Persuading a pessimist: Simplicity and robustness

Abstract

The signals used in persuasion mechanisms in practice typically satisfy two well-studied simple properties: (i) they partition an ordered state space into intervals, and (ii) they do not recommend lower actions at higher states. These properties have been studied—often separately—in the Bayesian persuasion literature, where conditions for the optimality of such signals are provided in various settings.The two properties can be defined only when the action and the state space are ordered. Under the proper ordering conditions, we show that the optimal signal features both of these properties, as well as robustness properties, when Receiver is a pessimist. A pessimistic receiver, rather than maximizing expected payoff, takes the action that guarantees the highest level of payoff. Through the notion of maxmin expected utility, our findings explain that simplicity and robustness of optimal signals can emerge from the ambiguity of the prior to Receiver.