Valuable Cheap Talk and Equilibrium Selection

Abstract

Intuitively, we expect that players who are allowed to engage in costless communication before playing a game would be foolish to agree on an inefficient outcome amongst the set of equilibria. At the same time, however, such pre-play communication has been suggested as a rationale for expecting Nash equilibria in general. This paper presents a plausible formal model of cheap talk that distinguishes and resolves these possibilities. Players are assumed to have an unlimited opportunity to send messages before playing an arbitrary game. Using an extension of fictitious play beliefs, minimal assumptions are made concerning which messages about future actions are credible and hence contribute to final beliefs. In this environment it is shown that meaningful communication among players leads to a Nash equilibrium (NE) of the action game. Within the set of NE, efficiency then turns out to be a consequence of imposing optimality on the cheap talk portion of the extended game. This finding contrasts with previous “babbling” results.