The Mathematics of Terrorism Risk: Equilibrium Force Allocations and Attack Probabilities (original) (raw)
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Strategic Analysis of Terrorism
Mathematical Methods in Counterterrorism, 2009
Two areas that are increasingly studied in the game-theoretic literature on terrorism and counterterrorism are collective action and asymmetric information. One contribution of this chapter is a survey and extension of continuous policy models with differentiable payoff functions. In this way, policies can be characterized as strategic substitutes (e. g., proactive measures), or strategic complements (e. g., defensive measures). Mixed substitute-complement models are also introduced. We show that the efficiency of counterterror policy depends upon (i) the strategic substitutes-complements characterization, and (ii) who initiates the action. Surprisingly, in mixed-models the dichotomy between individual and collective action may disappear. A second contribution is the consideration of a signaling model where indiscriminant spectacular terrorist attacks may erode terrorists' support among its constituency, and proactive government responses can create a backlash effect in favor of terrorists. A novel equilibrium of this model reflects the well-documented ineffectiveness of terrorism in achieving its stated goals.
The economics of terrorism against two targets
Applied Economics Letters, 2012
A terrorist without capacity constraints attacks two independent targets. As the target defence efficiency decreases, the target first increases its defence, and thereafter decreases and eventually does not defend because of the high cost. With terrorist capacity constraints, targets become interdependent. The attack gets gradually shifted towards the most vulnerable target. When only the most vulnerable target is attacked, only
European Journal of Operational Research, 2009
Probabilistic uncertainty is caused by ''chance'', whereas strategic uncertainty is caused by an adverse interested party. Using linear impact functions, the problems of allocating a limited resource to defend sites that face either probabilistic risk or strategic risk are formulated as optimization problems that are solved explicitly. The resulting optimal policies differ-under probabilistic risk, the optimal policy is to focus the investment of resources on priority sites where they yield the highest impact, while under strategic risk, the best policy is to spread the resources so as to decrease the potential damage level of the most vulnerable site(s). Neither solution coincides with the commonly practiced proportionality allocation scheme.
Governments' and Terrorists' Defense and Attack in a T -Period Game
Decision Analysis, 2011
W e analyze how a government allocates its resources between attacking to downgrade a terrorist's resources and defending against a terrorist attack. Analogously, the terrorist allocates its resources between attacking a government's asset and defending its own resources. A two-stage game is considered where the government moves first and the terrorist moves second. We show that (a) when the terrorist's resources are low, the government attacks the terrorist's resources sufficiently to deter the terrorist from attacking and does not defend; (b) when the terrorist's resources are high, both the government and terrorist defend and attack. We analyze T periods of the two-stage game between two myopic players. First we assume no linkages between periods. We show that after an attack the government may enjoy incoming resources, which deter the terrorist for some periods. Between periods the terrorist's resources may change because of arithmetically and geometrically changing incoming funds. We allow the government's and the terrorist's resources to be determined randomly in each time period. We also allow the government's resources in one period to depend on the terrorist's attacks in earlier time periods for three dynamics, where the terrorist's resources are drawn from a normal distribution or change arithmetically or geometrically.
Games, 2021
This paper derives a dynamic path of ongoing terror attacks as a function of terrorists’ capacity and a target government’s counterterror capacity. The analysis provides several novel insights and characterizations. First, the effect of counterterror policy is limited. Second, proactive counterterror policy affects the depreciation (fatigue) of terrorists’ capacity, and defensive counterterror policy limits the worst-case scenario. Third, fluctuations in the time path of attacks are a function of terrorists’ time preferences and adjustment costs of changing tactics, which are policy invariant. Indeed, in our model, the oscillations of terror attacks occur irrespective of the government’s counterterror stance. Fourth, collective action inefficiencies associated with the underprovision of proactive counterterror policies and overprovision of defensive ones are further exacerbated by our finding that proactive counterterror policy is the more effective of the two. Hence, the more effec...
Balancing Defending and Attacking—Both Governments’ and Terrorists’ Problem
2009
Abstract We analyze how a government allocates resources between defending against a terrorist attack and attacking a terrorist's resource, and how a terrorist allocates resources between attacking a government's asset and defending its resource. A two-stage game is considered where the government moves first. When the terrorist's resource is small, the government attacks the terrorist's resource to deter the terrorist. When the terrorist's resource is intermediate, the terrorist attacks and defends, while the government only attacks.
Terrorism and the optimal defense of networks of targets
2008
This paper examines a game-theoretic model of attack and defense of multiple networks of targets in which there exist intra-network strategic complementarities among targets. The defender's objective is to successfully defend all of the networks and the attacker's objective is to successfully attack at least one network of targets. In this context, our results highlight the importance of modeling asymmetric attack and defense as a conflict between "fully" strategic actors with endogenous entry and force expenditure decisions as well as allowing for general correlation structures for force expenditures within and across the networks of targets.
Governments' and Terrorists' Defense and Attack in a
Decis Anal, 2011
W e analyze how a government allocates its resources between attacking to downgrade a terrorist's resources and defending against a terrorist attack. Analogously, the terrorist allocates its resources between attacking a government's asset and defending its own resources. A two-stage game is considered where the government moves first and the terrorist moves second. We show that (a) when the terrorist's resources are low, the government attacks the terrorist's resources sufficiently to deter the terrorist from attacking and does not defend; (b) when the terrorist's resources are high, both the government and terrorist defend and attack. We analyze T periods of the two-stage game between two myopic players. First we assume no linkages between periods. We show that after an attack the government may enjoy incoming resources, which deter the terrorist for some periods. Between periods the terrorist's resources may change because of arithmetically and geometrically changing incoming funds. We allow the government's and the terrorist's resources to be determined randomly in each time period. We also allow the government's resources in one period to depend on the terrorist's attacks in earlier time periods for three dynamics, where the terrorist's resources are drawn from a normal distribution or change arithmetically or geometrically.
©2011 INFORMS Governments ’ and Terrorists ’ Defense and Attack in a T-Period Game
2016
We analyze how a government allocates its resources between attacking to downgrade a terrorist’s resourcesand defending against a terrorist attack. Analogously, the terrorist allocates its resources between attacking a government’s asset and defending its own resources. A two-stage game is considered where the government moves first and the terrorist moves second. We show that (a) when the terrorist’s resources are low, the gov-ernment attacks the terrorist’s resources sufficiently to deter the terrorist from attacking and does not defend; (b) when the terrorist’s resources are high, both the government and terrorist defend and attack. We analyze T periods of the two-stage game between two myopic players. First we assume no linkages between peri-ods. We show that after an attack the government may enjoy incoming resources, which deter the terrorist for some periods. Between periods the terrorist’s resources may change because of arithmetically and geometrically changing incoming fun...