Single level approach to solve Stackelberg Mean Field Games
Abstract
In this talk, we introduce the bi-level Stackelberg mean field game problem between a principal and a mean field of agents evolving on a continuous state space and discuss how to write it 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 in order to optimize her own objective. We analyze this game by using a probabilistic approach. We then rewrite this bi-level problem as a single-level problem and propose a numerical approach to solve the Stackelberg mean field game. We look at different financial applications such as the systemic risk model for a regulator and many banks and optimal contract between a principal and a large number of agents. (This is a joint work with Mathieu Lauriere.)
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