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Hypergraphon mean field games

Cui, Kai; KhudaBukhsh, Wasiur R.; Koeppl, Heinz

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Authors

Kai Cui

Heinz Koeppl



Abstract

We propose an approach to modeling 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 epidemic control problem.

Recent developments in the field of complex systems have shown that real-world multi-agent systems are often not restricted to pairwise interactions, bringing to light the need for tractable models allowing higher-order interactions. At the same time, the complexity of analysis of large-scale multi-agent systems on graphs remains an issue even without considering higher-order interactions. An increasingly popular and tractable approach of analysis is the theory of mean field games. We combine mean field games with higher-order structure by means of hypergraphons, a limiting description of very large hypergraphs. To motivate our model, we build a theoretical foundation for the limiting system, showing that the limiting system has a solution and that it approximates finite, sufficiently large systems well. This allows us to analyze otherwise intractable, large hypergraph games with theoretical guarantees, which we verify using two examples of rumor spreading and epidemics control.

Citation

Cui, K., KhudaBukhsh, W. R., & Koeppl, H. (2022). Hypergraphon mean field games. Chaos, 32(11), Article 113129. https://doi.org/10.1063/5.0093758

Journal Article Type Article
Acceptance Date Oct 24, 2022
Online Publication Date Nov 10, 2022
Publication Date 2022-11
Deposit Date Nov 11, 2022
Publicly Available Date Nov 11, 2022
Journal Chaos: An Interdisciplinary Journal of Nonlinear Science
Print ISSN 1054-1500
Electronic ISSN 1089-7682
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 32
Issue 11
Article Number 113129
DOI https://doi.org/10.1063/5.0093758
Keywords Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics
Public URL https://nottingham-repository.worktribe.com/output/13463397
Publisher URL https://aip.scitation.org/doi/10.1063/5.0093758

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