Bier Vicki M
Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, USA.
Risk Anal. 2007 Jun;27(3):607-20. doi: 10.1111/j.1539-6924.2007.00906.x.
We study a strategic model in which a defender must allocate defensive resources to a collection of locations, and an attacker must choose a location to attack. The defender does not know the attacker's preferences, while the attacker observes the defender's resource allocation. The defender's problem gives rise to negative externalities, in the sense that increasing the resources allocated to one location increases the likelihood of an attack at other locations. In equilibrium, the defender exploits these externalities to manipulate the attacker's behavior, sometimes optimally leaving a location undefended, and sometimes preferring a higher vulnerability at a particular location even if a lower risk could be achieved at zero cost. Key results of our model are as follows: (1) the defender prefers to allocate resources in a centralized (rather than decentralized) manner; (2) as the number of locations to be defended grows, the defender can cost effectively reduce the probability of a successful attack only if the number of valuable targets is bounded; (3) the optimal allocation of resources can be nonmonotonic in the relative value of the attacker's outside option; and (4) the defender prefers his or her defensive allocation to be public rather than secret.
我们研究一种战略模型，其中防御者必须将防御资源分配到一系列地点，而攻击者必须选择一个地点进行攻击。防御者不知道攻击者的偏好，而攻击者能观察到防御者的资源分配情况。防御者的问题会产生负外部性，即增加分配到一个地点的资源会增加其他地点遭受攻击的可能性。在均衡状态下，防御者利用这些外部性来操纵攻击者的行为，有时会最优地不设防某个地点，有时即使可以零成本实现更低风险，也会选择在特定地点有更高的脆弱性。我们模型的关键结果如下：（1）防御者倾向于以集中（而非分散）的方式分配资源；（2）随着要防御的地点数量增加，只有当有价值目标的数量有界时，防御者才能以成本有效的方式降低成功攻击的概率；（3）资源的最优分配在攻击者外部选择的相对价值上可能是非单调的；（4）防御者更倾向于其防御分配是公开的而非秘密的。
