Hypergraphon Mean Field Games. (arXiv:2203.16223v3 [cs.GT] UPDATED)

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, …

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