  This paper studies approximate solutions to large-scale linear quadratic
stochastic games with homogeneous nodal dynamics parameters and heterogeneous
network couplings within the graphon mean field game framework in [2]-[4]. A
graphon time-varying dynamical system model is first formulated to study the
finite and then limit problems of linear quadratic Gaussian graphon mean field
games (LQG-GMFG). The Nash equilibrium of the limit problem is then
characterized by two coupled graphon time-varying dynamical systems. Sufficient
conditions are established for the existence of a unique solution to the limit
LQG-GMFG problem. For the computation of LQG-GMFG solutions two methods are
established and employed where one is based on fixed point iterations and the
other on a decoupling operator Riccati equation; furthermore, two corresponding
sets of solutions are established based on spectral decompositions. Finally, a
set of numerical simulations on networks associated with different types of
graphons are presented.

Systems and Control;Systems and Control;Optimization and Control