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

Author

Listed:
  • 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.

Suggested Citation

  • V. Bhaskar & George J. Mailath & Stephen Morris, 2006. "Purification in the Infinitely-Repeated Prisoners’ Dilemma, Second Version," PIER Working Paper Archive 07-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Aug 2007.
    • Handle: RePEc:pen:papers:07-024
    as

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    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/working-papers/07-024.pdf
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    References listed on IDEAS

    as
    1. Bhaskar, V. & van Damme, Eric, 2002. "Moral Hazard and Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 16-39, January.
    2. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 135-149.
    3. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    4. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, vol. 45(2), pages 369-374, November.
    5. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    6. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, March.
    7. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
    8. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Purification; belief-free equilibria; repeated games;
    All these keywords.

    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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