An Attacker–defender Resource Allocation Game with Substitution and Complementary Effects

Abstract

The United States is funding homeland security programs with a large budget (e.g., 74.4 billion for FY 2019). A number of game‐theoretic defender–attacker models have been developed to study the optimal defense resource allocation strategies for the government (defender) against the strategic adversary (attacker). However, to the best of our knowledge, the substitution or complementary effects between different types of defensive resources (e.g., human resource, land resource, and capital resource) have not been taken into consideration even though they exist in practice. The article fills this gap by studying a sequential game‐theoretical resource allocation model and then exploring how the joint effectiveness of multiple security investments influences the defensive budget allocation among multiple potential targets. Three false belief models have been developed in which only the defender, only the attacker, and both the defender and attacker hold false beliefs about the joint effectiveness of resources. Regression analysis shows that there are significant substitution effects between human and capital resources. The results show that the defender will suffer a higher loss if he fails to consider the substitution or complementary effects. Interestingly, if the attacker holds a false belief while the defender does not, the defender will suffer an even higher loss, especially when the resources are substitutes. However, if both the attacker and defender hold false beliefs, there will be lower loss when resources are complementary. The results also show that the defender should allocate the highly effective resource when the resources substitute each other. This article provides some new insights to the homeland security resource allocation.

Counterterrorism resource allocation during a pandemic: The effects of dynamic target valuations when facing a strategic terrorist

“…Following Aziz et al. (2020) and Wang and Bier (2016), we assume that the total valuation of a target consists of two components: (i) the valuation of all lives (i.e., the casualties that could result from a successful attack at the target), and (ii) the valuation of damaged property. Clearly, the former component (i.e., valuation of all lives) of a target's value directly depends on the population flow at a target.…”

“…Property losses are available directly from GTD, and as suggested by Aziz et al. (2020), incomplete data can be imputed by calculating the average value of property losses for each category of incidents (i.e., minor, major, catastrophic, and unknown). Following the treatments of Bier et al.…”

“…In particular, for casualty-related losses, we follow CREATE (2011) and Zycher (2003), and set $6 million as the value of a life lost, and $40,000 as the value of an injury. Property losses are available directly from GTD, and as suggested by Aziz et al (2020), incomplete data can be imputed by calculating the average value of property losses for each category of incidents (i.e., minor, major, catastrophic, and unknown). Following the treatments of Bier et al (2008), Wang and Bier (2016), and Guan and Zhuang (2016), we adopt the targets' expected losses as their original valuations.…”

“…In the counterterrorism literature (Aziz et al., 2020; Dong et al., 2021; Institute for Economics & Peace [IEP], 2014; Wang & Bier, 2016), the total valuation of a target usually consists of two parts: casualties and the property damages, and the former part directly depends on the population flow at a specific target. Given that the primary motivation behind many terrorist attacks is to inflict casualties (Phillips, 2013), the value of a specific target should closely depend on the number of people who are occupying that target.…”

Deterrence against Terrorist Attacks in Sports‐Mega Events: A Method to Identify the Optimal Portfolio of Defensive Countermeasures

“…They use a sequential game to minimize expected loss and assume the adversary will always attack. Aziz, He, and Zhuang (2020) adopt a sequential game to explore the effectiveness of considering the complementary or substitute effect of a joint allocation of human and capital resources when protecting multiple targets. The authors conclude that highly effective resources should be used when the resources substitute each other.…”