Communication with Detectable Deceit

I analyze a model of communication in which players have no common interest, messages are cheap talk, but the deceit is detectable with positive probability. The sender observes his type and sends a message to the receiver. If he lies, his message becomes inconsistent with positive probability. In any informative equilibrium, the intermediate types of the sender reveal themselves, while the extreme types of the sender pool. The amount of information revealed increases with the detectability of lies. In the extreme cases, the model encompasses cheap talk (no information revelation) and verifiable evidence (full information revelation). I extend the model to a T-period game and show that there exists an equilibrium in which the probability of informative communication is positive in each period. In each period, only the highest types reveal the truth, and the threshold for truthtelling decreases with time. The receiver suffers from multiple rounds of communication when the probability of lie detection is high enough and benefits otherwise. Hence, when lie detectability is high, the receiver would like to commit to not giving second chances.