Generalized Principal-Agency: Contracts, Information, Games and Beyond

TL;DR

This paper generalizes the principal-agent problem to include infinite action spaces and additional constraints, unifying various design problems and providing efficient algorithms for optimal mechanism design.

Contribution

It extends the revelation principle and develops a polynomial-time algorithm for a broad class of principal-agent models, simplifying and unifying previous approaches.

Findings

Unified several principal-agent problems under a general model.

Developed a polynomial-time algorithm for optimal mechanism design.

Identified complexity differences among various constrained design problems.

Abstract

In the principal-agent problem formulated by Myerson'82, agents have private information (type) and make private decisions (action), both of which are unobservable to the principal. Myerson pointed out an elegant linear programming solution that relies on the revelation principle. This paper extends Myerson's results to a more general setting where the principal's action space can be infinite and subject to additional design constraints. Our generalized principal-agent model unifies several important design problems including contract design, information design, and Bayesian Stackelberg games, and encompasses them as special cases. We first extend the revelation principle to this general model, based on which a polynomial-time algorithm is then derived for computing the optimal mechanism for the principal. This algorithm not only implies new efficient solutions simultaneously for all the aforementioned special cases but also significantly simplifies previously known algorithms designed for special cases. Inspired by the recent interest in the algorithmic design of a single contract and menu of contracts, we study such constrained design problems to our general principal-agent model. In contrast to the above unification, our results here illustrate the other facet of diversity among different principal-agent design problems and demonstrate how their different structures can lead to different complexities: some are tractable whereas others are APX-hard. Finally, we reveal an interesting connection of our model to the problem of information acquisition for decision making and study its algorithmic properties in general.