贝叶斯说服与密码学（英）

Pablo D.Azar Bayesian Persuasion and CryptographyPablo D. AzarFederal Reserve Bank of New York Staff Reports, no.1194May 2026https://doi.org/10.59576/sr.1194 Abstract Bayesian Persuasion assumes that a sender can commit ex ante to an information structureand thenrelease the realized signal ex post. This paper asks when that commitmenttechnology can itself beimplemented. After observing the state, a sender who alsoobserves the realized signal can suppressunfavorable draws even if every disclosedsignal is verifiably correct. We define Receiver-PrivateCertified Bayesian Persuasion, abenchmark in which the receiver obtains the signal and a certificate ofcorrect generationwhile the sender does not learn the realized branch of the experiment. The maintheorem shows that this benchmark is equivalent in cryptographic power to securetwo-party computation.Thus cryptography is not merely an implementation devicefor persuasion; when the sender must beprevented from changing the signal sent to thereceiver, hiding the signal from the sender is necessary. Instress-test applications, theprimitive removes ex post discretion over which realized disclosure reachesdepositors. JEL classification:D82, D83, G28Keywords:Bayesian Persuasion, stress testing, central bank communications 1 .IN T R O D U C T I O N How should a regulator disclose information about banks when disclosure itself changesthe probability of distress? Stress tests are meant to discipline weak banks and reassuremarkets, but the same information can coordinate withdrawals when investors fear thatothers will run. This is precisely the tradeoff studied in Bayesian Persuasion (Kamenicaand Gentzkow, 2011): a sender designs an information structure to shape a receiver’sbeliefs and actions.In the stress-test setting, the sender is a regulator, the receiver is adepositor or market participant, and the hidden state is a bank’s balance sheet. Full opacityblunts market discipline; full transparency can create inefficient runs. The relevant designproblem is therefore neither concealment nor full disclosure, but a randomized stress-testrule that separates states enough to discipline banks while pooling them enough to avoidself-fulfilling panic. Randomized disclosure is useful only if the regulator can bind itself before learningwhat it will reveal.In Bayesian Persuasion, the sender chooses a signaling rule beforethe state is realized, then observes the state, and then releases a signal drawn from thecommitted rule. That commitment assumption is the source of the model’s force. Withoutit, the environment moves toward cheap talk (Crawford and Sobel, 1982): after observingthe state, the sender would like to send whichever message is best ex post, and the receiverwould understand this incentive. In the stress-test setting, a public announcement of atesting methodology is therefore not enough. Depositors must also believe that the realizeddisclosure was actually generated by the announced randomized procedure. A public commitment to such a rule is not renegotiation-proof. After observing the state,the regulator may want to replace the prescribed draw with a more favorable signal. Even ifeach disclosed signal can be certified as drawn from the announced rule, the regulator maystill observe the realized draw and suppress disclosure after an unfavorable realization.Conditional on disclosure, the receiver would then see a selected distribution rather thanthe distribution promised ex ante. The problem is therefore not only to verify that a releasedsignal is valid, but to prevent signal-contingent control over whether it is released. Thebenchmark implicitly asks for a mediator that sees the state, draws the signal according tothe committed rule, gives the realized signal to the receiver, and does not return ex postdiscretion over which draw gets released. This paper addresses the problem by introducingReceiver-Private Certified Bayesian Per-suasion. A certified persuasion mechanism implements the committed experiment ratherthan merely announcing it: after the state is realized, it draws the signal prescribed bythe announced rule and gives the receiver both the signal and a certificate that the drawwas generated correctly. The key restriction is receiver privacy. The sender does not learnthe realized signal or the certificate before delivery, and therefore cannot condition disclo-sure on whether the random draw is favorable. Certified Bayesian Persuasion is thus the commitment benchmark isolated above: it makes the receiver able to verify the realizeddisclosure while removing the ex post channel through which the sender can grind overrandomized disclosures. We implement Certified Bayesian Persuasion using secure two-party computation. Se-cure computation lets two parties jointly evaluate a committed rule while revealing onlythe outputs specified by that rule. In our setting, it lets the mechanism authenticate thestate, sample the prescribed stress-test signal, and give the re