Communication with Detectable Deceit

Abstract

Cheap-talk lies are at risk of being detected. We investigate the implications of this fact in a communication game in which players have no common interests and messages are cheap, but deceit is detectable with positive probability. In particular, when the sender makes a claim that is not true, with positive probability the receiver learns that the claim is a lie. We show that partially informative equilibria exist because lie detection generates an endogenous cost from lying consisting of being confused with lower types in equilibrium. In any informative equilibrium, the moderate and the highest types tell the truth, while the lowest types lie claiming to be the highest types. We show that more information may be revealed if the sender is given an opportunity to prepare a lie in advance and thereby decrease its detectability. We analyze an extension in which the sender may make multiple attempts at convincing the receiver, and show that if lie detectability is high, the receiver may benefit from committing to listening to the sender only once. And finally, we analyze a two-sender version of the model, and show that senders will exaggerate their claims only if the state disadvantages them sufficiently.