Bayesian signaling

This paper introduces private sender information in a sender-receiver game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing di¤erences related to the precision of signals and use these to fully characterize the set of equilibria selected by the D1 criterion. The sender’s equilibrium strategy consists of signals which 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 payo¤-relevant state. Whether the equilibrium signals are separating or fully disclosing is completely determined by the optimality properties of fully disclosing signals. Incentive compatibility requires the sender to use suboptimal signals in any equilibrium which is not fully disclosing and then generates a cost for the sender in comparison to a full information benchmark in which the receiver knows the sender’s type. Keywords: Bayesian Persuasion, Signaling, Information Transmission. JEL Classi…cation: D82, D83, D86. Acknowledgement: I thank Carlos Oyarzun, Cristoph Vanberg and seminar participants at the University of Heidelberg for many helpful comments and suggestions. Department of Economics, University of Heidelberg. Address: Bergheimer str. 58, 69115, Heidelberg, Germany. Email: [email protected]. Phone: +49 6221 54-3171. Fax: +49 6221 54-2997