Camouflage strategy of a Stackelberg game based on evolution rules

•Consider the cascading effect to define the value of the node and analyze the result of the offensive and defensive game.•We propose an evolutionary rule to optimize the camouflage strategy and improve the defense effect.•There is an optimal value for the setting of the penalty coefficient.•Unilaterally improving camouflage ability is not improving the defensive effect. The importance of critical infrastructure makes it a target of attacks in the new era. Using the Stackelberg game model, we analyze the offensive and defensive security issues of critical infrastructure from a network perspective. Considering the impact of cascading failure, nodes are divided into two categories according to the cost-efficiency ratio. High cost-efficiency (HCE) nodes are the initial protection nodes, and each initial protection node sets up an agent to manage the defense resources. The defense resources can achieve two effects: protection and camouflage. Complete defense can avoid failure after being attacked. Partial defenses can avoid the attacker's attack by camouflage, and the effect of camouflage is related to the amount of defense resources. We propose an evolution model to realize the optimal allocation of resources through the evolutionary game of the agents, and analyze the influence of three parameters on evolution. The results show that the initial willingness of the agent will affect the result of evolution only when it is small. If the willingness exceeds a critical value, the result of evolution is only affected by the penalty coefficient and camouflage coefficient. To optimize the overall defense effect, the penalty coefficient and camouflage coefficient must cooperate, which is explained by the causal relationship between the agent's behavior and decisions.