The stability degree analysis of profiles for networked evolutionary games with switching topology

Abstract

In this paper, we investigate the stability degree of profiles for a class of networked evolutionary games (NEGs) with switching topology using the semi-tensor product of matrices. Firstly, we calculate the algebraic form of NEGs with switching topology, whose strategy updating rule is myopic best response adjustment rule and network updating rule is voting principle. Secondly, the strong stability degree and weak stability degree of a profile are defined, and some necessary and sufficient conditions to detect whether a profile is strong or weak k−degree stable are provided. Furthermore, we propose the state feedback controller algorithms to guarantee that a profile is strong or weak k−degree stable, respectively. Finally, a numerical example is provided to illustrate the effectiveness of our results.