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The Folk Theorem with Private Monitoring

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  • Hitoshi Matsushima

    (Faculty of Economics, University of Tokyo)

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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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2001/2001cf123.pdf
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Bibliographic Info

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
Date of revision:
Handle: RePEc:tky:fseres:2001cf123

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References

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  1. Hitoshi Matsushima, 1998. "Multimarket Contact, Imperfect Monitoring, and Implicit Collusion," CIRJE F-Series CIRJE-F-24, CIRJE, Faculty of Economics, University of Tokyo.
  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. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo.
  4. V. Bhaskar & Ichiro Obara, 2000. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Econometric Society World Congress 2000 Contributed Papers 1330, Econometric Society.
  5. Fudenberg, D. & Levine, D.K. & Maskin, E., 1989. "The Folk Theorem With Inperfect Public Information," Working papers 523, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. 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.
  7. Hitoshi Matsushima, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo.
  8. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
  9. 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.
  10. Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part II: revelation through communication," Economics Letters, Elsevier, vol. 35(3), pages 257-261, March.
  11. Matsushima, Hitoshi, 1989. "Efficiency in repeated games with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 48(2), pages 428-442, August.
  12. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
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Cited by:
  1. Hitoshi Matsushima, 2000. "Small Verifiability in Long-Term Relationships," CIRJE F-Series CIRJE-F-98, CIRJE, Faculty of Economics, University of Tokyo.
  2. 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.
  3. Hitoshi Matsushima, 2001. "The Folk Theorem with Private Monitoring," CIRJE F-Series CIRJE-F-123, CIRJE, Faculty of Economics, University of Tokyo.

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