Credible Persuasion

Abstract

We propose a new notion of credibility for Bayesian persuasion problems. A disclosure policy is credible if the Sender cannot profit from tampering with her messages while keeping the message distribution unchanged. Using optimal transport theory, we show that for every profile of Sender's disclosure policy and Receiver's strategy, the credibility of the profile is equivalent to a cyclical monotonicity condition on its induced distribution over states and actions. We provide conditions on when credibility considerations completely shut down informative communication, as well as settings where the Sender is guaranteed to benefit from credible persuasion. We apply our results to a classic setting of asymmetric information-the market for lemons. It is well-known that market outcome in such a setting may be inefficient due to adverse selection (Akerlof, 1970): despite common knowledge of gain from trade, some cars may not be traded. If the seller can commit to a disclosure policy to persuade the buyers, she can completely solve the market inefficiency by perfectly revealing 0 to the buyers. However, we show that if the buyers can only observe the message distribution of the seller's disclosure policy, but not exactly how these messages are generated, then the seller cannot credibly disclose any useful information to the buyer. Our paper offers foundations for studying Bayesian persuasion in a number of settings. One example is when the Sender's payoff is state-independent: in these cases, our results imply that all disclosure policies are credible, so the full-commitment assumption in the Bayesian persuasion approach is nonessential as long as the message distribution is observable. Another example is when the Sender's payoff is supermodular, in which case all monotone disclosure policies are credible.