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The Folk Theorem for Repeated Games with Observation Costs

Author

Listed:
  • Eiichi Miyagawa

    (Department of Economics, Columbia University)

  • Yasuyuki Miyahara

    (Graduate School of Business Administration, Kobe University)

  • Tadashi Sekiguchi

    (Institute of Economic Research, Kyoto University)

Abstract
This paper studies repeated games with private monitoring where players make optimal decisions with respect to costly monitoring activities, just as they do with respect to stage-game actions. We consider the case where each player can observe other players' current-period actions accurately only if he incurs a certain level of disutility. In every period, players decide whether to monitor other players and whom to monitor. We show that the folk theorem holds for any finite stage game that satisfies the standard full dimensionality condition and for any level of observation costs. The theorem also holds under general structures of costless private signals and does not require explicit communication among the players. Therefore, tacit collusion can attain efficient outcomes in general repeated games with private monitoring if perfect private monitoring is merely feasible, however costly it may be.

Suggested Citation

  • 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.
    • Handle: RePEc:kyo:wpaper:597
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    2. repec:kbb:dpaper:2011-44 is not listed on IDEAS
    3. Flesch, János & Perea, Andrés, 2009. "Repeated games with voluntary information purchase," Games and Economic Behavior, Elsevier, vol. 66(1), pages 126-145, May.
    4. Goeschl, Timo & Jarke, Johannes, 2014. "Trust, but verify? When trustworthiness is observable only through (costly) monitoring," WiSo-HH Working Paper Series 20, University of Hamburg, Faculty of Business, Economics and Social Sciences, WISO Research Laboratory.
    5. Hino, Yoshifumi, 2018. "A folk theorem in infinitely repeated prisoner's dilemma with small observation cost," MPRA Paper 90381, University Library of Munich, Germany.
    6. McLean, Richard & Obara, Ichiro & Postlewaite, Andrew, 2014. "Robustness of public equilibria in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 153(C), pages 191-212.
    7. 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.
    8. Miklós-Thal, Jeanine & Schumacher, Heiner, 2013. "The value of recommendations," Games and Economic Behavior, Elsevier, vol. 79(C), pages 132-147.
    9. Miyahara, Yasuyuki & Sekiguchi, Tadashi, 2013. "Finitely repeated games with monitoring options," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1929-1952.
    10. David Rahman, 2012. "But Who Will Monitor the Monitor?," American Economic Review, American Economic Association, vol. 102(6), pages 2767-2797, October.
    11. Fujiwara-Greve, Takako & Okuno-Fujiwara, Masahiro & Suzuki, Nobue, 2012. "Voluntarily separable repeated Prisonerʼs Dilemma with reference letters," Games and Economic Behavior, Elsevier, vol. 74(2), pages 504-516.
    12. Sawa, Ryoji, 2021. "A stochastic stability analysis with observation errors in normal form games," Games and Economic Behavior, Elsevier, vol. 129(C), pages 570-589.
    13. Yasuyuki Miyahara & Tadashi Sekiguchi, 2016. "Finitely Repeated Games with Automatic and Optional Monitoring," Discussion Papers 2016-12, Kobe University, Graduate School of Business Administration.
    14. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    15. Heller, Yuval, 2015. "Instability of Equilibria with Imperfect Private Monitoring," MPRA Paper 64468, University Library of Munich, Germany.
    16. Sonntag, Axel & Zizzo, Daniel John, 2019. "Personal accountability and cooperation in teams," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 428-448.
    17. Awaya, Yu, 2014. "Community enforcement with observation costs," Journal of Economic Theory, Elsevier, vol. 154(C), pages 173-186.
    18. Goeschl, Timo & Jarke, Johannes, 2017. "Trust, but verify? Monitoring, inspection costs, and opportunism under limited observability," Journal of Economic Behavior & Organization, Elsevier, vol. 142(C), pages 320-330.
    19. Lehrer, Ehud & Solan, Eilon, 2018. "High frequency repeated games with costly monitoring," Theoretical Economics, Econometric Society, vol. 13(1), January.
    20. repec:pra:mprapa:64485 is not listed on IDEAS
    21. 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.
    22. Flesch, J. & Perea ý Monsuwé, A., 2007. "Repeated games with voluntary information purchase," Research Memorandum 057, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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    More about this item

    Keywords

    Repeated games; private monitoring; costly monitoring; tacit collusion; communication; secret price cuts;
    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
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • K21 - Law and Economics - - Regulation and Business Law - - - Antitrust Law
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L40 - Industrial Organization - - Antitrust Issues and Policies - - - General

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