Nash Equilibrium Seeking of Monotone N-Coalition Games

被引:0
作者
Chao Sun [1 ]
Bo Chen [2 ]
Jianzheng Wang [2 ]
Guoqiang Hu [1 ]
机构
[1] Nanyang Technological University,School of Electrical and Electronic Engineering
[2] Zhejiang University of Technology,Department of Automation
关键词
Cooperation and competition; Nash equilibrium seeking; -coalition game; regularization;
D O I
10.1007/s11424-025-4486-8
中图分类号
学科分类号
摘要
This study aims to solve the Nash equilibrium (NE) seeking problem for monotone N-coalition games. The authors assume that the gradient mapping of the game is monotone but not necessarily strictly or strongly monotone. Such a merely monotone assumption presents significant challenges to NE seeking, since the basic gradient descent method may fail to converge. The authors start with a regularization-based projected gradient dynamical system in a general non-cooperative game framework and analyze the convergence of the dynamics under different scenarios. Then, the authors develop NE seeking algorithms for monotone N-coalition games with undirected and connected inner-coalition communication graphs. Asymptotic convergence to the least-norm NE is proven. The convergence rate of the algorithm for an analytic mapping is provided. Furthermore, the authors propose a novel regularization-based dynamical system that allows different parameters among the coalitions. Rigorous analysis and a numerical example are provided to illustrate the effectiveness of the proposed method.
引用
收藏
页码:874 / 901
页数:27
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