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Efficiency in Repeated Games Revisited: The Role of Private Strategies

  • Michihiro Kandori

    (Department of Economics)

  • Ichiro Obara

    (University of Tokyo)

Most theoretical or applied research on repeated games with imperfect monitoring has restricted attention to public strategies; strategies that only depend on history of publicly observable signals, and perfect public equilibrium (PPE); sequential equilibrium in public strategies. The present paper sheds light on the role of private strategies; strategies that depend on players' own actions in the past as well as observed public signals. Our main finding is that players can sometimes make better use of information by using private strategies and efficiency in repeated games can often be drastically improved. We illustrate this for both games with a small signal space (Anti-folk theorem example) and games with a large signal space, for which the Folk Theorem holds. Our private strategy can be regarded as a machine which consists of two states. We provide two di erent characterizations of our two-state machine equilibrium for general two-person repeated games with imperfect public monitoring.

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Paper provided by UCLA Department of Economics in its series UCLA Economics Working Papers with number 826.

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Date of creation: 01 Jan 2003
Date of revision:
Handle: RePEc:cla:uclawp:826
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  1. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  2. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  3. Ichiro Obara, . "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics.
  4. Michihiro Kandori, 1999. "Check Your Partners' Behavior by Randomization: New Efficiency Results on Repeated Games with Imperfect Monitoring," CIRJE F-Series CIRJE-F-45, CIRJE, Faculty of Economics, University of Tokyo.
  5. George J. Mailath & Stephen Morris, 1999. "Repeated Games with Almost-Public Monitoring," CARESS Working Papres almost-pub, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences, revised 01 Sep 2000.
  6. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
  7. Michihiro Kandori & Ichiro Obara, 2003. "Less is More: An Observability Paradox in Repeated Gamess," CIRJE F-Series CIRJE-F-246, CIRJE, Faculty of Economics, University of Tokyo.
  8. George J. Mailath & Steven A. Matthews & Tadashi Sekiguchi, 2001. "Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring," Penn CARESS Working Papers e7304519c6d1562163dbaf181, Penn Economics Department.
  9. Ichiro Obara, 2007. "The Full Surplus Extraction Theorem with Hidden Actions," Levine's Bibliography 843644000000000137, UCLA Department of Economics.
  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. David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation for Research in Economics, Yale University.
  12. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  13. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  14. Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society.
  15. Radner, Roy & Myerson, Roger & Maskin, Eric, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 59-69, January.
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