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Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games

Zimmermann, Jan ; Tatarenko, Tatiana ; Willert, Volker ; Adamy, Jürgen (2022):
Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games. (Preprint)
Darmstadt, DOI: 10.26083/tuprints-00019664,

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Item Type: Report
Origin: Secondary publication
Status: Preprint
Title: Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games
Language: English

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.

Place of Publication: Darmstadt
Collation: 8 Seiten
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Robotics (from 01.08.2022 renamed Control Methods and Intelligent Systems)
Date Deposited: 08 Mar 2022 12:21
Last Modified: 02 Mar 2023 10:12
DOI: 10.26083/tuprints-00019664
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-196641
Additional Information:

arXiv:2102.09406 [eess.SY], Submitted on 18 Feb 2021

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19664
PPN: 492785872
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