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Efficiency in Repeated Games Revisited: The Role of Private Strategies

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  • Michihiro Kandori

    (Faculty of Economics, University of Tokyo)

  • Ichiro Obara

    (Department of Economics, UCLA)

Abstract

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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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-255.

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Length: 45 pages
Date of creation: Dec 2003
Date of revision:
Handle: RePEc:tky:fseres:2003cf255

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  1. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
  2. 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.
  3. George Mailath & Stephen Morris, . "Repeated Games with Almost-Public Monitoring," Penn CARESS Working Papers 6bf0f633ff55148107994e092, Penn Economics Department.
  4. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
  5. 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.
  6. Ichiro Obara, . "The Full Surplus Extraction Theorem with Hidden Actions," UCLA Economics Online Papers 374, UCLA Department of Economics.
  7. Michihiro Kandori & Ichiro Obara, 2006. "Less is more: an observability paradox in repeated games," International Journal of Game Theory, Springer, vol. 34(4), pages 475-493, November.
  8. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
  9. 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.
  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. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  12. 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.
  13. Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society.
  14. Ichiro Obara, . "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics.
  15. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
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