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A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification

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  • Doraszelski, Ulrich
  • Escobar, Juan

Abstract

This paper develops a theory of regular Markov perfect equilibria in dynamic stochastic games. We show that almost all dynamic stochastic games have a finite number of locally isolated Markov perfect equilibria that are all regular. These equilibria are essential and strongly stable. Moreover, they all admit purification.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6805.

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Date of creation: Apr 2008
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Handle: RePEc:cpr:ceprdp:6805
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Keywords: computation; dynamic stochastic games; essentiality; estimation; finiteness; genericity; Markov perfect equilibrium; purifiability; regularity; repeated games; strong stability;

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Find related papers by JEL classification:
  • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
  • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
  • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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  1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, 06.
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  11. Victor Aguirregabiria & Pedro Mira, 1999. "Swapping the Nested Fixed-Point Algorithm: a Class of Estimators for Discrete Markov Decision Models," Computing in Economics and Finance 1999 332, Society for Computational Economics.
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  24. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, vol. 45(2), pages 369-374, November.
  25. 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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Cited by:

  1. Hannu Salonen & Hannu Vartiainen, 2011. "On the Existence of Markov Perfect Equilibria in Perfect Information Games," Discussion Papers 68, Aboa Centre for Economics.
  2. John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A Dynamic Model of Leap-Frogging Investments and Bertrand Price Competition," 2012 Meeting Papers 370, Society for Economic Dynamics.
  3. Victor Aguirregabiria, 2009. "A Method for Implementing Counterfactual Experiments in Models with Multiple Equilibria," Working Papers tecipa-381, University of Toronto, Department of Economics.
  4. Breitmoser, Yves, 2012. "Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma," MPRA Paper 41731, University Library of Munich, Germany.
  5. Demian Pouzo & Ignacio Presno, 2012. "Sovereign default risk and uncertainty premia," Working Papers 12-11, Federal Reserve Bank of Boston.
  6. Ignacio Esponda & Demian Pouzo, 2014. "An Equilibrium Framework for Players with Misspecified Models," Papers 1411.1152, arXiv.org.
  7. V. Bhaskar & George J. Mailath & Stephen Morris, 2012. "A Foundation for Markov Equilibria with Finite Social Memory," PIER Working Paper Archive 12-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Fedor Iskhakov & John Rust & Bertel Schjerning & Jean-Robert Tyran, 2014. "Recursive Lexicographical Search: Finding all Markov Perfect Equilibria of Finite State Directional Dynamic Games," Discussion Papers 14-16, University of Copenhagen. Department of Economics.
  9. John Duggan, 2011. "Noisy Stochastic Games," RCER Working Papers 562, University of Rochester - Center for Economic Research (RCER).
  10. Ron Borkovsky & Ulrich Doraszelski & Yaroslav Kryukov, 2012. "A dynamic quality ladder model with entry and exit: Exploring the equilibrium correspondence using the homotopy method," Quantitative Marketing and Economics, Springer, vol. 10(2), pages 197-229, June.
  11. Victor Aguirregabiria & Pedro Mira, 2013. "Identification of Games of Incomplete Information with Multiple Equilibria and Common Unobserved Heterogeneity," Working Papers tecipa-474, University of Toronto, Department of Economics.
  12. Escobar, Juan F., 2013. "Equilibrium analysis of dynamic models of imperfect competition," International Journal of Industrial Organization, Elsevier, vol. 31(1), pages 92-101.
  13. Fedor Iskhakov & John Rust & Bertel Schjerning, 2013. "The Dynamics of Bertrand Price Competition with Cost-Reducing Investments," Discussion Papers 13-05, University of Copenhagen. Department of Economics.
  14. V. Bhaskar & George J. Mailath & Stephen Morris, 2012. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 12-043, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  15. Wang, Hefei, 2012. "Costly information transmission in continuous time with implications for credit rating announcements," Journal of Economic Dynamics and Control, Elsevier, vol. 36(9), pages 1402-1413.
  16. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
  17. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).

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