Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring

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V. Bhaskar ; Ichiro Obara (2000)
  • Subject:
    arxiv: Physics::Physics and Society | Computer Science::Computer Science and Game Theory
    acm: TheoryofComputation_MISCELLANEOUS

We analyze the infinitely repeated prisoners' dilemma with imperfect private monitoring and discounting. The main contribution of this paper is to construct ``belief-based'' strategies, where a player's continuation strategy is a function only of his beliefs. This simplifies the analysis considerably, and allows us to explicitly construct sequential equilibria for such games, thus enabling us to invoke the one-step deviation principle of dynamic programming. By doing so, we prove that one can approximate the efficient payoff in any prisoners' dilemma game provided that the monitoring is sufficiently accurate. Furthermore, for a class of prisoners' dilemma games, one can approximate every individually rational feasible payoff. These results require that monitoring be sufficiently accurate, but only require a uniform lower bound on the discount rate.
  • References (10)

    [1] V. Bhaskar, The Robustness of Repeated Game Equilibria to Incomplete Payo Information, mimeo, 1999.

    [2] V. Bhaskar, Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems, Review of Economic Studies, 65 (1998) , 135-149.

    [3] Bhaskar, V., and E. van Damme, Moral Hazard and Private Monitoring, mimeo, 1997.

    [4] O. Compte, Communication in repeated games with imperfect private monitoring, Econometrica, 66 (1998),597-626.

    [5] D. Fudenberg, D. Levine and E. Maskin, The Folk Theorem with Imperfect Public Information, Econometrica, 62 (1994), 997-1040.

    [6] J. Harsanyi, Games with Randomly Disturbed Payo s: A New Rationale for Mixed-Strategy Equilibrium Points, International Journal of Game Theory 2 (1973), 1-23.

    [7] M. Kandori, and H. Matsushima, Private Observation, Communication and Collusion, Econometrica, 66 (1998), 627-652.

    [8] G.Mailath, and S. Morris, Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective, mimeo, 1997.

    [9] M. Piccione, The repeated prisoners' dilemma with imperfect private monitoring, mimeo, 1998.

    [10] T. Sekiguchi, E ciency in the Prisoners' Dilemma with Private Monitoring, Journal of Economic Theory,76 (1997), 345-361.

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