Attack-defense game for critical infrastructure considering the cascade effect

Highlights: • Propose a network offensive and defensive game model considering the impact of the cascade effect;. • Simplify the calculation space of network game strategy through node classification. • Both pure strategy and mixed strategy are carried out for the theoretical analysis and simulation of four kinds of optimization problems. • The equilibrium solution of the strategy is related to the structural properties of the network. The important status of critical infrastructure makes it a target of attacks in the new era. Based on game theory, we analyze the offensive and defensive issues of critical infrastructure from a network perspective, and we propose a network offensive and defensive game model considering the impact of the cascade effect. We first establish a two-player game model for an attacker and a defender acting simultaneously. The nodes are categorized to achieve the transformation of the focus of the game from decision-making for the nodes to resource allocation, thereby simplifying the calculation space of the network game strategy. Both pure strategy and mixed strategy are carried out for the theoretical analysis and simulation of four kinds of optimization problems. With the pure strategy, the initial decision equilibrium is that the attacker's strategy is to attack the Equal Cost-Effective ratio nodes (ECE nodes), and the defender defends the High Cost-Efficient ratio nodes (HCE nodes). At this point, the defender's payoff is 0. With the mixed strategy, different optimization problems have different equilibrium solutions. In particular, the attacker adds a new equilibrium solution for the strategy with the cascading effect, which is related to the structural properties of the network. For the defender, the strategy is different when maximizing his/her own profit or minimizing the attacker's benefit. This can explain how the attacker and the defender can achieve a win-win situation.