Persuasion with Ambiguous Communication

This paper explores whether and to what extent ambiguous communication can be beneficial to the sender in a persuasion problem, when the receiver (and possibly the sender) is ambiguity averse. We provide a concavification-like characterization of the sender's optimal ambiguous communication. The characterization highlights the necessity of using a collection of experiments that form a splitting of an obedient (i.e., incentive compatible) experiment. Some experiments in the collection must be Pareto-ranked in the sense that both players agree on their payoff ranking. The existence of a binary such Pareto-ranked splitting is necessary for ambiguous communication to benefit the sender, and, if an optimal Bayesian persuasion experiment can be split in this way, this is sufficient for an ambiguity-neutral sender as well as the receiver to benefit. Such gains are impossible when the receiver has only two actions. The possibility of gains is substantially robust to (non-extreme) sender ambiguity aversion.