Title: A Single-level Deep Learning Approach to Solve Stackelberg Mean Field Game Problems
Abstract: In many real-life policy making applications, the principal (i.e., governor or regulator) wants to find the optimal policies for a large population of interacting agents who optimize their own objectives in a game theoretical framework. However, it is well known that finding an equilibrium in a game with a large number of agents is a challenging problem because of the increasing number of interactions among agents. In this talk, we introduce the Stackelberg mean field game problem to approximate the game between a principal and a large number of agents. Then, we discuss how to rewrite this bi-level problem as a single-level problem to propose an efficient numerical solution. In the model, the agents in the population 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 her own objective. After analyzing this game by using a probabilistic approach, we rewrite this bi-level problem as a single-level problem and propose a deep learning approach to solve the Stackelberg mean field game. We look at different applications such as the systemic risk model for a regulator and many banks and an optimal contract problem between a project manager and a large number of employees.
