Distributed Nash Equilibrium Seeking in Two-Coalition Zero-Sum Games Under Edge Agreements

This paper investigates the Nash equilibrium seeking problem in two coalitions of agents constrained by edge agreements, where all agents within the same coalition are collectively cooperative to minimize the sum of their individual costs. The edge agreements are linear constraints imposed by adjace...

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Bibliographic Details
Published in:IEEE transactions on automatic control pp. 1 - 8
Main Authors: Lei, Daning, Wang, Jiamin, Liu, Jian, Xi, Jianxiang, Zheng, Yuanshi
Format: Journal Article
Language:English
Published: IEEE 2025
Subjects:
Consensus control
Cost function
Costs
Distributed algorithm
Distributed algorithms
edge agreements
Formation control
Games
Heuristic algorithms
Nash equilibrium
Training
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This paper investigates the Nash equilibrium seeking problem in two coalitions of agents constrained by edge agreements, where all agents within the same coalition are collectively cooperative to minimize the sum of their individual costs. The edge agreements are linear constraints imposed by adjacent agents, which integrate several coordination control objects (e.g., consensus control, cluster consensus control and formation control) into a unified framework. We first propose a distributed algorithm based on the Rosen's gradient projection method and subgradient for Nash equilibrium seeking. Then, it is strictly proved that the proposed algorithm can solve the distributed Nash equilibrium seeking problem under edge agreements. Finally, a simulation example is provided to validate the effectiveness of the algorithm.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2025.3597241