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

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  • Ulrich Doraszelski
  • Mark Satterthwaite
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    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, 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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    Bibliographic Info

    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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    References

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    1. Cabral, L. & Riordan, M., 1992. "The Learning Curve, Market Dominance and Predatory Pricing," Papers 39, Boston University - Industry Studies Programme.
    2. MERTENS, Jean-François, . "Stochastic games," CORE Discussion Papers RP -1587, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. Bergin, J & Bernhardt, D, 1995. "Anonymous Sequential Games: Existence and Characterization of Equilibria," Economic Theory, Springer, vol. 5(3), pages 461-89, May.
    5. David Besanko & Ulrich Doraszelski, 2002. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," Computing in Economics and Finance 2002 196, Society for Computational Economics.
    6. 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.
    7. 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.
    8. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, January.
    9. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, Elsevier.
    10. Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, EconWPA, revised 03 Jun 1999.
    11. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    12. 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.
    13. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
    14. repec:att:wimass:9106 is not listed on IDEAS
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    Cited by:
    1. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    2. Ulrich Doraszelski & Kenneth L. Judd, 2005. "Avoiding the Curse of Dimensionality in Dynamic Stochastic Games," NBER Technical Working Papers 0304, National Bureau of Economic Research, Inc.
    3. Jean-Pierre Dubé & Günter Hitsch & Puneet Manchanda, 2005. "An Empirical Model of Advertising Dynamics," Quantitative Marketing and Economics, Springer, vol. 3(2), pages 107-144, June.
    4. Wei Tan, 2006. "The Effects of Taxes and Advertising Restrictions on the Market Structure of the U.S. Cigarette Market," Review of Industrial Organization, Springer, vol. 28(3), pages 231-251, 05.
    5. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2005. "Markov perfect industry dynamics with many firms," Working Paper Series 2005-23, Federal Reserve Bank of San Francisco.
    6. Gabriel Weintraub & C. Lanier Benkard & Ben Van Roy, 2005. "Markov Perfect Industry Dynamics with Many Firms," NBER Working Papers 11900, National Bureau of Economic Research, Inc.
    7. AMIR, Rabah & LAMBSON, Val E., 2004. "Imperfect competition, integer constraints and industry dynamics," CORE Discussion Papers 2004042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Victor Aguirregabiria & Gustavo Vicentini, 2006. "Dynamic Spatial Competition Between Multi-Store Firms," Working Papers tecipa-253, University of Toronto, Department of Economics.
    9. Shi Qi, 2008. "Advertising, Entry Deterrence, and Industry Innovation," Working Papers 2008-1, University of Minnesota, Department of Economics, revised 03 2008.

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