Ex-post Individually Rational Bayesian Persuasion
Jiahao Zhang, Shuran Zheng, Renato Paes Leme, Zhiwei Steven Wu
TL;DR
This paper introduces ex-post individually rational (ex-post IR) Bayesian persuasion, where signals must not decrease the sender's payoff relative to no disclosure after observing the state. It shows that ex-post IR constraints are linear and solvable via linear programming, and provides a geometric concave/ quasiconcave-closure view of optimal schemes. The authors prove no sender utility gap under ex-post IR for several nontrivial game classes, notably trading games and credence-market scenarios, and they compare ex-post IR with other credibility models, showing that ex-post IR and credible persuasion sit between standard Bayesian persuasion and cheap talk in terms of sender payoff. The results offer practical methods for designing robust signaling policies under credibility constraints and deepen our understanding of when commitment costs can be avoided while maintaining trust.
Abstract
In the Bayesian persuasion model, a sender can convince a receiver to choose an alternative action to the one originally preferred by the receiver. A crucial assumption in this model is the sender's commitment to a predetermined information disclosure policy (signaling scheme) and the receiver's trust in this commitment. However, in practice, it is difficult to monitor whether the sender adheres to the disclosure policy, and the receiver may refuse to follow the persuasion due to a lack of trust. Trust becomes particularly strained when the receiver knows that the sender will incur obvious losses when truthfully following the protocol. In this work, we propose the notion of ex-post individually rational (ex-post IR) Bayesian persuasion: after observing the state, the sender is never asked to send a signal that is less preferred than no information disclosure. An ex-post IR Bayesian persuasion policy is more likely to be truthfully followed by the sender, thereby providing stronger incentives for the receiver to trust the sender. Our contributions are threefold. First, we demonstrate that the optimal ex-post IR persuasion policy can be efficiently computed through a linear program, while also offering its geometric characterization. Second, we show that surprisingly, for non-trivial classes of games, the requirement of ex-post IR constraints does not incur any cost to the sender's utility. Finally, we compare ex-post IR Bayesian persuasion to other information disclosure models that ensure different notions of credibility.