Result: Nash equilibrium seeking over directed graphs

Title:
Nash equilibrium seeking over directed graphs
Authors:
Yutao Tang, Peng Yi, Yanqiong Zhang, Dawei Liu
Source:
Autonomous Intelligent Systems, Vol 2, Iss 1, Pp 1-8 (2022)
Publisher Information:
Springer, 2022.
Publication Year:
2022
Collection:
LCC:Electronic computers. Computer science
LCC:Computer engineering. Computer hardware
Subject Terms:
Nash equilibrium, Directed graph, Exponential convergence, Proportional control, Distributed computation, Electronic computers. Computer science, QA75.5-76.95, Computer engineering. Computer hardware, TK7885-7895
Document Type:
Academic journal article
File Description:
electronic resource
Language:
English
ISSN:
2730-616X
Relation:
https://doaj.org/toc/2730-616X
DOI:
10.1007/s43684-022-00026-2
Access URL:
https://doaj.org/article/bf201d0e6fbc458d8588bcd6d0bc49a1
Accession Number:
edsdoj.bf201d0e6fbc458d8588bcd6d0bc49a1
Database:
Directory of Open Access Journals

Further Information

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.