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.摘要创新点基于矩阵半张量积这一新工具,本文研究了有限网络演化博弈中策略组合的稳定度分析问题。 主要创新在于: (1) 提出了玩家策略组合的 k 度稳定性的概念, (2) 针对最优模仿策略调整规则, 为博弈的演化过程建立一个严格的动力学方程, 并将其转化为代数形式, (3) 得到了策略组合 k 度稳定的两个充分必要条件, 在 MATLAB 的帮助下这些条件都是很容易验证的, 并且给出一个计算策略组合稳定度的算法。