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

  • Ulrich Doraszelski
  • Mark Satterthwaite
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    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, con- trary to Ericson & Pakes's (1995) assertion. This is problematic because the existing algorithms cannot cope with mixed strategies. To establish a firm basis for computing dynamic industry equilibria, we introduce ¯rm 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 cuto® entry/exit strate- gies and is computationally no more demanding than the original game of complete information. Building on our basic existence result, we first show that a symmetric and anonymous MPE exists under appropriate assumptions on the model's primitives. Sec- ond, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, MPEs in cuto® entry/exit strategies converge to MPEs in mixed entry/exit strategies of the game of complete information. Next, we provide a condition on the model's primitives that ensures the existence of a MPE in pure investment strategies. Finally, we provide the first example of multiple symmetric and anonymous MPEs in this literature.

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    Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1383.

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    Date of creation: Nov 2003
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    Handle: RePEc:nwu:cmsems:1383
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    1. repec:att:wimass:9106 is not listed on IDEAS
    2. Luis M.B. Cabral & Michael Riordan, 1992. "The Learning Curve, Market Dominance and Predatory Pricing," Papers 0039, Boston University - Industry Studies Programme.
    3. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
    4. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, Elsevier.
    5. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
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    7. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
    8. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    9. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
    10. Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, EconWPA, revised 03 Jun 1999.
    11. Chakrabarti, Subir K., 2003. "Pure strategy Markov equilibrium in stochastic games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 693-724, September.
    12. Bergin, J & Bernhardt, D, 1995. "Anonymous Sequential Games: Existence and Characterization of Equilibria," Economic Theory, Springer, vol. 5(3), pages 461-89, May.
    13. Gowrisankaran, Gautam, 1999. "Efficient representation of state spaces for some dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1077-1098, August.
    14. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-81, September.
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