Optimal Coordination in Generalized Principal-Agent Problems: A Revisit and Extensions

In the principal-agent problem formulated in [Myerson 1982], agents have private information (type) and make private decisions (action), both of which are unobservable to the principal. Myerson pointed out an elegant solution that relies on the revelation principle, which states that without loss of generality optimal coordination mechanisms of this problem can be assumed to be truthful and direct. Consequently, the problem can be solved by a linear program when the support sets of the action and type spaces are finite. In this paper, we extend Myerson's results to the setting where the principal's action space might be infinite and subject to additional design constraints. This 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 present a revelation principle for this general model, based on which a polynomial-time algorithm is derived for computing the optimal coordination mechanism. This algorithm not only implies new efficient algorithms simultaneously for all the aforementioned special cases but also significantly simplifies previous approaches in the literature.