Persuasive signalling

We present a model of persuasive signalling, where a privately-informed sender selects from a class of signals with different precision to persuade a receiver to take one of two actions, where higher precision is more costly. The sender’s information could be either favourable or unfavourable. The receiver observes both the sender’s choice of signal and a random realization of the signal. We show that all plausible equilibria must involve some pooling and any informative signal must be associated with an optimistic posterior. When the receiver is ex ante pessimistic or indifferent, the only plausible equilibrium is semi-separating, with levels of precision independent of the prior. Finally, we investigate the sender’s optimal persuasion policy–choice of signal before (commitment) or after (discretion) he learns his type. We show that the sender is indifferent between commitment and discretion when the prior is optimistic, prefers discretion to commitment when the prior is sufficiently pessimistic, and could either prefer discretion or commitment when the prior is neutral.