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A folk theorem in infinitely repeated prisoner's dilemma with small observation cost

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  • Hino, Yoshifumi

Abstract

We consider an infinitely repeated prisoner's dilemma under costly monitoring. If a player observes his opponent, then he pays an observation cost and knows the action chosen by his opponent. If a player does not observe his opponent, he cannot obtain any information about his opponent's action. Furthermore, no player can statistically identify the observational decision of his opponent. We prove efficiency without any signals. Then, we extend the idea with a public randomization device and we present a folk theorem for a sufficiently small observation cost when players are sufficiently patient.

Suggested Citation

  • Hino, Yoshifumi, 2018. "A folk theorem in infinitely repeated prisoner's dilemma with small observation cost," MPRA Paper 96010, University Library of Munich, Germany, revised 13 Sep 2019.
    • Handle: RePEc:pra:mprapa:96010
    as

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    File URL: https://mpra.ub.uni-muenchen.de/96010/6/MPRA_paper_96010.pdf
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    References listed on IDEAS

    as
    1. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    2. Bhaskar, V. & van Damme, Eric, 2002. "Moral Hazard and Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 16-39, January.
    3. Johannes Hörner & Wojciech Olszewski, 2009. "How Robust is the Folk Theorem?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1773-1814.
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    8. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    9. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
    10. Glenn Ellison, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(3), pages 567-588.
    11. Miyagawa, Eiichi & Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2008. "The folk theorem for repeated games with observation costs," Journal of Economic Theory, Elsevier, vol. 139(1), pages 192-221, March.
    12. Yamamoto, Yuichi, 2007. "Efficiency results in N player games with imperfect private monitoring," Journal of Economic Theory, Elsevier, vol. 135(1), pages 382-413, July.
    13. Hino, Yoshifumi, 2019. "An efficiency result in a repeated prisoner’s dilemma game under costly observation with nonpublic randomization," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 47-53.
    14. 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.
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    More about this item

    Keywords

    Costly observation; Efficiency; Folk theorem; Prisoner's dilemma;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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