Cyber risk has become a critical financial threat in today's interconnected digital economy. This paper introduces a cyber-risk management framework for networked digital systems that combines the strategic behavior of players with contagion dynamics within a security game. We address the problem of optimally allocating cybersecurity resources across a network, focusing on the heterogeneous valuations of nodes by attackers and defenders, some areas may be of high interest to the attacker, while others are prioritized by the defender. We explore how this asymmetry drives attack and defense strategies and shapes the system's overall resilience. We extend a method to determine optimal resource allocation based on simple network metrics weighted by the defender's and attacker's risk profiles. We further propose risk measures based on contagion paths and analyze how propagation dynamics influence optimal defense strategies. Numerical experiments explore risk versus cost efficient frontiers varying network topologies and risk profiles, revealing patterns of resource allocation and cyber deception effects. These findings provide actionable insights for designing resilient digital infrastructures and mitigating systemic cyber risk.

翻译：网络风险已成为当今互联数字经济中的关键金融威胁。本文提出了一种面向网络化数字系统的网络风险管理框架，该框架将参与者的策略行为与安全博弈中的传播动力学相结合。我们研究了在网络中优化分配网络安全资源的问题，重点关注攻击者和防御者对节点的异质价值评估——某些区域可能对攻击者具有高价值，而其他区域则被防御者优先保护。我们探讨了这种不对称性如何驱动攻防策略并塑造系统的整体韧性。我们扩展了一种基于简单网络度量的方法来确定最优资源分配，这些度量通过防御者和攻击者的风险分布进行加权。进一步提出了基于传播路径的风险度量，并分析了传播动力学如何影响最优防御策略。通过数值实验探究了不同网络拓扑和风险分布下的风险-成本效率前沿，揭示了资源分配模式和网络欺骗效应。这些发现为设计韧性数字基础设施和缓解系统性网络风险提供了可操作的见解。