Hypergraphon Mean Field Games
This work addresses the challenge of analyzing complex multi-agent systems with higher-order interactions for researchers in game theory and network science, representing a novel extension rather than an incremental improvement.
The authors tackled the problem of modeling large-scale multi-agent systems with interactions beyond pairwise connections by introducing hypergraphon mean field games, proving theoretical properties like existence and approximate Nash equilibria, and extending numerical algorithms to compute these equilibria. They empirically verified their approach on social rumor spreading and epidemics control problems.
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.