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Private Monitoring with Infinite Histories

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  • Christopher Phelan
  • Andrzej Skrzypacz

Abstract

This paper develops new recursive methods for studying stationary sequential equilibria in games with private monitoring. We first consider games where play has occurred forever into the past and develop methods for analyzing a large class of stationary strategies, where the main restriction is that the strategy can be represented as a finite automaton. For a subset of this class, strategies which depend only on the players’ signals in the last k periods, these methods allow the construction of all pure strategy equilibria. We then show that each sequential equilibrium in a game with infinite histories defines a correlated equilibrium for a game with a start date and derive simple necessary and sufficient conditions for determining if an arbitrary correlation device yields a correlated equilibrium. This allows, for games with a start date, the construction of all pure strategy sequential equilibria in this subclass.

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Bibliographic Info

Paper provided by www.najecon.org in its series NajEcon Working Paper Reviews with number 843644000000000079.

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Date of creation: 02 Jun 2007
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Handle: RePEc:cla:najeco:843644000000000079

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References

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  1. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, 03.
  2. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics.
  3. George J. Mailath & Stephen Morris, 2004. "Coordination Failure in Repeated Games with Almost-Public Monitoring," Cowles Foundation Discussion Papers 1479, Cowles Foundation for Research in Economics, Yale University.
  4. George J Mailath & Stephen Morris, 1999. "Repeated Games with Almost Public Monitoring," Levine's Working Paper Archive 2107, David K. Levine.
  5. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
  6. Martin W. Cripps & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," PIER Working Paper Archive 04-031, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2004.
  7. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  8. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  9. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  10. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
  11. Compte, Olivier, 2002. "On Failing to Cooperate When Monitoring Is Private," Journal of Economic Theory, Elsevier, vol. 102(1), pages 151-188, January.
  12. 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.
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Cited by:
  1. Olivier Compte & Andrew Postlewaite, 2008. "Repeated Relationships with Limits on Information Processing," Levine's Working Paper Archive 122247000000002307, David K. Levine.
  2. Andrew Postlewaite & Olivier Compte, 2009. "Plausible Cooperation, Second Version," PIER Working Paper Archive 10-039, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 16 Dec 2010.
  3. Josh Cherry & Lones Smith, 2009. "Unattainable Payoffs for Repeated Games of Private Monitoring," Levine's Working Paper Archive 814577000000000284, David K. Levine.
  4. Michihiro Kandori & Ichiro Obara, 2007. "Finite State Equilibria in Dynamic Games," 2007 Meeting Papers 253, Society for Economic Dynamics.

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