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

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.