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. The sender can benefit from communication if and only if she prefers one of these equilibria to the no-communication outcome. Similar equilibria exist when the receiver can check multiple dimensions.