Nash equilibrium seeking over directed graphs

Autonomous Intelligent Systems

Dawei Liu¹  Peng Yi²  Yutao Tang³  Yanqiong Zhang⁴ 

[1] China Research and Development Academy of Machinery Equipment;Department of Control Science and Engineering, Tongji University;School of Artificial Intelligence, Beijing University of Posts and Telecommunications;School of Automation, Hangzhou Dianzi University;

关键词: Nash equilibrium;    Directed graph;    Exponential convergence;    Proportional control;    Distributed computation;   

DOI  :  10.1007/s43684-022-00026-2

来源: DOAJ

【 摘 要 】

Abstract 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.

【 授权许可】

Unknown