Efficiency in Repeated Games Revisited: The Role of Private Strategies

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Efficiency in Repeated Games Revisited: The Role of Private Strategies

Author Info

Michihiro Kandori (Faculty of Economics, University of Tokyo)
Ichiro Obara (Department of Economics, UCLA)

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Ichiro Obara

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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Publisher 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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Article
- 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)
Paper
- Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics. [Downloadable!]
- Michihiro Kandori & Ichiro Obara, 2004. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Levine's Bibliography 122247000000000055, UCLA Department of Economics. [Downloadable!]

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-01-05 (All new papers)
NEP-MAC-2004-01-05 (Macroeconomics)

References listed on IDEAS
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.:

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. [Downloadable!]
Other versions:
- Michihiro Kandori & Ichiro Obara, 2006. "Less is more: An Observability Paradox in Repeated Games," Levine's Bibliography 321307000000000342, UCLA Department of Economics. [Downloadable!]
- 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. [Downloadable!] (restricted)
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)
Other versions:
- Abreu, D. & Milgrom, P. & Pearce, D., 1990. "Information And Timing In Repeated Partnerships," Papers e-90-14, Stanford - Hoover Institution.
- David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation, Yale University. [Downloadable!]
Ichiro Obara, . "Endogenous Monitoring," UCLA Economics Online Papers 398, UCLA Department of Economics. [Downloadable!]
Other versions:
- Michihiro Kandori & Ichiro Obara, 2004. "Endogeous Monitoring," 2004 Meeting Papers 752, Society for Economic Dynamics.
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.
Other versions:
- 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. [Downloadable!]
- George J. Mailath & Stephen Morris, 2000. "Repeated Games with Almost-Public Monitoring," Econometric Society World Congress 2000 Contributed Papers 0661, Econometric Society. [Downloadable!]
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- George J. Mailath & Stephen Morris, 1999. "Repeated Games with Almost-Public Monitoring," Cowles Foundation Discussion Papers 1236, Cowles Foundation, Yale University. [Downloadable!]
- George Mailath & Stephen Morris, . "Repeated Games with Almost-Public Monitoring," Penn CARESS Working Papers 6bf0f633ff55148107994e092, Penn Economics Department. [Downloadable!]
- George J Mailath & Stephen Morris, 1999. "Repeated Games with Almost Public Monitoring," Levine's Working Paper Archive 2107, David K. Levine. [Downloadable!]
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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)
Other versions:
- Green, Edward J. & Porter, Robert H., 1982. "Noncooperative Collusion Under Imperfect Price Information," Working Papers 367, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
Ehud Lehrer, 1988. "Internal Correlation in Repeated Games," Discussion Papers 800, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Other versions:
- Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
Ichiro Obara, 2000. "Private Strategy and Efficiency: Repeated Partnership Games Revisited," Econometric Society World Congress 2000 Contributed Papers 1449, Econometric Society. [Downloadable!]
Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September. [Downloadable!] (restricted)
Other versions:
- Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine. [Downloadable!]
- 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.
- Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine. [Downloadable!]
Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January. [Downloadable!] (restricted)
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)
Other versions:
- Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society. [Downloadable!]
- 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!]
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, Blackwell Publishing, vol. 53(1), pages 59-69, January. [Downloadable!] (restricted)
Ichiro Obara, . "The Full Surplus Extraction Theorem with Hidden Actions," UCLA Economics Online Papers 374, UCLA Department of Economics. [Downloadable!]
Other versions:
- Ichiro Obara, 2006. "The Full Surplus Extraction Theorem with Hidden Actions," Levine's Bibliography 122247000000001206, UCLA Department of Economics. [Downloadable!]
- Ichiro Obara, 2007. "The Full Surplus Extraction Theorem with Hidden Actions," Levine's Bibliography 843644000000000137, UCLA Department of Economics. [Downloadable!]
Massimiliano Amarante, 2002. "Equivalence of public mixed-strategies and private behavior strategies in games with public monitoring," Discussion Papers 0102-49, Columbia University, Department of Economics. [Downloadable!]
repec:bep:thecon:v:2:y:2002:i:1:p:1046-1046 is not listed on IDEAS
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. [Downloadable!]
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)

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