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A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games


  • V. Bhaskar

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

  • George J. Mailath

    () (Department of Economics, University of Pennsylvania)

  • Stephen Morris

    () (Department of Economics, Princeton University)


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.

Suggested Citation

  • 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.
  • Handle: RePEc:pen:papers:12-043

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    References listed on IDEAS

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    13. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters,in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111 World Scientific Publishing Co. Pte. Ltd..
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    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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. P. Jean-Jacques Herings & Harold Houba, 2016. "The Condorcet paradox revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 141-186, June.
    3. Marina Azzimonti, 2011. "Barriers to Investment in Polarized Societies," American Economic Review, American Economic Association, vol. 101(5), pages 2182-2204, August.
    4. 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).
    5. Matros, Alexander & Smirnov, Vladimir, 2016. "Duplicative search," Games and Economic Behavior, Elsevier, vol. 99(C), pages 1-22.

    More about this item


    Markov; bounded recall; purification;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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