Foundations of Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity

In this paper we show that existence of a Markov perfect equilibrium (MPE) in the Ericson & Pakes (1995) model of dynamic competition in an oligopolistic industry with investment, entry, and exit requires admissibility of mixed entry/exit strategies, contrary to their assertion. This is problematic because the existing algorithms cannot cope with mixed strategies. To establish a solid foundation for computing dynamic industry equilibria, we introduce firm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. We show that the resulting game of incomplete information always has a MPE in cutoff entry/exit strategies and is computationally no more demanding than the original game of complete information. In addition, we provide a condition on the model's primitives that ensures that the MPE is in pure investment strategies. Building on this basic existence result, we first show that a symmetric and anonymous MPE exists under appropriate assumptions on the model's primitives. Second, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, MPEs in cutoff entry/exit strategies converge to MPEs in mixed entry/exit strategies of the game of complete information. Finally, we provide the first example of multiple symmetric and anonymous MPEs in this literature