Defending Against a Stockpiling Terrorist

Abstract

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.

ACKNOWLEDGMENTS

This research was partially supported by the United States Department of Homeland Security through the National Center for Risk and Economic Analysis of Terrorism Events (CREATE) under award number 2010-ST-061-RE0001. However, any opinions, findings, and conclusions or recommendations in this document are those of the authors and do not necessarily reflect views of the United States Department of Homeland Security, or CREATE.

Notes

For analytical tractability one asset is considered. The model also applies for collections of assets interpreted as a joint asset. One example of a collection of assets is the four targets of the 9/11 attack; that is, the World Trade Center's North and South Towers, the Pentagon, and the White House (which was not hit). Focusing on one asset means that we do not analyze how the government and terrorist substitute resources across assets. See Enders and Sandler (2004), Hausken (2006), Bier et al. (2007, 2008), and Hao et al. (2009) for when a government allocates defense to a collection of locations and a terrorist chooses a location to attack.

The terrorist earns U = 1 from attacking only in period 1 when W < 0.28 and 0.75 < W < 0.83 and attacking only in period 10 when 1.20 < W < 1.34 and W > 3.62.

This follows because inserting W = 0.74, R = 15, and T = 10 into (21)–(23) implies R ₁ = 4.10, R ₂ = 3.04, R ₃ = 2.25, R ₄ = 1.66, R ₅ = 1.23, R ₆ = 0.91, R ₇ = 0.67, R ₈ = 0.50, R ₉ = 0.37, R ₁₀ = 0.27, and the cases are determined from Figure 2d.