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The Folk Theorem with Private Monitoring

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

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Abstract

This paper investigates infinitely repeated prisoner-dilemma games, where the discount factor is less than but close to 1. We assume that monitoring is imperfect and private, and players' private signal structures satisfy the conditional independence. We require almost no conditions concerning the accuracy of private signals. We assume that there exist no public signals and no public randomization devices, and players cannot communicate and use only pure strategies. It is shown that the Folk Theorem holds in that every individually rational feasible payoff vector can be approximated by a sequential equilibrium payoff vector. Moreover, the Folk Theorem holds even if each player has no knowledge of her opponent's private signal structure.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-123.

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Length: 33 pages
Date of creation: Jul 2001
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Handle: RePEc:tky:fseres:2001cf123

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  1. 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)
  2. George J. Mailath & Stephen Morris, . ""Repeated Games with Imperfect Private Monitoring: Notes on a Coordination Perspective''," CARESS Working Papres 98-07, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
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  3. Radner, Roy, 1985. "Repeated Principal-Agent Games with Discounting," Econometrica, Econometric Society, vol. 53(5), pages 1173-98, September. [Downloadable!] (restricted)
  4. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  5. Jeffrey C. Ely & Juuso Valimaki, 1999. "A Robust Folk Theorem for the Prisoner's Dilemma," Discussion Papers 1264, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  6. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-33, November. [Downloadable!] (restricted)
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  7. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  8. 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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  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. Hitoshi Matsushima, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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  11. Matsushima, Hitoshi, 1989. "Efficiency in repeated games with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 48(2), pages 428-442, August. [Downloadable!] (restricted)
  12. 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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  13. 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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  14. 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!]
  15. 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)
  16. 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.
  17. Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society. [Downloadable!]
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  1. Atila Abdulkadiroglu & Kim-Sau Chung, 2002. "Mechanism design with tacit collusion," Discussion Papers 0102-68, Columbia University, Department of Economics. [Downloadable!]
  2. Kim-Sau Chung, 2002. "Optimal Repeated Auction with Tacit Collusion (joint with Atila Abdulkadiroglu)," Theory workshop papers 357966000000000093, UCLA Department of Economics. [Downloadable!]
  3. Hitoshi Matsushima, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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