Optimal Network Location in Infinite Horizon LQG Graphon Mean Field Games

We propose to study a class of infinite horizon linear quadratic Gaussian Graphon Mean Field Games (GM-FGs) inspired by the infinite horizon Mean Field Games in [1]. Graphon Mean Field Games (GMFGs) are non-uniform generalizations of Mean Field Games where the non-uniformity of agents is characterized by the nodes on which they are located in a network. Under mild conditions, we obtain for almost every node, an analytical expression for the cost at GMFG equilibrium, and propose a necessary and sufficient condition under which a particular node in the network is associated with the minimal cost at GMFG equilibrium.