Learning Graphon Mean Field Games and Approximate Nash Equilibria

Understand

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents.

• So far, results have been largely limited to graphon mean field systems with continuous-time diffusive or jump dynamics, typically without control and with little focus on computational methods.
• We propose a novel discrete-time formulation for graphon mean field games as the limit of non-linear dense graph Markov games with weak interaction.
• On the theoretical side, we give extensive and rigorous existence and approximation properties of the graphon mean field solution in sufficiently large systems.