The success of Bayesian persuasion relies on the key assumption that the sender will commit to a predetermined information disclosure policy (signaling scheme). However, in practice, it is usually difficult for the receiver to monitor whether the sender sticks to the disclosure policy, which makes the credibility of the sender's disclosure policy questionable. The sender's credibility is particularly tenuous when there are obvious deviations that benefit the sender. In this work, we identify such a deviation: the sender may be unwilling to send a signal that will lead to a less desirable outcome compared to no information disclosure. We thus propose the notion of ex-post individually rational (ex-post IR) Bayesian persuasion: after observing the state, the sender is never required to send a signal that will make the outcome worse off (compared to no information disclosure). An ex-post IR Bayesian persuasion policy is more likely to be truthfully followed by the sender, and thus more credible for the receiver. Our contribution is threefold. Firstly, we demonstrate that the optimal ex-post IR Bayesian persuasion policy can be efficiently computed through a linear program, while also offering geometric characterizations of this optimal policy. Second, we show that surprisingly, for non-trivial classes of games, the imposition of ex-post IR constraints does not affect the sender's expected utility. Finally, we compare ex-post IR Bayesian persuasion to other information disclosure models that ensure different notions of credibility.

翻译：贝叶斯说服的成功依赖于一个关键假设：发送者将承诺执行预定的信息披露策略（信号方案）。然而在实践中，接收者通常难以监控发送者是否坚持该披露策略，这使得发送者披露策略的可信度存疑。当存在明显有利于发送者的偏离行为时，其可信度尤为脆弱。本研究识别出此类偏离行为：与不披露信息相比，发送者可能不愿发送会导致较差结果的信号。为此，我们提出事后个体理性（ex-post IR）贝叶斯说服概念：在观测到状态后，发送者绝不会被要求发送会使结果（相对于不披露信息）更差的信号。事后IR贝叶斯说服策略更可能被发送者诚实遵循，因而对接收者更具可信性。我们的贡献体现在三个方面：首先，证明最优事后IR贝叶斯说服策略可通过线性规划高效求解，并给出该最优策略的几何特征刻画；其次，令人惊奇地发现，对于非平凡博弈类别而言，施加事后IR约束并不会影响发送者的期望效用；最后，将事后IR贝叶斯说服与其它确保不同可信度概念的信息披露模型进行比较。