Information Design in the Principal-Agent Problem (2209.13688v2)

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.