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 preplay 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.
Highlights
Self-enforcing agreements—those for that no party has any incentive to break given that all others comply—should be carried out even if they are not binding in a formal sense. This is the defining characteristic of the standard Nash equilibrium concept, and one of the common justifications for this concept is that if players are allowed to communicate before playing a game, they could hardly reasonably agree on an outcome not satisfying this criterion
Recall that a Nash equilibrium constitutes for each player a set of strategies and beliefs, such that the strategies are the best responses to beliefs and the beliefs are correct
But distinctly different track of reasoning, it is natural to wonder why agents would ever agree on an inefficient outcome, assuming that they had the chance to talk in the first place
Summary
Self-enforcing agreements—those for that no party has any incentive to break given that all others comply—should be carried out even if they are not binding in a formal sense. The main reason for the difference is that those previous studies looked for equilibria of the extended communication game as a whole—for instance, by assuming that the full strategies of all players are known This allows equilibrium strategies in which no value is placed even on seemingly mutually informative communication, whereas the model below presupposes the impossibility of ignoring beneficial interchange. The model does not impose beliefs about the cheap talk stage, it still must make some assumption about beliefs held upon entering the action game Another approach that will destroy the babbling equilibria is to assume an arbitrarily small, but positive cost to sending messages—this is a restriction on the environment rather than on the structure of equilibrium or on belief formation.
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