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Purification in the Infinitely-Repeated Prisoners’ Dilemma, Second Version

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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

This paper investigates the Harsanyi (1973)-purifiability of mixed strategies in the repeated prisoners’ dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of one-period memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners’ dilemma with private monitoring. We find that any such strategy profile is not the limit of one-period memory equilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable.

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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 07-024.

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Length: 23 pages
Date of creation: 13 Jul 2006
Date of revision: 20 Aug 2007
Handle: RePEc:pen:papers:07-024

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Keywords: Purification; belief-free equilibria; repeated games;

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  1. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-255, CIRJE, Faculty of Economics, University of Tokyo.
  2. Damme, E.E.C. van & Bhaskar, V., 1997. "Moral hazard and private monitoring," Discussion Paper, Tilburg University, Center for Economic Research 1997-98, Tilburg University, Center for Economic Research.
  3. 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.
  4. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
  5. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  6. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(2), pages 369-374, November.
  7. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 84-105, January.
  8. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 76(2), pages 345-361, October.
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