论文标题
部分可观测时空混沌系统的无模型预测
Economics and Optimal Investment Policies of Attackers and Defenders in Cybersecurity
论文作者
论文摘要
在我们的时期，网络安全已成为国家和企业层面上大量比例的话题。我们的论点是，经济观点和投资决策是确定斗争结果的重要因素。为了建立我们的经济框架，我们从戈登和勒布的开拓性工作中借用，在这些工作中，防守者最佳地交易投资以降低其系统违规的可能性。我们的双向模型还具有一个攻击者，被认为是理性的，并且在决策中也受到经济考虑的指导，后卫对此做出了回应。我们的模型是对在美国冷战期间提出的模型的简化改编。我们的模型也可能被视为stackelberg游戏，从分析的角度来看，这是一个最大的问题，其中已知的分析必须与不连续的行为抗衡。我们简单模型的复杂性植根于其固有的非线性，更是如此，更重要的是，在优化中，目标函数的非转换性。攻击者行动的可能性极大地增加了防守者的风险，而辩护人的理性，风险中立的最佳投资总体上大大超过了单方面的Gordon-Loeb模型预测的最佳投资。我们获得了三种简洁的决策类型，这些决策类型将所有辩护人的最佳投资决策分类。同样，随着其系统的最初脆弱性的变化，辩护人的最佳决策表现出不连续的行为。分析补充了广泛的数值插图。我们的模型的结果为将来的工作开放了几种主要途径。
In our time cybersecurity has grown to be a topic of massive proportion at the national and enterprise levels. Our thesis is that the economic perspective and investment decision-making are vital factors in determining the outcome of the struggle. To build our economic framework, we borrow from the pioneering work of Gordon and Loeb in which the Defender optimally trades-off investments for lower likelihood of its system breach. Our two-sided model additionally has an Attacker, assumed to be rational and also guided by economic considerations in its decision-making, to which the Defender responds. Our model is a simplified adaptation of a model proposed during the Cold War for weapons deployment in the US. Our model may also be viewed as a Stackelberg game and, from an analytic perspective, as a Max-Min problem, the analysis of which is known to have to contend with discontinuous behavior. The complexity of our simple model is rooted in its inherent nonlinearity and, more consequentially, non-convexity of the objective function in the optimization. The possibilities of the Attacker's actions add substantially to the risk to the Defender, and the Defender's rational, risk-neutral optimal investments in general substantially exceed the optimal investments predicted by the one-sided Gordon-Loeb model. We obtain a succinct set of three decision types that categorize all of the Defender's optimal investment decisions. Also, the Defender's optimal decisions exhibit discontinuous behavior as the initial vulnerability of its system is varied. The analysis is supplemented by extensive numerical illustrations. The results from our model open several major avenues for future work.
