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This paper studies linear quadratic graphon mean field games (LQ-GMFGs) withcommon noise, in which a large number of agents are coupled via a weightedundirected graph. One special feature, compared with the well-studied graphonmean field games, is that the states of agents are described by the dynamicsystems with the idiosyncratic noises and common noise. The limit LQ-GMFGs withcommon noise are formulated based on the assumption that these graphs lie in asequence converging to a limit graphon. By applying the spectral decompositionmethod, the existence of solution 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 problemis constructed.

Linear-Quadratic Graphon Mean Field Games with Common Noise