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Communication games, sequential equilibrium, and mediators

Author

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  • Geffner, Ivan
  • Halpern, Joseph Y.

Abstract

We consider k-resilient sequential equilibria, strategy profiles where no player in a coalition of at most k players believes that it can increase its utility by deviating, regardless of its local state. We prove that all k-resilient sequential equilibria that can be implemented with a trusted mediator can also be implemented without the mediator if n>3k. These results match the lower bounds given by Abraham et al. (2008) for implementing a Nash equilibrium without a mediator (which are easily seen to apply to implementing a sequential equilibrium) and improve the results of Gerardi (2004), who showed that, in the case that k=1, a sequential equilibrium can be implemented in synchronous systems if n≥5.

Suggested Citation

  • Geffner, Ivan & Halpern, Joseph Y., 2024. "Communication games, sequential equilibrium, and mediators," Journal of Economic Theory, Elsevier, vol. 221(C).
    • Handle: RePEc:eee:jetheo:v:221:y:2024:i:c:s0022053124000966
    DOI: 10.1016/j.jet.2024.105890
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    References listed on IDEAS

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    1. Imre Bárány, 1992. "Fair Distribution Protocols or How the Players Replace Fortune," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 327-340, May.
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    5. Gerardi, Dino & Myerson, Roger B., 2007. "Sequential equilibria in Bayesian games with communication," Games and Economic Behavior, Elsevier, vol. 60(1), pages 104-134, July.
    6. Robert J. Aumann, 2025. "Correlated Equilibrium as an Expression of Bayesian Rationality," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 7, pages 175-200, World Scientific Publishing Co. Pte. Ltd..
    7. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
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    Cited by:

    1. Helmuts Azacis & Péter Vida, 2025. "A Byzantine Agreement Protocol for Game Theorists," Thema Working Papers 2025-04, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    2. Gerardi, Dino, 2025. "Interim pre-play communication," Economics Letters, Elsevier, vol. 251(C).
    3. Ivan Geffner & Caspar Oesterheld & Vincent Conitzer, 2025. "Maximizing Social Welfare with Side Payments," Papers 2508.07147, arXiv.org.

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