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

Author

Listed:
  • Ulrich Doraszelski
  • Mark Satterthwaite

Abstract

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

Suggested Citation

  • Ulrich Doraszelski & Mark Satterthwaite, 2004. "Foundations of Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," 2004 Meeting Papers 189, Society for Economic Dynamics.
  • Handle: RePEc:red:sed004:189
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    File URL: http://pubweb.northwestern.edu/~udo390/existence.pdf
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    Cited by:

    1. AMIR, Rabah & GARCIA, Filomena & KNAUFF, Malgorzata, 2006. "Endogenous heterogeneity in strategic models: symmetry-breaking via strategic substitutes and nonconcavities," CORE Discussion Papers 2006008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Davis, Peter, 2006. "Estimation of quantity games in the presence of indivisibilities and heterogeneous firms," Journal of Econometrics, Elsevier, vol. 134(1), pages 187-214, September.

    More about this item

    Keywords

    dynamic competition; Markov perfect equilibrium;

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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