Persuasion with costly precision

Abstract

We study a sender’s optimal choice of precision when he selects from a class of random signals to persuade a receiver to accept his request, with higher costs associated with higher precision. The receiver observes both the precision and a random realization of the signal. We consider two situations: commitment, where the sender chooses the precision of his signal before observing any private information; and discretion, where the sender privately observes favourable or unfavourable information before choosing precision. We show that, under commitment, a positive level of precision is possible only when receiver is ex-ante neutral or slightly pessimistic about the sender. Under discretion, as long as the receiver is not convinced ex ante that he should accept the sender, there exists a unique plausible equilibrium, in which each type of sender’s payoff is independent of how pessimistic the receiver is about the sender. We then analyze optimal persuasion by comparing the sender’s payoff from discretion and that from commitment. We demonstrate that the more reluctant the receiver is to accept the sender, the more likely the sender prefers discretion to commitment. Finally, we show that whenever the sender prefers commitment to discretion, the receiver prefers the opposite.