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

2022/02/16 by Bayraktar, Erhan, Wu, Ruoyu, Zhang, Xin · 3 citations
#49N80 #60F25 #91A06 #91A15 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.08163

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.

Cited by

• An Overview of Some Extensions of Mean Field Games beyond Perfect Homogeneity and Anonymity
• A non-exchangeable mean field control problem with controlled interactions
• Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls

Related

• Probabilistic Analysis of Graphon Mean Field Control
• LQG Graphon Mean Field Games: Analysis via Graphon Invariant Subspaces
• Stochastic Graphon Games with Jumps and Approximate Nash Equilibria
• Finite State Graphon Games with Applications to Epidemics
• Stochastic Graphon Games: II. The Linear-Quadratic Case