Dynamic Consistency in Ambiguous Persuasion

Abstract

Beauchene, Li, and Li (2019) show that ambiguous persuasion can lead to a higher expected ex-ante value for the Sender than the standard Bayesian persuasion. Ambiguity arises due to a set of communication devices chosen by the Sender. However, they claim, that there is no gain of ambiguous persuasion if the Receiver behaves in a dynamically consistent way. This paper shows that we can restrict without loss of generality to messages that produce recommended actions or synonyms of recommended actions. Using this result, we can define rectangular beliefs on a general state space. We show that given these rectangular beliefs, the Receiver behaves in a dynamically consistent way and the optimal strategies of Beauchene et al. (2019) form a Perfect Bayesian Equilibrium. Hence, the gain of ambiguous persuasion arises due to ambiguity aversion and not due to dynamically inconsistent behavior.