Large Network-Coupled Mean Field Games and Associated Network Centralities

Explore a comprehensive seminar on large network-coupled mean field games and their associated network centralities. Delve into models, properties, and low-complexity solutions for mean field games with extensive network couplings. Examine approximate solutions to large-scale linear quadratic stochastic games featuring heterogeneous network couplings within the graphon mean field game framework. Investigate the formulation of a graphon dynamical system model to study finite and limit problems of linear quadratic graphon mean field games. Learn how the Nash equilibrium of the limit problem is characterized by two coupled graphon dynamical systems. Discover two computational methods for solutions: one based on fixed point iterations and another on a decoupling operator Riccati equation. Explore the establishment of two corresponding sets of low-complexity solutions based on graphon spectral decompositions. Understand how the equilibrium Nash values of these dynamic games lead to the introduction of fixed-point centralities for large networks, identifying important and influential nodes. Examine the connections between these new centralities and existing ones in network analysis.