, and adoption never leaves the seed. That field has a high equilibrium at $94\%$, but it lies beyond a tipping point at $59\%$. With $\sigma=0.5$ adoption is fastest, with half the field in by period 6, but it ends at $78\%$, below the $94\%$ a homogeneous field could reach, because dispersion also leaves more rivals whose costs are too high ever to adopt.

![Figure 12: Comparative dynamics of the diffusion parameters. Payoffs stay fixed at γ=0.05, β=0.4, α=0.3, r=2, ε=0.2, θ=0.5, k=8, c=0.6, σ=0.3, Q=−∞, W=0. The technology is demonstrated once usage reaches xv, and the baseline has p0=0.8, xv=8%, x0=2%, λ0=0.1, λ=0.3 and τ=0. Open circles mark demonstrations. Darker lines are higher values; the solid, thicker line is the baseline. Each panel changes only the parameter in its title.](https://rencryptofish.com/images/forcing-technologies/sweep_diffusion.png)

Figure 12: Comparative dynamics of the diffusion parameters. Payoffs stay fixed at $\gamma=0.05$, $\beta=0.4$, $\alpha=0.3$, $r=2$, $\varepsilon=0.2$, $\theta=0.5$, $k=8$, $c=0.6$, $\sigma=0.3$, $Q=-\infty$, $W=0$. The technology is demonstrated once usage reaches $x_{v}$, and the baseline has $p_{0}=0.8$, $x_{v}=8\%$, $x_{0}=2\%$, $\lambda_{0}=0.1$, $\lambda=0.3$ and $\tau=0$. Open circles mark demonstrations. Darker lines are higher values; the solid, thicker line is the baseline. Each panel changes only the parameter in its title.

Figure [12](https://rencryptofish.com/posts/forcing-technologies#A5.F12) adds a demonstration phase to the same technology and varies the diffusion parameters. In the baseline, prior beliefs sustain adoption up to a ceiling of $14.8\%$, the visibility threshold is $8\%$, and the demonstration comes in period 9. The parameters split into three groups.

- *Whether: $p_{0}$ and $x_{v}$.* They set the ceiling and the threshold of Proposition [9](https://rencryptofish.com/posts/forcing-technologies#Thmproposition9). Lowering the prior to $0.65$ drops the ceiling to $6.9\%$, below $x_{v}$, so the technology never becomes visible and adoption stays at $7\%$. Raising the threshold to $16\%$, above the ceiling, does the same. In the other direction, $p_{0}=0.95$ or $x_{v}=4\%$ brings the demonstration forward to period 4 or 3.

- *When: $x_{0}$ and $\lambda_{0}$.* These move the demonstration date but not the destination. With no seed the demonstration comes in period 10, and a seed of $10\%$, above $x_{v}$, makes it immediate. Slow pre-demonstration adjustment ($\lambda_{0}=0.04$) delays it to period 21, and fast adjustment ($\lambda_{0}=0.3$) brings it to period 3. Every one of these paths heads for the same $72\%$ rest point.

- *How fast, and sometimes how far: $\lambda$ and $\tau$.* The post-demonstration speed $\lambda$ sets the steepness of take-off: half the field adopts by period 19 with $\lambda=0.6$, and fewer than half by period 50 with $\lambda=0.15$. Because the baseline map rises, $\lambda$ does not change where adoption ends. Under an eroding edge it would (Appendix [E.8](https://rencryptofish.com/posts/forcing-technologies#A5.SS8)). Transitory shocks do change where adoption ends. A rival whose persistent cost exceeds the gain still adopts in a period when its shock is favorable, and it cannot undo that. With $\tau=0.15$, adoption passes the $72\%$ rest point and reaches $93\%$. The same shocks bring the demonstration forward, to period 3.

The payoff parameters determine the available incentives; the diffusion parameters determine whether and when actors act on them. The exceptions are $\lambda$ under an eroding edge and $\tau$, which also change where adoption ends.

### E.10 Weighting the rivals and partners that matter

A global adoption percentage can miss the relevant pressure. One large customer, dominant marketplace or close competitor may matter more than dozens of distant users. Assign weight $w_{ij}$ to actor $j$’s influence on actor $i$, and let $a_{j}=1$ if $j$ has adopted. Then the exposure is

$$
x_{i}=\frac{\sum_{j}w_{ij}a_{j}}{\sum_{j}w_{ij}}.
$$

This is the network-weighted counterpart of the share $x$ (Galeotti et al., [2010](https://rencryptofish.com/posts/forcing-technologies#bib.bib18)). Contest and exclusion exposure use a competition network, and network gains use a compatibility network, which need not coincide. A gatekeeper is a node with very large weight, which is why exclusion often looks like a step. On a star network, seeding the hub can tip adoption at parameters where seeding one leaf does not. Who adopts matters more than how many. On general networks the contest is zero-sum only pairwise, so welfare is computed from realized payoffs.

## Appendix F Counters: a third choice

So far a rival that does not adopt simply holds out, and every other response is folded into the constant $Q$. Many forcing technologies, however, meet a counter: torpedoes and mines against battleships, ad-blockers against advertising, speed bumps against latency arbitrage, detection against synthetic media. A counter differs from a second positional technology in two ways. It is worthless unless someone has adopted the technology it counters. And it works by taking away the adopter’s edge rather than by adding an edge of its own. This section adds the counter as a third choice.

### F.1 Protection against the loss

A counter pays for the loss it avoids. If exposure would cost $0.10$ per period, a defense that shields $80\%$ of that loss saves $0.08$. At a cost of $0.05$, it leaves its user $0.03$ better off than remaining unprotected. With no exposure it saves nothing and still costs $0.05$. These illustrative amounts show why a counter’s value depends on deployment of the technology it counters. Each rival adopts the forcing technology (A), adopts a counter (K), or does neither (N). Let $x$ and $y$ be the shares of adopters and counterers. A counter with *efficacy* $\varphi\in[0,1]$ shields a share $\varphi$ of its holder’s stake from the contest. Adopters can raid only the unshielded pool, which holds the adopters, the plain holdouts, and the unshielded $1-\varphi$ of each counterer. Within that pool the prize is divided in proportion to strength, as in Section [1](https://rencryptofish.com/posts/forcing-technologies#S1). The contest terms are therefore the base model’s, evaluated at the adopters’ share of the pool,

$$
\tilde{x}\equiv\frac{x}{1-\varphi y},
$$

with $\tilde{x}=0$ when $x=0$ (including the fully shielded corner), and the three payoffs are

$\displaystyle U_{A}$

$\displaystyle=p\Big{[}\gamma+\beta x+\frac{\alpha(1-\tilde{x})}{D(\tilde{x})}\Big{]}-c,\qquad U_{N}=-\,p\,\frac{\alpha\tilde{x}}{D(\tilde{x})}-\varepsilon\,\Phi(x),$

(13)

$\displaystyle U_{K}$

$\displaystyle=-\,p\,(1-\varphi)\,\frac{\alpha\tilde{x}}{D(\tilde{x})}-\varepsilon\,\Phi(x)-c_{K}.$

Counterers still lack the technology, so exclusion applies to them as to plain holdouts. The outside option of Section [1](https://rencryptofish.com/posts/forcing-technologies#S1) is switched off in this section. The full counter $\varphi=1$ is its within-segment analogue: it shelters the whole stake at cost $c_{K}$ but leaves its holder in the segment and subject to the gatekeeper, which is why a counter cannot disarm exclusion (Corollary [4](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary4)) while an outside option can (Corollary [1](https://rencryptofish.com/posts/forcing-technologies#Thmcorollary1)). Counter costs are log-logistic with mean $c_{K}$ and dispersion $\sigma_{K}$, independent of adoption costs. Each rival takes the best of the three choices, and both commitments are exclusive and irreversible. The gross gains from adopting and from countering, over doing neither and before a rival’s own cost, are

$$
z_{A}(x,y)=p\Big{[}\gamma+\beta x+\frac{\alpha}{D(\tilde{x})}\Big{]}+\varepsilon\,\Phi(x),\qquad z_{K}(x,y)=p\,\varphi\,\frac{\alpha\tilde{x}}{D(\tilde{x})}.
$$

The counter is worth the share $\varphi$ of the loss that a plain holdout would suffer.

The simpler alternative, giving counterers a strength $k$ in the same pool, does not produce a counter. Such a “counter” would pay even when no one has adopted. And adoption would lower its value rather than raise it, because in a proportional-share contest every strength-raising investment substitutes for every other (Proposition [1](https://rencryptofish.com/posts/forcing-technologies#Thmproposition1)). That is a second positional technology. Shielding distinguishes a counter from another investment in competitive strength, and the full counter $\varphi=1$ plays the role of a counter as strong as the edge.

A counter changes the incentives of the rivals who have not protected themselves. Each additional shield concentrates the contest on the remaining exposed stakes, increasing the reason for other holdouts to counter. The defense can become hard to avoid in its own right.

Countering also makes adoption less attractive relative to buying protection. When the edge erodes ($r>1$), it reduces the adoption gain relative to doing nothing as well. In the linear limit it lowers the adopter’s and plain holdout’s payoffs by the same amount. The contest still cancels across all three groups, so counter costs remain in the welfare total.

### F.2 Whether protection makes adoption avoidable

At full adoption, a rival that drops the technology need not hold out unprotected; it can counter instead. With $p=1$ and the mean-cost rival, its gain from adopting over the best non-adopting response is

$$
\Delta_{K}(1)=\Delta(1)-\max\Big{\{}0,\ \frac{\varphi\alpha}{r}-c_{K}\Big{\}}.
$$

(14)

The technology is forced against the counter if $\Delta_{K}(1)>0$. The counter *disarms* it if $\Delta(1)>0\geq\Delta_{K}(1)$, that is, if $c_{K}\leq\varphi\alpha/r-\Delta(1)$. A counter does not change the first-mover test at $x=0$: with no deployed technology to defend against, a non-adopter gains nothing from countering.

The limit is practical as well as mathematical. A counter can end an arms race over a positional edge. It cannot end a network good or a gatekeeper’s mandate, because no rival’s counter restores the compatibility or admissibility that holding out forfeits.

### F.3 The head start of the original technology

Because a counter is worthless until the technology spreads, the two diffuse in sequence. Figure [13](https://rencryptofish.com/posts/forcing-technologies#A6.F13) shows this for the selective-forcing technology of Figure [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) ($V=0.3$, $r=4$, $c=0.4$), with dispersed costs and a counter with $\varphi=0.8$ and $c_{K}=0.05$. In the first period $30\%$ of rivals adopt and no one counters. Counters spread from the second period, once $43\%$ have adopted, and by period 15 almost no plain holdouts remain. The path ends with $52\%$ adopters and $48\%$ counterers, against $68\%$ adopters without the counter. Panel (c) shows what happens to the contest. The adopter’s edge erodes further than without the counter, to $0.04$ rather than $0.09$. Plain holdouts lose *more* than without the counter ($0.215$ against $0.201$), although fewer rivals adopt, because adopters’ raids concentrate on them. That displacement is why every holdout ends up countering.

The static equilibrium, which ignores the order in which rivals commit, would hold adoption to $21\%$. Irreversibility again separates the path from the static equilibrium. Many of the rivals who would rather counter at the end adopted at the start, when the counter was worthless. The gap is larger in the decisive arms race of Figure [14](https://rencryptofish.com/posts/forcing-technologies#A6.F14)(a) ($V=0.9$, $r=2$, $\gamma=0.1$, $c=0.3$). There a counter with $\varphi=0.9$ and $c_{K}=0.05$ disarms the technology ($\Delta_{K}(1)=-0.105$) and would hold adoption to $45\%$ in the static equilibrium. Along the path, adoption still reaches $83\%$, against $97\%$ without the counter. Slowing adjustment to $\lambda=0.02$ lowers that only to $81\%$, because the counter’s value grows only as fast as adoption itself. Under these irreversible commitments, a counter can stop further spread but cannot reverse earlier adoption. Whether forward-looking rivals who anticipate the counter would wait for it is the same open question as for overshoot (Observation [1](https://rencryptofish.com/posts/forcing-technologies#Thmobservation1)).

![Figure 13: Selective forcing with a counter (V=0.3, r=4, c=0.4, σ=0.3; counter φ=0.8, cK=0.05, σK=0.3; x0=2%, λ=0.3). (a) The state space. Left of the blue curve, adopting pays for more rivals than have adopted. Right of the orange curve, countering pays for more rivals than have countered. The path (one dot per period) moves right first and turns up only once adoption makes the counter pay. It ends far from the static equilibrium, and short of the open circle, where adoption ends without a counter. (b) Shares over time. (c) Contest payoffs of the mean rival of each kind, with and without the counter. Here α=0.9, γ=β=ε=0, p=1, Q=−∞, W=τ=0; no rivals initially hold a counter.](https://rencryptofish.com/images/forcing-technologies/counter_dynamics.png)

Figure 13: Selective forcing with a counter ($V=0.3$, $r=4$, $c=0.4$, $\sigma=0.3$; counter $\varphi=0.8$, $c_{K}=0.05$, $\sigma_{K}=0.3$; $x_{0}=2\%$, $\lambda=0.3$). (a) The state space. Left of the blue curve, adopting pays for more rivals than have adopted. Right of the orange curve, countering pays for more rivals than have countered. The path (one dot per period) moves right first and turns up only once adoption makes the counter pay. It ends far from the static equilibrium, and short of the open circle, where adoption ends without a counter. (b) Shares over time. (c) Contest payoffs of the mean rival of each kind, with and without the counter. Here $\alpha=0.9$, $\gamma=\beta=\varepsilon=0$, $p=1$, $Q=-\infty$, $W=\tau=0$; no rivals initially hold a counter.

### F.4 Whether protection pays for itself

Protecting a user from a transfer loss redistributes the contest; it does not create value for the rival group by itself. The counter enters that group’s welfare through its cost. It raises rivals’ welfare only by deterring adoption whose cost exceeds its standalone and network value. Figure [14](https://rencryptofish.com/posts/forcing-technologies#A6.F14) maps the welfare change over the counter’s efficacy and cost. In both technologies, cheap, effective counters raise welfare, by up to $0.06$ in the arms race and $0.08$ under selective forcing. Under selective forcing, however, a wide band of moderately priced counters lowers welfare, by up to $0.017$. Holdouts buy them to cut losses that are transfers to adopters, and they deter little adoption. Such a counter is a second arms race layered on the first. In the arms race the corresponding losses are negligible, because few rivals are left holding out to buy the counter. The question for a regulator weighing a counter is therefore not whether it protects those who buy it, but whether it deters enough adoption to pay for itself.

![Figure 14: Change in rivals’ welfare from making a counter available, by efficacy φ and mean cost cK (σK=0.3; welfare at period 80 from a 2% seed with λ=0.3). (a) Decisive arms race (V=0.9, r=2, γ=0.1, c=0.3, σ=0.3). Below the dashed line the counter disarms the technology, ΔK⁢(1)≤0. (b) Selective forcing (V=0.3, r=4, c=0.4, σ=0.3). The ring marks the counter of Figure 13. Solid curves separate gains (blue) from losses (red). In both panels, β=ε=W=τ=0, p=1, Q=−∞, and γ=0 in (b); counters start at zero and adjust at the same speed as adopters.](https://rencryptofish.com/images/forcing-technologies/counter_welfare.png)

Figure 14: Change in rivals’ welfare from making a counter available, by efficacy $\varphi$ and mean cost $c_{K}$ ($\sigma_{K}=0.3$; welfare at period 80 from a $2\%$ seed with $\lambda=0.3$). (a) Decisive arms race ($V=0.9$, $r=2$, $\gamma=0.1$, $c=0.3$, $\sigma=0.3$). Below the dashed line the counter disarms the technology, $\Delta_{K}(1)\leq 0$. (b) Selective forcing ($V=0.3$, $r=4$, $c=0.4$, $\sigma=0.3$). The ring marks the counter of Figure [13](https://rencryptofish.com/posts/forcing-technologies#A6.F13). Solid curves separate gains (blue) from losses (red). In both panels, $\beta=\varepsilon=W=\tau=0$, $p=1$, $Q=-\infty$, and $\gamma=0$ in (b); counters start at zero and adjust at the same speed as adopters.

The extension keeps three restrictions worth relaxing. Commitments are exclusive and irreversible, so counterers cannot later adopt, and adopters cannot abandon the technology once counters spread. The obsolescence that ends many forcing technologies needs both. The model also excludes an outside option alongside the counter, so rivals cannot choose to leave the segment. Finally, it restricts counter adoption to members of the rival group. Counters adopted by outsiders, such as users’ ad-blockers, or aimed at threats from outside the rival set, such as quantum attacks for post-quantum cryptography, act instead through a standalone gain that changes over time, which the model does not yet allow.

## Appendix G Who gains when another rival adopts

For a firm’s decision, the relevant comparison is its own two payoffs. For an industry body, an investor assessing the whole market, or a policymaker, add the effects on everyone inside the chosen boundary. That sum is the welfare calculation, and it is the buyer-side accounting that the company arguments in the main text deliberately leave aside.

Suppose the technology works and adoption is assigned to the cheapest share $x$. Let $C(x)=\int_{0}^{x}c(q)\,dq$ be their total cost. Rival welfare is

$$
W_{R}(x)=\gamma x+\beta x^{2}+(1-x)h(x)-C(x),\qquad h(x)=\begin{cases}-\varepsilon\Phi(x),&x<x_{Q},\\ Q,&x\geq x_{Q}.\end{cases}
$$

(15)

Read the terms as direct gains, network gains, holdouts’ exclusion or sheltering costs, and adoption costs. Here $h$ records the holdout component left after contest transfers cancel; it is not the exposed holdout’s entire payoff. On a historical path where adopters are not the cheapest actors, use the costs actually incurred.

The contest terms cancel from aggregate welfare. Winning business from a rival may justify your investment, but that transfer adds nothing to rivals’ combined payoff. Exclusion is different: the lost value is not captured elsewhere in the group. Sheltering also carries a real loss relative to the original baseline.

Add outsiders explicitly:

$$
W_{S}(x)=W_{R}(x)+\eta x.
$$

Customers can gain from lower prices or better service even when competing suppliers’ returns fall. A collective wish to stop competing is therefore not enough to establish a social case for stopping adoption.

The marginal question is whether *one more* adoption helps. Before sheltering, the difference between its social gain and its private gain is

$$
\underbrace{W_{S}^{\prime}(x)-\Delta(x;c(x))}_{\text{social gain minus privategain}}=\underbrace{\beta x+\eta}_{\text{benefits to others}}-\underbrace{\left[\frac{\alpha}{D(x)}+(1-x)\varepsilon\Phi^{\prime}(x)\right]}_{\text{losses imposed on others}}.
$$

The actor misses the network benefit it gives existing adopters and the benefit it gives outsiders. It also ignores the competitive loss it imposes and any extra exclusion pressure on remaining holdouts. At an interior allocation where the next adopter is indifferent, more adoption reduces welfare when the second bracket exceeds the first. This is the private–social wedge proved in Appendix [D](https://rencryptofish.com/posts/forcing-technologies#A4).

The result allows both too much and too little adoption. A positional incentive can offset an otherwise insufficient network incentive; with only exclusion and no network or outsider benefit, the marginal private equilibrium over-adopts. Once holdouts have sheltered, the competitive and exclusion terms disappear from the marginal comparison. These are statements about an additional adoption, not a substitute for comparing the total value of different adoption levels.

## Appendix H What changes as a market matures

A decision can change because the technology improves, holdouts leave, customers raise their expectations or suppliers lose pricing power. Those changes can look like ordinary diffusion in an adoption chart. The following extensions separate them. They are scenarios to investigate, not additional channels estimated in the historical fits.

### H.1 A technology can move from doubtful to necessary to routine

Let maturity $m$ change benefits and costs. In the threshold restriction with $W=0$, write $G(m)=c(m)-\gamma(m)$ and $S(m)=\varepsilon(m)$. A possible sequence is

$$
G(m)>S(m)\quad\longrightarrow\quad 0<G(m)<S(m)\quad\longrightarrow\quad G(m)<0.
$$

Initially even maximum exposure does not justify adoption. At intermediate maturity adoption needs competitive pressure. Eventually it pays without that pressure. This is a window of *competitive compulsion*, not necessarily a window of forcing: the final technology can still satisfy $\Delta(1)>0$. Nor is the sequence inevitable. Costs, outside options and the competitive stake can move in different directions, and a technology may never enter the middle regime.

The related business lifecycle is differentiator, necessity, then infrastructure. In the contest, the differentiating return disappears as rivals catch up even with fixed primitives. Falling costs or new standards can then make the capability routine, while a new generation creates a fresh positional edge. This connects successive forcing episodes to the Red Queen process of competition and organizational learning (Barnett and Hansen, [1996](https://rencryptofish.com/posts/forcing-technologies#bib.bib25)). The distinction is observable: estimate whether a technology’s three signs change as its cost and performance change, rather than interpreting every change in its adoption rate as movement along one fixed curve. A forecast of rapid improvement can also raise the value of waiting for the next generation, so improving prospects need not accelerate purchases of the current one.

### H.2 Holdouts can adopt or disappear

Suppose twenty firms adopt and eighty hold out. If holdouts then leave faster, adoption among the survivors rises even if no additional firm buys the technology. An industry can become almost fully adopted without most initial holdouts ever adopting. Let $A_{t}$ and $N_{t}$ count active adopters and active holdouts, with $\bar{x}_{t}=A_{t}/(A_{t}+N_{t})$. In continuous time, let $h_{t}$ be the holdout adoption hazard and $d_{A},d_{N}$ the exit hazards. With no entry or reversal,

$$
\dot{A}_{t}=h_{t}N_{t}-d_{A}A_{t},\qquad\dot{N}_{t}=-h_{t}N_{t}-d_{N}N_{t},
$$

so

$$
\dot{\bar{x}}_{t}=h_{t}(1-\bar{x}_{t})+\bar{x}_{t}(1-\bar{x}_{t})(d_{N}-d_{A}).
$$

(16)

The first term is adoption within the population. The second is selection: if holdouts exit faster, the active-adopter share rises even with $h_{t}=0$. With entry rates $b_{A},b_{N}$, add $[(1-\bar{x}_{t})b_{A}-\bar{x}_{t}b_{N}]/(A_{t}+N_{t})$. Market-share measures require a further decomposition for growth among surviving firms.

The outside option $Q$ describes a response by members of the original field; it does not change the denominator of the baseline’s $x$. Equation ([16](https://rencryptofish.com/posts/forcing-technologies#A8.E16)) describes a different statistic. Estimation should retain the original cohort, report exits and alliances separately, and also report adoption among survivors. Entry, failure and changes in output weights must not be fitted as if they were individual adoption decisions. Strategic anticipation and selection can coexist, but only the former requires that rivals foresee the threat.

### H.3 Expectations can outlast the deployments that created them

A capability can become necessary because customers learn to expect it. Fast delivery, easy returns and online service illustrate the mechanism: an attribute can move from an attractive extra to a minimum requirement, in the terminology of Kano et al. ([1984](https://rencryptofish.com/posts/forcing-technologies#bib.bib26)). A simple extension introduces an expectation state $b_{t}\in[0,1]$,

$$
b_{t+1}=b_{t}+\rho\max\{0,x_{t}-b_{t}\},\qquad 0<\rho\leq 1,
$$

and makes a holdout’s demand loss depend on $b_{t}$. Expectations follow adoption upward and persist if adoption subsequently recedes. The same current share can then exert different pressure after different histories; $x_{t}$ alone no longer describes the state.

Replacing $\varepsilon\Phi(x_{t})$ by $\varepsilon\Phi(b_{t})$ approximates a penalty that no rival captures. If lost demand goes to adopting rivals, however, that portion is a transfer and must be entered on their payoff curve as well. If buyers enjoy better service, their gain belongs in social welfare. Customer pressure should therefore be decomposed rather than automatically counted as exclusion waste. Repeated customer surveys, purchasing behavior and holdout revenues can distinguish an expectation ratchet from a platform’s explicit access rule.

### H.4 Why a necessary capability need not pay its company

A customer may need a compatible capability while retaining several competing suppliers. That can make adoption widespread without giving any one company durable pricing power. Forcing describes the user’s alternatives; value capture describes who supplies the response and at what price. Let a company charge $f$ per period, on top of the user’s real implementation cost $c_{i}^{\mathrm{res}}$. The private cost is $c_{i}=c_{i}^{\mathrm{res}}+f$, while company profit is $fx-K_{v}(x)$ for supply cost $K_{v}$. When the company lies inside the social accounting boundary, fees cancel between users and company; implementation and supply costs do not. The forcing inequalities place no lower bound on the company’s markup. A compulsory open standard supplied competitively can be indispensable and earn little rent.

Interoperability can lower implementation costs and increase the compatibility gain while making alternative suppliers more useful. Adoption of the capability may rise while dependence on one implementation falls. In the base model a better outside option caps the holdout’s loss. In a company-choice extension, a rival implementation may preserve network benefits too, which the segment-exit option $Q$ does not represent. The appropriate company test is

$$
U(A)-\max\{U(B),U(\text{multihome}),U(\text{exit})\}.
$$

It can fall even while the gain from adopting *some* compatible technology rises. Adoption share, switching costs and supplier margins should therefore be measured separately. Neither widespread compliance nor a large forcing margin is an estimate of company profit.

### H.5 Different stakes and repeated upgrades change the decision

Cost dispersion is only one source of asymmetry. An incumbent may have more customers and capital at risk, yet also face a larger conversion cost; an entrant may choose an unexposed niche. These effects pull in different directions, so incumbency alone does not order forcing. Actor-level stakes, exposures and outside options are needed. In a heterogeneous contest, multiplying each rival’s payoff by an unrelated stake need not preserve zero sum. A consistent extension must allocate a common prize or specify bilateral transfers whose gains and losses cancel.

Binary adoption also leaves out repeated investment after everyone has joined. For comparison, take $n\geq 2$ symmetric rivals choosing expenditure $e_{i}\geq 0$ for a fixed total prize $\mathcal{V}>0$, with payoff

$$
\pi_{i}=\mathcal{V}\frac{e_{i}}{\sum_{j}e_{j}}-e_{i}.
$$

The symmetric interior equilibrium is $e^{*}=\mathcal{V}(n-1)/n^{2}$, so total expenditure is $\mathcal{V}(n-1)/n$. The first-order condition is $\mathcal{V}(n-1)e^{*}/(ne^{*})^{2}=1$, and the payoff is strictly concave in own expenditure when rivals spend positively. Everyone participates, yet rivalry continues to consume resources. This standard contest benchmark (Tullock, [1980](https://rencryptofish.com/posts/forcing-technologies#bib.bib5)) shows why universal adoption does not establish that an arms race has ended. The binary model’s fixed $r$ captures one discrete upgrade, not the equilibrium intensity of subsequent upgrades. Expenditure, quality and release frequency are therefore necessary complements to adoption dates.

## Appendix I Evidence that separates pressure from value

An adoption curve shows that enough actors found switching worthwhile. It does not say whether they gained productivity, won business from holdouts or escaped a penalty. In the linear specification, the private gain depends on $\gamma+\alpha$. Moving value from the direct benefit $\gamma$ to the contest edge $\alpha$ leaves the adoption incentive unchanged, while lowering aggregate value.

For example, a direct benefit of $0.3$ and an edge of $0.2$ can produce the same adoption path as a direct benefit of $0.1$ and an edge of $0.4$, with no outside option, $W=0$ and the other settings held fixed. The second case creates $0.2$ less value per adopter. A better fit to adoption alone cannot choose between them. Proposition [12](https://rencryptofish.com/posts/forcing-technologies#Thmproposition12) states the exact equivalence conditions.

Figure [15](https://rencryptofish.com/posts/forcing-technologies#A9.F15) shows three such pairs. In panel (a), moving $0.2$ from the standalone gain $\gamma$ to the edge $\alpha$ leaves adoption unchanged in every period, before the demonstration and after it. Welfare, however, is lower by $0.2\,x_{t}$, so one technology leaves rivals roughly where they started and the other costs them $0.11$. In panel (b), a standalone gain lower by $0.1$ and a waiting value of $0.1$ produce the same path, because both lower the switching gain by the same amount. Adopters realize $\gamma$, but no one realizes $W$, so welfare differs by $0.1\,x_{t}$; and only $\gamma$ enters the payoff gap, so the technology with the waiting value is forced for more rivals yet adopted no faster. In panel (c), a network gain and an exclusion penalty with $k=0$ produce the same switching gain once the technology is demonstrated, and they end at the same $92\%$. Beliefs scale only the network gain, though, so before the demonstration exclusion drives adoption to $81\%$ while the network good reaches $38\%$. Welfare differs in sign: the network good is worth $0.52$ to rivals, while exclusion leaves them slightly worse off.

![Figure 15: Parameter pairs that adoption data cannot tell apart. Top: share adopted. Bottom: rivals’ mean payoff when the technology works. (a) γ and α trade places (β=0.2, c=0.6, σ=0.3, p0=0.5, xv=8%). (b) A standalone gain against a waiting value (α=0.2, β=0.2, c=0.6, σ=0.3, the technology known to work). (c) A network gain against exclusion with a linear pressure curve (γ=0.3, c=0.4, σ=0.5, p0=0.4, exogenous demonstration at t=10). In (a) and (b) the paths coincide exactly. In (c) the adoption incentives coincide only once beliefs are settled, and the paths converge after the demonstration; welfare remains different. In all panels r=1, Q=−∞, τ=0, and any unlisted payoff channel or waiting value is zero. Panels (a,b) use x0=2%, λ=0.3, with λ0=0.1 in (a); (c) uses x0=5% and λ0=λ=0.4.](https://rencryptofish.com/images/forcing-technologies/equivalence.png)

Figure 15: Parameter pairs that adoption data cannot tell apart. Top: share adopted. Bottom: rivals’ mean payoff when the technology works. (a) $\gamma$ and $\alpha$ trade places ($\beta=0.2$, $c=0.6$, $\sigma=0.3$, $p_{0}=0.5$, $x_{v}=8\%$). (b) A standalone gain against a waiting value ($\alpha=0.2$, $\beta=0.2$, $c=0.6$, $\sigma=0.3$, the technology known to work). (c) A network gain against exclusion with a linear pressure curve ($\gamma=0.3$, $c=0.4$, $\sigma=0.5$, $p_{0}=0.4$, exogenous demonstration at $t=10$). In (a) and (b) the paths coincide exactly. In (c) the adoption incentives coincide only once beliefs are settled, and the paths converge after the demonstration; welfare remains different. In all panels $r=1$, $Q=-\infty$, $\tau=0$, and any unlisted payoff channel or waiting value is zero. Panels (a,b) use $x_{0}=2\%$, $\lambda=0.3$, with $\lambda_{0}=0.1$ in (a); (c) uses $x_{0}=5\%$ and $\lambda_{0}=\lambda=0.4$.

Diffusion histories therefore cannot classify a technology as wasteful or productive. The model indicates what can:

- *Adopter outcomes* as adoption spreads trace $U_{A}(x)+c$. Their slope separates network gains (rising) from contest erosion (falling).

- *Holdout outcomes* trace $U_{N}(x)$. Their shape identifies the contest’s $(\alpha,r)$ through the zero-sum restriction that ties it to the adopter curve, and separates the exclusion penalty $\varepsilon\Phi$. A floor at which holdout outcomes stop falling, together with the exits, alliances and specializations that accompany it, identifies the outside option $Q$.

- *Belief variation* also helps, because beliefs scale the technology channels but not exclusion. Pre-demonstration adoption separates $\varepsilon\Phi(x)$ from $p\beta x$ even when the two coincide after the demonstration.

- *Bans and joint disarmament*, such as the 1971 cigarette television advertising ban or the 2010 swimsuit ban, inform $y_{R}$ when their effects on costs and outcomes can be separated from changes in pricing, entry and other rules; Farr et al. ([2001](https://rencryptofish.com/posts/forcing-technologies#bib.bib27)) show how an advertising ban raised cigarette makers’ profits while leaving the social verdict to the smoking externality. Outsider outcomes inform $\eta$.

- *Shocks to rivals’ adoption* that are excluded from the focal rival’s payoff, such as rival-specific infrastructure access, regulatory eligibility or rollout timing, are needed to separate forcing from common shocks. This is the reflection problem (Manski, [1993](https://rencryptofish.com/posts/forcing-technologies#bib.bib16); Brock and Durlauf, [2001](https://rencryptofish.com/posts/forcing-technologies#bib.bib17)).

Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) implements Bayesian estimation case by case for aggregate series, using the continuum dynamics implied by the hazard and an observation-error likelihood. Hierarchical pooling and joint estimation with actor-period panels remain extensions. They should be preceded by recovery experiments on panels simulated by simulate\_agents, rather than inferred to work from aggregate fit alone.

### I.1 What to measure before assigning a forcing label

The unit of analysis is a capability, an actor set and a time period. “AI” or “crypto” is too broad. For each case, record who competes with whom, what counts as productive adoption, which alternatives remain feasible, and whether the denominator is an original cohort, surviving actors, output or transactions. Define the network before looking at the adoption outcome. A regulator’s deadline is an event that may change exclusion, expected benefits or beliefs; it is not automatically evidence that the technology’s productivity has been demonstrated.

Payoffs should first be measured in the domain’s natural flow units, such as annual profit, operating cost per unit of output, or a stated utility scale. A logit hazard identifies utility relative to the shock scale $\tau$: multiplying all payoff amounts, costs, waiting values and $\tau$ by the same positive constant leaves the hazard unchanged. Fix a scale or anchor it with outcome data. The normalized stake in Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) permits within-case interpretation; it does not make one unit of naval capability equal one unit of customer-service output.

Report several derived quantities rather than one forcing score:

- *Current switching margin*: $M_{i}(x,p)=\Delta(x;c_{i},p)-W_{i}$, together with the gain from adopting alone. A positive margin can be ordinary standalone adoption.

- *Endpoint lock-in*: $F_{i}=\Delta(1;c_{i},1)$ against the best specified non-adopting response, or $\Delta_{K}(1)$ when counters are available. This is distinct from whether the path can reach full adoption.

- *Thresholds and their accessibility*: report every relevant crossing of $M_{i}=0$ and, for a population cascade, the unstable crossings of $g_{p}(x)=x$. A selective contest can have a downward crossing; an outside option can produce a jump. Neither has the threshold model’s single upward tipping exposure.

- *Sensitivity and timing*: the slope of the switching gain at a continuous crossing, the size of a jump when applicable, and time from a defined demonstration to a specified adoption share. Report non-attainment and the observation horizon rather than dropping cases that never reach that share.

- *Welfare and uncertainty*: $W_{R}(x_{T})$, $W_{S}(x_{T})$ and their full-adoption counterparts, with posterior probabilities such as $\Pr(M_{i}>0\mid\text{data})$, $\Pr(F_{i}>0\mid\text{data})$ and $\Pr(y_{S}<0\mid\text{data})$.

Margins and slopes require a common economic normalization for cross-case comparison. Exposure thresholds are dimensionless but still depend on the actor set and network. Calendar times also reflect construction times and adjustment frictions. None of these statistics by itself identifies the strength of competitive causation.

The order of evidence.

Start with a record for each actor in each period: orders and use, real costs, output or financial outcomes, relevant rivals’ adoption, counters, alliances and exits. This is the actor-period panel. Estimate an adoption hazard with actor and time controls, then seek a shock that shifts rivals’ adoption without directly shifting the focal actor’s payoff. Lagged exposure alone does not solve common shocks or anticipation. Fit the structural channels only after specifying that causal design. Separate observation error from behavioral shocks; use cross-sectional cost data to distinguish persistent dispersion from slow adjustment.

Validation should test recovery on simulated panels, predictions for later periods or held-out actors, alternative network weights and actor sets, and sensitivity to cost distributions and prior bounds. A hierarchical model may pool diffusion parameters among comparable cases, but should not manufacture precision by pooling unrelated utility scales. Fit linear, threshold and flexible pressure specifications on the same observations. A low in-sample error from a flexible curve is evidence of descriptive fit, not evidence that competitive exposure caused adoption. The case studies below specify outcomes that could reject their proposed channel, so a prospective application can fail rather than merely be relabeled after the fact.

## Appendix J What the historical adoption curves tell us

The central finding from 14 historical cases is that fitting adoption is much easier than explaining where its value comes from. The fuller model often traces almost the same path as the simpler one, and the split between productive value and competitive transfers remains sensitive to prior assumptions.

The data were rebuilt from traceable sources. The earlier series had 108 observations, including 30 estimates, and used only the linear restriction; Appendix [Q](https://rencryptofish.com/posts/forcing-technologies#A17) retains those reproduction benchmarks. The findings below use the updated series and full-model fits.

### J.1 Traceable observations

Each case has a directory with a source registry, the observations, and the snapshots they were read from. Every source is recorded with its URL, its access date, its licence, and the SHA-256 hash of the snapshot. Wikipedia pages are fetched at a pinned revision, so the snapshot never changes.

Every value is a row that cites one source, and there are two kinds:

- A value typed from a page carries a verbatim quote, and a verification step checks that the quote appears in the snapshot’s text.

- A value parsed by code is re-derived from the snapshot by the case’s collector. The machine-readable sources are the Firefox telemetry files behind the Let’s Encrypt statistics, the Census Bureau’s Business Trends and Outlook Survey spreadsheets, the IEA electric-vehicle data, the USDA *Agricultural Statistics* table, Wikipedia infoboxes, and one chart digitized from its image.

Count-based cases (dreadnoughts, frequent-flyer programs, nuclear weapons, armed drones) are recorded actor by actor, including a disarmament event in the nuclear series. Their series is the share of a fixed field currently holding the technology, not the share among survivors.

The rebuilt data use 80 source records. They hold 295 rows: 183 parsed by code, 111 transcribed with verified quotes, and one excluded note row (Table [33](https://rencryptofish.com/posts/forcing-technologies#A20.T33)). The fitted series have 350 points in all, with 75 dated adoption or disarmament events in the four count cases sampled on an annual or monthly grid. Only three rows are estimates, down from 30, and 58 rows are kept but excluded because they use a different definition. Openly licensed snapshots are committed with the code. Copyrighted pages, and the one oversized scan, are kept locally and can be re-fetched; their hashes and supporting quotations are recorded.

Several inherited series changed materially:

- *Hybrid corn* is now the complete official series, 28 annual values from the 1962 *Agricultural Statistics*. It replaces seven estimates, two of them off by five points.

- *Frequent-flyer programs*: all eight carriers are now dated from sources, and seven of the eight had a program within four months of American’s, not within twenty.

- *Containers*, *swimsuits* and *armed drones* each now use a single definition in place of a composite.

- *Nuclear weapons* now follows one source, Bleek’s coding of acquisition, for both the dates and the field.

### J.2 How to read the estimates

The fits describe the recorded adoption paths under a specified model. They do not estimate causal losses imposed on rivals. Some parameters were restricted using prior judgments, and the uncertainty intervals are conditional on those restrictions and the observation-error assumptions.

The model sets the gross gain from staying adopted at full adoption to one, so a mean-cost actor is forced when $c<1$. It allows a nonlinear contest, temporary shocks and, for HTTPS and RFID, exclusion. It does not fit outside options, counters, changing fundamentals or reversals. Repeated observations of the same adoption event are not independent experiments.

The numerical settings, prior ranges and likelihood are in Appendix [K](https://rencryptofish.com/posts/forcing-technologies#A11). The reported $\Delta$AIC values are AIC-style fit diagnostics evaluated at posterior modes, not formal model-selection tests. Read them as a check on whether the extra flexibility materially changes the fitted curve.

### J.3 Historical customer value across the lifecycle

Section [1](https://rencryptofish.com/posts/forcing-technologies#S1) defines the customer budget $B(x,p)$, the ceiling on what a company can charge. The figures below apply it to the historical parameter posteriors. They say how the ceiling moved as each market filled; they say nothing about prices, shares or margins, which the fits do not observe.

Figure [16](https://rencryptofish.com/posts/forcing-technologies#A10.F16) follows that customer value from low adoption to a mature market. It holds the current parameter posterior fixed and assumes effectiveness has been demonstrated, $p=1$. The orange dot is 5% adoption and the blue square is 95%; the unadopted share falls from 95% to 5% between them. When the curve falls, early customers have an advantage over unprepared rivals that later customers cannot obtain. When it rises, network gains or exclusion make the product more valuable as adoption spreads. The balance, at a fixed belief, is

$$
\frac{\partial B}{\partial x}=p\left[\beta-\frac{\alpha(r-1)}{(1+(r-1)x)^{2}}\right]+\varepsilon\Phi^{\prime}(x).
$$

For example, the container fit’s median customer benefit rises from about $0.49$ at 5% adoption to $0.97$ at 95%; the dreadnought fit falls from about $1.94$ to $1.02$. The curves and bands meet at one because the normalization fixes that endpoint. Before proof, use $p<1$ in ([2](https://rencryptofish.com/posts/forcing-technologies#S1.E2)); the chart’s proven-effectiveness assumption is not an estimate of an early investor’s confidence. The fitted belief model only permits a jump to successful demonstration, so it also misses the risk of a disappointing trial.

![Figure 16: Estimated gross adoption benefit at different adoption shares. Each curve is the gross benefit of adopting rather than holding out, before all adoption costs, under the full-history parameter posterior and p=1. Dots mark 5% adoption and squares 95%; bands are pointwise 90% posterior intervals. The vertical axis is logarithmic. Each case is normalized to B⁢(1,1)=1, so levels compare value with that case’s mature-market benchmark, not dollar market sizes. These are conditional lifecycle scenarios, including stages not observed in a case’s data; they are not historical investor beliefs, price forecasts or estimated supplier returns.](https://rencryptofish.com/images/forcing-technologies/calibration_lifecycle.png)

Figure 16: Estimated gross adoption benefit at different adoption shares. Each curve is the gross benefit of adopting rather than holding out, before all adoption costs, under the full-history parameter posterior and $p=1$. Dots mark 5% adoption and squares 95%; bands are pointwise 90% posterior intervals. The vertical axis is logarithmic. Each case is normalized to $B(1,1)=1$, so levels compare value with that case’s mature-market benchmark, not dollar market sizes. These are conditional lifecycle scenarios, including stages not observed in a case’s data; they are not historical investor beliefs, price forecasts or estimated supplier returns.

### J.4 Market maturation versus learning about the market

Two things can change between an early investment and a later review. More customers adopt, moving the opportunity along a lifecycle curve. New evidence can also change the estimated curve itself. The model holds its structural parameters fixed within a case; a revised posterior is a change in our estimate, not evidence that the underlying parameter physically changed.

Figure [17](https://rencryptofish.com/posts/forcing-technologies#A10.F17) isolates the second effect. It compares a fit using only the early adoption observations with a fit using the latest recorded history. Both estimates evaluate $B(0.1,1)$: the same 10% adoption and proven effectiveness. Any movement therefore comes from the parameter estimate, rather than from moving further through the market. The numerical companion also records each parameter’s posterior and customer value at the actual adoption share and fitted belief in each window.

The early window ends at the last recorded point before adoption first exceeds 20%. This defines low penetration, not time since invention or a particular financing round. Nine cases have distinct early and later windows. AI use among all US firms and the RFID mandate remain below that threshold, so their early and latest windows coincide. Gen AI in large organizations, HTTPS and LZR suits have no observations below the threshold; the chart leaves their early estimate absent. Some early windows have only one observation and mostly reflect the priors.

These are retrospective refits with today’s priors held fixed. Observation dates are not verified publication dates, and the cases were selected with hindsight. They show how restricting the adoption history changes this model’s estimates; they do not reconstruct the information available to an investor on that date. A genuine investment backtest would also need archived data vintages, contemporaneous priors, failed technologies, and supplier prices, costs and valuations. Appendix [K](https://rencryptofish.com/posts/forcing-technologies#A11) records the windowing and sampling method.

![Figure 17: How adding later observations revises the estimate of early customer value. Circles use the early observation window; squares use the latest window. Both evaluate the same gross benefit at 10% adoption and p=1. Lines span separate 90% posterior intervals, not an interval for the difference between estimates. Missing early coverage is labeled; a single square also marks cases whose latest observation is still in the early window. The same present-day priors and observation model are used in both fits. These retrospective comparisons isolate information-window changes under those assumptions, not investable historical returns.](https://rencryptofish.com/images/forcing-technologies/calibration_early_updates.png)

Figure 17: How adding later observations revises the estimate of early customer value. Circles use the early observation window; squares use the latest window. Both evaluate the same gross benefit at 10% adoption and $p=1$. Lines span separate 90% posterior intervals, not an interval for the difference between estimates. Missing early coverage is labeled; a single square also marks cases whose latest observation is still in the early window. The same present-day priors and observation model are used in both fits. These retrospective comparisons isolate information-window changes under those assumptions, not investable historical returns.

### J.5 The full-adoption endpoint

Figure [2](https://rencryptofish.com/posts/forcing-technologies#S1.F2) in Section [1.2](https://rencryptofish.com/posts/forcing-technologies#S1.SS2) presents the historical endpoint estimates. Payoffs use the within-case normalization $a+\beta+\gamma+\varepsilon=1$, so a mean-cost actor wants to stay adopted at full adoption when $\Delta(1)=1-c>0$. The rival group’s payoff relative to no adoption is $y_{R}=\gamma+\beta-c$. Nuclear weapons and RFID lie left of zero, where full adoption would not sustain itself for a mean-cost actor.

The plotted dots pair the marginal posterior medians, and the bars show separate 5th–95th percentile intervals, not joint 90% regions. Distinguishing dominant from tipping adoption also requires $\Delta(0)$. For a supplier investor, the endpoint describes customers’ mature-market incentives and the rival group’s payoff; the lifecycle and value-capture questions above remain necessary. The estimates come from the stored derived summaries in data/cases/\*/fit.json; exact plotted values are exported to paper/tables/calibration\_scatter.csv.

### J.6 Three findings to use with care

Figures [18](https://rencryptofish.com/posts/forcing-technologies#A10.F18) and [19](https://rencryptofish.com/posts/forcing-technologies#A11.F19) and Table [22](https://rencryptofish.com/posts/forcing-technologies#A10.T22) support three practical conclusions.

*A more elaborate model can fit almost the same curve.* Adding contest curvature and exclusion changes the fitted paths little. HTTPS shows the largest improvement: its error falls from $0.015$ to $0.011$, but not enough to offset the extra-parameter penalty in the AIC-style diagnostic. This says the adoption series offer little reason to prefer the added flexibility. It does not show that those mechanisms are absent.

*The data say little about whether the value is productive or positional.* In every case, the uncertainty about the positional share changes little from the prior. Most series also say little about how decisive the contest is. A good adoption fit therefore leaves the welfare classification dependent on assumptions supplied before fitting. The detailed comparisons and their dependence caveats are in Appendix [K](https://rencryptofish.com/posts/forcing-technologies#A11).

*Even a high probability of forcing needs its assumptions beside it.* Twelve cases give at least $95\%$ probability that a mean-cost actor would keep the technology at full adoption. Several prior cost ranges already implied that result, so these are not twelve independent confirmations. Nuclear weapons and the RFID mandate are the exceptions; within the fitted model, their partial adoption is explained by costs. Outside options or changing enforcement could offer other explanations. HTTPS also splits between dominant and tipping patterns, at $58\%$ and $42\%$, rather than receiving a certain label.

Use these fits to describe paths and locate unanswered questions. Before relying on a welfare classification, vary the prior ranges, cost distribution and treatment of repeated observations, and add outcomes for adopters and holdouts. Reproducing the stored calculations verifies the arithmetic; it does not establish causal validity or predictive performance on new cases.

![Figure 18: Full-model calibration on the rebuilt series. Bands are conditional 90% posterior intervals of the adoption path, the solid line is the posterior median, and the dashed line is the linear model at its posterior mode. Each panel’s ΔAIC is the AIC-style diagnostic described in the text, comparing the full model with the linear model plus the transitory shock. Crosses mark alternative definitions excluded from the fit. These curves summarize posterior draws rather than one parameter set: fitted settings and priors are specified in Appendix K, and each case’s complete fitted summaries are stored in data/cases/\<case\>/fit.json.](https://rencryptofish.com/images/forcing-technologies/calibration_paths.png)

Figure 18: Full-model calibration on the rebuilt series. Bands are conditional 90% posterior intervals of the adoption path, the solid line is the posterior median, and the dashed line is the linear model at its posterior mode. Each panel’s $\Delta$AIC is the AIC-style diagnostic described in the text, comparing the full model with the linear model plus the transitory shock. Crosses mark alternative definitions excluded from the fit. These curves summarize posterior draws rather than one parameter set: fitted settings and priors are specified in Appendix [K](https://rencryptofish.com/posts/forcing-technologies#A11), and each case’s complete fitted summaries are stored in data/cases/\<case\>/fit.json.

Table 22: Full-model calibration. Panel A: $n$ is the number of fitted series points; RMSE is evaluated at the posterior modes. $\Delta$AIC compares the linear model plus the transitory shock with the linear model ($\tau$), and the full model with the linear model plus the shock ($r,\varepsilon$); negative favours the larger model. Panel B: posterior medians and 90% intervals, with the most probable region of Table [1](https://rencryptofish.com/posts/forcing-technologies#S1.T1) and its probability. A dash denotes exclusion fixed at zero. Prior-bound diagnostics remain in the stored fit summaries; source counts are in Table [33](https://rencryptofish.com/posts/forcing-technologies#A20.T33).

**A. Descriptive fit**

<table><thead><tr><th></th> <th></th> <th colspan="2">RMSE</th> <th colspan="2">$\Delta$AIC</th></tr> <tr><th>Case</th> <th>$n$</th> <th>Linear</th> <th>Full</th> <th>$\tau$</th> <th>$r,\varepsilon$</th></tr></thead> <tbody><tr><th>Clap skates</th> <th>6</th> <td>0.007</td> <td>0.006</td> <td>+1.8</td> <td>+2.1</td></tr> <tr><th>Container</th> <th>15</th> <td>0.032</td> <td>0.031</td> <td>+1.9</td> <td>+1.9</td></tr> <tr><th>Hybrid corn</th> <th>28</th> <td>0.017</td> <td>0.017</td> <td>+1.8</td> <td>+2.0</td></tr> <tr><th>Dreadnought</th> <th>18</th> <td>0.049</td> <td>0.049</td> <td>+2.0</td> <td>+2.0</td></tr> <tr><th>Armed drones</th> <th>64</th> <td>0.021</td> <td>0.021</td> <td>+2.0</td> <td>+2.0</td></tr> <tr><th>Frequent flyer</th> <th>32</th> <td>0.059</td> <td>0.059</td> <td>+1.8</td> <td>+2.0</td></tr> <tr><th>Gen AI (large orgs)</th> <th>5</th> <td>0.031</td> <td>0.031</td> <td>+2.0</td> <td>+2.0</td></tr> <tr><th>AI (all US firms)</th> <th>54</th> <td>0.004</td> <td>0.004</td> <td>+2.0</td> <td>+2.0</td></tr> <tr><th>HTTPS</th> <th>14</th> <td>0.015</td> <td>0.011</td> <td>+2.8</td> <td>+6.1</td></tr> <tr><th>LZR suit</th> <th>3</th> <td>0.041</td> <td>0.041</td> <td>+2.0</td> <td>+2.0</td></tr> <tr><th>MLB analytics</th> <th>4</th> <td>0.017</td> <td>0.017</td> <td>+2.0</td> <td>+2.0</td></tr> <tr><th>China NEVs</th> <th>11</th> <td>0.009</td> <td>0.009</td> <td>+2.3</td> <td>+2.0</td></tr> <tr><th>Nuclear</th> <th>91</th> <td>0.031</td> <td>0.031</td> <td>+2.0</td> <td>+1.8</td></tr> <tr><th>RFID mandate</th> <th>5</th> <td>0.000</td> <td>0.000</td> <td>+2.0</td> <td>+8.0</td></tr></tbody></table>

**B. Posterior summaries**

| Case | $r$ | $c$ | $\varepsilon$ | Modal region ($P$) |
| --- | --- | --- | --- | --- |
| Clap skates | 1.30 \[1.02, 2.40\] | 0.25 \[0.15, 0.30\] | – | arms race (0.97) |
| Container | 1.50 \[1.04, 3.51\] | 0.66 \[0.56, 0.70\] | – | coordination (0.93) |
| Hybrid corn | 1.49 \[1.03, 3.34\] | 0.35 \[0.22, 0.47\] | – | productive (1.00) |
| Dreadnought | 1.99 \[1.09, 7.33\] | 0.30 \[0.16, 0.48\] | – | arms race (0.97) |
| Armed drones | 2.25 \[1.08, 8.52\] | 0.18 \[0.11, 0.36\] | – | productive (0.87) |
| Frequent flyer | 1.86 \[1.10, 6.76\] | 0.20 \[0.09, 0.29\] | – | productive (0.51) |
| Gen AI (large orgs) | 1.60 \[1.05, 5.08\] | 0.43 \[0.21, 0.50\] | – | productive (0.97) |
| AI (all US firms) | 1.60 \[1.04, 4.75\] | 0.80 \[0.56, 0.98\] | – | arms race (0.55) |
| HTTPS | 1.50 \[1.02, 3.70\] | 0.79 \[0.66, 0.89\] | 0.28 \[0.03, 0.38\] | arms race (0.57) |
| LZR suit | 1.88 \[1.04, 6.82\] | 0.03 \[0.01, 0.05\] | – | productive (0.50) |
| MLB analytics | 1.88 \[1.06, 7.82\] | 0.23 \[0.11, 0.34\] | – | arms race (0.78) |
| China NEVs | 1.39 \[1.02, 2.80\] | 0.49 \[0.33, 0.59\] | – | productive (0.71) |
| Nuclear | 1.13 \[1.01, 1.55\] | 1.19 \[1.03, 1.29\] | – | inert (0.53) |
| RFID mandate | 1.57 \[1.04, 3.05\] | 1.64 \[1.13, 1.96\] | 0.21 \[0.02, 0.38\] | inert (1.00) |

## Appendix K Calibration assumptions and estimation settings

The fit normalizes the gross gain from staying adopted at full adoption to one: $a+\beta+\gamma+\varepsilon=1$ with $a=\alpha/r$. With no outside option, the mean-cost rival’s forcing test is then $c<1$ for every $r$. The linear payoff restriction also sets exclusion to zero.

The free parameters and their priors are:

- the positional share $a$, uniform on the inherited range, with $\beta$ and $\gamma$ splitting the remainder in the inherited ratio;

- the contest’s decisiveness $r$, half-normal on $\log r$ with scale one, truncated at $\log r=3$;

- the cost level $c$ and dispersion $\sigma$;

- the prior belief $p_{0}$, the visibility threshold $x_{v}$, the two adjustment speeds $\lambda_{0}$ and $\lambda$, and the seed $x_{0}$;

- the transitory shock $\tau$, half-normal with scale $0.05$.

The exclusion share $\varepsilon$ and its shape $(\theta,k)$ are free only for the two cases whose history includes a gatekeeper penalty, HTTPS and the RFID mandate; elsewhere $\varepsilon$ is fixed at zero. The waiting value $W$ is fixed at zero rather than separately inferred from benefits using adoption shares alone (Proposition [12](https://rencryptofish.com/posts/forcing-technologies#Thmproposition12)). The outside option is switched off, because no series records a sheltered share. Counters, learning from unfavorable evidence, endogenous exit and changing technological fundamentals are also outside these fits.

Uniform ranges for the diffusion parameters are the inherited ones, except where the rebuilt data moved them. Each change is recorded, with its reason, in the case’s metadata file. The main ones are a new seed where the series now starts at zero, a rescaled visibility threshold where the field changed, and nuclear effectiveness treated as known from the start in 1945 rather than inferred from a visibility threshold.

Each observation is normal around a numerical approximation to the continuum path, using 400 cost bins and linear interpolation at fractional periods. Its standard deviation is

$$
s(x)=\sqrt{0.01^{2}+(0.05\,x)^{2}}
$$

for stated and derived values, with $x$ evaluated at the observed share, and $0.05$ for estimates. For actor counts the standard deviation is half an actor; for the two series that stay below 10% it is set to match their precision. These are specified error scales, not survey-based sampling errors.

The posterior is sampled with the ensemble sampler of the emcee package, run for 10,000 steps with at least 40 walkers started at the posterior mode. Two restrictions are fitted at their own modes for comparison: the linear model ($r=1$, $\varepsilon=\tau=0$), and the linear model with the transitory shock.

The displayed $\Delta$AIC values are AIC-style diagnostics, computed as $2\Delta k-2\Delta\log L$ at the posterior modes. Because these are not unrestricted maximum-likelihood estimates, the values should not be interpreted as formal AIC model selection. The likelihood also treats sampled series points as conditionally independent. In count-based cases, many points repeat information from the same adoption events; the 350 points are not 350 independent experiments. Serial dependence, changing survey definitions and the nuclear reversal can make uncertainty larger than these intervals suggest. The irreversible model cannot reproduce a disarmament decline exactly.

### K.1 Lifecycle curves and retrospective observation windows

The investor figures use separate joint posterior draws stored under data/lifecycle/; the original data/cases/\*/fit.json summaries remain unchanged. The lifecycle curves evaluate $B(x,1)$ over $x=0,0.01,\ldots,1$ for each draw from a new full-history sample. Quantiles are taken after that transformation. Using joint draws preserves dependence among parameters when calculating the uncertainty bands.

The early observation window includes every fitted row through the last timestamp before the first observed share above 20%. A later decline does not reopen the early window. If the first observation is already above 20%, no early fit is produced; if the threshold is never crossed, the early and latest windows are identical. The likelihood uses only the retained rows and their original error scales, and its simulation horizon is shortened to cover that window. Automated checks verify that changing later observations does not change the early-window likelihood. This prevents later observations from entering the early likelihood but does not remove hindsight from the case priors, data revisions, definitions or case selection.

Each distinct window uses the same case priors, payoff normalization, likelihood and 400 cost bins as the main calibration. An early-window posterior mode is fitted using only that window; the latest-window sampler starts from the stored full-history mode. Each ensemble runs for 10,000 steps with at least 40 walkers, discards the first third and thins by five. Both the initial walker distribution and the sampler’s random state have explicit seeds. A reproducible selection of 4,000 joint draws is saved for the transformations and figures. Acceptance rates, autocorrelation estimates, approximate effective sample sizes, input hashes and code hashes accompany each fit. These finite-run diagnostics do not establish convergence across modes; the comparisons remain exploratory, conditional on the same prior and dependence limitations as the main calibration.

For the observation-window comparison, both posteriors are evaluated at $x=0.1,p=1$, which separates an estimate revision from a change in lifecycle position. The accompanying state table instead evaluates the gross benefit, net adoption incentive and adopter payoff at the last *observed* adoption share in each window, using that draw’s fitted belief at the corresponding model period. This is a model-based reconstruction, not an observed investor belief. The state table does not turn the binary demonstration rule into a general learning model.

The scripts scripts/fit\_lifecycle.py and scripts/calibration\_assets.py regenerate the window fits, figures and numerical companions. The curve table records the pointwise bands; the window table records dates, sample counts, observed adoption and state estimates; the parameter table records the joint draws’ marginal summaries. These are paper/tables/lifecycle\_curves.csv, lifecycle\_windows.csv and lifecycle\_parameters.csv, respectively. None contains observed supplier prices, margins or investment returns.

![Figure 19: Posterior of the contest’s decisiveness r by case against its prior (gray band, 90%). The right column is the ratio of posterior to prior standard deviation of log⁡r; near one, the posterior has contracted little. The intervals are conditional on the prior and observation model.](https://rencryptofish.com/images/forcing-technologies/calibration_r.png)

Figure 19: Posterior of the contest’s decisiveness $r$ by case against its prior (gray band, 90%). The right column is the ratio of posterior to prior standard deviation of $\log r$; near one, the posterior has contracted little. The intervals are conditional on the prior and observation model.

### K.2 Detailed posterior comparisons

Figure [18](https://rencryptofish.com/posts/forcing-technologies#A10.F18) and Table [22](https://rencryptofish.com/posts/forcing-technologies#A10.T22) report the fits. Three findings stand out.

*The additional channels make little difference to descriptive fit.* The full model’s paths are nearly indistinguishable from the linear model’s (Figure [18](https://rencryptofish.com/posts/forcing-technologies#A10.F18)). Against the linear model with the transitory shock, the contest and exclusion channels lower the AIC-style diagnostic in no case. Their $\Delta$AIC is about $+2$ almost everywhere. HTTPS and the RFID mandate, the two cases with a free exclusion channel, are higher still ($+6.1$ and $+8.0$). HTTPS gains the most: the additional channels cut its RMSE from $0.015$ to $0.011$, with an exclusion share of $0.28$ \[$0.03$, $0.38$\], but not enough to offset the four-parameter penalty in this diagnostic. Adding the transitory shock alone also improves fit little. These comparisons do not establish that the omitted mechanisms are absent.

*Most series weakly constrain the contest’s decisiveness.* Figure [19](https://rencryptofish.com/posts/forcing-technologies#A11.F19) compares the posterior and prior. For seven cases the ratio of standard deviations of $\log r$ is between $0.89$ and $1.06$: dreadnoughts, drones, frequent-flyer programs, swimsuits, MLB analytics and both gen-AI series. Six cases have ratios of $0.46$ to $0.70$: clap skates, the RFID mandate, Chinese electric vehicles, hybrid corn, containers and HTTPS. All six pull $r$ toward one. Nuclear weapons, with 91 sampled points over 81 years, has the narrowest interval, $[1.01,1.55]$, and a ratio of $0.24$; the dependence caveat is particularly relevant there. For the positional share $a$, the ratios remain between $0.96$ and $1.02$ in every case. Thus the split that determines waste remains strongly dependent on its prior. This is an empirical weak-identification result, not a proof that nonlinear contest parameters can never be identified from a sufficiently informative path.

*Endpoint forcing is more concentrated than the channel decomposition, conditional on the priors.* Twelve cases assign at least 95% posterior probability to $\Delta(1)=1-c>0$ for the mean-cost rival. This is not twelve independent confirmations of forcing: several prior cost ranges already lie wholly below one. The closest call is AI use among all US firms, whose 5th percentile of $\Delta(1)$ is $+0.02$. Nuclear weapons has median $c=1.19$, and the RFID mandate has $c=1.64$. Under the fitted restrictions, cost heterogeneity accounts for their partial adoption; alliance sheltering or changing enforcement could provide other explanations. The waste sign $y=\gamma+\beta-c$ inherits the weakly constrained split $a$, so the region labels in Table [22](https://rencryptofish.com/posts/forcing-technologies#A10.T22) are conditional on prior judgments. The adoption pattern is sensitive too: with weakly constrained $r$ and a prior restricted to $r\geq 1$, $\Delta(0)=\gamma+ar-c$ can be larger than in the linear restriction. HTTPS splits between dominant and tipping patterns (58% and 42%).

The calibration illustrates the value of the outcome-data strategy in Appendix [I](https://rencryptofish.com/posts/forcing-technologies#A9). Adoption histories constrain some combinations of relative costs and diffusion parameters while leaving welfare classifications sensitive to assumptions. Parameters whose 90% interval approaches a prior bound are recorded with the calibration; they include beliefs, adjustment rates, visibility thresholds and the container cost level. Sensitivity to these bounds, the prior on $r$, the cost distribution and time-series dependence remains necessary before treating the reported classifications as robust empirical findings. The stored sampler diagnostics and replay checks establish reproducibility of the reported calculations, not convergence under every alternative specification or out-of-sample validity.

## Appendix L Parameter reference

Section [B.7](https://rencryptofish.com/posts/forcing-technologies#A2.SS7) gives the visual walkthrough: how each main payoff parameter moves the two curves, what it does to adoption, and whether it adds collective value. This appendix supplies the distributional details and a compact reference. For numerical illustrations, the figure panels state changed parameters and their captions state the settings held fixed. The plotted values and complete payoff settings for Figures [1](https://rencryptofish.com/posts/forcing-technologies#S1.F1) and [6](https://rencryptofish.com/posts/forcing-technologies#A2.F6) are also exported to paper/tables/payoff\_examples.csv.

The main text uses $c$ for the mean-cost rival. Individual costs are represented by the quantile function

$$
c(q)=c\,\kappa(\sigma)\left(\frac{q}{1-q}\right)^{\sigma},\qquad\kappa(\sigma)=\frac{\sin(\sigma\pi)}{\sigma\pi},
$$

with the continuous limit $\kappa(0)=1$. This log-logistic distribution has mean $c$ and dispersion $0\leq\sigma<1$. The cost of assigning adoption to the cheapest share $x$ is $C(x)=\int_{0}^{x}c(q)\,dq=c\,I_{x}(1+\sigma,1-\sigma)$, where $I_{x}$ is the regularized incomplete beta function. On an irreversible path, use the costs of the actual adopters instead.

The exclusion curve is a logistic centered at $\theta$ with steepness $k$, normalized to $\Phi(0)=0$ and $\Phi(1)=1$. Its $k=0$ limit is $\Phi(x)=x$. The table is a reference for changing one parameter while holding the others fixed; real technologies can change several features at once.

Table 23: Parameter guide. Panel A gives effects on the three summary numbers in ([9](https://rencryptofish.com/posts/forcing-technologies#A2.E9)) for the mean-cost rival, holding other parameters fixed. Except for the $Q$ and $p$ rows, use $p=1$ and no outside option. The $r$ and $p$ signs assume nonnegative technology benefits; negative positional effects can reverse them. Panel B describes the adoption path, not the payoffs conditional on known effectiveness (Appendix [E](https://rencryptofish.com/posts/forcing-technologies#A5)).

<table><thead><tr><th></th> <th>Meaning</th> <th>Example</th> <th>$\Delta(0)$</th> <th>$\Delta(1)$</th> <th>Shape of $\Delta(x)$</th> <th>$y_{R}$</th></tr></thead> <tbody><tr><td colspan="7"><em>A. Payoff parameters</em></td></tr> <tr><td>$\gamma$</td> <td>standalone gain to an adopter</td> <td>containers’ lower handling cost</td> <td>$+$</td> <td>$+$</td> <td>level</td> <td>$+$</td></tr> <tr><td>$\beta$</td> <td>network gain from other adopters</td> <td>more container-ready ports</td> <td>$0$</td> <td>$+$</td> <td>rises</td> <td>$+$</td></tr> <tr><td>$\alpha$</td> <td>positional edge of a lone adopter</td> <td>one dreadnought against older fleets</td> <td>$+$</td> <td>$+$</td> <td>falls if $r&gt;1$</td> <td>$0$</td></tr> <tr><td>$r$</td> <td>erosion of the edge, $\alpha&gt;0$ fixed</td> <td>the same initial advantage wears away sooner</td> <td>$0$</td> <td>$-$</td> <td>lower for $x&gt;0$</td> <td>$0$</td></tr> <tr><td>$\varepsilon$</td> <td>penalty on holdouts that no rival captures</td> <td>browsers flagging non-HTTPS sites</td> <td>$0$</td> <td>$+$</td> <td>rises near $\theta$</td> <td>$0^{a}$</td></tr> <tr><td>$\theta$, $k$</td> <td>where and how abruptly exclusion bites</td> <td>a warning introduced at low rather than high market adoption</td> <td>$0$</td> <td>$0$</td> <td>moves and sharpens the rise</td> <td>$0^{a}$</td></tr> <tr><td>$c$</td> <td>mean adoption cost</td> <td>building a new fleet; retooling a port</td> <td>$-$</td> <td>$-$</td> <td>level</td> <td>$-$</td></tr> <tr><td>$\sigma$</td> <td>dispersion of adoption costs</td> <td>incumbents with installed fleets against entrants</td> <td>$0$</td> <td>$0$</td> <td>spreads rivals around it</td> <td>$0$</td></tr> <tr><td>$Q$</td> <td>value of the outside option ($\leq 0$): ally, specialize, exit the segment</td> <td>slower traders leaving the instruments that latency arbitrage contests</td> <td>$0^{c}$</td> <td>$-^{c}$</td> <td>caps the rise; the edge vanishes at $x_{Q}$</td> <td>$0$</td></tr> <tr><td>$\eta$</td> <td>gain to outsiders per adopter</td> <td>shippers’ freight rates; users’ security</td> <td>$0$</td> <td>$0$</td> <td>none</td> <td>$0^{b}$</td></tr> <tr><td>$p$</td> <td>belief that the technology works</td> <td>an untested battleship design</td> <td>$+$</td> <td>$+$</td> <td>scales $\gamma$, $\beta$, $\alpha$</td> <td>$0$</td></tr> <tr><td colspan="3"><em>B. Diffusion parameters</em></td> <td colspan="4">Main effect on the adoption path</td></tr> <tr><td>$p_{0}$</td> <td>belief before the demonstration</td> <td>confidence in an untested design</td> <td colspan="4">sets the ceiling $x_{L}$; dormancy if $x_{L}\leq x_{v}$</td></tr> <tr><td>$x_{v}$</td> <td>usage that demonstrates the technology</td> <td>first use in combat; a public benchmark</td> <td colspan="4">dormancy if above $x_{L}$; a later date near it</td></tr> <tr><td>$x_{0}$</td> <td>seed, held by the cheapest rivals</td> <td>a sponsor’s first orders</td> <td colspan="4">an earlier demonstration; immediate if $x_{0}\geq x_{v}$</td></tr> <tr><td>$\lambda_{0}$</td> <td>adjustment speed before the demonstration</td> <td>trials and pilot purchases</td> <td colspan="4">when the demonstration comes, not whether</td></tr> <tr><td>$\lambda$</td> <td>adjustment speed after it</td> <td>build times; budget cycles</td> <td colspan="4">speed of take-off; also the final level if the edge erodes</td></tr> <tr><td>$\tau$</td> <td>scale of transitory shocks</td> <td>budget windows; changes of leadership</td> <td colspan="4">adoption creeps past the rest point</td></tr> <tr><td>$W_{0}$, $\omega$, $\kappa_{W}$</td> <td>waiting value: a constant, its rise with belief uncertainty, its erosion by the edge</td> <td>waiting for a rival’s trial to fail</td> <td colspan="4">delays adoption and silences it before the demonstration; never enters payoffs or the classification</td></tr> <tr><td colspan="3"><em>C. Counter parameters (Appendix <a href="https://rencryptofish.com/posts/forcing-technologies#A6">F</a>)</em></td> <td colspan="4">Main effect</td></tr> <tr><td>$\varphi$</td> <td>share of a counterer’s stake shielded from adopters’ edge</td> <td>mines against battleships; ad-blocking</td> <td colspan="4">lowers the gain from adopting; disarms if $c_{K}\leq\varphi\alpha/r-\Delta(1)$</td></tr> <tr><td>$c_{K}$, $\sigma_{K}$</td> <td>mean and dispersion of counter costs</td> <td>building a mine flotilla</td> <td colspan="4">whether holdouts counter, and whether the counter pays for itself</td></tr></tbody> <tfoot><tr><th colspan="7"><sup>a</sup>Exclusion costs holdouts $(1-x)\,\varepsilon\,\Phi(x)$ during the transition, though not at either end. <sup>b</sup>Raises $y_{S}$ one for one. <sup>c</sup>For $Q&lt;0$, $\Delta(0)$ is unchanged; at $Q=0$ sheltering is immediate and removes the initial contest return. Raising $Q$ lowers $\Delta(1)$ only when the outside option binds. At fixed $V$ rather than fixed $\alpha$, increasing $r$ raises both endpoint gains because $\alpha=V(r-1)$; see Section <a href="https://rencryptofish.com/posts/forcing-technologies#A2.SS7">B.7</a>.</th></tr></tfoot></table>

## Appendix M Deployment conditions across fourteen markets

Table [24](https://rencryptofish.com/posts/forcing-technologies#A13.T24) compares deployment conditions across fourteen markets. It asks why adoption pays, where deployment stands and what constrains it. Those questions establish an adoption opportunity; evidence about holdout margins, retention or access is needed to establish economic forcing. Productive tools such as robots and software assistance can develop that pressure, while a network can attract adopters without yet damaging holdouts. Section [6](https://rencryptofish.com/posts/forcing-technologies#S6) and Appendix [N](https://rencryptofish.com/posts/forcing-technologies#A14) assess investment priorities across sixteen opportunities. The sources behind each readiness row are cited in the third column.

*Scaling* means established deployment in the named segment. *Selective* means expansion depends on local economics or workflow. *Phased* marks an active regulatory or technical transition. *Partners needed* means several parties still need to align.

Table 24: Fourteen markets compared on the buyer’s question, with sources as of October 2026. Deployment status describes maturity within the stated population; it says nothing about company profitability.

| Market / decision | Why adoption can pay | Where the market is today | Scale verdict | Main constraint |
| --- | --- | --- | --- | --- |
| Support assistance | Cost and service: less work per resolved case; rivals can raise service expectations. | 2026 company survey: 66% report AI agents in their organization (Salesforce, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib40)); a field study found 15% more issues resolved per hour (Brynjolfsson et al., [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib29)). | **Scaling** in repeatable queues. | Prove lower cost per durable resolution after escalation and repeat contacts. |
| Software assistance | Productivity and speed: useful output survives imitation; release advantages may fade. | Commercial tools; METR’s February 2026 update cannot reliably quantify current gains (Becker et al., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib619)). | **Selective** by workflow. | Review and rework can absorb gains; measure delivery through deployment. |
| Clinical note drafting | Time savings: less clerical work remains useful even when all clinics adopt. | 2026 study of 8,581 clinicians: 13.4 minutes less record work per eight scheduled patient hours; observational (Rotenstein et al., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib42)). | **Selective** with clinician review. | Corrections, integration and a buyer able to retain the benefit of time saved. |
| Warehouse robots | Cost competition: throughput and unit-cost gains survive imitation. | Amazon reported its millionth robot in June 2025 (Dresser, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib43)); five million industrial robots in service globally (International Federation of Robotics, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib44)). | **Scaling** in structured facilities. | Utilization, site conversion, integration and maintenance costs. |
| Precision spraying | Input savings: less herbicide at comparable weed control; rivals can lower costs. | Deere reports over five million acres treated in 2025 (John Deere, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib45)). | **Scaling** in suitable crops. | Acreage, weed control, equipment access and local payback. |
| Instant bank payments | Network reach: faster funds plus access to relevant counterparties. | RTP processed 2.27 million payments on May 1, 2026 (The Clearing House, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib46)); FedNow settled about 5.0 million transfers in 2026 Q2 (Federal Reserve Financial Services, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib47)). | **Scaling** on established rails. | Sending access, fraud controls, liquidity and 24-hour operations. |
| Stablecoin settlement | Route savings: faster settlement pays if full costs beat available bank routes. | Visa: over \$20 billion annualized settlement rate, September 2026 (Visa, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib48)). | **Selective** by corridor. | Redemption, conversion costs and local liquidity; compare full routes. |
| E-invoicing (France) | Coordination and mandate: shared formats save work; phased rules add pressure. | Receiving phase began September 2026; issuance phases continue in 2027 (Ministère de l’Économie, [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib49), [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib50)). | **Phased** rollout. | Partner activation, data quality and exceptions; no sanctions in 2026. |
| Electronic bills of lading | Coordination: faster transfer and finance pay when the whole shipment chain accepts them. | DCSA: about 11% electronic issuance in 2025; interoperability advanced in 2026 (Digital Container Shipping Association, [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib51); Guy, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib52)). | **Partners needed** across the chain. | Banks, shippers and carriers must align legal acceptance and operating procedures. |
| Passkeys | Defense: lower login friction and fraud can benefit every adopter. | FIDO participants: 36% of successful sign-ins in its October 2026 index (FIDO Alliance, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib53)). | **Scaling** in online services. | Enrollment, recovery and weak fallbacks can limit realized protection. |
| Post-quantum migration | Future protection and compatibility: rivals do not create the quantum threat. | Cloudflare: over two-thirds of human TLS traffic protected, April 2026 (Goldberg and Paul, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib54)); NCSC targets 2028/2031/2035 (National Cyber Security Centre, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib55)). | **Phased** beyond supported connections. | Inventory and legacy systems; protected web traffic does not cover every asset. |
| Insurance telematics | Selection: informed insurers can attract safer risks from less informed rivals. | Commercial programs such as Snapshot; availability varies by state (Progressive, [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib56); National Association of Insurance Commissioners, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib57)). | **Selective** within an established market. | Consent, data access, permitted pricing and policy renewals. |
| Procurement negotiation | Bargaining and labor: admin savings persist; price gains may shrink as suppliers respond. | Pactum reports over 50 enterprise customers (Pactum, [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib58); Uprety, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib59)). | **Selective** in bounded categories. | Supplier response and retention; test gains after both sides automate. |
| Grid storage / flexible demand | Energy shifting: useful flexibility persists; competing assets can erode revenue. | US utility batteries: nearly 52 GW in June 2026 (U.S. Energy Information Administration, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib60)); aggregation access varies locally (Electric Reliability Council of Texas, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib61)). | **Scaling** storage; **selective** aggregation. | Contracts, market access and interconnection; stress-test falling price spreads. |

Several additional candidates require separate consideration. Agent commerce and content provenance are candidates whose forcing mechanism still lacks a link: a transaction lost without an accepted credential, or an enforced platform rule with a measurable holdout effect. C2PA’s 2026 specification work supplies infrastructure rather than that evidence (Coalition for Content Provenance and Authenticity, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib62), [n.d.](https://rencryptofish.com/posts/forcing-technologies#bib.bib30)). Further evidence of lost transactions or enforced access requirements is needed to establish a forcing mechanism in agent commerce or content provenance. Polygenic embryo screening has a positional story and no validated effect to buy (Turley et al., [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib34)). Proof-of-work mining is an established contest benchmark; the main comparison separates miners’ returns from security benefits and equipment suppliers’ receipts (Section [4](https://rencryptofish.com/posts/forcing-technologies#S4)).

## Appendix N Investment directions: parameters, evidence and capital

This appendix sets out the evidence, assumptions and capital requirements for sixteen investment opportunities. Parameters are constructed annual scenarios, not fitted estimates. The four sectors are crypto, AI, fintech and greenfield (other markets). The opportunities include companies, networks, physical assets and financing arrangements; the appropriate investment instrument depends on the rights and returns available.

### N.1 The plotted coordinates

For each representative actor, $c=q+\kappa$ and

$$
F=\gamma+\beta+\alpha/r+\varepsilon-c,\qquad y_{R}=\gamma+\beta-c,\qquad y_{R}^{ext}=y_{R}-h(1).
$$

The current decision is

$$
M=p\left[\gamma+\beta x+\frac{\alpha}{1+(r-1)x}\right]+\varepsilon x-c-W.
$$

Here $\Phi(x)=x$ is a screening assumption. $p,x,W$ are subjective benefit haircuts, exposure and waiting values; they are not estimated success probabilities, measured adoption or actual calendar deadlines. A positive endpoint does not imply a positive current purchase decision.

Figure [20](https://rencryptofish.com/posts/forcing-technologies#A14.F20) plots the scenarios on the base model’s endpoint grid. Figure [21](https://rencryptofish.com/posts/forcing-technologies#A14.F21) applies the common producer revenue loss. All scenarios for a direction use its original plan central $B_{1}=\gamma+\beta+\alpha/r+\varepsilon$ as a fixed normalizer. This preserves comparability across revisions within that direction; it does not compare dollar market size across directions. Joined downside/central/upside points are joint scenarios, not an adoption path or a confidence interval.

Table 25: Working-case annual parameters and endpoints, in \$000 per representative actor. All cases are unvalidated scenarios. Public evidence constrains the assumptions for C1, A1, F2 and G1; $M$ includes the stated discounts to expected benefits and the value of waiting.

<table><tbody><tr><td>ID</td> <td>$\gamma$</td> <td>$\beta$</td> <td>$\alpha$</td> <td>$r$</td> <td>$\varepsilon$</td> <td>$c$</td> <td>$h(1)$</td> <td>$F$</td> <td>$y_{R}-h(1)$</td> <td>$M$</td></tr> <tr><td>C1</td> <td>400</td> <td>0</td> <td>0</td> <td>1</td> <td>0</td> <td>240</td> <td>320</td> <td>160</td> <td>-160</td> <td>0</td></tr> <tr><td>C2</td> <td>100</td> <td>0</td> <td>600</td> <td>3</td> <td>0</td> <td>200</td> <td>0</td> <td>100</td> <td>-100</td> <td>90</td></tr> <tr><td>C3</td> <td>800</td> <td>500</td> <td>0</td> <td>1</td> <td>0</td> <td>700</td> <td>200</td> <td>600</td> <td>400</td> <td>-238</td></tr> <tr><td>C4</td> <td>40</td> <td>30</td> <td>200</td> <td>4</td> <td>0</td> <td>150</td> <td>0</td> <td>-30</td> <td>-80</td> <td>-92</td></tr> <tr><td>A1</td> <td>100</td> <td>0</td> <td>0</td> <td>2</td> <td>0</td> <td>200</td> <td>0</td> <td>-100</td> <td>-100</td> <td>-220</td></tr> <tr><td>A2</td> <td>2,400</td> <td>0</td> <td>0</td> <td>1</td> <td>0</td> <td>1,000</td> <td>1,920</td> <td>1,400</td> <td>-520</td> <td>380</td></tr> <tr><td>A3</td> <td>800</td> <td>0</td> <td>0</td> <td>1</td> <td>0</td> <td>600</td> <td>0</td> <td>200</td> <td>200</td> <td>-350</td></tr> <tr><td>A4</td> <td>50</td> <td>300</td> <td>0</td> <td>1</td> <td>0</td> <td>200</td> <td>100</td> <td>150</td> <td>50</td> <td>-210</td></tr> <tr><td>F1</td> <td>400</td> <td>100</td> <td>0</td> <td>1</td> <td>0</td> <td>250</td> <td>240</td> <td>250</td> <td>10</td> <td>30</td></tr> <tr><td>F2</td> <td>750</td> <td>0</td> <td>0</td> <td>1</td> <td>0</td> <td>600</td> <td>0</td> <td>150</td> <td>150</td> <td>-300</td></tr> <tr><td>F3</td> <td>125</td> <td>125</td> <td>0</td> <td>1</td> <td>0</td> <td>175</td> <td>75</td> <td>75</td> <td>0</td> <td>-172</td></tr> <tr><td>F4</td> <td>500</td> <td>0</td> <td>600</td> <td>2</td> <td>0</td> <td>500</td> <td>400</td> <td>300</td> <td>-400</td> <td>0</td></tr> <tr><td>G1</td> <td>200</td> <td>0</td> <td>0</td> <td>1</td> <td>0</td> <td>160</td> <td>160</td> <td>40</td> <td>-120</td> <td>-30</td></tr> <tr><td>G2</td> <td>1,000</td> <td>0</td> <td>0</td> <td>1</td> <td>0</td> <td>600</td> <td>400</td> <td>400</td> <td>0</td> <td>-100</td></tr> <tr><td>G3</td> <td>150</td> <td>0</td> <td>0</td> <td>1</td> <td>300</td> <td>250</td> <td>0</td> <td>200</td> <td>-100</td> <td>-135</td></tr> <tr><td>G4</td> <td>1,500</td> <td>0</td> <td>3,000</td> <td>3</td> <td>0</td> <td>1,500</td> <td>600</td> <td>1,000</td> <td>-600</td> <td>-300</td></tr></tbody></table>

The central cases for C1, A1, F2 and G1 make conservative assumptions where evidence is missing. C1 includes operational savings and fees but no network premium; A1 includes administrative savings but no bargaining advantage; F2 assumes net fraud prevention without an additional network benefit; and G1 counts capacity gains only when they generate revenue or reduce costs. The positive upside for A1 still illustrates the hypothesis that an experiment could establish; it is not supported merely by its presence on the figure.

![Figure 20: Sixteen directions on the original endpoint grid. Upper right: adoption pays and the rival group gains; lower right: adoption pays and the group loses; lower left: full adoption is not sustained. Upper left is infeasible with these nonnegative channels. Points are constructed scenarios; the source tables provide exact values and direction names.](https://rencryptofish.com/images/forcing-technologies/investment_execution_paper_grid.png)

Figure 20: Sixteen directions on the original endpoint grid. Upper right: adoption pays and the rival group gains; lower right: adoption pays and the group loses; lower left: full adoption is not sustained. Upper left is infeasible with these nonnegative channels. Points are constructed scenarios; the source tables provide exact values and direction names.

![Figure 21: The same working cases after assumed common price pass-through. Hollow dots are before h; filled dots subtract h⁢(1) vertically. Adoption incentives do not change. A2, C1 and G1 can have positive adoption incentives while producer profits decline. This is not a finding of social waste or a measured price equilibrium.](https://rencryptofish.com/images/forcing-technologies/investment_execution_paper_passthrough.png)

Figure 21: The same working cases after assumed common price pass-through. Hollow dots are before $h$; filled dots subtract $h(1)$ vertically. Adoption incentives do not change. A2, C1 and G1 can have positive adoption incentives while producer profits decline. This is not a finding of social waste or a measured price equilibrium.

### N.2 Directions across the four sectors

The following table distinguishes the source of adoption pressure from the business that could earn revenue from it. “Option” means an identifiable missing observation could change the decision. “Stop” applies to the generic proposition specified, not every use of the underlying technology.

Table 26: Mechanisms, value capture and decisions after public research.

| Direction | Possible forcing mechanism | Position that can retain value | Decision |
| --- | --- | --- | --- |
| C1: corridor payouts | Lower completed-payout cost or better availability erodes rival margin | Local redemption/liquidity plus embedded distribution | Conditional advance |
| C2: orderflow rights | Solvers compete over a fixed trading contribution pool | Application or wallet with durable orderflow and fee rights | Option with distribution |
| C3: collateral mobility | Accepted claims free funding and allow tighter quotes | Bank/custodian or neutral connection with acceptance and financing | Requires a partner |
| C4: proof-carrying services | Buyers favor verifiable computation and exclude weaker claims | Specialized prover or buyer-recognized verification workflow | Stop generic thesis; paid-workload option |
| A1: seller negotiation | Rival sellers gain contribution or terms | Vertical commercial authority and audited transaction outcomes | Experiment only |
| A2: operated services | Cost/service competition reduces holdout viability | Service operator’s contracts and reliable completion | Advance narrow diligence |
| A3: agent authority | Exposed firms suffer attacks or lose required access | Cross-platform enforcement beyond incumbent coverage | Benchmark / option |
| A4: outcome acceptance | Accepted evidence and guarantees enable trade | Trusted acceptance workflow; separately, capitalized risk carrier | Small option |
| F1: continuous treasury | Better liquidity use tightens prices and service | Embedded bank/PSP controls and customer access | Requires access to customers |
| F2: shared fraud signals | Changing threats increase exposed accounts’ expected loss | Useful receiving-account labels with operational rights | Requires a partner |
| F3: agent-payment guarantees | Merchants lose valuable transactions without accepted risk coverage | Guarantor or dispute operator with capital and claims control | Reject a generic protocol fee; investigate a paid guarantee |
| F4: continuous SME credit | Faster selection takes attractive borrowers from slower lenders | Lender/data partner with outcomes, funding and customer relationship | Requires data access and capital |
| G1: industrial cells | Lower cost or lead time takes work from comparable plants | Repeatable integrator, field service and equipment finance | Advance one application |
| G2: flexible power | Usable power determines competitive service capacity | Accepted flexibility and access/payment rights | Advance subject to enforceable contracts |
| G3: insurability retrofits | Insurer/lender conditions change property economics | Recognized retrofit service and financing channel | Requires enforceable contracts |
| G4: autonomous formulation | Qualified products undercut cost or improve performance | Qualified IP, validation and industrial scale-up | Requires a qualified product |

Crypto.

The payoff units are, respectively, a PSP with \$200m annual eligible flow (C1), a solver/market maker (C2), an institution with \$200m eligible collateral (C3), and a supplier of verifiable computation (C4). C2 assumes a \$300k contested contribution pool and $r=3$, giving $\alpha=600$; Flashbots’ refund design demonstrates why gross orderflow is not retained protocol receipts (Flashbots, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib673)). C3 assumes release of 10% of collateral at a 4% funding spread ($\gamma=800$), plus a separately unverified \$500k acceptance/netting benefit. J.P. Morgan and Agorá establish functionality and experimentation, not those amounts (J.P. Morgan, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib675); Bank for International Settlements, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib642)). C4 assumes 400 avoided verification hours at \$100 plus speculative acceptance/contest gains. Succinct proves execution of specified programs; it does not establish true inputs or a token-holder distribution (Succinct, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib674)).

AI.

A1’s actor is a \$50m industrial supplier; its \$100k administration saving alone does not cover \$200k cost. A2’s actor is the mature \$20m service firm, distinct from the new-business funnel. A3 assumes \$2m attributable incident loss and 40% incremental prevention, a particularly uncertain expected-loss input. NIST’s identity project is not a mandate, and Microsoft offers a licensed incumbent alternative (NIST, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib670); Microsoft Learn, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib669)). A4 assumes \$50k direct saving and \$300k reusable acceptance value against \$200k cost; setting $\beta=0$ makes $F=-150$. AI insurance supplies a market analogue, not proof of a new acceptance-network toll (Munich Re, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib671)).

Fintech.

F1 starts with \$50m prefunding: releasing 20% at 4% gives $\gamma=400$, with another \$100k network benefit left unverified. FedNow’s native functionality is an alternative (Federal Reserve, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib677)). F2’s \$5m residual loss must be measured after existing controls and actual loss allocation. F3 uses a hypothetical \$50m agent-payment flow and \$125k each of direct and network benefit; AP2 does not verify that paid volume (Google, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib672)). A \$100k gross guarantee fee less \$60k claims, \$10k risk capital/transfer and \$10k transaction operations leaves only \$20k before other delivery costs. F4 assumes a \$100m credit book with 50bp operating/risk benefit and a separate contest edge. Historical mortgage evidence does not validate current SME selection or through-cycle losses (Fuster et al., [2018](https://rencryptofish.com/posts/forcing-technologies#bib.bib678)).

Greenfield.

G1’s unit is a production cell, G2’s a 20MW site. G3 uses a \$100m commercial property portfolio: \$100k assumed premium savings plus \$50k uninsured-loss reduction, and a separate \$300k enforced access penalty. California’s mitigation guidance does not establish that commercial contract; without $\varepsilon$, $F=-100$ (California Department of Insurance, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib679)). G4 assumes \$100m of affected industrial product sales, 1.5% direct cost improvement and a \$1.5m contest stake with $r=3$. Laboratory results do not establish qualification, yield or royalties. The A-Lab correction and autonomous chemistry evidence motivate investment in validation and qualified-product ownership, while challenging automatic discovery-value claims (Szymanski et al., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib681); Dai et al., [2024](https://rencryptofish.com/posts/forcing-technologies#bib.bib680)).

### N.3 Commercial scale and financing

The assumed customer pools are scenarios, not verified market sizes. Do not sum overlapping budgets: C1/F1 share payment buyers, A3/A4/F3 can sit in one transaction, and F2/F4 can use related data. A token waterfall must separately deduct rebates, execution, security, incentives and dilution before identifying any enforceable holder claim.

The narrower C1 cross-check starts from the dated \$226bn global B2B run rate. Assumed filters of 20% origin/segment relevance, 50% eligible payout use and 40% accessibility leave \$9.04bn flow; 10% entrant share at 6bp yields \$0.54m. Only the starting global estimate is source-derived. The original eventual pool implied \$240bn of adopted eligible flow and therefore cannot be called a verified current subset of that estimate.

Table 27: Constructed month-24 outcomes and capital envelopes, \$m unless stated. Annualized service/equipment receipts are not all software ARR. Debt and funding terms are assumed, not offers.

|  | Active units | Annualized receipts | Peak equity | With 25% buffer | Unfinanced need |
| --- | --- | --- | --- | --- | --- |
| A2 | 65.4 | 3.27 | 3.25 | 4.06 | 3.25 |
| G1 | 28.9 | 2.89 | 3.93 | 4.91 | 7.10 |
| C1 | 4.6 | 0.55 | 3.76 | 4.69 | 4.69 |
| G2 | 4.0 | 1.00 | 5.59 | 6.99 | 5.59 |
| F2 | 7.1 | 2.12 | 6.04 | 7.55 | 6.04 |
| A1 | 42.7 | 4.27 | 2.06 | 2.58 | 2.06 |

Each monthly path starts with no installed base and includes sales delay, installation capacity, churn, delivery costs, acquisition/onboarding, fixed expense and receivables. Equipment purchases, depreciation, amortizing debt and operating liquidity are accounted for separately. Customer counts are fractional expected cohorts under assumed conversion, not scheduled installations. No acquisition purchase price, terminal value or data-center construction is included.

The seller-negotiation scenario projects attractive supplier revenue, but its assumed customer savings do not cover adoption costs. All five other paths still consume cash at month 24. A 50% fee cut with unchanged direct costs makes A2 and G1 economic gross profit negative; slow acquisition can reduce asset purchases and funding while also shrinking the business. Neither a fast sales curve nor low burn substitutes for customer economics.

### N.4 Falsification and reproducibility

The script removes unmonetized benefit, sets network and exclusion channels to zero, changes waiting and implementation cost, and distinguishes reducing $r$ at fixed $\alpha$ from reducing it at fixed $V$, where $\alpha=V(r-1)$. Shelter uses the base model’s capped endpoint loss; a compatible supplier is compared directly. No price ceiling is interpreted as a realized price forecast.

The productivity deadline is fragile. Under the industrial-cell assumptions, $h(1)=160$ is less than initial profit 180, so the hypothesized holdout break-even lies beyond full adoption and there is no finite deadline. A2’s 15-month latest-start illustration remains conditional on its assumed diffusion rate; it is not a calendar forecast.

Public failures and alternatives are included where found, but no verified profitable non-adopter panel was obtained for the six initial fields. A company’s silence about a technology is not evidence of holding out. The assessment is based on public sources. Interviews, customer invoices, randomized comparisons and private underwriting records are still needed.

Running scripts/investment\_execution.py with the paper dependency group regenerates 48 endpoint cases, 218 parameter stresses, 432 monthly cohort rows, figures and tables. It checks endpoints against the repository model and reconciles financing, depreciation, fee compression and customer stock/flows. The accompanying executed notebook and public-source ledger are in data/investment\_directions/execution/.

## Appendix O AI and crypto: evidence and accounting boundaries

The case study in Section [4](https://rencryptofish.com/posts/forcing-technologies#S4) uses primary research, protocol specifications, company disclosures and documented product terms. The research ledger is data/investor/research/R20\_ai\_crypto\_platforms.md; source-level claims, dates and limitations are in data/investor/evidence.json. The source cutoff is October 20, 2026. Historical observations retain their original periods; documentation without a publication date describes the version accessed that day. The cases were selected for their mechanisms and cannot estimate the success rate of investments across either industry.

### O.1 What each receipt measures

A payment must be assigned to its recipient before it can support a claim about capture. Bitcoin block rewards combine issuance and user fees. Issuance transfers purchasing power to miners and is not customer sales. On Ethereum, the base-fee burn reduces supply, whereas priority fees and issuance enter validator economics differently. Solana’s fee documentation likewise distinguishes the burned and validator portions. Hyperliquid’s trading fees, deployer receipts and assistance-fund mechanism need to be separated from HyperEVM gas, whose documentation specifies burning both base and priority fees (Hyperliquid, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib613)). These mechanisms do not make protocol dashboards equivalent to audited income statements. Token appreciation, market capitalization and assets deposited in contracts are different stocks; trading fees are flows. Neither the stocks nor gross fees establish a holder’s contractual cash-flow entitlement or a supplier’s net profit.

For AI, recognized revenue, annualized revenue, contracted backlog, capital expenditure and financing commitments answer different questions. A run rate is not a completed year’s sales. Capital expenditure buys assets used over multiple periods; depreciation and utilization affect operating returns. Hyperscaler capital budgets also support other workloads. Adding a lab’s purchases to its cloud provider’s investment and the hardware company’s sales counts successive links in the same spending chain. The main section therefore uses NVIDIA’s reported Data Center revenue as evidence of upstream receipts, without allocating all of it to a contest or treating a corporate gross margin as a segment margin.

The same boundary applies to research costs. DeepSeek’s training estimate prices specified GPU-hours; it excludes earlier research and experiments. Comparable lab economics would require personnel, data, failed runs, inference, support, financing and subsequent model generations. The public sources reviewed here do not provide a consistent, audited model-level cost panel for the five providers. We therefore make no cross-provider profitability ranking and no estimate of the share of AI spending that is socially wasteful.

### O.2 Cloud investment and the cash that funds it

The large cloud providers can fund expansion from existing businesses as well as external capital. Table [28](https://rencryptofish.com/posts/forcing-technologies#A15.T28) reconciles selected full-year cash flows. Each row covers the whole company and its stated fiscal period; none isolates AI investment or the return on a particular model. The final column is operating cash less the specified property-and-equipment outflow, before acquisitions, financing flows and other investing uses.

Table 28: Selected realized cloud-provider cash flows, in US\$ billions. Different fiscal periods and capital-spending definitions are retained explicitly.

| Company and year ended | Operating cash | Cash PP&E | Difference |
| --- | --- | --- | --- |
| Alphabet, December 31, 2025 | 164.7 | 91.4 | 73.3 |
| Amazon, December 31, 2025 | 139.5 | 128.3 | 11.2 |
| Microsoft, June 30, 2026 | 182.9 | 115.9 | 67.0 |

Sources: company releases (Alphabet Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib499); Amazon.com, Inc., [2026e](https://rencryptofish.com/posts/forcing-technologies#bib.bib631); Microsoft Corporation, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib632)). Amazon nets property sales and incentives against purchases; Alphabet reports purchases and Microsoft reports cash additions. Differences are calculated from unrounded amounts, then rounded. These outflows exclude noncash asset additions.

Leases make the distinction consequential. On its July 2026 call, Microsoft reported quarterly capital expenditure of \$41 billion, finance leases of \$5.6 billion and cash paid for property and equipment of \$35.8 billion. It also explained that revised asset lives would shift some future datacenter leases from finance to operating classification: the latter do not enter its headline capex measure (Microsoft Corporation, [2026a](https://rencryptofish.com/posts/forcing-technologies#bib.bib633)). A lower reported capex path can therefore reflect accounting treatment while future payment obligations remain. Contractual commitments, depreciation, utilization and operating cash must be checked together. These disclosures also show why a claim about loss-making independent laboratories cannot be extended to every participant financing the race.

### O.3 Announcements, financing and realized operations

The September 22, 2025 OpenAI–NVIDIA announcement described a letter of intent for at least 10 GW of systems and an intended investment of up to \$100 billion, deployed progressively (OpenAI, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib580)). Those were announcement terms, not a record of delivered capacity or recognized sales; the initial announcement cannot establish its subsequent completion. The FTC’s January 2025 study of cloud/model partnerships identified arrangements requiring developers to spend substantial parts of their partners’ investment on those partners’ cloud services (Federal Trade Commission Staff, [2025](https://rencryptofish.com/posts/forcing-technologies#bib.bib628)). Such links can finance useful capacity while making the buyer and supplier financially interdependent. They require tracing rather than summing headline commitments.

Core Scientific provides a realized bridge between the two sectors. Its 2025 annual filing separates colocation, self-mining and hosted-mining revenue, and separates passed-through power fees within colocation (Core Scientific, Inc., [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib626)). The observed revenue shift supports a change in the use of sites and power. It does not imply that announced multiyear contract values were received in 2025, that all converted sites were operational, or that an ordinary mining site meets an AI customer’s cooling, networking and reliability requirements. Customer funding of a conversion also changes the allocation of construction and credit risk.

### O.4 Events that change different parts of the mechanism

China’s 2021 restrictions affected where mining could operate. Cambridge’s October account reports a sharp June fall in global hashrate, partial recovery in July and August, and changes in geographic shares (Rauchs, [2021](https://rencryptofish.com/posts/forcing-technologies#bib.bib629)). Its geographic estimates came from participating mining pools; they do not fully observe concealed activity. Ethereum’s 2022 Merge changed which method could produce valid blocks on Ethereum itself. The estimated reduction in its energy use belongs to that consensus transition, not to Bitcoin or the whole crypto industry (Ethereum.org Contributors, [2026b](https://rencryptofish.com/posts/forcing-technologies#bib.bib604)). The two events changed different mechanisms: China’s restrictions relocated mining, while Ethereum replaced proof-of-work.

The analogous AI branches include changes in efficiency, access to weights, chip access and customer demand. The conditional table is not an equilibrium solution for these branches. Capital renewal, entry and exit, heterogeneous capacity, strategic subsidies and changes in the total prize are outside the base adoption model. Its illustrative payoff calculation demonstrates why a positive incentive to adopt cannot identify the sign of the field’s aggregate gain. It cannot estimate consumer surplus, environmental costs, security benefits or the spillovers of model research.

### O.5 Measurements still needed to distinguish the hypotheses

A platform-retention study needs fixed cohorts, periods and definitions. For each chain, measure fee-paying users and developers retained after incentives, the applications they actually use, and whether liquidity is duplicated or migrated. Separate trading volume from net deposits and useful settlement; remove known wash trading, automated repetition and consensus votes before comparing activity. For models, measure retained paid workloads and successful outcomes at a fixed quality threshold after credits end or a competing model launches. Record routing across providers, evaluation costs and failures, rather than counting API accounts as exclusive customers.

The public evidence establishes mechanisms and some realized outcomes, but does not supply those matched cohorts across all nine cases. In particular, Hyperliquid’s fee-routing rules establish a possible path from activity to token supply changes; they do not establish sustained external-application retention. Electric Capital’s repository data observe open-source contributions, with overlapping chain attribution, rather than exclusive customer relationships (Electric Capital, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib614)). The absence of a comparable panel is a limit on the conclusion, not evidence that the network effect is absent.

For a payout corridor, measure delivered local purchasing power and availability time after every conversion and fee. Stripe’s Remote account supplies a reported benefit and a concrete workflow; it supplies neither randomized evidence nor a published cohort of repeat users and complete redemption costs (Stripe, [2026](https://rencryptofish.com/posts/forcing-technologies#bib.bib625)). For AI tasks, measure completion quality and review time as well as speed. The support study and METR’s evolving experiment answer narrower questions than economy-wide productivity. These measurements would test the investment hypotheses.

### O.6 Forecast definitions, assumptions and resolution

The October 20, 2026 register contains eleven capability fields and separate entries for October 20, 2031 and October 20, 2036. It is stored in data/ai\_crypto\_forecasts/forecasts.csv; definitions, source records and assumptions are adjacent. The research ledger is data/investor/research/R21\_ai\_crypto\_forecasts.md. All twenty-two entries are qualitative conditional forecasts. The observed quantities, external projections, customer claims and posted offers in observations.csv are explicitly distinguished. None is treated as a fitted actor-level panel.

The commercial-field event compares annual operating profit with a no-technology counterfactual in constant purchasing power, controlling for common shocks. It follows the original 2026 cohort including exits, with entrants reported separately. Nonprofitable firms, traders’ execution costs and service-access measures need separate denominators and cannot be pooled into this profit-ratio event. The central convention is at least 10% loss for at least 50% of the field over eight consecutive quarterly intervals, after the best feasible non-adopting response and with an economically feasible adoption response. We vary loss thresholds over 5, 10 and 20%, and reach over 25, 50 and 75%. Actual resolution requires matched actor outcomes and implementation costs. Missing observations leave an event unresolved.

Pressure reached by a horizon means that some qualifying eight-quarter window has completed. Pressure active at a horizon requires the final eight quarters to qualify. A 2026 observation does not establish the preceding persistence history, and a declining loss can still represent an active event. The register records current pressure separately from the expected mechanism of further change. It does not claim measured customer counts, aggregate dollars at risk, onset dates or probability calibration.

#### O.6.1 What the reproducible calculations establish

The script scripts/ai\_crypto\_forecasts.py supplies mechanism stress tests, not parameter estimates behind the qualitative tiers. There are eleven constructed branches across six mechanisms, each observed at the origin and forty quarterly endpoints. Linear interpolation joins the input knots in Table [29](https://rencryptofish.com/posts/forcing-technologies#A15.T29). Payoffs remain annual flows; the script does not compound them as quarterly returns. Exposure is imposed conditionally rather than generated by diffusion. Replacement states therefore do not purport to solve ten years of irreversible adoption.

Each artificial field has cost multipliers $0.5,1,1.5$ with weights $0.25,0.5,0.25$. These are assumptions, not estimates of firm heterogeneity. Conditional effectiveness is $p=1$; it is not an event probability. No weights are assigned to branches, which overlap and cannot be added into forecast probabilities. The calendar, thresholds and complete input paths are frozen in JSON; the output includes both the level of loss and its change from 2026.

For ordinary model branches, the script uses the existing payoff functions, with $\Phi(x)=x$, $\alpha=V(r-1)$ and an additional common price loss $h=\rho\gamma x$. That loss reduces both adopter and holdout profits and cancels from their switching difference. The genuine-exit branch uses the model’s outside option and removes departed contest stakes; a compatible competing provider is not that exit. To avoid an unsupported combination, the script rejects simultaneous common price pressure and a finite outside option. The defense branch instead sets

$$
U_{N}=-L_{\mathrm{attack}},\qquad U_{A}=-(1-\varphi)L_{\mathrm{attack}}-c,\qquad M=\varphi L_{\mathrm{attack}}-c-W.
$$

Here $L_{\mathrm{attack}}$ is incremental expected loss after existing controls. This is separate-population accounting, not an application of the strategic-counter theorem.

An artificial cohort qualifies only when holdout loss exceeds the chosen threshold, switching margin is positive and post-adoption operating profit remains positive. The additional viability condition prevents a beneficial but still insolvent response from being counted as feasible. All remaining alternatives are conditional assumptions of the branch; these calculations do not establish that real firms lack other responses.

Table 29: Assumed input knots at 2026 / 2031 / 2036, with linear quarterly interpolation. All payoff flows use baseline-profit units. Unlisted $V,\beta,\varepsilon,\rho,W$ are zero and unlisted $r=1$. These are mechanism tests, not estimates.

| **Stress test** | **Assumed parameter path** |
| --- | --- |
| Workflow price competition: Savings transmitted | x=0.15/0.6/0.85; gamma=0.5/0.9/1.2; c=0.3/0.35/0.4; rho=0.2/0.6/0.8; wait=0.03/0.03/0.03 |
| Workflow price competition: Weak transmission | x=0.15/0.6/0.85; gamma=0.5/0.9/1.2; c=0.3/0.6/0.9; rho=0.1/0.1/0.05; wait=0.03/0.03/0.03 |
| Capacity contest: Continuing contest | x=0.5/0.85/0.95; gamma=0.15/0.3/0.45; V=0.6/0.3/0.2; r=2/3/3; c=0.25/0.3/0.35; wait=0.02/0.02/0.02 |
| Capacity contest: Feasible exit | x=0.5/0.85/0.95; gamma=0.15/0.3/0.45; V=0.6/0.3/0.2; r=2/3/3; c=0.25/0.3/0.35; wait=0.02/0.02/0.02; Q=-0.2/-0.08/-0.05 |
| Payout corridor: Corridor advantage | x=0.1/0.5/0.75; gamma=0.2/0.4/0.45; beta=0.05/0.1/0.15; c=0.12/0.18/0.16; rho=0.25/0.7/0.8; wait=0.01/0.01/0.01 |
| Payout corridor: Bank substitution | x=0.1/0.5/0.75; gamma=0.2/0.12/0.08; beta=0.05/0.05/0.04; c=0.12/0.18/0.16; rho=0.25/0.4/0.3; wait=0.01/0.01/0.01 |
| Compatible access: Access dependence | x=0.1/0.6/0.85; gamma=0.03/0.1/0.1; beta=0.4/0.6/0.8; eps=0/0.3/0.5; c=0.1/0.15/0.15; wait=0.01/0.01/0.01 |
| Compatible access: Optional connection | x=0.1/0.6/0.85; gamma=0.03/0.1/0.1; beta=0.4/0.6/0.8; c=0.1/0.15/0.15; wait=0.01/0.01/0.01 |
| External attack defense: Adapting threat | threat=0.05/0.3/0.6; efficacy=0.7/0.7/0.7; c=0.08/0.12/0.15; wait=0.01/0.01/0.01 |
| External attack defense: Bundled protection | threat=0.05/0.08/0.06; efficacy=0.7/0.7/0.7; c=0.08/0.12/0.15; wait=0.01/0.01/0.01 |
| Benefits without forcing: Useful but optional | x=0.1/0.6/0.9; gamma=0.3/0.3/0.3; beta=0.4/0.4/0.4; c=0.1/0.1/0.1 |

Table 30: Constructed stress tests, not empirical forecasts. Loss and its change from 2026 are percentage points of baseline annual operating profit. Event: 10% loss, 50% reach, eight completed quarters. By / active distinguishes attainment from persistence.

| **Assumed mechanism / branch** | **2031 loss / change** | **2036 loss / change** | **2031 by / active** | **2036 by / active** |
| --- | --- | --- | --- | --- |
| Workflow price competition: Savings transmitted | 32.4 / +30.9 | 81.6 / +80.1 | Yes / Yes | Yes / Yes |
| Workflow price competition: Weak transmission | 5.4 / +4.7 | 5.1 / +4.3 | No / No | No / No |
| Capacity contest: Continuing contest | 18.9 / -1.1 | 13.1 / -6.9 | Yes / Yes | Yes / Yes |
| Capacity contest: Feasible exit | 8.0 / -12.0 | 5.0 / -15.0 | Yes / No | Yes / No |
| Payout corridor: Corridor advantage | 14.0 / +13.5 | 27.0 / +26.5 | No / No | Yes / Yes |
| Payout corridor: Bank substitution | 2.4 / +1.9 | 1.8 / +1.3 | No / No | No / No |
| Compatible access: Access dependence | 18.0 / +18.0 | 42.5 / +42.5 | No / No | Yes / Yes |
| Compatible access: Optional connection | 0.0 / +0.0 | 0.0 / +0.0 | No / No | No / No |
| External attack defense: Adapting threat | 30.0 / +25.0 | 60.0 / +55.0 | Yes / Yes | Yes / Yes |
| External attack defense: Bundled protection | 8.0 / +3.0 | 6.0 / +1.0 | No / No | No / No |
| Benefits without forcing: Useful but optional | 0.0 / +0.0 | 0.0 / +0.0 | No / No | No / No |

The stress tests distinguish the size of a loss from its duration. In the constructed payout branch, endpoint loss reaches 14% in 2031 but has not remained material long enough to pass the two-year test. The access branch likewise has a high endpoint before completing the required window. In the exit branch, pressure is reached before 2031 but is no longer active at either horizon. Direct and network benefits alone never create holdout loss. The full 198 threshold–horizon results in scenario\_sensitivity.csv expose these distinctions; they are not 198 independent forecasts.

Capture requires another comparison. With $c=q+\kappa$, the holdout-based ceiling is $q\leq B-\kappa-W$, but a compatible supplier can impose a tighter bound. For example, if avoiding the holdout produces gross value $0.50$ and other implementation cost is $0.10$, the ceiling before waiting is $0.40$. If an equally effective alternative costs $0.12$ in total and the focal product still requires $0.10$ of other costs, the focal supplier can charge at most $0.02$ at equal quality. These assumed numbers illustrate why capability forcing need not imply protocol rent. Actual gross profit then deducts service costs, and capital-intensive suppliers must fund replacement and earn returns on their invested capital.

#### O.6.2 Evidence boundaries and the next resolution

The source register retains publication and observation periods. The support-study entry uses the published-version sample and effect, without mixing earlier working-paper numbers. Census’s broadened question is a series break. The IEA’s 2030 number is an external projection, IFR counts include conventional industrial robots, incident reports are selected cases, and an advertised API price is not sales. Source-specific limitations are retained alongside the observations.

The forecasts lack interviews, a complete panel covering adopters, holdouts and exits, calibrated loss distributions and prospective validation. Consequently no parameter recovery, held-out forecast accuracy, probability calibration or industry-wide capture estimate is reported. The numerical tests verify economic accounting and event-window logic, not prediction accuracy. A future quantitative edition must first identify the relevant exposure and obtain the outcomes needed to distinguish direct value, contest transfer and exclusion.

The next review should establish cohorts and measurement contracts in 2027; test pass-through, retention and incremental security losses in 2028; and apply the candidate-specific 2029 reversal tests before upgrading broad claims. Dated revisions should retain the original forecasts and record failed candidates and exits, allowing later assessment against the planned milestones.

## Appendix P Where the framework comes from

The model is a binary choice with externalities in the sense of Schelling ([1973](https://rencryptofish.com/posts/forcing-technologies#bib.bib1), [1978](https://rencryptofish.com/posts/forcing-technologies#bib.bib2)), with heterogeneous thresholds as in Granovetter ([1978](https://rencryptofish.com/posts/forcing-technologies#bib.bib3)). The distinction between a rival’s adoption raising one’s *incentive* to adopt and raising one’s *payoff* is the strategic-complements distinction of Bulow et al. ([1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib4)), and the threshold structure of games with strategic complements is that of Milgrom and Roberts ([1990](https://rencryptofish.com/posts/forcing-technologies#bib.bib427)). The two earlier reduced forms each measure only one side of it. Network and compatibility forcing follow Katz and Shapiro ([1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib6), [1986](https://rencryptofish.com/posts/forcing-technologies#bib.bib430)), Farrell and Saloner ([1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib7), [1986](https://rencryptofish.com/posts/forcing-technologies#bib.bib431)) and Arthur ([1989](https://rencryptofish.com/posts/forcing-technologies#bib.bib8)); two-sided pricing of the crossing follows Rochet and Tirole ([2003](https://rencryptofish.com/posts/forcing-technologies#bib.bib421)); switching costs and lock-in follow Klemperer ([1987](https://rencryptofish.com/posts/forcing-technologies#bib.bib426)), Shapiro and Varian ([1999](https://rencryptofish.com/posts/forcing-technologies#bib.bib422)) and Farrell and Klemperer ([2007](https://rencryptofish.com/posts/forcing-technologies#bib.bib433)). The positional channel is a proportional-share contest in the tradition of Tullock ([1980](https://rencryptofish.com/posts/forcing-technologies#bib.bib5)); its welfare consequences are the positional arms races of Hirsch ([1976](https://rencryptofish.com/posts/forcing-technologies#bib.bib9)) and Frank ([2011](https://rencryptofish.com/posts/forcing-technologies#bib.bib10)), the rank-order tournaments of Lazear and Rosen ([1981](https://rencryptofish.com/posts/forcing-technologies#bib.bib420)), the winner-take-all markets of Frank and Cook ([1995](https://rencryptofish.com/posts/forcing-technologies#bib.bib429)) and the races of Harris and Vickers ([1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib428)). Adoption timing under rivalry follows Reinganum ([1981](https://rencryptofish.com/posts/forcing-technologies#bib.bib11)) and Fudenberg and Tirole ([1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib12)), and the waiting value draws on Dixit and Pindyck ([1994](https://rencryptofish.com/posts/forcing-technologies#bib.bib13)). Diffusion curves follow Griliches ([1957](https://rencryptofish.com/posts/forcing-technologies#bib.bib14)) and Bass ([1969](https://rencryptofish.com/posts/forcing-technologies#bib.bib15)); the cost curves of Section [2.3](https://rencryptofish.com/posts/forcing-technologies#S2.SS3) follow Wright ([1936](https://rencryptofish.com/posts/forcing-technologies#bib.bib423)) and Arrow ([1962](https://rencryptofish.com/posts/forcing-technologies#bib.bib424)). Teece ([1986](https://rencryptofish.com/posts/forcing-technologies#bib.bib418)) explains when innovators can retain returns, while Sutton ([1991](https://rencryptofish.com/posts/forcing-technologies#bib.bib419)) links market concentration to endogenous sunk costs. Reference dependence in customers’ expectations follows Kahneman and Tversky ([1979](https://rencryptofish.com/posts/forcing-technologies#bib.bib432)), and information cascades, the wave that carries no payoff information, follow Bikhchandani et al. ([1992](https://rencryptofish.com/posts/forcing-technologies#bib.bib425)). On the empirical side, identification of peer effects in adoption faces the reflection problem of Manski ([1993](https://rencryptofish.com/posts/forcing-technologies#bib.bib16)), and the hazard here is a dynamic relative of the discrete-choice social-interactions model of Brock and Durlauf ([2001](https://rencryptofish.com/posts/forcing-technologies#bib.bib17)). Network exposure follows Galeotti et al. ([2010](https://rencryptofish.com/posts/forcing-technologies#bib.bib18)). Demonstration thresholds under noisy beliefs connect to global games (Carlsson and van Damme, [1993](https://rencryptofish.com/posts/forcing-technologies#bib.bib19); Morris and Shin, [1998](https://rencryptofish.com/posts/forcing-technologies#bib.bib20)). Institutional and fad-driven adoption (DiMaggio and Powell, [1983](https://rencryptofish.com/posts/forcing-technologies#bib.bib21); Abrahamson and Rosenkopf, [1993](https://rencryptofish.com/posts/forcing-technologies#bib.bib22)) motivates the treatment of belief-driven “false forcing”. For artificial intelligence, Armstrong et al. ([2016](https://rencryptofish.com/posts/forcing-technologies#bib.bib23)) model a racing game of the arms-race type.

Three further connections clarify the extensions. Competitive learning can repeatedly erode a rival’s advantage, as in the Red Queen account of Barnett and Hansen ([1996](https://rencryptofish.com/posts/forcing-technologies#bib.bib25)). Customer requirements can differ between attractive features and minimum expectations (Kano et al., [1984](https://rencryptofish.com/posts/forcing-technologies#bib.bib26)). And evidence that collective restrictions raise producer profits need not establish a social gain, as the cigarette-advertising analysis of Farr et al. ([2001](https://rencryptofish.com/posts/forcing-technologies#bib.bib27)) shows. These connections help separate the transmission of competitive pressure from its consequences for customers, entry and successive generations of technology.

## Appendix Q Earlier models and reproduction benchmarks

The exact parameter restrictions are stated in Proposition [11](https://rencryptofish.com/posts/forcing-technologies#Thmproposition11). The threshold model retains exclusion pressure and the linear model holds the contest gap constant.

The threshold calibration reproduces in full; thirteen of the fourteen linear-model fits reproduce to the precision of the stored parameters. All 15 threshold-model technologies match in $G$, in current pressure $S\Phi(x)$, and in status. Thirteen of the 14 fitted linear-model series reproduce their demonstration date, $T_{50}$, $T_{90}$, final share and RMSE within the five-decimal rounding of the stored fits (Figure [22](https://rencryptofish.com/posts/forcing-technologies#A17.F22), Table [31](https://rencryptofish.com/posts/forcing-technologies#A17.T31)).

The fourteenth, nuclear weapons, does not, and the reason is substantive. Its fit sets $x_{0}=x_{v}$ and $F_{c}(p_{0}z)\approx x_{0}$ to five decimals. A $5\times 10^{-6}$ change in $x_{v}$ decides whether a demonstration ever happens, so the fitted demonstration date is not identified. In the terms of Proposition [9](https://rencryptofish.com/posts/forcing-technologies#Thmproposition9), the fit puts the visibility threshold at the pre-demonstration ceiling $x_{L}$, which is where the demonstration date in Figure [9](https://rencryptofish.com/posts/forcing-technologies#A5.F9)(c) diverges.

![Figure 22: Four of the 14 historical diffusion series with the unified model’s fitted paths (r=1, ε=0, so the paths coincide with the linear model’s fits). Payoff parameters appear in Table 31; the complete case-specific settings, including beliefs, seeds and adjustment speeds, are stored in data/claude\_cases.json and data/claude\_fits.json.](https://rencryptofish.com/images/forcing-technologies/fits.png)

Figure 22: Four of the 14 historical diffusion series with the unified model’s fitted paths ($r=1$, $\varepsilon=0$, so the paths coincide with the linear model’s fits). Payoff parameters appear in Table [31](https://rencryptofish.com/posts/forcing-technologies#A17.T31); the complete case-specific settings, including beliefs, seeds and adjustment speeds, are stored in data/claude\_cases.json and data/claude\_fits.json.

Table 31: Inherited calibration of 14 historical cases under the linear restriction ($r=1$, $\varepsilon=W=0$, no outside option). $W(x_{T})$ is realized rival welfare at the end of the series relative to $x=0$. <sup>†</sup>Sensitive to the rounding of stored parameters (see text).

| Case | $\alpha$ | $\beta$ | $\gamma$ | $c$ | $\sigma$ | RMSE | $T_{50}$ | $\Delta(0)$ | $\Delta(1)$ | $y$ | $W(x_{T})$ | Region |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Hybrid corn | 0.35 | 0.05 | 0.60 | 0.20 | 0.15 | 0.019 | 10 yr | $+0.75$ | $+0.80$ | $+0.45$ | $+0.43$ | productive |
| HTTPS | 0.45 | 0.25 | 0.30 | 0.80 | 0.15 | 0.014 | 4 yr | $-0.05$ | $+0.20$ | $-0.25$ | $-0.17$ | wasteful bandwagon |
| Dreadnought | 0.90 | 0.00 | 0.10 | 0.15 | 0.10 | 0.043 | 4 yr | $+0.85$ | $+0.85$ | $-0.05$ | $-0.05$ | arms race |
| Container | 0.10 | 0.60 | 0.30 | 0.49 | 0.58 | 0.035 | 16 yr | $-0.09$ | $+0.51$ | $+0.41$ | $+0.50$ | coordination |
| MLB analytics | 0.85 | 0.00 | 0.15 | 0.10 | 0.10 | 0.015 | 6 yr | $+0.90$ | $+0.90$ | $+0.05$ | $+0.05$ | productive |
| Frequent flyer | 0.80 | 0.05 | 0.15 | 0.08 | 0.10 | 0.035 | 7 mo | $+0.87$ | $+0.92$ | $+0.12$ | $+0.11$ | productive |
| LZR suit | 1.00 | 0.00 | 0.00 | 0.05 | 0.34 | 0.021 | 3 mo | $+0.95$ | $+0.95$ | $-0.05$ | $-0.05$ | arms race |
| Clap skates | 0.90 | 0.00 | 0.10 | 0.24 | 0.38 | 0.005 | 12 yr | $+0.76$ | $+0.76$ | $-0.14$ | $-0.12$ | arms race |
| Nuclear<sup>†</sup> | 1.00 | 0.00 | 0.00 | 1.00 | 0.19 | 0.022 | 52 yr | $-0.002$ | $-0.002$ | $-1.00$ | $-0.39$ | inert |
| Armed drones<sup>†</sup> | 0.65 | 0.00 | 0.35 | 0.21 | 0.25 | 0.057 | 25 yr | $+0.79$ | $+0.79$ | $+0.14$ | $+0.12$ | productive |
| China NEVs | 0.45 | 0.20 | 0.35 | 0.60 | 0.15 | 0.012 | 10 yr | $+0.20$ | $+0.40$ | $-0.05$ | $-0.02$ | arms race |
| Gen AI (large orgs) | 0.40 | 0.10 | 0.50 | 0.50 | 0.54 | 0.025 | 4 qtr | $+0.40$ | $+0.50$ | $+0.10$ | $+0.25$ | productive |
| AI (all US firms) | 0.25 | 0.15 | 0.60 | 0.99 | 0.24 | 0.003 | – | $-0.14$ | $+0.01$ | $-0.24$ | $+0.02$ | wasteful bandwagon |
| RFID mandate | 0.20 | 0.50 | 0.30 | 2.00 | 0.26 | 0.002 | – | $-1.50$ | $-1.00$ | $-1.20$ | $-0.001$ | inert |

The inherited calibration should be read with three caveats.

- The static split of $(\alpha,\beta,\gamma)$ was set by judgment and ban evidence, not estimated. By Proposition [12](https://rencryptofish.com/posts/forcing-technologies#Thmproposition12) the diffusion fits cannot check it.

- Region labels use the mean-cost rival. Cases with a plateau below full adoption have $c$ pushed up by the fit, and HTTPS’s “wasteful bandwagon” label comes from its assumed positional share $\alpha=0.45$, not from evidence. That label is a candidate for re-estimation, not a finding.

- These are reproduction benchmarks, not the paper’s updated estimates. Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) rebuilds the historical series and reports fits allowing $r\neq 1$, transitory shocks and, where relevant, exclusion.

Why the earlier dreadnought interpretations differed.

The two reduced forms disagree on whether a lone dreadnought was worth building. The threshold calibration has $\Delta(0)=-G=-0.33$, while the linear calibration has $\Delta(0)=\gamma+\alpha-c=+0.85$. In the unified model the disagreement is over $\Delta(0)=p[\gamma+\alpha]-c$: whether the first mover’s positional edge $\alpha$ is counted, and whether incumbents’ installed fleets, which are part of their $c$, outweighed it. That is an empirical question about the adopter curve at low $x$, Britain’s relative position in 1906–1909, rather than a definitional one.

## Appendix R Learning and forward-looking timing

Appendix [E.3](https://rencryptofish.com/posts/forcing-technologies#A5.SS3) describes the decision implications. These equations specify possible extensions; they are not the adoption rule used for the historical fits.

One way to allow both favorable and unfavorable evidence is a binary quality state $\zeta\in\{0,1\}$ and a signal $Y_{t}$ with state-dependent density $\ell_{\zeta}$. Beliefs update by

$$
p_{t+1}=\frac{p_{t}\ell_{1}(Y_{t})}{p_{t}\ell_{1}(Y_{t})+(1-p_{t})\ell_{0}(Y_{t})}.
$$

Signal likelihoods must account for the pilot’s positional advantage and its selected cost. Otherwise the inference confuses success against unprepared rivals with value after they respond. The jump to $p=1$ is the limiting case of conclusive favorable evidence, not a general learning law. Downward revisions can halt new adoption while leaving earlier commitments stranded. Institutional pressures can also persist after a technological disappointment, because exclusion is not multiplied by $p$ in ([8](https://rencryptofish.com/posts/forcing-technologies#A1.E8)); this connects mistaken technological expectations to institutional bandwagons (Abrahamson and Rosenkopf, [1993](https://rencryptofish.com/posts/forcing-technologies#bib.bib22); DiMaggio and Powell, [1983](https://rencryptofish.com/posts/forcing-technologies#bib.bib21)).

Anticipation is a separate issue. Let $s$ contain exposure, beliefs, costs and any announced deadline, and let $\delta\in(0,1)$ discount future flows. With irreversible adoption, an optimal-stopping formulation is

$$
J_{A}(s)=U_{A}(s)+\delta\,\operatorname{E}[J_{A}(s^{\prime})\mid s],\qquad J(s)=\max\{J_{A}(s),\ U_{N}(s)+\delta\,\operatorname{E}[J(s^{\prime})\mid s]\}.
$$

Here $J$ is the value while still free to wait and $J_{A}$ is the value after commitment. The transition law must incorporate rivals’ strategies for this to be a timing game (Fudenberg and Tirole, [1985](https://rencryptofish.com/posts/forcing-technologies#bib.bib12); Rust, [1987](https://rencryptofish.com/posts/forcing-technologies#bib.bib24)). The historical fits use the myopic hazard defined in Appendix [E](https://rencryptofish.com/posts/forcing-technologies#A5). A future cutoff can bring investment forward when installation takes time or capacity must be reserved. With instantaneous, freely available installation, a future penalty alone need not justify paying today’s operating cost early. Empirically, order dates, installation dates and productive-use dates should therefore be recorded separately. Adoption before measured rival use may reflect anticipation rather than an absent competitive effect.

## Appendix S Reproducibility

The model is src/forcing/model.py. Each result is checked in tests/:

<table><tbody><tr><td>Result</td> <td>Test</td></tr> <tr><td>Section <a href="https://rencryptofish.com/posts/forcing-technologies#S1">1</a></td> <td>test_payoffs_are_relative_to_the_status_quo</td></tr> <tr><td></td> <td>test_outside_option_caps_the_loss_and_withdraws_the_stake</td></tr> <tr><td>Lemma <a href="https://rencryptofish.com/posts/forcing-technologies#Thmlemma1">1</a></td> <td>test_contest_is_zero_sum</td></tr> <tr><td></td> <td>test_welfare_is_mean_payoff_and_ignores_the_contest</td></tr> <tr><td>Lemma <a href="https://rencryptofish.com/posts/forcing-technologies#Thmlemma2">2</a></td> <td>test_contest_slope_has_the_sign_of_minus_alpha_r_minus_one</td></tr> <tr><td></td> <td>test_small_edge_limit_is_the_linear_contest</td></tr> <tr><td></td> <td>test_decisive_contest_makes_the_holdout_loss_a_step</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition1">1</a></td> <td>test_contests_alone_never_tip</td></tr> <tr><td>Definition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmdefinition1">1</a></td> <td>test_classification_ignores_the_waiting_value</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition2">2</a></td> <td>test_selective_forcing_closed_form</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition3">3</a></td> <td>test_shakeout_closed_form</td></tr> <tr><td></td> <td>test_outside_option_stops_adoption_at_the_shakeout</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition4">4</a></td> <td>test_exclusion_raises_forcing_but_not_full_adoption_welfare</td></tr> <tr><td>Corollary <a href="https://rencryptofish.com/posts/forcing-technologies#Thmcorollary1">1</a></td> <td>test_outside_option_caps_the_loss_and_withdraws_the_stake</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition5">5</a></td> <td>test_private_social_wedge</td></tr> <tr><td>Propositions <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition6">6</a>, <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition7">7</a></td> <td>test_ban_criterion_includes_exclusion</td></tr> <tr><td></td> <td>test_interior_allocation_beats_both_endpoints</td></tr> <tr><td></td> <td>test_contest_waste_vanishes_at_cost_extremes</td></tr> <tr><td></td> <td>test_tax_receipts_are_transfers</td></tr> <tr><td>Appendices <a href="https://rencryptofish.com/posts/forcing-technologies#A5.SS2">E.2</a>, <a href="https://rencryptofish.com/posts/forcing-technologies#A8">H</a></td> <td>test_pilot_return_separates_edge_and_network</td></tr> <tr><td></td> <td>test_selection_can_raise_adoption_without_conversion</td></tr> <tr><td></td> <td>test_continuous_contest_equilibrium</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition8">8</a></td> <td>test_linear_dynamics_match</td></tr> <tr><td></td> <td>test_homogeneous_costs_give_the_logit_hazard</td></tr> <tr><td></td> <td>test_persistent_heterogeneity_makes_the_hazard_fall</td></tr> <tr><td>Appendix <a href="https://rencryptofish.com/posts/forcing-technologies#A5.SS5">E.5</a></td> <td>test_failed_seeds_freeze_rather_than_unravel</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition9">9</a></td> <td>test_demonstration_needs_visibility_below_the_ceiling</td></tr> <tr><td>Appendix <a href="https://rencryptofish.com/posts/forcing-technologies#A5.SS7">E.7</a></td> <td>test_waiting_value_sharpens_the_demonstration_cliff</td></tr> <tr><td>Observation <a href="https://rencryptofish.com/posts/forcing-technologies#Thmobservation1">1</a></td> <td>test_aggregate_recursion_is_exact_only_for_monotone_thresholds</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition10">10</a></td> <td>test_counter_nests_the_base_model</td></tr> <tr><td></td> <td>test_counter_dynamics_nest_the_base_dynamics</td></tr> <tr><td></td> <td>test_counter_contest_is_zero_sum</td></tr> <tr><td></td> <td>test_counter_welfare_is_the_mean_payoff</td></tr> <tr><td></td> <td>test_counter_complements_adoption_and_other_counters</td></tr> <tr><td></td> <td>test_countering_leaves_the_linear_contests_gain_from_adopting_unchanged</td></tr> <tr><td></td> <td>test_full_counter_restores_the_split</td></tr> <tr><td>Corollary <a href="https://rencryptofish.com/posts/forcing-technologies#Thmcorollary4">4</a></td> <td>test_disarmament_test_with_a_counter</td></tr> <tr><td>Appendix <a href="https://rencryptofish.com/posts/forcing-technologies#A6">F</a></td> <td>test_counter_shares_match_sampled_rivals</td></tr> <tr><td></td> <td>test_counter_dynamics_match_a_finite_population</td></tr> <tr><td></td> <td>test_counters_arrive_late_and_stop_rather_than_reverse_adoption</td></tr> <tr><td></td> <td>test_a_counter_raises_welfare_only_by_deterring_adoption</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition11">11</a></td> <td>test_threshold_model_is_a_special_case</td></tr> <tr><td></td> <td>test_threshold_calibration_table_reproduces</td></tr> <tr><td></td> <td>test_linear_model_is_a_special_case</td></tr> <tr><td></td> <td>test_linear_fits_reproduce</td></tr> <tr><td></td> <td>test_nuclear_fit_sits_on_a_knife_edge</td></tr> <tr><td>Proposition <a href="https://rencryptofish.com/posts/forcing-technologies#Thmproposition12">12</a></td> <td>test_adoption_data_cannot_split_alpha_from_gamma</td></tr> <tr><td></td> <td>test_adoption_data_cannot_split_standalone_gain_from_waiting</td></tr> <tr><td></td> <td>test_belief_separates_exclusion_from_network_gains</td></tr> <tr><td></td> <td>test_utility_rescaling_preserves_adoption</td></tr> <tr><td>Appendix <a href="https://rencryptofish.com/posts/forcing-technologies#A10">J</a></td> <td>test_archived_map_likelihoods_reproduce</td></tr></tbody></table>

Figures and Table [31](https://rencryptofish.com/posts/forcing-technologies#A17.T31) are generated by scripts/paper\_assets.py. The four worked cases in Section [7](https://rencryptofish.com/posts/forcing-technologies#S7) are regenerated by scripts/investor\_assets.py. The contest, detection and invoice cases use the planning assumptions in data/investor/scenarios.json; their purchase margins are checked against forcing.gain, and the contest field path comes from forcing.simulate. The fulfillment case uses data/investor/productivity.json, the explicit extension in src/forcing/productivity.py, and scripts/productivity\_assets.py. Its deployment trajectory and price response are assumptions, not estimates from the base model. That script can also be run separately to regenerate Table [15](https://rencryptofish.com/posts/forcing-technologies#S7.T15), its CSV, the timing sensitivity CSV and the supplier summary JSON. Tests in tests/test\_productivity.py check the separation of switching gain from holdout loss, the viability ceiling, the customer transfer, and the disappearance of the timing threshold under low pass-through.

Every source cited in the investor sections is registered in data/investor/evidence.json. Calibration figures and tables are generated by scripts/calibration\_assets.py from the stored fit summaries. These record input and code hashes. The input-integrity checks and a replay of all 42 stored posterior-mode likelihoods verify the assembled calibration against the current code; they do not replace convergence or sensitivity checks on the posterior sampling.

## Appendix T Data sources

Every series in Appendix [J](https://rencryptofish.com/posts/forcing-technologies#A10) is rebuilt by

uv run python -m forcing.collect all

which, for each case:

1. re-downloads every snapshot;

2. re-derives parsed rows from the snapshots;

3. verifies hashes, quotes, values and schema;

4. builds the fitted series.

scripts/fit\_cases.py then writes each calibration with the hashes of its inputs and of the code. A test fails if any committed calibration was fitted from inputs that have since changed.

Table [33](https://rencryptofish.com/posts/forcing-technologies#A20.T33) summarizes the rows and how they were obtained:

- *Crawled* sources were fetched byte for byte by code.

- *Captured* sources were saved from a browser session, because the publisher blocks scripts.

- *Parsed* rows were derived by code.

- *Quoted* rows were transcribed with a verbatim quote checked against the snapshot.

Flags count rows that are stated, derived, estimated, and excluded. The list that follows gives every source used, by case; the source registries add access dates, hashes and Wayback Machine captures.

Table 33: Provenance of the rebuilt data.

<table><tbody><tr><td></td> <th colspan="4">Sources</th> <th></th> <th colspan="2">Rows</th> <td></td></tr> <tr><th>Case</th> <th>All</th> <th>Crawled</th> <th>Captured</th> <th>Manual</th> <th>Fitted table</th> <th>Parsed</th> <th>Quoted</th> <th>Flags s/d/e/b</th></tr> <tr><td>Clap skates</td> <td>5</td> <td>5</td> <td>0</td> <td>0</td> <td>7 values</td> <td>0</td> <td>7</td> <td>1/4/1/1</td></tr> <tr><td>Container</td> <td>3</td> <td>3</td> <td>0</td> <td>0</td> <td>18 values</td> <td>15</td> <td>3</td> <td>0/15/0/3</td></tr> <tr><td>Hybrid corn</td> <td>1</td> <td>1</td> <td>0</td> <td>0</td> <td>28 values</td> <td>28</td> <td>0</td> <td>28/0/0/0</td></tr> <tr><td>Dreadnought</td> <td>10</td> <td>10</td> <td>0</td> <td>0</td> <td>8 events</td> <td>8</td> <td>0</td> <td>0/8/0/0</td></tr> <tr><td>Armed drones</td> <td>11</td> <td>11</td> <td>0</td> <td>0</td> <td>48 events</td> <td>13</td> <td>52</td> <td>0/48/0/17</td></tr> <tr><td>Frequent flyer</td> <td>11</td> <td>10</td> <td>1</td> <td>0</td> <td>8 events</td> <td>1</td> <td>7</td> <td>0/8/0/0</td></tr> <tr><td>Gen AI (large orgs)</td> <td>5</td> <td>5</td> <td>0</td> <td>0</td> <td>10 values</td> <td>0</td> <td>10</td> <td>4/0/1/5</td></tr> <tr><td>AI (all US firms)</td> <td>2</td> <td>2</td> <td>0</td> <td>0</td> <td>77 values</td> <td>77</td> <td>0</td> <td>54/0/0/23</td></tr> <tr><td>HTTPS</td> <td>5</td> <td>5</td> <td>0</td> <td>0</td> <td>24 values</td> <td>24</td> <td>0</td> <td>0/14/0/10</td></tr> <tr><td>LZR suit</td> <td>4</td> <td>4</td> <td>0</td> <td>0</td> <td>5 values</td> <td>0</td> <td>5</td> <td>2/1/0/2</td></tr> <tr><td>MLB analytics</td> <td>7</td> <td>7</td> <td>0</td> <td>0</td> <td>5 values</td> <td>0</td> <td>5</td> <td>1/2/1/1</td></tr> <tr><td>China NEVs</td> <td>5</td> <td>5</td> <td>0</td> <td>0</td> <td>15 values</td> <td>11</td> <td>4</td> <td>11/0/0/4</td></tr> <tr><td>Nuclear</td> <td>3</td> <td>3</td> <td>0</td> <td>0</td> <td>11 events</td> <td>6</td> <td>5</td> <td>0/11/0/0</td></tr> <tr><td>RFID mandate</td> <td>8</td> <td>8</td> <td>0</td> <td>0</td> <td>14 values</td> <td>0</td> <td>13</td> <td>4/1/0/9</td></tr></tbody></table>

<table><thead><tr><th>Source</th> <th>Method</th> <th>Licence</th></tr></thead> <tbody><tr><td colspan="3"><strong>Clap skates</strong></td></tr> <tr><td>Jos J. de Koning (Vrije Universiteit Amsterdam), in Sportscience News (1997). Background to the slapskate: Fifteen years of slapskate history, biomechanical backgrounds, first results and recent developments. <a href="http://www.sportsci.org/news/news9703/slapxtra.htm">http://www.sportsci.org/news/news9703/slapxtra.htm</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>International Skating Union (2026). Speed Skating and the clap skate revolution. <a href="https://isu-skating.com/speed-skating/news/speed-skating-and-the-clap-skate-revolution/">https://isu-skating.com/speed-skating/news/speed-skating-and-the-clap-skate-revolution/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Olympedia (OlyMADMen) (2026). Speed Skating at the 1998 Winter Olympics (overview). <a href="https://www.olympedia.org/editions/46/sports/SSK">https://www.olympedia.org/editions/46/sports/SSK</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Stephen Seiler (Sportscience News) (1997). The new Dutch ”Slapskates”: Will They Revolutionize Speed Skating Technique?. <a href="http://www.sportsci.org/news/news9703/slapskat.htm">http://www.sportsci.org/news/news9703/slapskat.htm</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td colspan="3"><strong>Containerization, North Atlantic &amp; UK</strong></td></tr> <tr><td>Daniel M. Bernhofen, Zouheir El-Sahli, Richard Kneller (2012). Estimating the effects of the container revolution on world trade (working paper, February 3, 2012; Figure 2: Changes in container utilization in the UK and Japan). <a href="http://economicsarchive.fiu.edu/events/2013/seminar-daniel-bernhofen/bek_container_feb-3-2013.pdf">http://economicsarchive.fiu.edu/events/2013/seminar-daniel-bernhofen/bek_container_feb-3-2013.pdf</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Benjamin Bridgman (Bureau of Economic Analysis) (2014). Why Containerization Did Not Reduce Ocean Trade Shipping Costs. <a href="https://www.aeaweb.org/conference/2015/retrieve.php?pdfid=3462&amp;tk=k5HEFitY">https://www.aeaweb.org/conference/2015/retrieve.php?pdfid=3462&amp;tk=k5HEFitY</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Frank Broeze (2002). The Globalisation of the Oceans: Containerisation from the 1950s to the Present, ch. ’1970s: conquering the world’ (Cambridge Core chapter page with extract). <a href="https://www.cambridge.org/core/books/globalisation-of-the-oceans/1970s-conquering-the-world/F87A212081653D8714A7393E7D008209">https://www.cambridge.org/core/books/globalisation-of-the-oceans/1970s-conquering-the-world/F87A212081653D8714A7393E7D008209</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td colspan="3"><strong>Hybrid corn, US</strong></td></tr> <tr><td>U.S. Department of Agriculture (Statistical Reporting Service) (1963). Agricultural Statistics 1962 (Table 46: Corn hybrids: Acreage of corn planted with hybrids, United States, 1933-60). <a href="https://esmis.nal.usda.gov/sites/default/release-files/j3860694x/vd66w276c/8c97kt28h/Agstat-04-23-1962.pdf">https://esmis.nal.usda.gov/sites/default/release-files/j3860694x/vd66w276c/8c97kt28h/Agstat-04-23-1962.pdf</a></td> <td>crawler</td> <td>public-domain</td></tr> <tr><td colspan="3"><strong>Dreadnought battleships</strong></td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: French battleship Courbet (revision 1374865778). <a href="https://en.wikipedia.org/w/index.php?title=French_battleship_Courbet&amp;oldid=1374865778&amp;action=raw">https://en.wikipedia.org/w/index.php?title=French_battleship_Courbet&amp;oldid=1374865778&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: HMS Dreadnought (1906) (revision 1374707991). <a href="https://en.wikipedia.org/w/index.php?title=HMS_Dreadnought_(1906)&amp;oldid=1374707991&amp;action=raw">https://en.wikipedia.org/w/index.php?title=HMS_Dreadnought_(1906)&amp;oldid=1374707991&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2025). Wikipedia: Italian battleship Dante Alighieri (revision 1323091977). <a href="https://en.wikipedia.org/w/index.php?title=Italian_battleship_Dante_Alighieri&amp;oldid=1323091977&amp;action=raw">https://en.wikipedia.org/w/index.php?title=Italian_battleship_Dante_Alighieri&amp;oldid=1323091977&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: Japanese battleship Settsu (revision 1375023838). <a href="https://en.wikipedia.org/w/index.php?title=Japanese_battleship_Settsu&amp;oldid=1375023838&amp;action=raw">https://en.wikipedia.org/w/index.php?title=Japanese_battleship_Settsu&amp;oldid=1375023838&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: Russian battleship Gangut (revision 1379253632). <a href="https://en.wikipedia.org/w/index.php?title=Russian_battleship_Gangut&amp;oldid=1379253632&amp;action=raw">https://en.wikipedia.org/w/index.php?title=Russian_battleship_Gangut&amp;oldid=1379253632&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: SMS Nassau (revision 1378184497). <a href="https://en.wikipedia.org/w/index.php?title=SMS_Nassau&amp;oldid=1378184497&amp;action=raw">https://en.wikipedia.org/w/index.php?title=SMS_Nassau&amp;oldid=1378184497&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: SMS Viribus Unitis (revision 1373687988). <a href="https://en.wikipedia.org/w/index.php?title=SMS_Viribus_Unitis&amp;oldid=1373687988&amp;action=raw">https://en.wikipedia.org/w/index.php?title=SMS_Viribus_Unitis&amp;oldid=1373687988&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: USS Michigan (BB-27) (revision 1377049957). <a href="https://en.wikipedia.org/w/index.php?title=USS_Michigan_(BB-27)&amp;oldid=1377049957&amp;action=raw">https://en.wikipedia.org/w/index.php?title=USS_Michigan_(BB-27)&amp;oldid=1377049957&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td colspan="3"><strong>Armed drones, states</strong></td></tr> <tr><td>Dan Gettinger (Center for the Study of the Drone at Bard College) (2019). The Drone Databook. <a href="https://dronecenter.bard.edu/files/2019/10/CSD-Drone-Databook-Web.pdf">https://dronecenter.bard.edu/files/2019/10/CSD-Drone-Databook-Web.pdf</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Drone Wars UK (2022). Armed drones proliferation update - May 2022. <a href="https://dronewars.net/2022/05/09/armed-drones-proliferation-update-may-2022/">https://dronewars.net/2022/05/09/armed-drones-proliferation-update-may-2022/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Drone Wars UK (2023). Armed drone proliferation update - March ’23. <a href="https://dronewars.net/2023/03/22/armed-drone-proliferation-update-march-23/">https://dronewars.net/2023/03/22/armed-drone-proliferation-update-march-23/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Drone Wars UK (2025). Armed Drone Proliferation: Continued Exports Leading to Civilian Casualties. <a href="https://dronewars.net/2025/03/03/armed-drone-proliferation-continued-exports-leading-to-civilian-casualties/">https://dronewars.net/2025/03/03/armed-drone-proliferation-continued-exports-leading-to-civilian-casualties/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Drone Wars UK (2025). Who has Armed Drones? (States operating armed MALE drones - updated March 2025). <a href="https://dronewars.net/who-has-armed-drones/">https://dronewars.net/who-has-armed-drones/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Drone Wars UK (2024). Who has Armed Drones? (Feb 2024 update; Wayback Machine capture 2024-04-10). <a href="https://web.archive.org/web/20240410090925id_/https://dronewars.net/who-has-armed-drones/">https://web.archive.org/web/20240410090925id_/https://dronewars.net/who-has-armed-drones/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>New America (2021). Countries that Have Drones (Datawrapper dataset, World of Drones). <a href="https://datawrapper.dwcdn.net/GwojV/9/dataset.csv">https://datawrapper.dwcdn.net/GwojV/9/dataset.csv</a></td> <td>crawler</td> <td>CC-BY</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: General Atomics MQ-1 Predator (revision 1376630226). <a href="https://en.wikipedia.org/w/index.php?title=General_Atomics_MQ-1_Predator&amp;oldid=1376630226&amp;action=raw">https://en.wikipedia.org/w/index.php?title=General_Atomics_MQ-1_Predator&amp;oldid=1376630226&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td colspan="3"><strong>Frequent-flyer programs</strong></td></tr> <tr><td>Georgia newspapers, via the Rawson Company clipping service (1981). Clippings: ’EAL Plans Discounts’ (Gwinnett Daily News) and ’Eastern To Reward Frequent Travelers’ (Atlanta Daily World), clipping-service stamps 6 Sep 1981. <a href="https://cdm16905.contentdm.oclc.org/digital/bl/dmwebservices/index.php?q=dmGetItemInfo/eastern/51840/xml">https://cdm16905.contentdm.oclc.org/digital/bl/dmwebservices/index.php?q=dmGetItemInfo/eastern/51840/xml</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Randy Petersen (InsideFlyer) (2006). The Big 2-5: Celebrating 25 Years of Frequent Flyer Programs. <a href="https://www.insideflyer.com/2006/05/12/the-big-2-5-celebrating-25-years-of-frequent-flyer-programs/">https://www.insideflyer.com/2006/05/12/the-big-2-5-celebrating-25-years-of-frequent-flyer-programs/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Randy Petersen (InsideFlyer) (2006). 60 Seconds with Mike Boynton, Delta Air Lines (retired). <a href="https://www.insideflyer.com/2006/04/25/60-seconds-with-mike-boynton-delta-air-lines-retired/">https://www.insideflyer.com/2006/04/25/60-seconds-with-mike-boynton-delta-air-lines-retired/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>The New York Times (1982). United Schedules Its Boeing 767’s (Company News), with correction of 30 Jul 1982. <a href="https://web.archive.org/web/20150524120028id_/https://www.nytimes.com/1982/07/29/business/united-schedules-its-boeing-767-s.html">https://web.archive.org/web/20150524120028id_/https://www.nytimes.com/1982/07/29/business/united-schedules-its-boeing-767-s.html</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Carole Shifrin (The Washington Post) (1981). Rewarding Frequent Flyers. <a href="https://www.washingtonpost.com/archive/lifestyle/travel/1981/10/25/rewarding-frequent-flyers/28d68e93-122c-4547-9bdb-79549b862223/">https://www.washingtonpost.com/archive/lifestyle/travel/1981/10/25/rewarding-frequent-flyers/28d68e93-122c-4547-9bdb-79549b862223/</a></td> <td>browser</td> <td>copyrighted</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: AAdvantage (revision 1376666546). <a href="https://en.wikipedia.org/w/index.php?title=AAdvantage&amp;oldid=1376666546&amp;action=raw">https://en.wikipedia.org/w/index.php?title=AAdvantage&amp;oldid=1376666546&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td colspan="3"><strong>Generative AI, large organisations</strong></td></tr> <tr><td>McKinsey &amp; Company (2023). The state of AI in 2023: Generative AI’s breakout year. <a href="https://web.archive.org/web/20260925170608id_/https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-state-of-ai-in-2023-generative-ais-breakout-year">https://web.archive.org/web/20260925170608id_/https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-state-of-ai-in-2023-generative-ais-breakout-year</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>McKinsey &amp; Company (2024). The state of AI in early 2024: Gen AI adoption spikes and starts to generate value. <a href="https://web.archive.org/web/20260614200348id_/https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-state-of-ai-2024">https://web.archive.org/web/20260614200348id_/https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-state-of-ai-2024</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>McKinsey &amp; Company (2025). The state of AI: How organizations are rewiring to capture value. <a href="https://web.archive.org/web/20250416052125id_/https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-state-of-ai">https://web.archive.org/web/20250416052125id_/https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-state-of-ai</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>McKinsey &amp; Company (2025). The state of AI in 2025: Agents, innovation, and transformation (PDF). <a href="https://web.archive.org/web/20260408014729id_/https://www.mckinsey.com/~/media/mckinsey/business%20functions/quantumblack/our%20insights/the%20state%20of%20ai/the-state-of-ai-in-2025-vf.pdf">https://web.archive.org/web/20260408014729id_/https://www.mckinsey.com/~/media/mckinsey/business%20functions/quantumblack/our%20insights/the%20state%20of%20ai/the-state-of-ai-in-2025-vf.pdf</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>McKinsey &amp; Company (2026). The state of AI in 2026: On the road to ROI (PDF). <a href="https://web.archive.org/web/20260915005927id_/https://www.mckinsey.com/~/media/mckinsey/business%20functions/quantumblack/our%20insights/the%20state%20of%20ai/the-state-of-ai-in-2026-on-the-road-to-roi-aug-2026.pdf">https://web.archive.org/web/20260915005927id_/https://www.mckinsey.com/~/media/mckinsey/business%20functions/quantumblack/our%20insights/the%20state%20of%20ai/the-state-of-ai-in-2026-on-the-road-to-roi-aug-2026.pdf</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td colspan="3"><strong>AI use, all US businesses</strong></td></tr> <tr><td>U.S. Census Bureau (2025). Business Trends and Outlook Survey: AI Core Questions (Original), 09/11/2023 to 10/05/2025. <a href="https://www.census.gov/hfp/btos/downloads/AI%20Core%20Questions.xlsx">https://www.census.gov/hfp/btos/downloads/AI%20Core%20Questions.xlsx</a></td> <td>crawler</td> <td>public-domain</td></tr> <tr><td>U.S. Census Bureau (2026). Business Trends and Outlook Survey: National (current questionnaire). <a href="https://www.census.gov/hfp/btos/downloads/National.xlsx">https://www.census.gov/hfp/btos/downloads/National.xlsx</a></td> <td>crawler</td> <td>public-domain</td></tr> <tr><td colspan="3"><strong>HTTPS page loads</strong></td></tr> <tr><td>Google (2026). Google Transparency Report: Percentage of pages loaded over HTTPS in Chrome by platform (JSON). <a href="https://transparencyreport.google.com/transparencyreport/api/v3/httpsreport/chromeusage/byos?series=page-load&amp;groupby=os">https://transparencyreport.google.com/transparencyreport/api/v3/httpsreport/chromeusage/byos?series=page-load&amp;groupby=os</a></td> <td>crawler</td> <td>unknown</td></tr> <tr><td>Internet Security Research Group (Let’s Encrypt); data from Mozilla Firefox telemetry (2026). current-https-adoption.csv (Firefox telemetry, daily, by country group). <a href="https://d1dfn7jg27m4cf.cloudfront.net/current-https-adoption.csv">https://d1dfn7jg27m4cf.cloudfront.net/current-https-adoption.csv</a></td> <td>crawler</td> <td>unknown</td></tr> <tr><td>Internet Security Research Group (Let’s Encrypt); data from Mozilla Firefox telemetry (2017). historical-https-adoption.csv (Firefox telemetry HTTP_PAGELOAD_IS_SSL, global, daily). <a href="https://d1dfn7jg27m4cf.cloudfront.net/historical-https-adoption.csv">https://d1dfn7jg27m4cf.cloudfront.net/historical-https-adoption.csv</a></td> <td>crawler</td> <td>unknown</td></tr> <tr><td colspan="3"><strong>Polyurethane swimsuits</strong></td></tr> <tr><td>Lisa Dillman (Los Angeles Times) (2008). As swim records fall, high-tech suit faces scrutiny. <a href="https://www.latimes.com/archives/la-xpm-2008-mar-27-sp-swim27-story.html">https://www.latimes.com/archives/la-xpm-2008-mar-27-sp-swim27-story.html</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Jason Tillotson (Swimming World) (2018). Eight Years Later, the Super Suit Era Still Plagues the Record Books. <a href="https://www.swimmingworldmagazine.com/news/eight-years-later-the-super-suit-era-still-plagues-the-record-books/">https://www.swimmingworldmagazine.com/news/eight-years-later-the-super-suit-era-still-plagues-the-record-books/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: LZR Racer (revision 1379269770). <a href="https://en.wikipedia.org/w/index.php?title=LZR_Racer&amp;oldid=1379269770&amp;action=raw">https://en.wikipedia.org/w/index.php?title=LZR_Racer&amp;oldid=1379269770&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td colspan="3"><strong>MLB analytics departments</strong></td></tr> <tr><td>ESPN; MLB section by Ben Baumer (2015). The Great Analytics Rankings (MLB: In a Moneyball world, a number of teams remain slow to buy into sabermetrics). <a href="https://web.archive.org/web/20160806162303id_/http://www.espn.com:80/espn/feature/story/_/id/12331388/the-great-analytics-rankings">https://web.archive.org/web/20160806162303id_/http://www.espn.com:80/espn/feature/story/_/id/12331388/the-great-analytics-rankings</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Ben Lindbergh and Rob Arthur (2016). Statheads Are The Best Free Agent Bargains In Baseball. <a href="https://web.archive.org/web/20160426203822id_/http://fivethirtyeight.com/features/statheads-are-the-best-free-agent-bargains-in-baseball/">https://web.archive.org/web/20160426203822id_/http://fivethirtyeight.com/features/statheads-are-the-best-free-agent-bargains-in-baseball/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td colspan="3"><strong>New-energy vehicles, China</strong></td></tr> <tr><td>Lei Kang, CnEVPost (2024). China’s NEV retail reaches record 945,000 in Dec, 7.74 million for full year 2023. <a href="https://cnevpost.com/2024/01/09/china-nev-retail-reaches-945000-in-dec/">https://cnevpost.com/2024/01/09/china-nev-retail-reaches-945000-in-dec/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>CnEVPost (2025). China NEV retail at record 1.38 million in Dec, preliminary CPCA data show. <a href="https://cnevpost.com/2025/01/08/china-nev-retail-dec-2024-preliminary-cpca-data/">https://cnevpost.com/2025/01/08/china-nev-retail-dec-2024-preliminary-cpca-data/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>CnEVPost (2026). China NEV retail sales rise 7% to 1.387 million units in Dec, preliminary CPCA data shows. <a href="https://cnevpost.com/2026/01/07/china-nev-retail-1-387-million-dec-2025-preliminary-cpca/">https://cnevpost.com/2026/01/07/china-nev-retail-1-387-million-dec-2025-preliminary-cpca/</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Our World in Data, from International Energy Agency, Global EV Outlook 2026 (2026). Share of new cars sold that are electric (grapher CSV). <a href="https://ourworldindata.org/grapher/electric-car-sales-share.csv?v=1&amp;csvType=full&amp;useColumnShortNames=true">https://ourworldindata.org/grapher/electric-car-sales-share.csv?v=1&amp;csvType=full&amp;useColumnShortNames=true</a></td> <td>crawler</td> <td>CC-BY</td></tr> <tr><td colspan="3"><strong>Nuclear weapons</strong></td></tr> <tr><td>Philipp C. Bleek (2017). When Did (and Didn’t) States Proliferate? Chronicling the Spread of Nuclear Weapons. <a href="https://www.belfercenter.org/sites/default/files/pantheon_files/files/publication/When%20Did%20%28and%20Didn%27t%29%20States%20Proliferate%3F_1.pdf">https://www.belfercenter.org/sites/default/files/pantheon_files/files/publication/When%20Did%20%28and%20Didn%27t%29%20States%20Proliferate%3F_1.pdf</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Wikipedia contributors (2026). Wikipedia: List of states with nuclear weapons (revision 1377913291). <a href="https://en.wikipedia.org/w/index.php?title=List_of_states_with_nuclear_weapons&amp;oldid=1377913291&amp;action=raw">https://en.wikipedia.org/w/index.php?title=List_of_states_with_nuclear_weapons&amp;oldid=1377913291&amp;action=raw</a></td> <td>crawler</td> <td>CC-BY-SA</td></tr> <tr><td colspan="3"><strong>Walmart RFID mandate</strong></td></tr> <tr><td>Associated Press (via TELECOM Digest) (2005). Wal-Mart: Radio Tags Keep Shelves Stocked. <a href="https://bio.nic.funet.fi/pub/mirrors/lcs.mit.edu/telecom-archives/TELECOM_Digest_Online2005-2/2288.html">https://bio.nic.funet.fi/pub/mirrors/lcs.mit.edu/telecom-archives/TELECOM_Digest_Online2005-2/2288.html</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Computerworld (2006). Wal-Mart details its RFID journey. <a href="https://www.computerworld.com/article/1720141/wal-mart-details-its-rfid-journey.html">https://www.computerworld.com/article/1720141/wal-mart-details-its-rfid-journey.html</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Perry Trunick (Material Handling &amp; Logistics) (2004). Wal-Mart rolls out RFID pilots. <a href="https://www.mhlnews.com/technology-automation/article/22033989/wal-mart-rolls-out-rfid-pilots">https://www.mhlnews.com/technology-automation/article/22033989/wal-mart-rolls-out-rfid-pilots</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Supply Chain Digest (2009). RFID News: Looking Back at the Wal-Mart RFID Timeline. <a href="https://www.scdigest.com/assets/On_Target/09-02-23-1.php">https://www.scdigest.com/assets/On_Target/09-02-23-1.php</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Michael Garry (Supermarket News) (2005). Wal-Mart: 57 Suppliers Meet January RFID Mandate. <a href="https://www.supermarketnews.com/supplier-news/wal-mart-57-suppliers-meet-january-rfid-mandate">https://www.supermarketnews.com/supplier-news/wal-mart-57-suppliers-meet-january-rfid-mandate</a></td> <td>crawler</td> <td>copyrighted</td></tr> <tr><td>Michael Garry (Supermarket News) (2008). Plugging Along. <a href="https://www.supermarketnews.com/grocery-technology/plugging-along">https://www.supermarketnews.com/grocery-technology/plugging-along</a></td> <td>crawler</td> <td>copyrighted</td></tr></tbody></table>