Signaling and mediation in games with common interests

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 other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.