Asymmetric Models of Sales

We broaden and develop the classic captive-and-shopper model of sales. Firstly, we allow for asymmetric marginal costs as well as asymmetric captive audiences. These asymmetries jointly determine the identities of the two or more firms we find compete (via randomized sales) to serve shoppers. In a leading case, the prices paid by shoppers fall following a cost rise for the firm that serves most of them. Secondly, we study asymmetric price adjustment opportunities via a two-stage game in which firms may cut but not raise their initial prices. In this setting (and in scenarios with risk aversion or endogenous move order) we predict the play of pure strategies and that a unique firm serves the shoppers. Despite the different pricing predictions across games, firms’ profits are equivalent. Welfare properties depend on whether firm asymmetry is predominantly on the supply side (costs) or on the demand side (captive audiences). Thirdly, we allow firms to choose production technologies via process innovations. One firm innovates distinctly more than others, attains a lower marginal cost, and ultimately serves the shoppers. We connect the distinctive asymmetric pattern of innovations to demand-side asymmetries and the shape of technology opportunity.