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

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  • V. Bhaskar
  • Ichiro Obara

Abstract

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.

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Paper provided by Penn Economics Department in its series Penn CARESS Working Papers with number d93eb6f40c65728f9e1a7b11423f1641.

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Handle: RePEc:cla:penntw:d93eb6f40c65728f9e1a7b11423f1641

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  1. George J. Mailath & Stephen Morris, 1998. "Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective," CARESS Working Papres imp-mon, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  2. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  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. Damme, E.E.C. van & Bhaskar, V., 1997. "Moral hazard and private monitoring," Discussion Paper 1997-98, Tilburg University, Center for Economic Research.
  5. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  6. Bhaskar, V., 1994. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Papers 9485, Tilburg - Center for Economic Research.
  7. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  8. Ichiro Obara, . "The Repeated Prisoner's Dilemma with Private Monitoring: a N-player case," CARESS Working Papres 99-13, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  9. Ellison, Glenn, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Review of Economic Studies, Wiley Blackwell, vol. 61(3), pages 567-88, July.
  10. Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society.
  11. 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.
  12. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  13. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
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