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We generalize the captive-and-shopper model of sales to allow asymmetries in production costs and captive audiences in an oligopoly. Both kinds of asymmetry determine the firms that compete (via randomized sales) to serve the price-comparing shoppers, while other firms exploit their captive audiences. In contrast to a model with symmetric costs (but asymmetric captive audiences) there are natural situations in which more than two firms use sales by engaging in pairwise battles across different price intervals. We then study the choice of production technologies via costly process innovations. A distinctive asymmetry emerges endogenously: one firm innovates more and becomes the dominant supplier of shoppers. The pattern of innovations connects to the size of firms’ captive bases and the shape of technological opportunity. We also provide a trio of extensions to consider costly acquisitions of captives and shoppers, and captives’ choice of captor.

Copyright ©2025 by the American Economic Association.

Large, generalist, technology firms—so-called “big-tech” firms—powerful in their primary market, routinely enter secondary markets consisting of specialist firms. Naturally, one might expect a specialist firm to be fiercely protective of its data as a way to maintain its market position in the secondary market. Counter to this intuition, we demonstrate that a specialist firm willingly shares its market data with an intruding generalist. We do so by developing a model of cross-market competition in which the data collected via consumer usage in one market can improve product quality in another. We show that a specialist firm shares its data to strategically create codependence between the two firms, thereby softening competition and transforming the generalist firm from a traditional competitor into a coopetitor. For the generalist intruder, data from the specialist firm substitute for its own investments in product quality in the secondary market. As such, the act of sharing data makes the generalist a stakeholder in the data collected by the specialist, and consequently in the specialist’s continued success. Moreover, although the firms benefit from data sharing, consumers can be worse off from weakened price competition and lower investments in innovation. Our results have managerial and policy implications, notably on account of backlash against data collection and the market power of big-tech firms.

© 2026, INFORMS

@The Author(s) 2025

© 2026 The Author(s), under exclusive license to Springer Nature Switzerland AG

We study a Bertrand oligopoly with asymmetric costs in which each seller has some “captive” buyers. In the limit as captive buyers vanish, the lowest-cost firm sells to all buyers at a price equal to the second-lowest marginal cost. However, the closest competing price arises from non-degenerate mixed strategies, firms play exclusively undominated strategies, and with positive probability all but one firm sets the monopoly price.

With permission of Elsevier