Multistage Games with Communication

TLDR

Multistage games with a central mediator can achieve communication equilibria where no player benefits from manipulating reports, and a stronger sequential version requires this property even after zero‑probability events. The authors define codominated actions and introduce predominant communication equilibria, obtained by iteratively eliminating codominated actions. They prove that a communication equilibrium is sequential precisely when it avoids codominated actions, and that predominant equilibria—those derived by eliminating codominated actions—always exist.

Abstract

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.