Information Design in the Principal-Agent Problem

TL;DR

This paper analyzes how information structures designed by regulators affect the implementation of actions in a principal-agent setting, providing a simple characterization and exploring the impact of noise and constraints on welfare and computational complexity.

Contribution

It offers a clear threshold-based characterization for action implementability under various information structures and examines the effects of noise and constraints on welfare and computational complexity.

Findings

Implementability characterized by utility thresholds

Welfare deteriorates with noisier information structures

Deciding implementability under constraints is NP-complete

Abstract

We study a variant of the principal-agent problem in which the principal does not directly observe the agent's effort outcome; rather, she gets a signal about the agent's action according to a variable information structure designed by a regulator. We consider both the case of a risk-neutral and of a risk-averse agent, focusing mainly on a setting with a limited liability assumption. We provide a clean characterization for implementability of actions and utility profiles by any information structure, which turns out to be simple thresholds on the utilities. We further study naturally constrained information structures in which the signal emitted from any action is either the action itself or some actions nearby. We show that the worst implementable welfare deteriorates gracefully as the information structure becomes noisier. Finally, we show that our clean characterization does not generalize to a larger class of signaling constraints. In fact, even deciding whether a certain action is implementable by some constrained information structure from this class is NP-complete in the general setting.