Attack–Defense Game Model with Multi-Type Attackers Considering Information Dilemma

Qi, Gaoxin; Li, Jichao; Xu, Chi; Chen, Gang; Yang, Kewei

doi:10.3390/e25010057

Cited by 9 publications

(1 citation statement)

References 27 publications

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“…Fu et al [20] established a Stackelberg game model based on camouflage strategies and proposed an evolutionary rule to optimize these strategies. Qi et al [21,22] proposed a link-hiding rule and analyzed its impact in terms of optimization within the context of dynamic attack and defense games played out on complex networks. Liu et al [23] established an attack-defensive game model based on a Stackelberg game under asymmetric information, obtaining a defensive resource allocation strategy to optimize the network robustness.…”

Section: Introductionmentioning

confidence: 99%

Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Dong,

Liu,

Ren

et al. 2023

Mathematics

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Critical infrastructure is essential for the stability and development of modern society, and a combination of complex network theory and game theory has become a new research direction in the field of infrastructure protection. However, existing studies do not consider the fuzziness and subjective factors of human judgment, leading to challenges when analyzing strategic interactions between decision makers. This paper employs interval-valued intuitionistic fuzzy numbers (IVIFN) to depict the uncertain payoffs in a Stackelberg game of infrastructure networks and then proposes an algorithm to solve it. First, we construct IVIFN payoffs by considering the different complex network metrics and subjective preferences of decision makers. Next, we propose a lexicographic algorithm to solve this game based on the concept of a strong Stackelberg equilibrium (SSE). Finally, we conduct experiments on target scale-free networks. Our results illustrate that in an SSE, for the defender in a weak position, it is better to defend nodes with high degrees. The experiments also indicate that taking fuzziness into account leads to higher SSE payoffs for the defender. Our work aims to solve a Stackelberg game with IVIFN payoffs and apply it to enhance the protection of infrastructure networks, thereby improving their overall security.

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Section: Introductionmentioning

confidence: 99%

Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Dong,

Liu,

Ren

et al. 2023

Mathematics

View full text Add to dashboard Cite

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Modelling attack and defense games in infrastructure networks with interval-valued intuitionistic fuzzy set payoffs

Dong,

Liu,

Ren

et al. 2024

Complex Intell. Syst.

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Infrastructure networks are critical components of contemporary society, and numerous approaches have been suggested for the selection of strategies to protect these networks. However, for uncertain environments, research on attack and defense game models for infrastructure networks is limited. Therefore, after reviewing the existing approaches, a method based on interval-valued intuitionistic fuzzy set (IVIFS) theory is proposed for attack and defense games in critical infrastructure networks. First, we present the process of constructing the game model proposed in this paper, which mainly includes the formulation of the cost model, the strategies, and the method of generating IVIFS payoffs. Next, the Nash equilibria of the game are identified by a pair of nonlinear programming models based on IVIFS theory. Finally, experiments are conducted on a target scale-free network, and an investigation into the variation patterns of the Nash equilibria under different circumstances is also conducted. We provide explanations for these variation patterns by considering payoffs from the perspective of mathematical programming models. Furthermore, we find that compared to the existing attack and defense game model with crisp payoffs, the model proposed in this paper leads to superior Nash equilibria. Our work is a preliminary attempt to analyse attack and defense games for infrastructure networks based on IVIFS theory, providing a method for assessing payoffs in uncertain environments for the attacker and defender. This topic deserves further study.

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Applying the Stackelberg game to assess critical infrastructure vulnerability: Based on a general multi-layer network model

Li,

Ji,

Wang

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Critical infrastructure systems (CIS) are closely related to human life. Attacks against CIS occur frequently, making accurate and effective protection of CIS essential. Vulnerability assessment is the primary issue to achieving this goal. The interconnected characteristic of CIS means that it is best represented by a multi-layer network, but a uniform model is absent. Game theory offers a suitable framework for researching intelligent confrontation. Previous research combining game theory and network science mainly focuses on a single-layer network and lacks a comprehensive assessment that combines qualitative and quantitative aspects of vulnerability. In this paper, we apply the Stackelberg game to the multi-layer network and comprehensively assess vulnerability based on game equilibrium to realize accurate protection. We first present a method for constructing a general model of the multi-layer network and introduce a multi-layer weighted factor to extend topological attribute metrics. Then, we design a Stackelberg game model for the multi-layer network. Furthermore, we qualitatively analyze the impact of multi-layer network characteristics on vulnerability and propose a method to quantify vulnerability. Experiments show that the vulnerability of the multi-layer network is greatly influenced by the multi-layer weighted factor, single-layer network type, and inter-layer coupling method. The quantitative value of network vulnerability does not rely entirely on the topology attributes on which the attack and defense costs depend but also relates to the resources available. Our work provides an adaptive model for CIS and gives a new approach to developing accurate protection based on comprehensive vulnerability assessment, which deserves further study.

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Attack–Defense Game Model with Multi-Type Attackers Considering Information Dilemma

Cited by 9 publications

References 27 publications

Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Modelling attack and defense games in infrastructure networks with interval-valued intuitionistic fuzzy set payoffs

Applying the Stackelberg game to assess critical infrastructure vulnerability: Based on a general multi-layer network model

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