Cost of Equity in Homeland Security Resource Allocation in the Face of a Strategic Attacker

Abstract

Hundreds of billions of dollars have been spent in homeland security since September 11, 2001. Many mathematical models have been developed to study strategic interactions between governments (defenders) and terrorists (attackers). However, few studies have considered the tradeoff between equity and efficiency in homeland security resource allocation. In this article, we fill this gap by developing a novel model in which a government allocates defensive resources among multiple potential targets, while reserving a portion of defensive resources (represented by the equity coefficient) for equal distribution (according to geographical areas, population, density, etc.). Such a way to model equity is one of many alternatives, but was directly inspired by homeland security resource allocation practice. The government is faced with a strategic terrorist (adaptive adversary) whose attack probabilities are endogenously determined in the model. We study the effect of the equity coefficient on the optimal defensive resource allocations and the corresponding expected loss. We find that the cost of equity (in terms of increased expected loss) increases convexly in the equity coefficient. Furthermore, such cost is lower when: (a) government uses per-valuation equity; (b) the cost-effectiveness coefficient of defense increases; and (c) the total defense budget increases. Our model, results, and insights could be used to assist policy making.

On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness

“…Furthermore, the expected damage is decreasing in d i , but increasing in a i and λ. Consider an exponential damage function Golalikhani & Zhuang, 2011;Nikoofal & Zhuang, 2012;Shan & Zhuang, 2013a) …”

“…We employ data from Willis, Morral, Kelly, and Medby (2005) which provide estimates of the expected annual terrorism losses to the seven most valuable urban areas of the United States (Table 2). We assume that the expected property loss represents the defender's valuation of the target Hao et al, 2009;Hu et al, 2011;Nikoofal & Zhuang, 2012;Shan & Zhuang, 2013a) and that the total defender budget is $270 million (Willis et al, 2005).…”

Análise de Risco Adversário para alocação de recursos de contraterrorismo

“…(Bier, 2006) Tradeoff analysis in the distribution of resources for the protection of several targets Analysis of how considering equity and efficiency impacts on the distribution of resources for the protection of various targets. (Shan & Zhuang, 2012) question. However, it is important to point out here that allocating resources to protect oneself from the worst scenario (the one the opponent has in mind to cause and the one the defense will seek to avoid) is not tantamount to protecting against all other less harmful scenarios.…”

On the value of terrorist’s private information in a government’s defensive resource allocation problem

“…Also, it has the following regularity properties: (i) P(D i , A i ) is twice differentiable with respect to A i and D i and (ii) lim A i →0 P(D i , A i ) = 0, and lim D i →∞ P(D i , A i ) = 0. An appropriate candidate for the damage probability function that parsimoniously satisfies the above properties is the cumulative exponential function (Gerchak and Safayeni, 1996;Bier et al, 2008;Golalikhani and Zhuang, 2011;Shan and Zhuang, 2013b):…”