Bayesian Persuasion: From Persuasion toward Counter-Suasion

We study the problem of Bayesian persuasion under receiver distrust. In the classical Bayesian persuasion problem introduced by Kamenica and Gentzkow [AER, 2011], there are two parties, a sender Alice and a receiver Bob, who engage in a one-way interaction from sender to receiver. The sender employs a signalling strategy so as to persuade or steer the receiver toward taking a certain action(s) with respect to a random state known only to her. Both parties are rational and seek to optimize their expected utilities; however, their utilities are intimately coupled as they are functions of the random state and the receiver's action. In this work, we initiate a systematic study of Bayesian persuasion when the receiver is distrustful of the sender. Extending the result of Kamenica and Gentzkow [AER, 2011], we present a necessary and sufficient criterion for the existence of a signalling scheme for persuasion under distrust. Interestingly, our results unveil the existence of a regime under a so-called ‘super-distrustful’ receiver when a rational sender should seek to ‘counter-persuade’ or employ ‘counter-suasion’ to derive maximal benefit.