École Nationale Supérieure de
Techniques Avancées

Abstract

Mean field games theory studies a class of stochastic games involving a large number of interacting players influenced by their average state. It has applications in finance, biology, energy storage... We propose new numerical schemes relying on machine learning techniques to solve mean field games. Our methods are based upon the resolution of McKean-Vlasov Forward-Backward Stochastic Differential Equations. We analyze the numerical behavior of our algorithms on several examples including non linear quadratic models. To the best of our knowledge, this work is the first one to address the resolution of such problems in high dimension.