Abstract
We study a model of terrorism and counterterrorism with three geographic target locations, in which the last location is chosen by the terrorists and is unknown to the defender. We find the choice of location and defender’s allocation of defensive resources to depend on whether the first two locations are attacked simultaneously or sequentially. In the sequential-move game, the final attack is closer to the low-valued target than it is in the simultaneous-move game. In addition, the defender chooses to defend only the location that is attacked first in the sequential game. Results from the model also can shed light on less provocative criminal events such as bank robberies and drug dealings.
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Notes
Comparatively, there are 4,935 attacks targeted a single geographic location, 3,002 attacks targeted two locations, 467 attacks targeted four locations, 228 attacks targeted five locations, and 553 attacks targeted six or more locations (authors’ calculation).
Game-theoretic models have provided important insights into the analyses of terrorism and counterterrorism. Notable examples include Sandler et al. (1983) and Bueno de Mesquita (2005a, b, c) on various interactions between government and terrorists, Cadigan and Schmitt (2010) on entry deterrence and terrorism, Bandyopadhyay and Sandler (2011) on the interplay between preemptive and defensive measures, Bandyopadhyay et al. (2011, 2014) on the relationship between foreign aid, terrorism, and counterterrorism, and Das and Chowdhury (2014) on deterrence and preemption. For recent surveys, see Sandler and Arce (2003), Sandler and Siqueira (2009), Sandler (2014, 2015), and Schneider et al. (2015).
Even though Bier et al. (2007) present a general model that can deal with more than two potential targets, the main derivation of their results is done in a two-target setting.
Alternatively, one may think of this scenario in the context of two local terrorist groups competing to show their loyalty to the leader by providing “additional” soldiers.
As outlined in Sect. 2.2, the current model assumes that the defender “chooses” the values of \(w_i\). As a result, whether defense may cause a reversal of valuations of the two locations can not be analyzed in the current framework.
The sufficient and necessary condition for \({\bar{d}}_1={\tilde{d}}_1\) is
$$\begin{aligned} {\left\{ \begin{array}{ll}w_1=2w_1-w_2;\\ w_1^2+w_2^2=4w_1^2-3w_1w_2+w_2^2;\end{array}\right. } \end{aligned}$$which hold true if \(w_1=w_2\).
It is straightforward to verify that
$$\begin{aligned} \frac{\partial ^2{\mathscr {L}}}{\partial w_i^2}=\frac{w_j(w_i+w_j)}{w_i^2(w_i+w_j)^2}>0; \end{aligned}$$and hence the second order condition of a minimization problem is satisfied.
In the movie, Texas Ranger Marcus Hamilton, played by Oscar-winning actor Jeff Bridges, needs to determine which branch of a bank will be attacked next by the Howard brothers. The Howard brothers had previously robbed three other branches of the same bank.
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Acknowledgements
We thank the editors and two anonymous referees for helpful comments, which have significantly improved the qualify of the paper. An earlier version of this paper was presented at Jinan University, South China Normal University, and the 28th International Conference on Game Theory. We thank seminar and conference participants especially Timothy Mathews, Shane Sanders, Xianbin Wang, and Zhibo Wang for helpful comments. Any remaining errors are ours.
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Jiao, Y., Luo, Z. A model of terrorism and counterterrorism with location choices. Public Choice 179, 301–313 (2019). https://doi.org/10.1007/s11127-018-0559-8
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DOI: https://doi.org/10.1007/s11127-018-0559-8