The Interval Structure of Optimal Disclosure

Abstract

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.

Leaks, Sabotage, and Information Design

“…Interestingly, the same result holds in the static persuasion model ofGuo and Shmaya (2018) under a set of regularity conditions, though for different reasons.…”

“…Another emerging strand of the literature has studied the effects of combining persuasion with a privately informed receiver. Kolotilin et al (2017), Kolotilin (2018), and Guo and Shmaya (2018) study static persuasion problems. In each paper, the receiver makes a binary decision to act or not, and the focus is on settings in which the sender has a (possibly stochastic) bias toward action relative to the receiver.…”

Buyer-Optimal Robust Information Structures

“…Like here, attention can be restricted to equilibria in which subsequent players have no incentive to add information (see also Perez-Richet and Skreta, 2018). Concerning disclosure to a receiver who is privately informed, Kolotilin, Li, Mylovanov, and Zapechelnyuk (2017) establish a payoff equivalence between experiments and mechanisms that provide an experiment conditional on a report by the receiver (see also Guo and Shmaya, 2017). One interpretation of our model is that the buyer observes the signal from the original information structure before the seller decides about her disclosure.…”

Persuasion Meets Delegation

“…Nonlinear delegation is considered in Holmström (1984), Alonso and Matouschek (2008), Amador and Bagwell (2013), and Amador, Bagwell, and Frankel (2018). Nonlinear persuasion is considered in Rayo and Segal (2010), Kamenica and Gentzkow (2011), Kolotilin (2018), Dworczak and Martini (2019), and Guo and Shmaya (2019).…”