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

Abstract

The ability to understand and predict the sequence of events leading to a terrorist attack is one of the main issues in developing preemptive defense strategies for homeland security. This article, explores the value of terrorist's private information on a government's defense allocation decision. In particular, two settings with different informational structures are considered. In the first setting, the government knows the terrorist's target preference but does not know whether the terrorist is fully rational in his target selection decision. In the second setting, the government knows the degree of rationality of the terrorist but does not know the terrorist's target preference. The government's equilibrium budget allocation strategy for each setting is fully characterized and it is shown that the government makes resource allocation decisions by comparing her valuation for each target with a set of thresholds. The Value Of Information (VOI) from the perspective of the government for each setting is derived. The obtained results show that VOI mainly depends on the government's budget and the degree of heterogeneity among the targets. In general, VOI goes to zero when the government's budget is high enough. However, the impact of heterogeneity among the targets on VOI further depends on whether the terrorist's target preference matches those of the government's or not. Finally, various extensions on the baseline model are performed and it is shown that the structural properties of budget allocation equilibrium still hold true.

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

“…A number of studies investigate signaling games where the defender updates her belief about the attacker's attributes (Arce & Sandler, 2007;Harvey & Sandler, 1993;Hausken & Zhuang, 2011;Overgaard, 1994;Zhuang, Bier, & Alagoz, 2010). There is also some research that investigates allocating defensive resources facing both strategic threats (e.g., strategic terrorists) and nonstrategic threats (e.g., natural disasters Golany, Kaplan, Marmur, & Rothblum, 2009;Levitin & Hausken, 2009;Powell, 2007b;Zhuang & Bier, 2007 and nonstrategic terrorists Hao, Jin, & Zhuang, 2009;Nikoofal & Gumus, 2015;Shan & Zhuang, 2013b). The only paper in this stream that investigates the impact of the attacker's private information on the robustness of the defender's budget allocation is Nikoofal and Zhuang (2012); however, it fails to compare the robustness of the defense system in a sequential game with that in a simultaneous game, and thus fails to study the tradeoff between secrecy and exposure.…”

Securing containerized supply chain through public and private partnership

“…Also, $$P_i(Y_{i},f,s_{i},A_{i})$$ has the following regularity properties: (i) $$P_i(Y_{i},f,s_{i},A_{i})$$ is twice differentiable with respect to $$A_{i}$$; (ii) $$\underset{A_{i}\rightarrow 0}{\lim }P_i(Y_{i},f,s_{i},A_{i})=0$$; and (iii) $${\lim }_{(f+s_{i})\rightarrow \infty }P_i(Y_{i},f,s_{i},A_{i})=0$$. An appropriate candidate for the probability of infiltration function satisfying the above properties is the cumulative exponential function (Bier et al., 2008; Gerchak & Safayeni, 1996; Nikoofal & Gümüs, 2015): $$$$\begin{equation} P_i(Y_{i},f,s_{i},A_{i})=1-\exp {\left(\frac{-\eta _i A_{i}}{Y_{i}{\left(f+s_{i}\right)}+z_i}\right)}. \end{equation}$$$$Note from Equation () that the adversary may infiltrate a nonmember's container with less effort than what is required for a member's container.…”

“…A more relevant stream of literature to our paper has cast the adversary as strategic in responding to the decisions and strategies of the securing party, whether public or private. In this line of work, a growing body of literature has studied mainly the logistic problem of resource allocation faced by governments defending themselves against terrorism—often framed as defender/attacker games (Baron et al., 2018; Golany et al., 2009; Hausken et al., 2009; Nikoofal & Gümüs, 2015; Powell, 2007a; Zhuang & Bier, 2007).…”

“…for the probability of infiltration function satisfying the above properties is the cumulative exponential function (Bier et al, 2008;Gerchak & Safayeni, 1996;Nikoofal & Gümüs, 2015):…”

Prevention of Terrorism–An Assessment of Prior POM Work and Future Potentials

“…Nikoofal and Gümüs (2015) study the impact of an unforeseeable terrorist’s information about the government’s spending priorities for the protection of targets. The authors show that (1) the value of information related to target preference is positive when the degree of information asymmetry is high enough; (2) the value of information enlarges the government’s budget at the beginning of the process; and later, decreases; (3) the value of information is correlated (both positive and negative) with the degree of heterogeneity between targets; and, (4) the value of target information is not altered by the effectiveness ratio of attack, but the impact of that ratio on the value of rationality depends on the actual nature of the terrorist.…”