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Learning the behavior of large agent populations is an important task fornumerous research areas. Although the field of multi-agent reinforcementlearning (MARL) has made significant progress towards solving these systems,solutions for many agents often remain computationally infeasible and lacktheoretical guarantees. Mean Field Games (MFGs) address both of these issuesand can be extended to Graphon MFGs (GMFGs) to include network structuresbetween agents. Despite their merits, the real world applicability of GMFGs islimited by the fact that graphons only capture dense graphs. Since mostempirically observed networks show some degree of sparsity, such as power lawgraphs, the GMFG framework is insufficient for capturing these networktopologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) whichbuilds on the graph theoretical concept of graphexes. Graphexes are thelimiting objects to sparse graph sequences that also have other desirablefeatures such as the small world property. Learning equilibria in these gamesis challenging due to the rich and sparse structure of the underlying graphs.To tackle these challenges, we design a new learning algorithm tailored to theGXMFG setup. This hybrid graphex learning approach leverages that the systemmainly consists of a highly connected core and a sparse periphery. Afterdefining the system and providing a theoretical analysis, we state our learningapproach and demonstrate its learning capabilities on both synthetic graphs andreal-world networks. This comparison shows that our GXMFG learning algorithmsuccessfully extends MFGs to a highly relevant class of hard, realisticlearning problems that are not accurately addressed by current MARL and MFGmethods.

Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach