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.

Matysková gratefully acknowledges funding from the Generalitat Valenciana (Prometeo/2021/073), the German Research Foundation DFG (CRC TR 224, project B02), the ERC-2015-STG H2020 (project 678081), and the Charles University (GA UK no. 178715). Montes gratefully acknowledges funding from the Ecole Polytechnique, the National Commission of Scientific and Technological Research of the Government of Chile (Ref. no. 72180147), the Labex MME-DII, and the University of Chile (proyecto anillo ACT 210005).