Checking Cheap Talk

TL;DR

This paper analyzes a sender-receiver game with a multidimensional state where the receiver can check one or more dimensions before acting, identifying influential equilibria that determine when communication benefits the sender.

Contribution

It introduces a class of influential equilibria in multidimensional state communication games, showing when sender communication is beneficial based on equilibrium selection.

Findings

Sender benefits from communication if equilibria favor revealing high-value components.

Existence of influential equilibria depends on the receiver's checking strategy.

Multiple dimensions checked can lead to similar equilibrium structures.

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.