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Correlated Equilibrium and Private Monitoring

  • Jeffrey C. Ely

In repeated games, simple strategies such as Grim Trigger, while strict equilibria when monitoring is perfect, can fail to be even approximate Nash equilibria when monitoring is private, yet arbitrarily close to perfect. That is, they fail to be robust to private monitoring. In this paper, it is shown that for a class of repeated Prisoner's Dilemma games these strategies, when viewed as (degenerate) correlated equilibria, are robust. In particular, even when monitoring is private and conditionally independent, as the signalling noise goes to zero, there is a sequence of correlated equilibria converging to the Grim Trigger strategies. The correlation device uses an information structure akin to that of Rubinstein's e-mail game.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1265.

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Date of creation: Apr 2000
Date of revision:
Handle: RePEc:nwu:cmsems:1265
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  1. George J Mailath & Stephen Morris, 2001. "Repeated Games with Almost-Public Monitoring," Levine's Working Paper Archive 625018000000000257, David K. Levine.
  2. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  3. Bhaskar, V. & van Damme, E.E.C., 2002. "Moral hazard and private monitoring," Other publications TiSEM 432fc615-feb9-4c90-8a14-e, Tilburg University, School of Economics and Management.
  4. 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.
  5. 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.
  6. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  7. 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.
  8. Bhaskar, V, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Wiley Blackwell, vol. 65(1), pages 135-49, January.
  9. Kyle Bagwell, 1992. "Commitment and Observability in Games," Discussion Papers 1014, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
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