Hypergraphon Mean Field Games

TL;DR

This paper introduces hypergraphon mean field games, a novel framework for modeling large multi-agent systems with complex interactions, extending traditional pairwise models to hypergraph structures, and provides theoretical and computational tools for analysis.

Contribution

It is the first work to develop mean field game theory on hypergraphs, extending to multi-layer systems, with proofs of well-foundedness and algorithms for equilibrium computation.

Findings

Established existence and approximate Nash equilibria for hypergraphon mean field games.

Extended numerical algorithms for computing equilibria in complex multi-agent systems.

Validated approach through social rumor spreading and epidemic control models.

Abstract

We propose an approach to modelling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly-interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game, showing both existence and approximate Nash properties. On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria. To verify our approach empirically, we consider a social rumor spreading model, where we give agents intrinsic motivation to spread rumors to unaware agents, and an epidemics control problem.