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A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games

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  • V. Bhaskar

    ()
    (Department of Economics, University College, London)

  • George J. Mailath

    ()
    (Department of Economics, University of Pennsylvania)

  • Stephen Morris

    ()
    (Department of Economics, Princeton University)

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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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 12-043.

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Length: 29 pages
Date of creation: 29 Oct 2012
Date of revision:
Handle: RePEc:pen:papers:12-043

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Keywords: Markov; bounded recall; purification;

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References

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  1. George J. Mailath & Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring," PIER Working Paper Archive 08-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
  3. V. Bhaskar & George J. Mailath & Stephen Morris, 2006. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Cowles Foundation Discussion Papers 1571, Cowles Foundation for Research in Economics, Yale University.
  4. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, Octomber.
  5. Drew Fudenberg & David Levine, 1987. "Reputation and Equilibrium Selection in Games With a Patient Player," Working papers 461, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Bhaskar, V., 1994. "Informational Constraints and the Overlapping Generations Model : Folk and Anti-Folk Theorems," Discussion Paper 1994-85, Tilburg University, Center for Economic Research.
  7. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Game Theory and Information 9707002, EconWPA.
  8. Akihiko Matsui & Kiminori Matsuyama, 1991. "An Approach to Equilibrium Selection," Discussion Papers 1065, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. 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.
  10. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
  11. 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.
  12. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
  13. Mailath, George J & Samuelson, Larry, 2001. "Who Wants a Good Reputation?," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 415-41, April.
  14. Morris, Stephen Morris & Takashi Ui, 2002. "Best Response Equivalence," Cowles Foundation Discussion Papers 1377, Cowles Foundation for Research in Economics, Yale University.
  15. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
  16. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
  17. 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.
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  22. Livshits, Igor, 2002. "On non-existence of pure strategy Markov perfect equilibrium," Economics Letters, Elsevier, vol. 76(3), pages 393-396, August.
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Citations

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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. Marina Azzimonti, 2011. "Barriers to Investment in Polarized Societies," American Economic Review, American Economic Association, vol. 101(5), pages 2182-2204, August.
  3. 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).

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