In this talk, we discuss a single-level numerical approach that uses machine learning techniques to solve bi-level Stackelberg mean field game problems between a principal and a mean field of agents. In Stackelberg mean field game, the mean field of agents play a non-cooperative game and choose their controls to optimize their individual objectives by interacting with the principal and other agents in the society through the population distribution. The principal can influence the resulting mean field game Nash equilibrium through incentives to optimize its own objective. This creates a bi-level problem where at the lower level, the equilibrium of the population given the policies of the principal is found and at the upper level, policy optimization of the principal is executed given the reactions of agents. We rewrite this bi-level problem between the principal and mean field of agents as a single-level problem to implement an efficient numerical approach to solve it.  We discuss the convergence of the solution of the single-level problem to the original problem. Later, we extend our numerical approach to a more generalized problem setting and discuss the experiment results on different applications.

(This is a joint work with Mathieu Lauriere.)