Implementing Mediators with Asynchronous Cheap Talk
This work addresses a foundational problem in game theory for researchers, focusing on incremental advancements by extending synchronous mediator implementation to asynchronous environments.
The paper investigates whether non-cooperative agents can achieve mediated equilibrium using only nonbinding pre-play communication (cheap talk) in asynchronous settings, establishing upper bounds for mediator implementation.
A mediator can help non-cooperative agents obtain an equilibrium that may otherwise not be possible. We study the ability of players to obtain the same equilibrium without a mediator, using only cheap talk, that is, nonbinding pre-play communication. Previous work has considered this problem in a synchronous setting. Here we consider the effect of asynchrony on the problem, and provide upper bounds for implementing mediators. Considering asynchronous environments introduces new subtleties, including exactly what solution concept is most appropriate and determining what move is played if the cheap talk goes on forever. Different results are obtained depending on whether the move after such "infinite play" is under the control of the players or part of the description of the game.