Cheap Talk and Lie Detection

This paper analyzes strategic interactions between cheap talk and lie detection and studies the optimal equilibrium for costly lie detection and its effectiveness. An informed sender wants to persuade an uninformed receiver to take high actions, but the receiver wants to match the action with the true state. The sender makes a claim about the state, and the receiver decides whether to incur a cost to inspect the truthfulness of the claim. We show that the receiver-optimal equilibrium partitions the state space into three intervals. Types in the top interval make precise and truthful claims about the state, which are mimicked by types in the bottom interval and randomly inspected. Types in the middle interval make a vague claim that is never inspected. We show that lie detection is more beneficial to the receiver than state verification because it provides incentives for moderate and high types to be truthful