标题： 基于信号博弈的CPS防御中的最优诱饵比例与收敛虚设博弈学习 显示英文标题

标题： Optimal Honeypot Ratio and Convergent Fictitious-Play Learning in Signaling Games for CPS Defense

摘要： 网络物理系统(CPSs)正面临日益增长的攻击浪潮。 为了实现有效的主动防御，本文将蜜罐部署建模为一个gamma固定信号博弈，在该博弈中节点存活状态作为唯一的信号，正常节点信号gamma是外生固定的。 我们定义了gamma-完美贝叶斯纳什均衡(gamma-PBNE)。 获得了所有gamma-PBNE的解析表达式，揭示了三种不同的均衡区域，这些区域取决于先验蜜罐比例。 此外，获得了最优蜜罐比例和联合最大化网络平均效用的信号策略。 为了捕捉随时间的战略互动，我们开发了一个离散时间虚拟博弈算法，该算法将贝叶斯信念更新与经验最佳响应相结合。 我们证明了只要蜜罐比例在最优值的非退化邻域内扰动，每条虚拟博弈路径都会收敛到防守者最优的gamma-PBNE。 数值结果证实了所提出方法的有效性，并展示了其在CPS防御中的适用性。 显示英文摘要

摘要： Cyber-Physical Systems (CPSs) are facing a fast-growing wave of attacks. To achieve effective proactive defense, this paper models honeypot deployment as a gamma-fixed signaling game in which node liveness serves as the only signal and normal-node signal gamma is exogenously fixed. We define the gamma-perfect Bayesian-Nash equilibrium (gamma-PBNE). Analytical expressions are obtained for all gamma-PBNEs, revealing three distinct equilibrium regimes that depend on the priori honeypot ratio. Furthermore, the optimal honeypot ratio and signaling strategy that jointly maximize the network average utility are obtained. To capture strategic interaction over time, we develop a discrete-time fictitious-play algorithm that couples Bayesian belief updates with empirical best responses. We prove that, as long as the honeypot ratio is perturbed within a non-degenerate neighbourhood of the optimum, every fictitious-play path converges to the defender-optimal gamma-PBNE. Numerical results confirm the effectiveness of the proposed method and demonstrate its applicability to CPS defense.