ABSTRACT

This work introduces Graphon Mean Field Game (GMFG) theory for the analysis of non-cooperative dynamical games involving agents modelled as controlled stochastic systems distributed over networks of unbounded size. One component is the profoundly influential new graphon theory of large networks and their infinite limits due to Laszlo Lovasz and coworkers which has already been employed in the central- ized control of asymptotically infinite networks of systems [Gao and Caines, CDC 2017, MTNS 2018]. The second component of the theory is that of asymptotically infinite populations of competing dynamical agents for which equilibria in the standard formulation are expressed in terms of the Mean Field Game equations of Huang, Caines and Malham ́e, and Lasry - Lions. The newly defined Graphon Mean Field Game (GMFG) equations significantly generalize the classical MFG PDEs since they describe the interaction of infinite populuations dis- tributed over infinite networks. In this talk we present existence and uniquenes results for the solutions of GMFG equations together with an epsilon-Nash theorem for the approximate equilibrium behaviour of large finite populations subject to infinite population GMFG feedback control. It is a joint work with Minyi Huang.