Communication games, sequential equilibrium, and mediators

Ivan Geffner and Joseph Y. Halpern

Journal of Economic Theory, 2024, vol. 221, issue C

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.

Keywords: Long cheap talk; Communication equilibrium; Paranoid beliefs; Mediators (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:221:y:2024:i:c:s0022053124000966

DOI: 10.1016/j.jet.2024.105890

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