1.1Four 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). 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, $\epsilon \mathrm{\Phi }(x)$.

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 says what changes when it is. The pressure curve $\mathrm{\Phi }$ 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,

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. Appendix A 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). 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.

1.2Three tests and four patterns

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

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 $\mathrm{\Delta }(1)>0$, competitively compelled when $\mathrm{\Delta }(0)\le 0$, and wasteful for the field when . 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 combines the first two tests with the third, and Figure 1 draws one technology of each kind.

Figure 2 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.

1.3Productivity 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

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 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.

1.4The price ceiling moves with adoption

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

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:

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 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.

1.5Two 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 $Q\le 0$. 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. The other is a counter, a defense that shields a share $\phi$ 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). 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 and 4). For a company, an exit is a lost customer and a counter may be a second product line.

1.6What each channel means for a company

Table 2 sets the five channels side by side as company business models.

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.

2.1Rivals 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; Lazear and Rosen, 1981; Frank and Cook, 1995). 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). 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, 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, and the Red Queen of Barnett and Hansen, in which rivals’ improvements offset one another while their costs remain (Barnett and Hansen, 1996).

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), 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, 2026d; Marketing Dive, 2026; Walmart Inc., 2026; Maplebear Inc., 2026). 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; Modern Retail, 2024), 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). 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). 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).

2.2Network 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, 1986; Farrell and Saloner, 1985, 1986; Arthur, 1989). 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). In the model this is $\beta x$. With identical costs, known effectiveness and no waiting value, a network-led tipping point occurs where $\mathrm{\Delta }(x_T)=0$ 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); by switching the default on for an installed base it already owns, as Stripe and Shopify did with stablecoin acceptance (Section 4); or by being large enough that its own adoption is the tip. Switching costs then hold the field where it tipped (Klemperer, 1987; Farrell and Klemperer, 2007).

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; U.S. Department of Justice, 2024). 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). 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). 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 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). 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.

2.3A 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; Arrow, 1962). 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). 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). That is a company target, not a measured industry effect. The fulfillment case in Section 7.2 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, 2025); new-energy vehicles were 47.9% of China’s vehicle sales in 2025, 16.5 million of them (CnEVPost, 2026). 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); renewables were 85.6% of the generating capacity the world added in 2025 (TaiyangNews, 2026). 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; inside.lighting, 2024). 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). 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.

2.4Expectations 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); 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). Appendix H.3 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); 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; Walmart Inc., 2026); 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). The surveys discussed in Section 3.2 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; Yeung, 2017). 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); evidence for an economic ratchet requires holdout losses attributable to the changed expectation, which is the row of Table 10 on holdouts losing share.

2.5Gatekeepers 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, $\epsilon \mathrm{\Phi }(x)$, 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 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; Roberti, 2003). 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). 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; CYBRA Corporation, 2026; R.R. Donnelley & Sons, 2024). 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; Impinj, Inc., 2026; edgar.tools, 2026; Avery Dennison Corporation, 2024; Hickey, 2025). 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; Meta Platforms, Inc., 2022; AppLovin Corporation, 2021). 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; PPC Land, 2025). 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 names: a gatekeeper that supplies the capability itself can displace vendors unless they offer additional value.

2.6Who 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). 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). That mechanism is consistent with some consolidation in defense and certificate operations, but does not establish its cause. The opportunities in Section 6 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.

3.1Arms 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 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; Steiner, 2010). 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); 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; Hardy, 2017). 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); ICE’s exchange data and connectivity line alone was $1.03 billion in 2025 (Intercontinental Exchange, Inc., 2026). 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).

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; Associated Press, 2009). 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). 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). 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); 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; BlueGamma, 2026); 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, 2026); and the reported single-terminal price rose to $31,980 a year from January 2025 (NeuGroup, 2024), 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). 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; Semrush Holdings, Inc., 2026a; Adobe Inc. and Semrush Holdings, Inc., 2025; Adobe, 2026); 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. 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, b; eMarketer, 2026), 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; 24/7 Wall St., 2026). Those outcomes do not isolate the effect of venue competition. Retail media, in Section 2.1, provides another example of venues selling placement directly.

The dreadnought race, whose falling ceiling Section 1 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; Wikipedia contributors, 2026a). 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; Grace’s Guide to British Industrial History, 2026). 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; Ballpark Digest, 2020). 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.

3.2A 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. 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, 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), 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 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.); Google folded Gemini into Workspace in January 2025 and Microsoft put Copilot into consumer Microsoft 365 the same week (Google Workspace, 2025; Rognier, 2025); 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; Decagon, 2026). 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 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 gives the mechanism and Appendix H.3 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); in April 2019 Amazon put about $800 million into a single quarter to make one-day delivery the default (The Motley Fool, 2019a); the same-day volumes of Section 2.4 are where that has reached, with 30-minute delivery following in May 2026 (Amazon.com, Inc., 2026b, a). 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), and in 2025 62% said faster shipping decides between retailers at the same price (Radial, Inc., 2025). 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; Investing.com, 2026); Target bought Shipt for $550 million in December 2017 (Target Corporation, 2017); 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, 2023a, 2023b). The independents that sell Prime-like fulfillment to everyone else raised at $1 billion (ShipBob, 2021) and $3 billion (Stord, May 2026) (ShipBob, 2021; TechCrunch, 2026): 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; Bessemer Venture Partners, 2025); 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; Associated Press, 2023); new questions on Stack Overflow fell from 1.34 million in 2022 to 109,000 in 2025 (PPC Land, 2026). 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, that a budget has become compulsory without any gatekeeper saying so.

3.3Coordination 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: 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; U.S. Department of Justice, 2021; Beltran, 2025). 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; JPMorganChase, 2025); 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). 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; Wackett, 2018). 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.

3.4Counters 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); 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); 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; Cloudflare, Inc., 2026). 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, 2026). 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), 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, 2026). Its July 2024 update crashed about 8.5 million Windows machines (TechCrunch, 2024), and the year still ended with recurring revenue up 23% and gross retention of 97% (CrowdStrike Holdings, Inc., 2025): 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: 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). 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); Australia’s under-16 ban took effect on December 10, 2025 and 4.7 million accounts were removed within days (The Register, 2026); and Texas’s app-store law came into force after the Supreme Court declined to block it in July 2026 (Wiley Rein LLP, 2026). A counter that leaves the compliance requirement unmet cannot disarm it (Corollary 4): 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, c; Persona, 2025; Borak, 2026). 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; Biometric Update, 2026b).

3.5Low 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 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; Schechter, 2018). Chrome 68 shipped on July 24, 2018 (Google, 2018): 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; Internet Security Research Group, 2025). 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; O’Brien et al., 2017). 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). 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; Palo Alto Networks, Inc., 2025). 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).

3.6Mandates 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). 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, 2020, 2022); 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; Srivastava, 2025). 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). 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; Lazarus, 2026; Bloomberg Law, 2025b). Drata, founded in 2020, passed $100 million in February 2025 (Drata, 2025).

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). 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, 2016, 2017b). 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). 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). Y2K is the same shape at a larger scale. Gartner put worldwide remediation spending at $300 to $600 billion (Edward W. Kelley, 1998); 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; Cognizant Technology Solutions Corp., 2001). Post-quantum migration (Section 6.5) 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, 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, 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). 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). 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). A French transmission startup would compete with the free and bundled offers described in Section 6.5.

4.1Payoffs 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 keeps these decisions separate.

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 $r$.

4.2Adoption: 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) 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). 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 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 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). 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). 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). Repeat use after all costs is the demand test.

4.3Four Layer 1 cases

4.4Five foundation-model strategies

A foundation model is a reusable model adapted to many downstream tasks (Bommasani and others, 2021). Reuse can support a platform, but the economics depend on what the provider controls besides the model. Table 6 summarizes the comparison; the following examples are dated demonstrations of different strategies, not a ranking of today’s model quality.

4.5The 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). 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). 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). 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). 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). 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). 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.

4.6A worked race and six possible outcomes

Consider one round of the model with $p=1$, $r=2$, $c=0.4$ and $\beta =\epsilon =0$, 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 states conditional branches that may overlap, with no assigned probabilities.

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). Cambridge’s October 2021 account of China’s mining restrictions reports geographic displacement and a partial recovery in global hashrate by August (Rauchs, 2021). 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.

4.7Forecasts 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 specifies sensitivity tests and identifies outcomes for which probabilities remain unestimated.

4.8What 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 records the accounting boundaries and remaining evidence gaps. Section 5 turns these cases into observable signals; the investment memos then ask which of those signals leaves room for a new company.

6.1Own 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, 2026). 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). That is not a controlled failure of AI. It is a reminder that distribution, finance and operating execution are part of the product.

6.2Make 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). 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; Symbotic / SEC Exhibit 99.1, 2025). 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.

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

6.4Negotiation and fraud services require further evidence

6.5Other investment opportunities and benchmarks

7.1Case 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): $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). 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), $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). The launch price clears until 66% of the brand’s rivals have a tool (Figure 4). 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.

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) 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). 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.

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.

7.2Case 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; Symbotic Inc., 2025). 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

With annual volume $N$, incumbent cost $C_0$, supplier price $q$ and other buyer cost $\kappa$, annual operating profits are

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: $\gamma =Ns$, $c=N(q+\kappa )$ 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.

The holdout breaks even at $x^{\ast }=(P_0-C_0)/(\rho s)=52.1\%$. 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. 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 $q\le P(x)-(C_0-s)-\kappa$, 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.

7.3Case 3: a detection layer sold into verification flows

This is the attack–defense branch of Section 4: 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 $\epsilon =0$. For the numerical illustration, assume external expected loss $L=\alpha x/(1-\phi y)$ and incremental avoided loss $z_K=\phi L$. 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, 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; Biometric Update, 2026a). The central scenario sets $x=0.2$, $y=0.1$, $\phi =0.8$ 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).

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). 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. 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.

A simple scale calculation would add Incode’s 4.1 billion checks and Socure’s 2.7 billion requests (Burt, 2025; Biometric Update, 2025). 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.

7.4Case 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, b)) cost it €240,000 of staff time; Billentis’s benchmarks put exceptions at 20 to 30% of paper invoices (Koch, 2017). It already has a compliant platform for the September 2026 mandate, because the accounting suites include one (Section 6.5). 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); 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.

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), 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.

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; Polish Ministry of Finance, 2026; German Federal Ministry of Finance, 2026; European Commission, 2025). 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); TeamSystem sold the suite above that exchange, and the exchange itself was free to use.