Bayesian Persuasion and Cryptography

Bayesian Persuasion assumes that a sender can commit ex ante to an information structure and then release the realized signal ex post. This paper asks when that commitment technology can itself be implemented. After observing the state, a sender who also observes the realized signal can suppress unfavorable draws even if every disclosed signal is verifiably correct. We define Receiver-Private Certified Bayesian Persuasion, a benchmark in which the receiver obtains the signal and a certificate of correct generation while the sender does not learn the realized branch of the experiment. The main theorem shows that this benchmark is equivalent in cryptographic power to secure two-party computation. Thus cryptography is not merely an implementation device for persuasion; when the sender must be prevented from changing the signal sent to the receiver, hiding the signal from the sender is necessary. In stress-test applications, the primitive removes ex post discretion over which realized disclosure reaches depositors.