TY - JOUR
T1 - Propagation of Chaos of Forward–Backward Stochastic Differential Equations with Graphon Interactions
AU - Bayraktar, Erhan
AU - Wu, Ruoyu
AU - Zhang, Xin
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/8
Y1 - 2023/8
N2 - 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.
AB - 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.
KW - Convergence of Nash equilibrium
KW - FBSDE
KW - Graphon mean field games
KW - Large population games
KW - Propagation of chaos
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U2 - 10.1007/s00245-023-09996-y
DO - 10.1007/s00245-023-09996-y
M3 - Article
AN - SCOPUS:85159851210
SN - 0095-4616
VL - 88
JO - Applied Mathematics and Optimization
JF - Applied Mathematics and Optimization
IS - 1
M1 - 25
ER -