Smooth, strategic communication

We study strategic communication between a Sender and Receiver who are both uncertain about their preferred actions. The Sender observes noisy signals about both players' ideal policies and then communicates with the Receiver. Even though Sender and Receiver disagree about ideal policies as a function of the Sender's information, we can show that: i) there are information structures such that in equilibrium the Sender credibly communicates his ideal policy and the Receiver correctly takes the Sender's advice at face value and ii) the unique outcome of Nash-bargaining over information structures induces precisely a situation where communication about ideal policies is credible. The resulting equilibrium features message strategies that are smooth in a subspace of the Sender's information. Smooth communication equilibria are extremely tractable. Senders with better aligned preferences are endogenously endowed with better information and therefore give more accurate advice.