Generalized Principal-Agency: Contracts, Information, Games and Beyond
Jiarui Gan, Minbiao Han, Jibang Wu, Haifeng Xu
TL;DR
The paper generalizes Myerson’s principal-agent framework to a convex, constraint-rich setting, unifying contract design, information design, Bayesian persuasion, and Stackelberg games under a single algorithmic lens. A strengthened revelation principle yields succinct, truthful, direct mechanisms, enabling a polynomial-time computation of the optimal coordination mechanism via convex programming in regular cases and an epsilon-approximation in irregular ones. It demonstrates broad tractability across several classic problems while identifying APX-hard and NP-hard boundaries in constrained or information-cost regimes, and links information acquisition to concavification with both tractable and hard instances. The work also clarifies when information-design problems can be solved efficiently and when intrinsic complexity prevents exact solutions, offering concrete algorithmic tools and hardness results that illuminate the computational landscape of principal-agent designs. Overall, the framework provides a coherent, scalable methodology for designing and analyzing complex contracts, signals, and leadership strategies in the presence of asymmetric information and strategic behavior.
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.