A dynamic entry and price game with capacity indivisibility

Strategic market interaction is here modelled as a two-stage game in which potential entrants choose capacities and active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are substantial economies of scale. In the simplest version of the model assuming a single production technique, the equilibrium of the game is shown to depend on the market size - namely, on total demand at a price equal to the minimum average cost - relative to the firm minimum efficient scale: if the market is sufficiently large, then the competitive price (the minimum of average cost) emerges at a subgame-perfect equilibrium of the game; if the market is not that large, then the firms randomize in prices on the equilibrium path of the game. The role of the market size for the competitive outcome is even more important for the case of two production techniques.