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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 (we describe a simple strategy profile that is a perfect public equilibrium of a repeated prisoner's dilemma with imperfect public monitoring, and yet is not an equilibrium for arbitrarily close games with private monitoring). If a perfect public equilibrium 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 David K. Levine in its series Levine's Working Paper Archive with number 2107.

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Date of creation: 09 Sep 1999
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Handle: RePEc:cla:levarc:2107

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  1. Mailath George J. & Matthews Steven A. & Sekiguchi Tadashi, 2002. "Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 2(1), pages 1-23, June.
  2. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  3. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-255, CIRJE, Faculty of Economics, University of Tokyo.
  4. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 40-69, January.
  5. Damme, E.E.C. van & Bhaskar, V., 1997. "Moral hazard and private monitoring," Discussion Paper, Tilburg University, Center for Economic Research 1997-98, Tilburg University, Center for Economic Research.
  6. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 627-652, May.
  7. Massimiliano Amarante, 2003. "Recursive structure and equilibria in games with private monitoring," Economic Theory, Springer, Springer, vol. 22(2), pages 353-374, 09.
  8. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer, Springer, vol. 20(3), pages 211-26.
  9. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  10. Compte, Olivier, 2002. "On Failing to Cooperate When Monitoring Is Private," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 151-188, January.
  11. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part I: anti-folk theorem without communication," Economics Letters, Elsevier, Elsevier, vol. 35(3), pages 253-256, March.
  12. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 597-626, May.
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