Graphon Mean Field Games and Their Equations
Peter E. Caines, Minyi Huang · SIAM Journal on Control and Optimization · 2021
The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks. Furthermore, the study of the decentralized control of such systems has been initiated in which graphon mean field games (GMFG) and the GMFG equations have been formulated for the analysis of noncooperative dynamic games on unbounded networks; in that work, existence and uniqueness results have been introduced for the GMFG equations, together with an $\epsilon$-Nash theory for GMFG systems which relates infinite population equilibria on infinite networks to finite population equilibria on finite networks. Those results are rigorously established in this paper.