  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.
