Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity

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Abstract
We provide a general model of dynamic competition in an oligopolistic industry with investment, entry, and exit. To ensure that there exists a computationally tractable Markov perfect equilibrium, we introduce flrm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. Our game of incomplete information always has an equilibrium in cutofi entry/exit strategies. In contrast, the existence of an equilibrium in the Ericson & Pakes (1995) model of in- dustry dynamics requires admissibility of mixed entry/exit strategies, contrary to the assertion in their paper, that existing algorithms cannot cope with. In addition, we provide a condition on the model's primitives that ensures that the equilibrium is in pure investment strategies. Building on this basic existence result, we flrst show that a symmetric equilibrium exists under appropriate assumptions on the model's primi- tives. Second, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, equilibria in cutofi entry/exit strategies converge to equilibria in mixed entry/exit strategies of the game of complete information. Finally, we provide the flrst example of multiple symmetric equilibria in this literature.