Zimmermann, Jan ; Tatarenko, Tatiana ; Willert, Volker ; Adamy, Jürgen (2022)
Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games.
doi: 10.26083/tuprints-00019664
Report, Zweitveröffentlichung, Preprint
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Kurzbeschreibung (Abstract)
We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to be virtual players that compete against each other in a non-cooperative game with respect to a coupled cost function. In such scenarios, the inner-cluster problem and the game between the clusters need to be solved simultaneously. Therefore, the resulting inter-cluster Nash Equilibrium should also be a minimizer of the social welfare problem inside the clusters. In this work, this setup is cast as a distributed optimization problem with sparse state information. Hence, critical information, such as the agent’s cost functions, remain private. We present a distributed algorithm that converges witha linear rate to the optimal solution. Furthermore, we apply our algorithm to an extended cournot game to verify our theoretical results.
| Typ des Eintrags: | Report |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Zimmermann, Jan ; Tatarenko, Tatiana ; Willert, Volker ; Adamy, Jürgen |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games |
| Sprache: | Englisch |
| Publikationsjahr: | 2022 |
| Publikationsdatum der Erstveröffentlichung: | 2021 |
| Kollation: | 8 Seiten |
| DOI: | 10.26083/tuprints-00019664 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/19664 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung |
| Kurzbeschreibung (Abstract): | We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to be virtual players that compete against each other in a non-cooperative game with respect to a coupled cost function. In such scenarios, the inner-cluster problem and the game between the clusters need to be solved simultaneously. Therefore, the resulting inter-cluster Nash Equilibrium should also be a minimizer of the social welfare problem inside the clusters. In this work, this setup is cast as a distributed optimization problem with sparse state information. Hence, critical information, such as the agent’s cost functions, remain private. We present a distributed algorithm that converges witha linear rate to the optimal solution. Furthermore, we apply our algorithm to an extended cournot game to verify our theoretical results. |
| Status: | Preprint |
| URN: | urn:nbn:de:tuda-tuprints-196641 |
| Zusätzliche Informationen: | arXiv:2102.09406 [eess.SY], Submitted on 18 Feb 2021 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Automatisierungstechnik und Mechatronik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Automatisierungstechnik und Mechatronik > Regelungsmethoden und Robotik (ab 01.08.2022 umbenannt in Regelungsmethoden und Intelligente Systeme) |
| Hinterlegungsdatum: | 08 Mär 2022 12:21 |
| Letzte Änderung: | 06 Dez 2023 09:30 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games. (deposited 08 Mär 2022 12:21) [Gegenwärtig angezeigt]
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