Bertrand-Edgeworth Duopoly: Multi-Market

Abstract

Nowadays most firms compete for multiple separate markets as opposed to a single market. Extant IO works mainly focus on these firms' cooperative behavior, assuming away their capacity constraints and studying the effect of potential multi-market retaliation upon these firms' collusive incentive. With the assumption that the firms have a single capacity constraint, which applies to the multiple separate markets they compete for, this paper sheds light on the effects of the capacity constraint and demand linkages across different markets in the context of a non-cooperative duopoly model. Different from the classical single market capacity-constrained price competition theory, which has three regions divided by three different types of price equilibria as we adjust the firms' capacity constraints, two asymmetric markets capacity-constrained price competition has five regions divided by five different types of price equilibria as we adjust the firms' capacity constraints. An interesting result is that the firms do not always set higher price in the big or rich market than the small or poor market. When the capacities are endogenously determined, we find that the classical single market result (Kreps and Scheinkman 1983) that the Cournot-Nash quantity is a subgame perfect Nash equilibrium cannot hold for the two asymmetric markets competition model. In sum, the results of the asymmetric markets capacity-constrained price competition may yield different implications on merger, price leadership, and collusive behavior.