Implementing Mediators with Asynchronous Cheap Talk

TL;DR

This paper explores how asynchronous communication affects the ability of non-cooperative agents to replicate mediator-based equilibria through cheap talk, providing upper bounds and analyzing different solution concepts.

Contribution

It extends the study of mediator implementation via cheap talk to asynchronous settings, addressing new challenges and subtleties introduced by asynchrony.

Findings

Asynchrony introduces new complexities in implementing mediators.

Upper bounds are established for mediator implementation in asynchronous environments.

Different results depend on how infinite cheap talk plays are interpreted.

Abstract

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.