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Bounding equilibrium payoffs in repeated games with private monitoring

Author

Listed:
  • Sugaya, Takuo

    (Graduate School of Business, Stanford University)

  • Wolitzky, Alexander

    (Department of Economics, MIT)

Abstract

We provide a simple sufficient condition for the existence of a recursive upper bound on (the Pareto frontier of) the sequential equilibrium payoff set at a fixed discount factor in two-player repeated games with imperfect private monitoring. The bounding set is the sequential equilibrium payoff set with perfect monitoring and a mediator. We show that this bounding set admits a simple recursive characterization, which nonetheless necessarily involves the use of private strategies. Under our condition, this set describes precisely those payoff vectors that arise in equilibrium for some private monitoring structure, if either non-stationary monitoring or communication is allowed.

Suggested Citation

  • Sugaya, Takuo & Wolitzky, Alexander, 2017. "Bounding equilibrium payoffs in repeated games with private monitoring," Theoretical Economics, Econometric Society, vol. 12(2), May.
    • Handle: RePEc:the:publsh:2270
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    References listed on IDEAS

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    1. 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.
    2. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    3. 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..
    4. William Fuchs, 2007. "Contracting with Repeated Moral Hazard and Private Evaluations," American Economic Review, American Economic Association, vol. 97(4), pages 1432-1448, September.
    5. repec:dau:papers:123456789/6103 is not listed on IDEAS
    6. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    7. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    8. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-948, July.
    9. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    10. Massimiliano Amarante, 2003. "Recursive structure and equilibria in games with private monitoring," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 353-374, September.
    11. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    12. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, September.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, September.
    13. Sekiguchi, Tadashi, 2002. "Existence of nontrivial equilibria in repeated games with imperfect private monitoring," Games and Economic Behavior, Elsevier, vol. 40(2), pages 299-321, August.
    14. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    15. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
    16. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    17. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    18. Renault, Jerome & Tomala, Tristan, 2004. "Communication equilibrium payoffs in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 49(2), pages 313-344, November.
    19. Mailath George J. & Matthews Steven A. & Sekiguchi Tadashi, 2002. "Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-23, June.
    20. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    21. Ehud Lehrer, 1992. "Correlated Equilibria in Two-Player Repeated Games with Nonobservable Actions," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 175-199, February.
    22. repec:dau:papers:123456789/6102 is not listed on IDEAS
    23. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Cited by:

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    2. Hörner, Johannes & Takahashi, Satoru, 2016. "How fast do equilibrium payoff sets converge in repeated games?," Journal of Economic Theory, Elsevier, vol. 165(C), pages 332-359.
    3. David Spector, 2017. "Cheap talk, monitoring and collusion," Working Papers hal-01975642, HAL.
    4. David Spector, 2022. "Cheap Talk, Monitoring and Collusion," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 60(2), pages 193-216, March.
    5. Sugaya, Takuo & Wolitzky, Alexander, 2018. "Bounding payoffs in repeated games with private monitoring: n-player games," Journal of Economic Theory, Elsevier, vol. 175(C), pages 58-87.
    6. Awaya Yu & Fukai Hiroki, 2020. "Monitoring and coordination for essentiality of money," The B.E. Journal of Macroeconomics, De Gruyter, vol. 20(1), pages 1-7, January.
    7. Daehyun Kim, 2019. "Comparison of information structures in stochastic games with imperfect public monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 267-285, March.

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    More about this item

    Keywords

    Repeated games; private monitoring;

    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

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