Bayesian signaling

This paper introduces private sender information into a sender-receiver game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing differences related to the precision of signals and use these to fully characterize the set of equilibria robust to the intuitive criterion. In particular, all such equilibria are either separating, i.e., the sender's choice of signal reveals his private information to the receiver, or fully disclosing, i.e., the outcome of the sender's chosen signal fully reveals the payoff-relevant state to the receiver. Incentive compatibility requires the high sender type to use sub-optimal signals and therefore generates a cost for the high sender type in comparison to a full information benchmark in which the receiver knows the sender's type. The receiver prefers the equilibrium outcome over this benchmark for large classes of monotonic sender preferences.