Cheap talk and lie detection

This study analyzes strategic interactions between cheap talk and lie detection, identifies the receiver-optimal equilibrium under costly lie detection, and evaluates its effectiveness. An informed sender seeks to persuade an uninformed receiver to choose higher actions, while the receiver aims to align the action as closely as possible with the true state. The sender issues a claim about the state, and the receiver then decides whether to incur a cost to inspect the claim’s truthfulness. We show that the receiver-optimal equilibrium partitions the state space into three intervals. Types in the upper interval make precise and truthful claims, which are mimicked by types in the lower interval and are subject to random inspection. Types in the middle interval make a vague claim that is never inspected. We further show that lie detection is more beneficial to the receiver than direct state verification, as it creates incentives for moderate and high types to communicate truthfully.