Communication, Risk and Efficiency in Games

This paper looks at simple games with one round of pre-play communication followed by a simultaneous move, complete information game. In these games the {\em curb} concept distinguishes among efficient equilibria according to their risk. The paper contains two major results. First, if only one of the players can talk, and that player's favorite outcome is a strict equilibrium in the underlying game, then, for a given size of the message space the corresponding payoffs will be the only curb equilibrium payoffs in the communication game, provided the communicating player's risk at that equilibrium is sufficiently low. Second, suppose that communicating players have a slight preference for strategies where messages communicate only their intent to play according to their preferred equilibrium. Then the curb concept distinguishes multi-sided from one-sided communication. Modifying payoffs in this way does not affect the results with one-sided communication. However with two-sided communication, and a unique strict common interest equilibrium in the underlying game, only the payoffs of that equilibrium are curb equilibrium payoffs in the communication game.