A Study on a Sequential One‐Defender‐N‐Attacker Game

Abstract

Government usually faces threat from multiple attackers. However, in the literature, researchers often model attackers as one monolithic player who chooses whether to attack, how much investment to spend, and on which target, instead of treating multiple attackers as independent agents. This modeling strategy may potentially cause suboptimal defense investment if the attackers have vastly different interests and preferences and may not be combined as one in theory. In this article, we develop a sequential game with complete information. This model considers one defender explicitly dealing with multiple unmergeable attackers. Thorough numerical experiments are conducted using ratio and exponential contest success functions under different scenarios. The result is also contrasted with the corresponding single attacker model to study the effect of mishandling multiple attackers. The propositions and observations drawn from the numerical experiments provide insights for government decision making with a better understanding of the attackers' behavior.

Firm investment decisions for information security under a fuzzy environment: a game-theoretic approach

“…The application of game theory to analyze the strategic choices of a firm in EIS literature has gained attention in recent times (Wu et al , 2017; Qian et al , 2018; Miaoui and Boudriga, 2019; Xu and Zhuang, 2019; Feng et al , 2020; Li and Xu, 2020; Peng et al , 2020; Wu et al , 2020; Zhai et al , 2020). Laszka et al (2015) provide a detailed literature review of existing research on strategic games under a full-information setting.…”

“…We observe that broadly two forms of probability functions are adopted in the extant game-theoretic EIS literature: BPF first proposed by Gordon and Loeb (2002), modified by Cavusoglu et al (2008) and used in a multitude of cybersecurity investment problems (Huang et al , 2008; Kim and Kim, 2016; Young et al , 2016; Ezhei and Ladani, 2017; Qian et al , 2017; Wu et al , 2017; Ezhei and Ladani, 2018; Qian et al , 2018; Miaoui and Boudriga, 2019; Dou et al , 2020; Feng et al , 2020; Gordon et al , 2020; Li and Xu, 2020; Wu et al , 2020). Contest success function (CSF) introduced in rent-seeking literature and widely applied by Hausken and associates (Hausken and Bier, 2011; Hausken and Zhuang, 2012; Hausken, 2017a; Hausken, 2017b; Hausken, 2017c; Hausken, 2019) and other scholars (Gao et al , 2014; Peng et al , 2016; Guan et al , 2017; Wu et al , 2018; Wu et al , 2019; Xu and Zhuang, 2019; Wu et al , 2020; Peng et al , 2020; Xiao et al , 2020; Zhai et al , 2020) for modeling defender-attacker problems. …”

“…Contest success function (CSF) introduced in rent-seeking literature and widely applied by Hausken and associates (Hausken and Bier, 2011; Hausken and Zhuang, 2012; Hausken, 2017a; Hausken, 2017b; Hausken, 2017c; Hausken, 2019) and other scholars (Gao et al , 2014; Peng et al , 2016; Guan et al , 2017; Wu et al , 2018; Wu et al , 2019; Xu and Zhuang, 2019; Wu et al , 2020; Peng et al , 2020; Xiao et al , 2020; Zhai et al , 2020) for modeling defender-attacker problems.…”

“…Recent studies in EIS have also dealt with game-theoretic modeling to investigate the strategies of the attackers and the firms (Hausken, 2014; Fielder et al , 2016; Hausken, 2017a; Hausken, 2017b; Hausken, 2017c; Wu et al , 2018; Hausken, 2019; Xiao et al , 2020; Zhai et al , 2020). While they have considered attack scenarios with multiple firms (Gao et al , 2015; Gao and Zhong, 2015; Huang and Behara, 2013) or between a single attacker and a firm (Cavusoglu and Raghunathan, 2004; Cavusoglu et al , 2008), most large breach incidents are not singular and may involve multiple attacker agents [5] (Xu and Zhuang, 2019).…”

Defender–Attacker Games with Asymmetric Player Utilities

“…We consider a two‐period game where the defender moves first and distributes its resources among y selected elements. For simplicity, we do not consider repeated interactions (Shan & Zhuang, ) or multiple attackers (Xu & Zhuang, ). The defender only discloses the number of protected elements y , so the attacker does not know precisely which elements are protected.…”