Checking Cheap Talk

Abstract

We consider a sender-receiver game in which the receiver's action is binary and the sender's preferences are state-independent. The state is multidimensional. The receiver can select one dimension of the state to check (i.e., observe) before choosing his action. We identify a class of influential equilibria in which the sender's message reveals which components of the state are highest, and the receiver selects one of these components to check. In these equilibria, the sender's message guides the receiver to check positively selected attributes. We provide conditions under which these equilibria are sender-optimal, Pareto efficient, or receiver-optimal among all equilibria.