Présentation sur YouTube.

This talk will present models, properties and low-complexity solutions to mean field games with large network couplings. More specifically, we will investigate approximate solutions to large-scale linear quadratic stochastic games with heterogeneous network couplings following the graphon mean field game framework. A graphon dynamical system model is first formulated to study the finite and then limit problems of linear quadratic graphon mean field games. The Nash equilibrium of the limit problem is then characterized by two coupled graphon dynamical systems. For the computation of solutions, two methods are employed where one is based on fixed point iterations and the other on a decoupling operator Riccati equation; furthermore, two corresponding sets of low-complexity solutions are established based on graphon spectral decompositions. The equilibrium Nash values of such dynamic games lead to the introduction of fixed-point centralities for large networks for identifying important and influential nodes, and the connections with existing centralities will be demonstrated.

Based on joint work with Peter E. Caines, Minyi Huang and Rinel Foguen Tchuendom.