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The Folk Theorem with Private Monitoring

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

Abstract

This paper investigates infinitely repeated prisoner-dilemma games, where the discount factor is less than but close to 1. We assume that monitoring is imperfect and private, and players' private signal structures satisfy the conditional independence. We require almost no conditions concerning the accuracy of private signals. We assume that there exist no public signals and no public randomization devices, and players cannot communicate and use only pure strategies. It is shown that the Folk Theorem holds in that every individually rational feasible payoff vector can be approximated by a sequential equilibrium payoff vector. Moreover, the Folk Theorem holds even if each player has no knowledge of her opponent's private signal structure.

Suggested Citation

  • Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2001cf123
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2001/2001cf123.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part I: anti-folk theorem without communication," Economics Letters, Elsevier, vol. 35(3), pages 253-256, March.
    4. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
    5. Matsushima, Hitoshi, 2001. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," Journal of Economic Theory, Elsevier, vol. 98(1), pages 158-178, May.
    6. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    7. Aoyagi, Masaki, 2002. "Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication," Journal of Economic Theory, Elsevier, vol. 102(1), pages 229-248, January.
    8. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part II: revelation through communication," Economics Letters, Elsevier, vol. 35(3), pages 257-261, March.
    9. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 57-89.
    10. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    11. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 40-69, January.
    12. Matsushima, Hitoshi, 1989. "Efficiency in repeated games with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 48(2), pages 428-442, August.
    13. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
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    Cited by:

    1. Gintis, Herbert, 2004. "Modeling cooperation among self-interested agents: a critique," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 33(6), pages 695-714, December.
    2. Hitoshi Matsushima, 2000. "Small Verifiability in Long-Term Relationships," CIRJE F-Series CIRJE-F-98, CIRJE, Faculty of Economics, University of Tokyo.
    3. Hitoshi Matsushima, 2002. "Repeated Games with Correlated Private Monitoring and Secret Price Cuts," CIRJE F-Series CIRJE-F-154, CIRJE, Faculty of Economics, University of Tokyo.
    4. Sekiguchi, Tadashi, 2002. "Existence of nontrivial equilibria in repeated games with imperfect private monitoring," Games and Economic Behavior, Elsevier, vol. 40(2), pages 299-321, August.

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