Bayesian persuasion with costly information acquisition

We consider a Bayesian persuasion model, in which the receiver can gather independent information about the state at a uniformly posterior-separable cost. We show that the sender provides information that prevents the receiver from gathering independent information in equilibrium. When the receiver faces a lower cost of information, her ‘threat’ of gathering independent information increases, thus decreasing the sender's power to persuade. Lower cost of information can also hurt the receiver, because the sender may provide strictly less information in equilibrium. Furthermore, we propose a solution method that can be used to solve our model in specific applications.