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 experiment, that is, whose recommendations are incentive compatible for the receiver. At least some of the experiments in the collection must be Pareto-ranked in the sense that both the sender and receiver 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. We show such gains are impossible when the receiver has only two actions available. Such gains persist even when the sender is ambiguity averse, as long as not too much more so than the receiver and not infinitely averse.