Communication games, sequential equilibrium, and mediators

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 media...

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Bibliographic Details
Published in:Journal of economic theory 2024-10, Vol.221, p.105890, Article 105890
Main Authors: Geffner, Ivan, Halpern, Joseph Y.
Format: Article
Language:English
Subjects:
Communication equilibrium
Long cheap talk
Mediators
Paranoid beliefs
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Summary: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.
ISSN:0022-0531
DOI:10.1016/j.jet.2024.105890