Nash equilibrium seeking over directed graphs
作者机构：School of Artificial IntelligenceBeijing University of Posts and TelecommunicationsBeijing100876China Department of Control Science and EngineeringTongji UniversityShanghai200092China Shanghai Institute of Intelligent Science and TechnologyTongji UniversityShanghai200092China School of AutomationHangzhou Dianzi UniversityHangzhou310018China China Research and Development Academy of Machinery EquipmentBeijing100086China.
出 版 物：《Autonomous Intelligent Systems》 (自主智能系统（英文）)
年 卷 期：2022年第2卷第1期
页 面：79-86页
核心收录：
基 金：This work was partially supported by the National Natural Science Foundation of China under Grants 61973043,62003239,and 61703368 Shanghai Sailing Program under Grant 20YF1453000 Shanghai Municipal Science and Technology Major Project No.2021SHZDZX0100 Shanghai Municipal Commission of Science and Technology Project No.19511132101.
主 题：Nash equilibrium Directed graph Exponential convergence Proportional control Distributed computation
摘 要：In this paper,we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game.Motivated by the recent consensus-based designs,we present a distributed algorithm with a proportional gain for weight-balanced directed graphs.By further embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the graph Laplacian,we extend it to the case with arbitrary strongly connected directed graphs having possible unbalanced weights.In both cases,the Nash equilibrium is proven to be exactly reached with an exponential convergence rate.An example is given to illustrate the validity of the theoretical results.
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