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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. Luis M.B. Cabral & Michael Riordan, 1992. "The Learning Curve, Market Dominance and Predatory Pricing," Papers 0039, Boston University - Industry Studies Programme.
    2. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
    3. 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.
    4. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, Spring.
    5. MERTENS, Jean-François, . "Stochastic games," CORE Discussion Papers RP -1587, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. 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.
    8. 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.
    9. Ariel Pakes, 2000. "A Framework for Applied Dynamic Analysis in I.O," NBER Working Papers 8024, National Bureau of Economic Research, Inc.
    10. repec:att:wimass:9106 is not listed on IDEAS
    11. Bergin, J & Bernhardt, D, 1995. "Anonymous Sequential Games: Existence and Characterization of Equilibria," Economic Theory, Springer, vol. 5(3), pages 461-89, May.
    12. Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, EconWPA, revised 03 Jun 1999.
    13. 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.
    14. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
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    Cited by:
    1. 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.
    2. 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.
    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. Pedro Mira & Victor Aguirregabiria, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers wp2007_0711, CEMFI.
    5. Ulrich Doraszelski & Kenneth L. Judd, 2005. "Avoiding the Curse of Dimensionality in Dynamic Stochastic Games," Harvard Institute of Economic Research Working Papers 2059, Harvard - Institute of Economic Research.
    6. Victor Aguirregabiria & Gustavo Vicentini, 2012. "Dynamic Spatial Competition Between Multi-Store Firms," Working Papers tecipa-457, University of Toronto, Department of Economics.
    7. Amir, Rabah & Lambson, Val E., 2007. "Imperfect competition, integer constraints and industry dynamics," International Journal of Industrial Organization, Elsevier, vol. 25(2), pages 261-274, April.
    8. 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.
    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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