Bayesian persuasion under partial commitment

The “full commitment” assumption in the Bayesian persuasion literature might not always hold: the sender might be tempted to deviate from an information structure to which he commits. To incorporate this possibility, I study a model in which the sender’s commitment to an information structure binds with an exogenously given probability less than one. This gives rise to a novel mode of communication which is between cheap talk and Bayesian persuasion. I focus on the welfare implication of partial commitment. Not surprisingly, the sender’s ex ante payoff weakly increases as the commitment probability increases. Then I show that, in the uniform-quadratic setting, both the sender and the receiver can be strictly better off as the mode of communication changes from cheap talk through communication under partial commitment to Bayesian persuasion. This Pareto-ranking holds for any level of the conflict of interests between two players. The sender’s opportunistic behavior under partial commitment undermines Pareto-optimal welfare achievable under Bayesian persuasion. The sender under partial commitment can improve upon the highest welfare under cheap talk via two contrasting classes of information structures: (1) one which involves truth-telling or (2) one which involves a pure noise-generating process.