Existence of equilibria in persuasion games with costly information acquisition

This paper studies public information disclosure in games with rationally inattentive players. We establish how the existence of an optimal sender's strategy depends on the nature of the receivers' information cost. When the receivers' cost is strongly Uniformly Posterior Separable (UPS), selecting the sender's most preferred equilibrium (SPE) for every interim belief guarantees a solution to the information design problem. We provide an example with a (non-strongly) UPS cost function in which an optimal sender's strategy does not exist despite the selection of the SPE.