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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 & Juuso Valimaki, 1999. "A Robust Folk Theorem for the Prisoner's Dilemma," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1264, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Cripps,M.W. & Mailath,G.J. & Samuelson,L., 2004. "Disappearing private reputations in long-run relationships," Working papers, Wisconsin Madison - Social Systems 5, Wisconsin Madison - Social Systems.
  3. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, Econometric Society, vol. 74(2), pages 499-519, 03.
  4. Stephen Morris & George J Mailath, 2005. "Coordination Failure in Repeated Games with Almost-Public Monitoring," 2005 Meeting Papers, Society for Economic Dynamics 25, Society for Economic Dynamics.
  5. Compte, Olivier, 2002. "On Failing to Cooperate When Monitoring Is Private," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 151-188, January.
  6. Glen Ellison, 2010. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Levine's Working Paper Archive 631, David K. Levine.
  7. George Mailath & Stephen Morris, . "Repeated Games with Almost-Public Monitoring," Penn CARESS Working Papers, Penn Economics Department 6bf0f633ff55148107994e092, Penn Economics Department.
  8. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 76(2), pages 345-361, October.
  9. Harold L. Cole & Narayana R. Kocherlakota, 2001. "Finite memory and imperfect monitoring," Staff Report, Federal Reserve Bank of Minneapolis 287, Federal Reserve Bank of Minneapolis.
  10. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
  11. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  12. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, 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, Elsevier, vol. 102(1), pages 70-83, January.
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Cited by:
  1. Andrew Postlewaite & Olivier Compte, 2008. "Repeated Relationships with Limits on Information Processing," PIER Working Paper Archive 08-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. Josh Cherry & Lones Smith, 2009. "Unattainable Payoffs for Repeated Games of Private Monitoring," Levine's Working Paper Archive 814577000000000284, David K. Levine.
  3. Michihiro Kandori & Ichiro Obara, 2007. "Finite State Equilibria in Dynamic Games," 2007 Meeting Papers, Society for Economic Dynamics 253, Society for Economic Dynamics.
  4. Olivier Compte & Andrew Postlewaite, 2010. "Plausible Cooperation,Third Version," PIER Working Paper Archive 13-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2012.

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