Hypergraphon Mean Field Games
- URL: http://arxiv.org/abs/2203.16223v1
- Date: Wed, 30 Mar 2022 11:57:16 GMT
- Title: Hypergraphon Mean Field Games
- Authors: Kai Cui, Wasiur R. KhudaBukhsh, Heinz Koeppl
- Abstract summary: We propose an approach to modelling large-scale multi-agent dynamical systems using the theory of mean-field games.
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.
On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria.
- Score: 27.56570458658299
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 an epidemic control
problem and a social rumor spreading model, where we give agents intrinsic
motivation to spread rumors to unaware agents.
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