Repeated Games with Observation Costs

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Repeated Games with Observation Costs

Author Info

Eiichi Miyagawa () (Columbia University - Department of Economics)
Yasuyuki Miyahara () (Columbia University)
Tadashi Sekiguchi () (Kobe University)

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Eiichi Miyagawa

Abstract

This paper analyzes repeated games in which it is possible for players to observe the other players' past actions without noise but it is costly. One's observation decision itself is not observable to the other players, and this private nature of monitoring activity makes it difficult to give the players proper incentives to monitor each other. We provide a sufficient condition for a feasible payoff vector to be approximated by a sequential equilibrium when the observation costs are sufficiently small. We then show that this result generates an approximate Folk Theorem for a wide class of repeated games with observation costs. The Folk Theorem holds for a variant of prisoners' dilemma, partnership games, and any games in which the players have an ability to "burn" small amounts of their own payoffs.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0203-14.

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Length: 38 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:clu:wpaper:0203-14

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Paper
- Eiichi Miyagawa & Yasuyuki Miyahara & Tadashi Sekiguchi, 2003. "Repeated Games with Observation Costs," KIER Working Papers 565, Kyoto University, Institute of Economic Research.

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.:

Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June. [Downloadable!] (restricted)
Kandori, Michihiro, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Blackwell Publishing, vol. 59(1), pages 63-80, January. [Downloadable!] (restricted)
Compte, Olivier, 2002. "On Failing to Cooperate When Monitoring Is Private," Journal of Economic Theory, Elsevier, vol. 102(1), pages 151-188, January. [Downloadable!] (restricted)
Aoyagi, Masaki, 2002. "Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication," Journal of Economic Theory, Elsevier, vol. 102(1), pages 229-248, January. [Downloadable!] (restricted)
Bhaskar, V. & van Damme, Eric, 2002. "Moral Hazard and Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 16-39, January. [Downloadable!] (restricted)
Other versions:
- V. Bhaskar & Eric van Damme, 1998. "Moral Hazard and Private Monitoring," Game Theory and Information 9809004, EconWPA. [Downloadable!]
Drew Fudenberg & David K Levine, 1999. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 81, David K. Levine. [Downloadable!]
Other versions:
- D. Fudenberg & D. K. Levine, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 627, David K. Levine. [Downloadable!]
- Fudenberg, D. & Levine, D.K., 1991. "Efficiency and Obsevability with Long-Run and Short-Run Players," Working papers 591, Massachusetts Institute of Technology (MIT), Department of Economics.
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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!]
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!]
Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March. [Downloadable!] (restricted)
Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
Matsushima, Hitoshi, 1991. "On the theory of repeated games with private information : Part I: anti-folk theorem without communication," Economics Letters, Elsevier, vol. 35(3), pages 253-256, March. [Downloadable!] (restricted)
Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-22, July. [Downloadable!] (restricted)
Ben-Porath, Elchanan & Kahneman, Michael, 1996. "Communication in Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 70(2), pages 281-297, August. [Downloadable!] (restricted)
Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January. [Downloadable!] (restricted)
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!]
- George J Mailath & Stephen Morris, 2001. "Repeated Games with Almost-Public Monitoring," NajEcon Working Paper Reviews 625018000000000257, www.najecon.org. [Downloadable!]
- 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.
- 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!]
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)
Other versions:
- V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department. [Downloadable!]
- 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. [Downloadable!]
Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May. [Downloadable!] (restricted)
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)
Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
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)

Full references

Cited by:
(explanations, 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.)

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.
Eiichi Miyagawa & Yasuyuki Miyahara & Tadashi Sekiguchi, 2004. "The folk theorem for repeated games with observation costs," Discussion Papers 0405-12, Columbia University, Department of Economics. [Downloadable!]
Other versions:
- Eiichi Miyagawa & Yasuyuki Miyahara & Tadashi Sekiguchi, 2004. "The Folk Theorem for Repeated Games with Observation Costs," KIER Working Papers 597, Kyoto University, Institute of Economic Research.

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