Signaling and Mediation in Games with Common Interests

Abstract

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential signals that stochastically depend on the actual state of nature. These signal not only provide the players with partial information about the state of nature but also serve as a correlation means.

Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the latter structure. This paper fully characterizes when one information structure is better than another with respect to various solution concepts. The solution concepts we refer to differ from each other in the scope of communication allowed between the players. The characterizations are phrased in terms of maps that take signals of one structure and (stochastically) translate them to signals of another structure.

Keywords: Bayesian games, common interest, garbling, information structure, equilibrium

JEL Classification: C72