Modelling And Analysis Of Attacker-defender Game In Complex Networks

With the acceleration in the emergence of networks in human society,modern society is increasingly dependent on some critical infrastructures.These critical infrastructures have not only become important military targets in times of war,but also been frequently threatened by terrorist activities.Therefore,how to protect these critical infrastructures is a great challenge for security agencies all over the world.In addition,the war under informatization conditions is no longer a discrete confrontation between guns and guns,and modern warfare is increasingly becoming a confrontation between systems and systems.Systematic attack has become the basic operational pattern of information warfare in the future.In military confrontations,how to formulate effective strategies to destroy the combat systems of the enemy to the greatest extent is a critical issue to resolve.In modern society,whether in a critical infrastructure network or a military combat system,the targets are not isolated.They are connected to each other,which forms a complex network,and the functionalities of the systems are heavily dependent on the network topologies.In recent years,the disintegration of complex networks and the protection of them have received extensive attentions respectively,but how to investigate these two aspects in a unified framework and analyze the attackerdefender game from the perspective of network science still need further research.To analyze the confrontations in complex networks,this thesis comprehensively used the knowledge of network science,game theory,graph theory,military operations research,computer simulation and other subject areas.It adopted the framework of game theory and considered the behaviors of both the attacker and the defender simultaneously.From the perspective of network science,it established three different game models,introduced the methods to solve them,and investigated the equilibrium results in depth.This thesis provided important theories and methods for military confrontations,antiterrorism activities,and protection of critical infrastructures.The main innovations and contributions of this dissertation are as follows:(1)Established the attacker-defender games from a network science perspective.The problems of disintegration and protection of complex networks have accumulated lots of researches in their respective fields.But in reality,there are many cases where both attackers and defenders may exist at the same time.Previous studies have not considered the process of this dynamic decision-making process.In addition,the attacker-defender games,especially the security games,have been widely used in practice,but they believe that the targets are isolated.In networks such as critical infrastructures,such assumptions are unreasonable.Therefore,this thesis established attacker-defender games from a network science perspective,defined the strategies and payoffs of both attackers and defenders based on the topology structures of the network,and studied the attacker-defender games in complex networks in depth.(2)Studied the static attacker-defender game under uniform cost condition.The uniform cost means that the costs of attacking or defending each target are equal,and the static game model is a game model in which both the attacker and the defender act simultaneously.This thesis first considered the situation of the whole strategies,that is,all the possible strategies for both sides,defined the strategies and payoffs of the game model,and proposed an algorithm for quickly building the payoff matrix according to the characteristics of the payoff functions.An iteration-based algorithm for obtaining the Nash equilibrium was introduced.This thesis also studied the game model based on two typical strategies,namely,the random strategy and the targeted strategy,introduced its solution method and analytical results.Besides,this thesis analyzed the equilibrium results of the two cases and found that in both cases,the attacker would not attack the most important nodes in the network with a high probability,while the defender would protect these targets with high probabilities.(3)Introduced a static attacker-defender game model under the condition of uneven cost.The cost-sensitive parameters are used to describe the non-uniformity of the costs.The static attacker-defender game model under the non-uniform cost condition is modeled as a two-player zero-sum game with complete information.It was assumed that both the attacker and defender consider only two typical strategies.This thesis introduced the simulation process and solution method.The experiments under different parameters were carried out in the model networks with different parameters.It was found that the cost-sensitive parameter had little effect on the attacker’s equilibrium strategy and he virtually always attacked randomly.However,the defender protected the most important targets with low cost-sensitive parameter,and changed to the random defense strategy when the cost-sensitive parameter was high.(4)Established a dynamic attacker-defender game model under the condition of uneven cost.This thesis also studied the Stackelberg game model,where the defender acted firstly,under the condition of uneven cost.It introduced the strategies and payoffs of the game,introduced the solution concept of Strong Stackelberg Equilibrium and its solution method.This thesis executed experimental simulations in the model network and found that both the attack and defense strategies in equilibriums were affected by the costsensitive parameters.When the cost-sensitive parameters were small,the defender first promised to adopt a mixed strategy,and the attacker’s best response was to choose the targeted attack strategy.When the cost-sensitive parameters were large,both the attacker and defender chose the random strategy.The first-mover advantage of the defender was also confirmed in this game.(5)Conducted empirical research on different game models.This thesis empirically analyzed the three game models in an empirical network,the USAir.The results showed that the attacker did not prefer to attack the most important targets under uniform cost,and the defender’s optimal strategy was to assign higher probabilities on protecting the most important targets.Under the condition of uneven cost,with the increase of cost-sensitive parameters in the static game model,the defender’s equilibrium strategies were changed from the targeted defense strategy to the random defense strategy,and the attacker was always inclined to the random attack strategy.In the dynamic game model,as the cost-sensitive parameter increased,the attacker’s equilibrium strategies changed from the targeted attack strategy to the random attack strategy,and the defender’s equilibrium strategies changed from a mixed strategy to the random defense strategy.