Efficiency, communication and honesty

We here develop a model of pre-play communication that generalizes the cheap-talk approach by allowing players to have a lexicographic preference, second to the payoffs in the underlying game, for honesty. We formalize this by way of an honesty (or truth) correspondence between actions and statements, and postulate two axioms met by natural languages. The model is applied to finite and symmetric two-player games and we establish that honest communication and play of the Pareto dominant Nash equilibrium together characterize the unique evolutionarily stable set in generic and symmetric n×n-coordination games. In particular, this holds even in Aumann's (1990) example of a Pareto dominant equilibrium that is not self-enforcing.