Language, meaning and games: a model of communication, coordination and evolution

Language is arguably a powerful coordination device in real-life interactions. We here develop a game-theoretic model of two-sided pre-play communication that generalizes the cheap-talk approach by way of introducing a meaning correspondence between messages and actions, and postulating two axioms met by natural languages. Deviations from this correspondence are called dishonest and players have a lexicographic preference for honesty, second to material payoffs. The model is first applied to finite and symmetric two-player games and we establish that, in generic and symmetric n x n -coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We discus Aumann’s (1990) example of a Pareto efficient equilibrium that is not self-enforcing. We also extend the approach to one-sided communication.