Stackelberg game in critical infrastructures from a network science perspective

Defending critical infrastructures has received enormous attentions by security agencies. Many infrastructures function as networks such as transportation and communication systems. It is necessary for us to protect them from a network science perspective. In many real-world scenarios, the attacker can observe the defender’s action and then choose its best strategy accordingly. Therefore, we propose a Stackelberg game where the defender commits to a strategy, either a pure strategy or a mixed one, and the attacker makes its choice after knowing the defender’s action. The strategies and payoffs in this game are defined on the basis of the topology structure of the network. For the convenience of analysis, only two attack and defense strategies, namely, targeted strategy and random strategy, are considered in this paper. The simulation results reveal that in infrastructures with a small cost-sensitive parameter, representing the degree to which costs increase with the importance of a target, the defender commits to a mixed strategy and the attacker’s best response is to attack hub nodes with the largest degrees. When the cost-sensitive parameter exceeds a threshold, both the defender and the attacker switch to the random strategy. We also implement experiments with different cost-sensitive parameters and find that the attack-cost-sensitive parameter is the key factor influencing the equilibrium strategies. Our work is a rudimentary attempt to analyze the Stackelberg game in protecting networked infrastructures and it is worth further study.