November 23, 2011
A government defends against a terrorist who attacks repeatedly and stockpiles its resources over time. The government defends an asset and attacks the terrorist’s resources. The terrorist defends its resources and attacks the government. We find four possible equilibrium solutions: (1) the government attacks only, deterring the terrorist; (2) both players defend and attack; (3) the government defends but does not attack, and the terrorist attacks only; and (4) the terrorist attacks a passive government. Understanding which factors impact the four cases is important in order to combat terrorism. The terrorist allocates its resources over T periods according to a geometric series with a stockpiling parameter. This article analyzes how the government and terrorist prefer low versus high stockpiling parameters and how these preferences interact with the other parameters such as the terrorist’s resources and the players’ asset valuations, unit defense and attack costs, and discount factors. If the terrorist’s resources are small, it can be deterred in each period. If the terrorist’s resources are extremely large, it allocates its resources equally across the T periods, whereas the government prefers a single attack. If the terrorist’s resources are intermediate, the terrorist would be deterred in each period if it allocated its resources equally across the T periods. It thus strikes a balance where it allocates much resources to early or late periods, to facilitate attacks, and accept being deterred in the other periods. As the future becomes less important, the terrorist attacks more in early periods.