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Communication games, sequential equilibrium, and mediators

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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. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. 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.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Forges, Francoise, 1990. "Universal Mechanisms," Econometrica, Econometric Society, vol. 58(6), pages 1341-1364, November.
    5. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    6. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
    7. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    8. 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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