Entry, Exit and Coordination with Mixed Strategies

A dynamic entry and exit game is studied, where, following Dixit and Shapiro (1986), firms play symmetric mixed strategies. Due to coordination considerations, the value of incumbency is increasing in the number of incumbent firms (up to the point where there is excess capacity). This feature of the problem complicates the study of a mixed strategy equilibrium, because the relevant payoffs are not monotonic functions of the randomization probabilities, as they are often implicitly assumed to be. It is shown that the payoff functions have an interesting dynamic structure, which allows the complete characterization of the equilibrium.