Propagation of Chaos of Forward-Backward Stochastic Differential Equations with Graphon Interactions

Abstract

In this paper, we study graphon mean field games using a system of forward-backward stochastic differential equations. We establish the existence and uniqueness of solutions under two different assumptions and prove the stability with respect to the interacting graphons which are necessary to show propagation of chaos results. As an application of propagation of chaos, we prove the convergence of n-player game Nash equilibrium for a general model, which is new in the theory of graphon mean field games.

Keywords: Large population games, graphon mean field games, propagation of chaos, FBSDE, convergence of Nash equilibrium