Our increasing dependence on infrastructure networks leads to growing concerns over the protection of these networks. Many methods have been proposed to select protective strategies by combining complex network theory and game theory. However, the misleading effect of hidden links is not considered in previous methods. This work creates an information gap between attackers and defenders by partly hiding network links to mislead the attacker in the game. We first introduce the rule of link hiding that depends on the nodes’ property, where the number of hidden links has a maximum value. Additionally, based on the Stackelberg game model, we establish an attack–defense game model with link hiding strategies considering node property and cost constraints. Finally, we conduct experiments in a scale-free network and an existing power grid. The experimental results show that the defender tends to combine first-mover advantage and link hiding to get a better payoff under more different costs of the nodes. Hiding half of the links in the existing power grid can effectively reduce network damage by about [Formula: see text]% on average, with the two sides investing the same resources. The effect of link hiding could be more obvious when the attacker owns more resources than the defender. When an attacker employs the high-degree attacking strategy, the proposed link hiding method can help the defender reduce the damage to the network by 12.2% compared to the link reconnecting method.

Today, people rely heavily on infrastructure networks. Attacks on infrastructure networks can lead to significant property damage and production stagnation. The game theory provides a suitable theoretical framework for solving the problem of infrastructure protection. Existing models consider only the beneficial effects that the defender obtains from information gaps. If the attacker’s countermeasures are ignored, the defender will become passive. Herein, we consider that a proficient attacker with a probability in the game can fill information gaps in the network. First, we introduce the link-hiding rule and the information dilemma. Second, based on the Bayesian static game model, we establish an attack–defense game model with multiple types of attackers. In the game model, we consider resource-consistent and different types of distributions of the attacker. Then, we introduce the solution method of our model by combining the Harsanyi transformation and the bi-matrix game. Finally, we conduct experiments using a scale-free network. The result shows that the defender can be benefited by hiding some links when facing a normal attacker or by estimating the distribution of the attacker correctly. The defender will experience a loss if it ignores the proficient attacker or misestimates the distribution.

No abstract

Complex systems widely exist in nature and human society. There are complex interactions between system elements in a complex system, and systems show complex features at the macro level, such as emergence, self-organization, uncertainty, and dynamics. These complex features make it difficult to understand the internal operation mechanism of complex systems. Networked modeling of complex systems is a favorable means of understanding complex systems. It not only represents complex interactions but also reflects essential attributes of complex systems. This paper summarizes the research progress of complex systems modeling and analysis from the perspective of network science, including networked modeling, vital node analysis, network invulnerability analysis, network disintegration analysis, resilience analysis, complex network link prediction, and the attacker-defender game in complex networks. In addition, this paper presents some points of view on the trend and focus of future research on network analysis of complex systems.

No abstract