Repeated communication with private lying costs

Abstract

I study a repeated communication game between a patient sender and a sequence of myopic receivers. The sender has persistent private information about his cost of lying. Each period, the sender privately observes an i.i.d. state and recommends an action. The receiver takes an action after observing this recommendation and the full history of states and recommendations. I provide conditions under which a sufficiently patient sender can attain his optimal commitment payoff in the repeated game. My results provide justifications for the commitment assumption in Bayesian persuasion models using a repeated communication game without any commitment. My results also imply that the sender's equilibrium payoff is not monotone with respect to the receiver's belief about his lying cost.