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Characterizing belief-free review-strategy equilibrium payoffs under conditional independence

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  • Yamamoto, Yuichi

Abstract

This paper proposes and studies a tractable subset of Nash equilibria, belief-free review-strategy equilibria, in repeated games with private monitoring. The payoff set of this class of equilibria is characterized in the limit as the discount factor converges to one for games where players observe statistically independent signals. As an application, we develop a simple sufficient condition for the existence of asymptotically efficient equilibria, and establish a folk theorem for N-player prisonerʼs dilemma. All these results are robust to a perturbation of the signal distribution, and hence remain true even under almost-independent monitoring.

Suggested Citation

  • Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:1998-2027
    DOI: 10.1016/j.jet.2012.05.016
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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. Johannes Hörner & Wojciech Olszewski, 2006. "The Folk Theorem for Games with Private Almost-Perfect Monitoring," Econometrica, Econometric Society, vol. 74(6), pages 1499-1544, November.
    3. Joseph E. Harrington & Andrzej Skrzypacz, 2011. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," American Economic Review, American Economic Association, vol. 101(6), pages 2425-2449, October.
    4. Drew Fudenberg & David K. Levine, 2008. "The Nash-threats folk theorem with communication and approximate common knowledge in two player games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 15, pages 331-343, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    7. Drew Fudenberg & David K. Levine, 2008. "Efficiency and Observability with Long-Run and Short-Run Players," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 13, pages 275-307, World Scientific Publishing Co. Pte. Ltd..
    8. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    9. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
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    11. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    12. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    13. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    14. 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.
    15. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    16. Radner, Roy, 1985. "Repeated Principal-Agent Games with Discounting," Econometrica, Econometric Society, vol. 53(5), pages 1173-1198, September.
    17. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    18. 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.
    19. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    20. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 191-217.
    21. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    22. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    23. 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.
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    Cited by:

    1. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.
    2. Jehiel, Philippe & Samuelson, Larry, 2023. "The analogical foundations of cooperation," Journal of Economic Theory, Elsevier, vol. 208(C).
    3. Ghidoni, Riccardo & Calzolari, Giacomo & Casari, Marco, 2017. "Climate change: Behavioral responses from extreme events and delayed damages," Energy Economics, Elsevier, vol. 68(S1), pages 103-115.
    4. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    5. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    6. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    7. Hino, Yoshifumi, 2018. "A folk theorem in infinitely repeated prisoner's dilemma with small observation cost," MPRA Paper 90381, University Library of Munich, Germany.
    8. 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.
    9. Heller, Yuval, 2015. "Instability of Equilibria with Imperfect Private Monitoring," MPRA Paper 64468, University Library of Munich, Germany.
    10. repec:pra:mprapa:64485 is not listed on IDEAS
    11. Joyee Deb & Takuo Sugaya & Alexander Wolitzky, 2020. "The Folk Theorem in Repeated Games With Anonymous Random Matching," Econometrica, Econometric Society, vol. 88(3), pages 917-964, May.
    12. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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    More about this item

    Keywords

    Repeated game; Private monitoring; Conditional independence; Belief-free review-strategy equilibrium; Prisonerʼs 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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