Ronayne Week Day #1: How Cost Asymmetry Reshapes Competitive Sales
Myatt & Ronayne: "Asymmetric Models of Sales" American Economic Journal: Microeconomics, Volume 18 (2026)
The dispersion of prices for similar products is a persistent regularity, often rationalised by the canonical captive-and-shopper model of sales. This model presents firms with a fundamental trade-off: pricing high to exploit captive customers or pricing low to capture price-comparing shoppers. David P. Myatt (London Business School) and David Ronayne (ESMT Berlin, Project A04) generalise this foundational model to allow for asymmetries in both production costs and captive audiences within an oligopoly, characterising a unique (equilibrium) prediction in this complex setting.
Their work challenges the established “two to tango” prediction in this setting—that only the two firms with the smallest captive audiences compete through randomised sales. The authors demonstrate that both cost and captive asymmetries determine which firms compete. Unlike symmetric models, there are natural situations where more than two firms use sales by engaging in pairwise battles across different price intervals. This complexity, sometimes resulting in a “thrango” pattern, can occur, for instance, when a firm with a relatively high marginal cost (one that is yet to harness production efficiencies) enters the market but possesses few captives (an undeveloped loyal customer base), generating a “hunger to attract shoppers” with discounted prices. The resulting pricing pattern involves marked dispersion, where a single, most aggressive firm mixes with a succession of fellow-discounting partners (aggression follows from having low costs or few captive customers, making the firm more willing and able to set low sale prices).
A second major contribution explores the endogenous emergence of asymmetry through costly process innovations that reduce a firm’s marginal cost. The analysis reveals that the incentive to reduce marginal cost is distinctly greater for the most aggressive firm. Even if firms are at first symmetric, exactly one firm chooses to innovate more, operates with a lower marginal cost, and becomes the uniquely dominant sale-price setter and supplier of shoppers. This innovation pattern is linked to firm size and technological opportunity. When technological opportunity is strong (meaning per-unit surplus reacts elastically to output), firms with the largest captive audiences innovate sufficiently to achieve the lowest marginal costs, enabling them to compete aggressively for shoppers. This inverse relationship (larger captive bases leading to lower marginal costs) is precisely the condition most conducive to seeing multiple firms engage in randomised sales in equilibrium.
David and David also extend and apply their results to settings including those in which firms pay, for example via costly advertising, to build their loyal-customer bases and how firms may compete in the presence of a “clearinghouse” such as a price comparison website.
Link: Asymmetric Models of Sales
