A Dynamic Entry and Price Game With Capacity Indivisibility

Abstract

Strategic market interaction is here modelled as a two-stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long-run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently 'large'), then the competitive price emerges at a subgame-perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques. . I wish to thank an anonymous referee, Paul Madden, and various seminar participants for helpful comments and suggestions. The usual disclaimers apply. 1 The assumption of concave demand, made by Kreps and Scheinkman (1983), is often relaxed in the subsequent literature, for example by assuming (strict) concavity of the revenue function of a capacityunconstrained monopolist (see, e.g., Davidson and Deneckere, 1986), without affecting most of the results.2 And total capacity differs from total demand at a price equal to marginal cost. 10 The lowest output that minimizes long-run average cost.