Costly Persuasion by a Partially Informed Sender

Abstract

I study a model of costly Bayesian persuasion by a privately and partially informed sender who conducts a public experiment. The cost of running an experiment is the expected reduction of a weighted log-likelihood ratio function of the sender's belief. This is microfounded by a Wald sequential sampling problem where good news and bad news cost differently. I focus on equilibria satisfying the D1 criterion. The equilibrium outcome depends crucially on the relative costs of drawing good and bad news in the experiment. If good news is not too costly compared to bad news, there exists a unique separating equilibrium, and the receiver learns more information thanks to sender private information. If good news is sufficiently costlier than bad news, the single-crossing property fails. There may exist pooling and partial pooling equilibria, and in some equilibria, the receiver learns less information compared to a benchmark with an uninformed sender.