Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(7): 2064-2073

https://doi.org/10.1007/s12555-023-0314-x

© The International Journal of Control, Automation, and Systems

Stable Degree Analysis for Profile of Networked Evolutionary Games With Disturbances

Ziyun Wang, Shihua Fu, Jianjun Wang, Ling Yu, and Xiaoyu Zhao*

Shandong University

Abstract

This paper studies the stable degree for profile of networked evolutionary games (NEGs) with disturbances by the semi-tensor product of matrices. Firstly, the algebraic formulation of an NEG with disturbances is established. Secondly, on the basis of algebraic formulation, some concepts about stable profile with disturbances are proposed, including strong k-degree stable and weak k-degree stable, and the corresponding criteria to detect the stable degree are presented. Thirdly, two algorithms for designing controls are given to make the stable profile achieves strong k-degree stable or weak k-degree stable. Finally, an example is given to illustrate the validity of the results.

Keywords Algebraic formulation, disturbances, networked evolutionary games, semi-tensor product of matrices, stable degree.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(7): 2064-2073

Published online July 1, 2024 https://doi.org/10.1007/s12555-023-0314-x

Copyright © The International Journal of Control, Automation, and Systems.

Stable Degree Analysis for Profile of Networked Evolutionary Games With Disturbances

Ziyun Wang, Shihua Fu, Jianjun Wang, Ling Yu, and Xiaoyu Zhao*

Shandong University

Abstract

This paper studies the stable degree for profile of networked evolutionary games (NEGs) with disturbances by the semi-tensor product of matrices. Firstly, the algebraic formulation of an NEG with disturbances is established. Secondly, on the basis of algebraic formulation, some concepts about stable profile with disturbances are proposed, including strong k-degree stable and weak k-degree stable, and the corresponding criteria to detect the stable degree are presented. Thirdly, two algorithms for designing controls are given to make the stable profile achieves strong k-degree stable or weak k-degree stable. Finally, an example is given to illustrate the validity of the results.

Keywords: Algebraic formulation, disturbances, networked evolutionary games, semi-tensor product of matrices, stable degree.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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