Choosing What to Protect

TLDR

The defender’s allocation problem creates negative externalities, as allocating more resources to one location raises attack likelihood at others. The study investigates a strategic model where a defender allocates resources to multiple locations while an attacker chooses a target. The defender is unaware of the attacker’s preferences, whereas the attacker observes the defender’s allocation. In equilibrium the defender exploits these externalities, sometimes leaving locations undefended or accepting higher vulnerability for zero cost, and the analysis shows that centralized allocation is preferred, cost‑effective reduction of attack probability requires bounded valuable targets, optimal allocation can be nonmonotonic in the attacker’s outside option, and a public allocation is favored over secrecy.

Abstract

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.