Moral Hazard in Delegated Bayesian Persuasion

TL;DR

This paper analyzes delegated Bayesian persuasion, characterizing optimal information design with incentive alignment, and explores how moral hazard and entropy costs affect the principal's ability to implement ideal experiments.

Contribution

It provides a novel characterization of first-best implementability conditions and introduces a virtual Bayesian persuasion framework for second-best solutions under agency frictions.

Findings

First-best implementability characterized by alignment conditions.

A partial characterization of the intermediate region where first-best is unattainable.

Explicit solutions derived for binary environments with entropy costs.

Abstract

We study delegated Bayesian persuasion: a principal incentivizes an intermediary to design information via outcome-contingent transfers, while the intermediary privately chooses the experiment subject to convex costs. We characterize first-best implementability through a pair of alignment conditions on the principal's and intermediary's payoff indices. A local condition on the support of the target experiment is necessary; a global affine alignment condition is sufficient. We show that the gap between them is non-empty and provide a partial characterization of the intermediate region. When the first-best is unattainable, the principal's problem admits a virtual Bayesian persuasion representation: the second-best experiment maximizes the same concavified objective as the first-best, with the principal's payoff index distorted by a single scalar shadow price that summarizes the entire agency friction. Under entropy costs, moral hazard compresses posterior dispersion whenever the intermediary's utility differs across the actions it recommends. Explicit closed-form solutions for posteriors, mixing weights, and the optimal transfer schedule are derived for binary environments.