Multistage Games with Communication

This paper considers multistage games with communication mechanisms that can be implemented by a central mediator. In a communication equilibrium, no player expects ex ante to gain by manipulating his reports or actions. A sequential communication equilibrium is a communication equilibrium with a conditional probability system under which no player could ever expect to gain by manipulation, even after zero-probability events. Codominated actions are defined. It is shown that a communication equilibrium is a sequential communication equilibrium if and only if it never uses codominated actions. Predominant communication equilibria are defined by iterative elimination of codominated actions and are shown to exist.