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Repeated Games with Almost-Public Monitoring

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  • George J. Mailath
  • Stephen Morris

Abstract

In repeated games with imperfect public monitoring, players can use public signals to coordinate their behavior perfectly, and thus support cooperative outcomes with the threat of punishments. But with even a small amount of private monitoring, players' private histories may lead them to have sufficiently different views of the world that such coordination on punishments is no longer possible. Even though grim trigger is a public perfect equilibrium (PPE) in games with public monitoring, it often fails to be an equilibrium in arbitrarily close games with private monitoring. If a PPE has players' behavior conditioned only on finite histories, then it induces an equilibrium in all close-by games with private monitoring. This implies a folk theorem for repeated games with almost-public almost-perfect monitoring.

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Paper provided by University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences in its series CARESS Working Papres with number almost-pub.

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Date of creation: Aug 1999
Date of revision: 01 Sep 2000
Handle: RePEc:wop:pennca:almost-pub

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  1. 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.
  2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  3. Compte, Olivier, 2002. "On Failing to Cooperate When Monitoring Is Private," Journal of Economic Theory, Elsevier, vol. 102(1), pages 151-188, January.
  4. V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department.
  5. George J. Mailath & Steven A. Matthews & Tadashi Sekiguchi, 2001. "Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring," Penn CARESS Working Papers e7304519c6d1562163dbaf181, Penn Economics Department.
  6. V. Bhaskar & Eric van Damme, 1998. "Moral Hazard and Private Monitoring," Game Theory and Information 9809004, EconWPA.
  7. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics.
  8. Massimiliano Amarante, 2003. "Recursive structure and equilibria in games with private monitoring," Economic Theory, Springer, vol. 22(2), pages 353-374, 09.
  9. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  10. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  11. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer, vol. 20(3), pages 211-26.
  12. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
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