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

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  • 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, 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.

Suggested Citation

  • Ulrich Doraszelski & Mark Satterthwaite, 2003. "Foundations of Markov-Perfect Industry Dynamics. Existence, Purification, and Multiplicity," Discussion Papers 1383, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1383
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    1. 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.
    2. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter.
    3. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 30, pages 1887-1966, Elsevier.
    4. Bergin, J & Bernhardt, D, 1995. "Anonymous Sequential Games: Existence and Characterization of Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 461-489, May.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    6. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, October.
    7. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-1281, September.
    8. Patricia Langohr, 2003. "Competitive Convergence and Divergence: Capability and Position Dynamics," Computing in Economics and Finance 2003 229, Society for Computational Economics.
    9. Rust, J., 1991. "Estimation of dynamic Structural Models: Problems and Prospects Part I : Discrete Decision Processes," Working papers 9106, Wisconsin Madison - Social Systems.
    10. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    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. Cabral, Luis M B & Riordan, Michael H, 1994. "The Learning Curve, Market Dominance, and Predatory Pricing," Econometrica, Econometric Society, vol. 62(5), pages 1115-1140, September.
    13. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, October.
    14. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, vol. 68(5), pages 1231-1248, September.
    15. 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.
    16. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    17. 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.
    18. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
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    3. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    4. Michael Cohen & Adam Rabinowitz, 2012. "An Empirical Analysis of Equilibrium Pricing and Advertising in the Ready-To-Eat Cereal Market," Working Papers 15, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    5. 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.
    6. Griffith, Rachel & Dubois, Pierre & O'Connell, Martin, 2014. "The Effects of Banning Advertising on Demand, Supply and Welfare: Structural Estimation on a Junk Food Market," CEPR Discussion Papers 9942, C.E.P.R. Discussion Papers.
    7. Dalida Kadyrzhanova & Antonio Falato, 2008. "Optimal CEO Incentives and Industry Dynamics," 2008 Meeting Papers 880, Society for Economic Dynamics.
    8. Victor Aguirregabiria & Gustavo Vicentini, 2006. "Dynamic Spatial Competition Between Multi-Store Firms," Working Papers tecipa-253, University of Toronto, Department of Economics.
    9. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Markov Perfect Industry Dynamics with Many Firms," Research Papers 1919r, Stanford University, Graduate School of Business.
    10. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    11. Pierre Dubois & Rachel Griffith & Martin O’Connell, 2018. "The Effects of Banning Advertising in Junk Food Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 396-436.
    12. Jean-Pierre Dubé & Günter Hitsch & Puneet Manchanda, 2005. "An Empirical Model of Advertising Dynamics," Quantitative Marketing and Economics (QME), Springer, vol. 3(2), pages 107-144, June.
    13. Shi Qi, 2008. "Advertising, Entry Deterrence, and Industry Innovation," Working Papers 2008-1, University of Minnesota, Department of Economics, revised 03 2008.
    14. 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.
    15. Ulrich Doraszelski & Sarit Markovich, 2004. "Advertising Dynamics and Competitive Advantage," Computing in Economics and Finance 2004 61, Society for Computational Economics.
    16. C. Lanier Benkard & Benjamin Van Roy & Gabriel Y. Weintraub, 2005. "Markov perfect industry dynamics with many firms," Working Paper Series 2005-23, Federal Reserve Bank of San Francisco.
    17. 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;The Industrial Organization Society, vol. 28(3), pages 231-251, May.
    18. Shi Qi, 2008. "Advertising, Entry Deterrence, and Industry Innovation," Levine's Working Paper Archive 122247000000002137, David K. Levine.

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