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The folk theorem for repeated games with observation costs

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  • Miyagawa, Eiichi
  • Miyahara, Yasuyuki
  • Sekiguchi, Tadashi

Abstract

The folk theorem literature has been relaxing the assumption on how much players know about each other's past action. Here we consider a general model where players can "buy" precise information. Every period, each player decides whether to pay a cost to accurately observe the actions chosen by other players in the previous period. When a player does not pay the cost, he obtains only imperfect private signals. Observational decisions are unobservable to others. Known strategies such as trigger strategies do not work since they fail to motivate players to pay for information. This paper shows that the folk theorem holds for any level of observation costs. Unlike existing folk theorems with private monitoring, ours imposes virtually no restriction on the nature of costless imperfect signals. The theorem does not use explicit or costless communication, thereby having implications on antitrust laws that rely on evidence of explicit communication. The main message is that accurate observation alone, however costly, enables efficient cooperation in general repeated games.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:139:y:2008:i:1:p:192-221
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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. Yuichi Yamamoto, 2012. "Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under ConditionalIndependence," PIER Working Paper Archive 12-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. 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.
    14. Yasuyuki Miyahara & Tadashi Sekiguchi, 2016. "Finitely Repeated Games with Automatic and Optional Monitoring," Discussion Papers 2016-12, Kobe University, Graduate School of Business Administration.
    15. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    16. Heller, Yuval, 2015. "Instability of Equilibria with Imperfect Private Monitoring," MPRA Paper 64468, University Library of Munich, Germany.
    17. Sonntag, Axel & Zizzo, Daniel John, 2019. "Personal accountability and cooperation in teams," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 428-448.
    18. Awaya, Yu, 2014. "Community enforcement with observation costs," Journal of Economic Theory, Elsevier, vol. 154(C), pages 173-186.
    19. 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.
    20. Lehrer, Ehud & Solan, Eilon, 2018. "High frequency repeated games with costly monitoring," Theoretical Economics, Econometric Society, vol. 13(1), January.
    21. repec:pra:mprapa:64485 is not listed on IDEAS
    22. 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.
    23. 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

    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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