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A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games

  • V. Bhaskar
  • George J. Mailathy
  • Stephen Morris

We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical non-cooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents’ payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player’s strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one long-run player, all purifiable equilibria are Markov.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 814577000000000178.

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Date of creation: 19 Mar 2009
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Handle: RePEc:cla:levarc:814577000000000178
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  1. Bhaskar, V, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Wiley Blackwell, vol. 65(1), pages 135-49, January.
  2. V. Bhaskar & George J. Mailath & Stephen Morris, 2004. "Purification in the Infinitely-Repeated Prisoners’ Dilemma," PIER Working Paper Archive 04-004, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
  4. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  5. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
  6. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
  7. Fudenberg, Drew & Levine, David K, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Econometrica, Econometric Society, vol. 57(4), pages 759-78, July.
  8. George J. Mailath & Larry Samuelson, . "Who Wants a Good Reputation?," Penn CARESS Working Papers a3e3219aee004bd237f8112f9, Penn Economics Department.
  9. Abhinay Muthoo & Kenneth Shepsle, 2010. "Information, institutions and constitutional arrangements," Public Choice, Springer, vol. 144(1), pages 1-36, July.
  10. Juan Escobar & Ulrich Doraszelski, 2008. "A Theory of Regular Markov Perfect Equilibria\\in Dynamic Stochastic Games: Genericity, Stability, and Purification," 2008 Meeting Papers 453, Society for Economic Dynamics.
  11. George J. Mailath & Stephen Morris, 2000. "Repeated Games with Almost-Public Monitoring," Econometric Society World Congress 2000 Contributed Papers 0661, Econometric Society.
  12. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
  13. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 463-77, April.
  14. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
  15. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
  17. Livshits, Igor, 2002. "On non-existence of pure strategy Markov perfect equilibrium," Economics Letters, Elsevier, vol. 76(3), pages 393-396, August.
  18. Roger Lagunoff & Akihiko Matsui, . ""An 'Anti-Folk Theorem' for a Class of Asynchronously Repeated Games''," CARESS Working Papres 95-15, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  19. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  20. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
  21. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-99, May.
  22. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
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