In recent years, evolutionary game theory has been gradually applied to analyze and predict network attack and defense for maintaining cybersecurity. The traditional deterministic game model cannot accurately describe the process of actual network attack and defense due to changing in the set of attack-defense strategies and external factors (such as the operating environment of the system). In this paper, we construct a stochastic evolutionary game model by the stochastic differential equation with Markov property. The evolutionary equilibrium solution of the model is found and the stability of the model is proved according to the knowledge of the stochastic differential equation. And we apply the explicit Euler numerical method to analyze the evolution of the strategy selection of the players for different problem situations. The simulation results show that the stochastic evolutionary game model proposed in this paper can get a steady state and obtain the optimal defense strategy under the action of the stochastic disturbance factor. In addition, compared with other kinds of literature, we can conclude that the return on security investment of this model is better, and the strategy selection of the attackers and defenders in our model is more suitable for actual network attack and defense.

中文翻译：

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网络攻防中的随机差分博弈模型研究

近年来，进化博弈论已逐渐应用于分析和预测网络攻击和防御以维护网络安全。传统的确定性博弈模型由于攻防策略集和外部因素（例如系统的运行环境）的变化而无法准确描述实际的网络攻防过程。本文利用具有马尔可夫性质的随机微分方程构建了一个随机演化博弈模型。根据随机微分方程的知识，找到了模型的演化平衡解，并证明了模型的稳定性。并且我们采用显式欧拉数值方法来分析针对不同问题情况的参与者策略选择的演变。仿真结果表明，本文提出的随机演化博弈模型可以在随机干扰因素的作用下，达到稳态并获得最优的防御策略。此外，与其他文献相比，我们可以得出结论，该模型的安全性投资回报率更高，并且该模型中的攻击者和防御者的策略选择更适合实际的网络攻击和防御。