研究了基于添加惩罚策略的囚徒困境 博弈的网络演化模型. 利用矩阵的半张量积方法, 建立了该 网络演化博弈的数学模型, 并结合逻辑的矩阵表达, 将该数学模型表示成动态逻辑系统并转化成代数形式. 然后, 对其动态演化过程进行分析, 讨论了最终合作水平. 最后, 通过例子对结论进行验证.

This paper investigates the modeling and analysis of network evolution based on prisoner's dilemma game with punishment strategy.\ Using the method of semi-tensor product of matrices ,\ the mathematical model of the networked evolutionary game is built .\ The networked evolutionary game is expressed as a logical dynamic system and then converted into its algebraic form rely on the matrix expression of logic and the method of seme-tensor product of matrices.\ Next,\ the dynamic evolution process is analysed and the final cooperation levels of the networked evolutionary game is discussed.\ Finally,\ an illustrative example is given to show the effectiveness of our main results.