Very large scale (finite) networks (VLSNs) linking large populations of dynamical agents are ubiquitous, with examples being given by electrical power grids, social media networks and epidemic transmission networks. VLSNs typically present problems of intractable complexity, however the emergence of the graphon theory of large network limits has enabled the development of Graphon Mean Field Game (GMFG) theory and the GMFG equations on the infinite limit structures of VLSNs provided by graphons. GMFG theory generalizes the standard MFG theory of large populations of non-cooperative agents on completely connected uniform networks to populations distributed over VLSNs. In particular, GMFG theory provides conditions for (i) the existence and uniqueness of Nash equilibria for infinite populations distributed over infinite networks, and (ii) epsilon-Nash equilibria for finite populations of dynamical systems distributed over VLSNs when subject to GMFG strategies. It is currently being developed for various classes of systems and networks.
Work with Minyi Huang