The Interval Structure of Optimal Disclosure

A sender persuades a receiver to accept a project by disclosing information about a payoff-relevant quality. The receiver has private information about the quality, referred to as his type. We show that the sender-optimal mechanism takes the form of nested intervals: each type accepts on an interval of qualities and a more optimistic type's interval contains a less optimistic type's interval. This nested-interval structure offers a simple algorithm to solve for the optimal disclosure and connects our problem to the monopoly screening problem. The mechanism is optimal even if the sender conditions the disclosure mechanism on the receiver's reported type.