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Repeated Games with Private Monitoring: Two Players

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Author Info
Hitoshi Matsushima (Faculty of Economics, University of Tokyo)

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Abstract

We investigate two-player infinitely repeated games where the discount factor is less than but close to unity. Monitoring is private and players cannot communicate. We require no condition concerning the accuracy of players' monitoring technology. We show the folk theorem for the prisoners' dilemma with conditional independence. We also investigate more general games where players' private signals are correlated only through an unobservable macro shock. We show that efficiency is sustainable for generic private signal structures when the size of the set of private signals is sufficiently large. Finally, we show that cartel collusion is sustainable in price-setting duopoly.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-242.

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Length: 40 pages
Date of creation: Oct 2003
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Handle: RePEc:tky:fseres:2003cf242

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January. [Downloadable!] (restricted)
  2. Radner, Roy, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," Review of Economic Studies, Blackwell Publishing, vol. 53(1), pages 43-57, January. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
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  4. Radner, Roy, 1985. "Repeated Principal-Agent Games with Discounting," Econometrica, Econometric Society, vol. 53(5), pages 1173-98, September. [Downloadable!] (restricted)
  5. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  6. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  7. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, UCLA Department of Economics. [Downloadable!]
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  8. Hitoshi Matsushima, 2002. "Repeated Games with Correlated Private Monitoring and Secret Price Cuts," CIRJE F-Series CIRJE-F-154, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  9. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, 03. [Downloadable!] (restricted)
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  10. George Mailath & Stephen Morris, . ""Repeated Games with Almost-Public Monitoring''," CARESS Working Papres 99-09, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
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  11. Aoyagi, Masaki, 2002. "Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication," Journal of Economic Theory, Elsevier, vol. 102(1), pages 229-248, January. [Downloadable!] (restricted)
  12. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
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  14. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  15. Matsushima, Hitoshi, 2001. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," Journal of Economic Theory, Elsevier, vol. 98(1), pages 158-178, May. [Downloadable!] (restricted)
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  16. Hitoshi Matsushima, 2000. "The Folk Theorem with Private Monitoring and Uniform Sustainability," CIRJE F-Series CIRJE-F-84, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  17. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October. [Downloadable!] (restricted)
  18. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer, vol. 18(1), pages 57-89.
  19. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January. [Downloadable!] (restricted)
  20. Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society. [Downloadable!]
  21. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. George J Mailath & Stephen Morris, 2006. "Coordination Failure in Repeated Games with Almost-Public Monitoring," Levine's Bibliography 122247000000001105, UCLA Department of Economics. [Downloadable!]
    Other versions:
  2. Wojciech Olszewski, 2007. "A Simple Exposition of Belief-Free Equilibria in Repeated Games," Economics Bulletin, Economics Bulletin, vol. 3(58), pages 1-16. [Downloadable!]
  3. Ichiro Obara, . "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. Michihiro Kandori, 2006. "Repeated Games, Entry in The New Palgrave Dictionary of Economics, 2nd Edition," CIRJE F-Series CIRJE-F-395, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. Michihiro Kandori, 2007. "Chicken in Prison: Weakly Belief-Free Equilibria in Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-491, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  6. Ichiro Obara, 2005. "Folk Theorem with Communication," UCLA Economics Online Papers 366, UCLA Department of Economics. [Downloadable!]
    Other versions:
  7. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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