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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.

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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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  1. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
  2. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
  3. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
  4. V. Bhaskar & George J. Mailath & Stephen Morris, 2004. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Cowles Foundation Discussion Papers 1451, Cowles Foundation for Research in Economics, Yale University.
  5. Drew Fudenberg & David K. Levine, 1995. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 103, David K. Levine.
  6. 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.
  7. 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.
  8. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  9. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. 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.
  11. 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.
  12. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 135-149.
  13. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
  14. repec:oup:restud:v:68:y:2001:i:2:p:415-41 is not listed on IDEAS
  15. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
  16. Livshits, Igor, 2002. "On non-existence of pure strategy Markov perfect equilibrium," Economics Letters, Elsevier, vol. 76(3), pages 393-396, August.
  17. repec:oup:restud:v:60:y:1993:i:2:p:463-77 is not listed on IDEAS
  18. repec:oup:restud:v:65:y:1998:i:1:p:135-49 is not listed on IDEAS
  19. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, July.
  20. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, July.
  21. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
  22. Abhinay Muthoo & Kenneth Shepsle, 2010. "Information, institutions and constitutional arrangements," Public Choice, Springer, vol. 144(1), pages 1-36, July.
  23. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
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