When Escalation is Inevitable: A Role of Thresholds in a Counterterrorism Game

A counterterrorism model is developed where a government and a terrorist allocate resources over two periods. Escalation to period 2 occurs if a threshold for the government’s period-1 damage is exceeded. Without escalation four scenarios exist, including deterrence and nonprovocation. With escalation and unitary contest intensity, both players’ fractions of their resources allocated to period 1 equal the sum of their potential period-1 damages divided by the sum of their potential damages in both periods. As the government’s resource superiority increases, the terrorist allocates all its resources to the period-1 attack, and the government deters escalation. Uniform distributions of the contest intensity and the government’s resource superiority over various intervals are considered. Observing that the terrorist’s utility may be U-shaped in the escalation threshold, the government is enabled to determine both its resource allocation and escalation threshold. The government prefers no threshold when it lacks resources and should always escalate, and when it has abundant resources and can deter. For intermediate resource superiority, the government prefers an intermediate threshold. Six game outcomes are shown where escalation is deterred for two disjoint intervals of the government’s resource superiority.