A Smooth, strategic communication

We study strategic information transmission in a Sender-Receiver game where players' optimal actions depend on the realization of multiple signals but the players disagree on the relative importance of each piece of news. We characterize a statistical environment - featuring symmetric loss functions and elliptically distributed parameters - in which the Sender's expected utility depends only on the first moment of his posterior. Despite disagreement about the use of underlying signals, we demonstrate the existence of equilibria in differentiable strategies in which the Sender can credibly communicate posterior means. The existence of smooth communication equilibria depends on the relative usefulness of the signal structure to Sender and Receiver, respectively. We characterize extensive forms in which the quality of information is optimally designed of equal importance to Sender and Receiver so that the best equilibrium in terms of ex ante expected payoffs is a smooth communication equilibrium. The quality of smooth equilibrium communication is entirely determined by the correlation of interests. Senders with better aligned preferences are endogenously endowed with better information and therefore give more accurate advice.