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This talk studies linear quadratic graphon mean field games (LQ-GMFGs) with common noise, in which a large number of agents are coupled via a weighted undirected graph. One special feature, compared with the well-studied graphon mean field games, is that the states of agents are described by the dynamic systems with the idiosyncratic noises and common noise. The limit LQ-GMFGs with common noise are formulated based on the assumption that these graphs lie in a sequence converging to a limit graphon. By applying the spectral decomposition method, the existence of Nash equilibrium for the formulated limit LQ-GMFGs is derived. Moreover, based on the adequate convergence assumptions, a set of $\epsilon$-Nash equilibrium strategies for the finite large population problem is constructed. Finally, an application is given for network security to illustrate our theoretical results.

Biography: Dr. Dexuan Xu received a Ph.D. in Mathematics from Sichuan University in 2025. His research focuses on large-population (mean-field) games and stochastic differential games.