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A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games

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

Abstract

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. George Mailath & Stephen Morris, . "Repeated Games with Almost-Public Monitoring," Penn CARESS Working Papers, Penn Economics Department 6bf0f633ff55148107994e092, Penn Economics Department.
  2. George Mailath & Wojciech Olszewski, 2008. "Folk theorems with Bounded Recall under(Almost) Perfect Monitoring," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
  4. Roger Lagunoff & Akihiko Matsu, . "Asynchronous Choice in Repeated Coordination Games," Penn CARESS Working Papers, Penn Economics Department 23a1aa461811b8f48b0334f6e, Penn Economics Department.
  5. V.V. Bhaskar, 2007. "Purification in the Infinitely-Repeated Prisoners' Dilemma," 2007 Meeting Papers, Society for Economic Dynamics 136, Society for Economic Dynamics.
  6. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 103(2), pages 334-350, April.
  7. Bhaskar, V., 1994. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Papers, Tilburg - Center for Economic Research 9485, Tilburg - Center for Economic Research.
  8. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 97-109, January.
  9. Mailath,G.J. & Samuelson,L., 1998. "Who wants a good reputation?," Working papers, Wisconsin Madison - Social Systems 19, Wisconsin Madison - Social Systems.
  10. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  14. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195300796, October.
  15. Fudenberg, Drew & Levine, David K, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Econometrica, Econometric Society, Econometric Society, vol. 57(4), pages 759-78, July.
  16. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, Econometric Society, vol. 56(3), pages 571-99, May.
  17. Abhinay Muthoo & Kenneth Shepsle, 2010. "Information, institutions and constitutional arrangements," Public Choice, Springer, Springer, vol. 144(1), pages 1-36, July.
  18. Roger Lagunoff & Akihiko Matsui, . ""An 'Anti-Folk Theorem' for a Class of Asynchronously Repeated Games''," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences 95-15, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
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  22. Livshits, Igor, 2002. "On non-existence of pure strategy Markov perfect equilibrium," Economics Letters, Elsevier, Elsevier, vol. 76(3), pages 393-396, August.
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Cited by:
  1. Herings P.J.J. & Meshalkin A. & Predtetchinski A., 2012. "A Folk Theorem for Bargaining Games," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Marina Azzimonti, 2011. "Barriers to Investment in Polarized Societies," American Economic Review, American Economic Association, American Economic Association, vol. 101(5), pages 2182-2204, August.
  3. Hannu Salonen & Hannu Vartiainen, 2011. "On the Existence of Markov Perfect Equilibria in Perfect Information Games," Discussion Papers, Aboa Centre for Economics 68, Aboa Centre for Economics.

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