Censorship as optimal persuasion

Abstract

We consider a Bayesian persuasion problem where a sender's utility depends only on the expected state. We show that upper censorship that pools the states above a cutoff and reveals the states below the cutoff is optimal for all prior distributions of the state if and only if the sender's marginal utility is quasi‐concave. Moreover, we show that it is optimal to reveal less information if the sender becomes more risk averse or the sender's utility shifts to the left. Finally, we apply our results to the problem of media censorship by a government.