Stable degree analysis for strategy profiles of evolutionary networked games

In this paper, we investigate the stable degree of strategy profile for evolutionary networked games by using the semi-tensor product method, and present a number of new results. First, we propose the concept of k-degree stability for strategy profiles based on a normal evolutionary networked game model. Second, using the semi-tensor product of matrices, we convert the game dynamics with "best imitate" strategy updating rule into an algebraic form. Third, based on the algebraic form of the game, we analyzed the stable degree of strategy profile, and proposed two necessary and sufficient conditions for the k-degree stability of strategy profile. Furthermore, we discuss the computation problem of the transient time within which a disturbed strategy profile can be restored, and also establish an algorithm for the verification of the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained in this paper are very effective.