Abstract: The random selection of network attack or defense strategy will cause that the system state changes randomly, the process of network attack and defense is certainly a multi-state confrontation also, whose gain matrix is different. This paper provides a new Markov evolutionary game model with multi-state and multi-agent, which uses Markov decision processes to describe the randomness and extend the game model from single-state to multi-state. After the formalization, this paper proves the existence of equilibrium strategy and gets the defense strategy by solving a corresponding nonlinear programming model. Finally, this paper takes a typical enterprise network attack process for example, does simulation analysis and deduction, the results show that this model can match the actual application, the evaluation results are accurate, and helpful to the development of the offensive and defensive game.

Key words: offensive and defensive evolution, evolutionary game, Markov game, network attack model, network security

摘要： 网络攻击或防御策略选取的随机性会导致系统状态变化的随机性，网络攻防的过程也定然是收益矩阵各不相同的多状态上的对抗。使用Markov决策过程对这一随机性进行刻画，将单状态的博弈模型扩展到多状态，形成了多状态多智能体的Markov演化博弈模型；在形式化建模的基础上，证明了均衡策略的存在；通过非线性规划的求解方法得到了攻防策略方案。最后以一个典型的企业网络攻防过程为例，使用该模型进行了仿真分析和推演，结果表明该模型符合实际应用，评估结果准确，有助于攻防博弈研究的发展。

关键词: 攻防演化, 演化博弈, Markov博弈, 网络攻击模型, 网络安全