Bayesian Persuasion

2590 Suppose one person, call him Sender, wishes to persuade another, call her Receiver, to change her action. If Receiver is a rational Bayesian, can Sender persuade her to take an action he would prefer over the action she was originally going to take? If Receiver understands that Sender chose what information to convey with the intent of manipulating her action for his own benefit, can Sender still gain from persuasion? If so, what is the optimal way to persuade? These questions are of substantial economic importance. As Donald McCloskey and Arjo Klamer (1995) emphasize, attempts at persuasion command a sizable share of our resources. Persuasion, as we will define it below, plays an important role in advertising, courts, lobbying, financial disclosure, and political campaigns, among many other economic activities. Consider the example of a prosecutor trying to convince a judge that a defendant is guilty. When the defendant is indeed guilty, revealing the facts of the case will tend to help the prosecutor’s case. When the defendant is innocent, revealing facts will tend to hurt the prosecutor’s case. Can the prosecutor structure his arguments, selection of evidence, etc. so as to increase the probability of conviction by a rational judge on average? Perhaps surprisingly, the answer to this question is yes. Bayes’s Law restricts the expectation of posterior beliefs but puts no other constraints on Bayesian Persuasion