Computable Markov-perfect industry dynamics

Authors


  • We are indebted to Lanier Benkard, David Besanko, Michaela Draganska, Dino Gerardi, Gautam Gowrisankaran, Ken Judd, Patricia Langohr, Andy Skrzypacz, and Eilon Solan for useful discussions. The comments of the editor, Joe Harrington, and two anonymous referees greatly helped to improve the article. Satterthwaite acknowledges gratefully that this material is based upon work supported by the National Science Foundation under grant no. 0121541 and by the General Motors Research Center for Strategy in Management at Kellogg. Doraszelski is grateful for the hospitality of the Hoover Institution during the academic year 2006/07 and financial support from the National Science Foundation under grant no. 0615615.

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 firm 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 cutoff entry/exit strategies. In contrast, the existence of an equilibrium in the Ericson and Pakes' model of industry dynamics requires admissibility of mixed entry/exit strategies, contrary to the assertion in their article, 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 first show that a symmetric equilibrium 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, equilibria in cutoff entry/exit strategies converge to equilibria in mixed entry/exit strategies of the game of complete information.

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