Informed Information Design

Abstract

A designer is privately informed about the state and chooses an information- disclosure mechanism to influence the decisions of multiple agents playing a game. We define interim-optimal mechanisms, a subset of incentive-compatible mechan- isms that are optimal in the sense that the informed designer cannot credibly find an alternative mechanism that strictly improves his interim payoff. We prove that an interim-optimal mechanism exists and that every interim-optimal mechanism is a perfect Bayesian equilibrium outcome of the informed-designer game. An ex- ante optimal mechanism may not be interim optimal, but it is when it is ex-post optimal. Likewise, the unraveling outcome in disclosure games is interim op- timal. We provide a belief-based characterization of interim-optimal mechanisms and compare them with ex-ante optimal ones in common economic environments. In settings with strategic complements and binary actions, every ex-ante optimal mechanism is interim optimal. We compare interim optimality to other solutions of informed-principal problems.

Keywords: Bayesian persuasion, core mechanism, Disclosure games, informed prin- cipal, interim information design, neutral optimum, strong neologism proof- ness, Unraveling, verifiable types

JEL Classification: C72, D82