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.

使用超图的概念和均值场博弈理论，提出了一种建模大规模多智能体动力系统的方法，可以跨超过两个 Agent 进行交互，该方法被扩展到多层设置中，并被用于社交舆论和传染病控制问题的实证研究。