LQG Graphon Mean Field Games: Graphon Invariant Subspaces

This paper studies approximate solutions to largescale linear quadratic stochastic games with homogeneous nodal dynamics and heterogeneous network couplings based on the graphon mean field game framework in [1]-[3]. A graphon time-varying dynamical system model is first formulated to study the limit problem of linear quadratic Gaussian graphon mean field games (LQG-GMFG). The Nash equilibrium to the limit problem is then characterized by two coupled graphon time-varying dynamical systems. Based on this characterization, we establish two sufficient conditions for the existence of a unique solution to the limit LQG-GMFG problem, and moreover we provide a new asymptotic error bound for applications of approximate solutions to finite-network games. Finally, simulation results on random networks are demonstrated