An Optimal Signaling Equilibrium

This paper analyses the optimal combination of costly and costless messages that a Sender uses in a signaling game if he is able to choose among all equilibrium communication strategies. We provide a complete characterization of the equilibrium that maximizes the Sender's ex ante expected utility in case of uniformly distributed types and quadratic loss functions. First, the Sender often wants to avoid money burning by using the most informative cheap talk communication strategy. Second, if he does burn money, he avoids separation and only re-arranges the existing intervals of the most informative cheap talk equilibrium, possibly adding one extra interval. Money burning takes place in the second interval only.