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Secret Correlation in Repeated Games with Imperfect Monitoring

Author

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  • Olivier Gossner

    (Paris-Jourdan Sciences Economiques, UMR CNRS-EHESS-ENPC-ENS 8545, 48 Boulevard Jourdan, 75014 Paris, France and MEDS, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, Illinois 60208-2001)

  • Tristan Tomala

    (CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris, Cedex 16, France)

Abstract

We characterize the maximum payoff that a team can guarantee against another in a class of repeated games with imperfect monitoring. Our result relies on the optimal tradeoff for the team between optimization of stage payoffs and generation of signals for future correlation.

Suggested Citation

  • Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
  • Handle: RePEc:inm:ormoor:v:32:y:2007:i:2:p:413-424
    DOI: 10.1287/moor.1060.0248
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    References listed on IDEAS

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    1. 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.
    2. JÊrÆme Renault & Tristan Tomala, 1998. "Repeated proximity games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 539-559.
    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. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Olivier Gossner & Tristan Tomala, 2012. "Repeated Games with Complete Information," Post-Print hal-00712075, HAL.
    6. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 431-456.
    7. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October.
    8. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    9. 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.
    10. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    11. Ehud Lehrer & Sylvain Sorin, 1992. "A Uniform Tauberian Theorem in Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 303-307, May.
    12. O. Gossner, 2000. "Sharing a long secret in a few public words," THEMA Working Papers 2000-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
    14. GOSSNER, Olivier, 1998. "Repeated games played by cryptographically sophisticated players," LIDAM Discussion Papers CORE 1998035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    16. 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.
    17. 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.
    18. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
    19. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    20. Yair Goldberg, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring: The Need for Nonstationary Strategies," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 425-435, May.
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    Cited by:

    1. Deb, Joyee & González-Díaz, Julio & Renault, Jérôme, 2016. "Uniform folk theorems in repeated anonymous random matching games," Games and Economic Behavior, Elsevier, vol. 100(C), pages 1-23.
    2. Bavly, Gilad & Peretz, Ron, 2019. "Limits of correlation in repeated games with bounded memory," Games and Economic Behavior, Elsevier, vol. 115(C), pages 131-145.
    3. Valizadeh, Mehrdad & Gohari, Amin, 2019. "Playing games with bounded entropy," Games and Economic Behavior, Elsevier, vol. 115(C), pages 363-380.
    4. Gossner, Olivier & Hörner, Johannes, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 63-84, January.
    5. Jérôme Renault & Tristan Tomala, 2011. "General Properties of Long-Run Supergames," Dynamic Games and Applications, Springer, vol. 1(2), pages 319-350, June.
    6. Heng Liu, 2017. "Correlation and unmediated cheap talk in repeated games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1037-1069, November.
    7. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    8. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series dp579, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    10. Olivier Gossner & Penélope Hernández & Ron Peretz, 2016. "The complexity of interacting automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 461-496, March.
    11. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 867-890, November.
    12. Bavly, Gilad & Neyman, Abraham, 2014. "Online concealed correlation and bounded rationality," Games and Economic Behavior, Elsevier, vol. 88(C), pages 71-89.

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