Markov Perfect Industry Dynamics With Many Firms

Authors

  • Gabriel Y. Weintraub,

    1. Decisions, Risk, and Operations Division, Columbia Business School, Columbia University, Uris Hall 402, 3022 Broadway, New York, NY 10027, U.S.A.; gweintraub@columbia.edu,
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  • C. Lanier Benkard,

    1. Graduate School of Business, Stanford University, 518 Memorial Way, Stanford, CA 94305-5015, U.S.A.; lanierb@stanford.edu,
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  • Benjamin Van Roy

    1. Dept. of Management Science and Engineering, Stanford University, 380 Panama Way, Stanford, CA 94305-4026, U.S.A.; bvr@stanford.edu
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    • We have had very helpful conversations with José Blanchet, Uli Doraszelski, Liran Einav, Hugo Hopenhayn, Ken Judd, Jon Levin, and Ariel Pakes, as well as seminar participants at Berkeley, Columbia, Duke, IIOC, Iowa, Informs, Kellogg, Minnesota, NYU, SITE, Stanford, Rochester, UCLA, UIUC, University of Chile, UT Austin, and Yale. We thank the editor and three anonymous referees for valuable suggestions. This research was supported by the Federal Reserve Bank of San Francisco, General Motors, the Lillie Fund, the National Science Foundation, and the Office of Naval Research.


Abstract

We propose an approximation method for analyzing Ericson and Pakes (1995)-style dynamic models of imperfect competition. We define a new equilibrium concept that we call oblivious equilibrium, in which each firm is assumed to make decisions based only on its own state and knowledge of the long-run average industry state, but where firms ignore current information about competitors' states. The great advantage of oblivious equilibria is that they are much easier to compute than are Markov perfect equilibria. Moreover, we show that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain “light-tail” condition, then oblivious equilibria closely approximate Markov perfect equilibria. This theorem justifies using oblivious equilibria to analyze Markov perfect industry dynamics in Ericson and Pakes (1995)-style models with many firms.

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