Persuasion with Ambiguous Communication

We explore whether ambiguous communication can be beneficial to the sender in persuasion games when the receiver is ambiguity averse and dynamically consistent. Splitting of obedient experiments into a convex combination of two Pareto-ranked experiments (those for which both players agree on a payoff ranking) plays a key role. That some obedient experiment can be split in this way is necessary for the sender to benefit. If an optimal Bayesian persuasion experiment can be split in this way, then any not-too-ambiguity-averse sender benefits. The sender never benefits from ambiguous communication when the receiver has only two actions. We identify a class of games in which our conditions fully characterize when the sender benefits and are generically satisfied when there are at least three actions.