On the Stable Degree of Strategy Profile in Finite Evolutionary Networked Games

This paper investigates the stable degree of strategy profile in evolutionary networked games by using the semi-tensor product method. First, based on a normal evolutionary networked game model, the concept for k-degree stability of strategy profile is proposed. Second, using the semi-tensor product of matrices, the game dynamics with "best imitate" strategy updating rule is converted into an algebraic form. Third, the stable degree of strategy profile is analyzed and a necessary and sufficient condition for k-degree stability of strategy profile is obtained. Meanwhile, an algorithm is presented to verify the stable degree of strategy profile. The study of an illustrative example shows that the new results obtained are effective.