Mean Field Games on Large Sparse Network Limits: Laplexion Dynamics on Graphexons

We consider dynamic games with large subpopulations distributed over large sparse graphs. Each agent on one hand has mean field coupling with all agents located within the same cluster and on the other hand receives impact from neighboring clusters via a graph Laplacian. We aim to derive tractable limit models when the sparse network size tends to infinity, which leads to higher order mean field interaction dynamics. This is justified by asymptotic analysis of the graph Laplacian operator within the large graph limits. Subsequently, the solution equation system of the Laplexion mean field game is obtained within the setting of infinite population and infinite network size.