Cui, Kai ; KhudaBukhsh, Wasiur R. ; Koeppl, Heinz (2022)
Hypergraphon mean field games.
In: Chaos: An Interdisciplinary Journal of Nonlinear Science, 32 (11)
doi: 10.1063/5.0093758
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2022 |
| Creators: | Cui, Kai ; KhudaBukhsh, Wasiur R. ; Koeppl, Heinz |
| Type of entry: | Bibliographie |
| Title: | Hypergraphon mean field games |
| Language: | English |
| Date: | 10 November 2022 |
| Publisher: | AIP Publishing |
| Journal or Publication Title: | Chaos: An Interdisciplinary Journal of Nonlinear Science |
| Volume of the journal: | 32 |
| Issue Number: | 11 |
| DOI: | 10.1063/5.0093758 |
| Corresponding Links: | |
| 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. |
| Uncontrolled Keywords: | emergenCITY_KOM |
| Additional Information: | Art.No.: 113129 |
| Divisions: | 18 Department of Electrical Engineering and Information Technology 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications 18 Department of Electrical Engineering and Information Technology > Self-Organizing Systems Lab LOEWE LOEWE > LOEWE-Zentren LOEWE > LOEWE-Zentren > emergenCITY |
| Date Deposited: | 27 Feb 2023 13:12 |
| Last Modified: | 13 May 2024 11:27 |
| PPN: | 507922441 |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
Available Versions of this Item
-
Hypergraphon mean field games. (deposited 30 Apr 2024 09:03)
- Hypergraphon mean field games. (deposited 27 Feb 2023 13:12) [Currently Displayed]
 |
Send an inquiry |
Options (only for editors)
 |
Show editorial Details |
Drucken
Impressum