Node-based infrastructure network game strategy generation method

Abstract

The application discloses a node-based infrastructure network game strategy generation method, and the method comprises the following steps: acquiring a topological structure of a real infrastructure network, constructing a false network through two methods of randomly adding and deleting edges and randomly adding and deleting nodes, and constructing network models of the real network and the false network; reasonably allocating resources of an attack side and a defense side, establishing cost constraints for the attack side and the defense side in attack and defense games; considering uncertain factors in whether an attack succeeds in the network attack and defense process, determining attack success rate constraints of each node of the network under unprotected conditions and protected conditions; obtaining a strategy set of the attack side and the defense side through the cost constraints, taking a maximum connected piece scale as a network performance evaluation index, and calculating benefits of the attack side and the defense side under respective strategies under the attack success rate constraints; converting the network attack and defense game model into a linear programming model, solving a mixed strategy Nash equilibrium solution, and projecting the result to nodes.

Description

Technical Field

[0001] The present invention relates to the technical field of complex network games in system engineering, and in particular to a node-based infrastructure network game strategy generation method. Background Art

[0002] In recent years, with rapid technological advancements, the scale of critical infrastructure, such as aviation, power, road, and communications networks, has grown exponentially. These networks play an increasingly crucial role in society's production and daily lives, making them vulnerable to becoming important military targets during wartime. In the context of combat operations involving attacks on critical infrastructure networks, traditional hierarchical command and control models struggle to process information and make decisions in a timely manner. Cyber ​​attack and defense game theory, a cutting-edge research topic in complex network science, provides a framework for addressing this issue, facilitating the rapid and efficient allocation of defensive resources.

[0003] Existing complex network attack and defense game models primarily assume that the attacker and defender possess symmetric and complete information about the target network's topology. This means that both sides possess complete and objective knowledge of the target network's real situation. In actual combat, battlefield conditions are constantly changing, and information channels are complex. It's impossible for both attackers and defenders to simultaneously possess complete information about the target network. The defender can actively spread false information to disrupt the attacker's decision-making, thus gaining a certain information advantage. Therefore, this paper addresses this information asymmetry by developing an asymmetric network attack and defense game model. By establishing constraints on attack and defense costs and attack success rates, we calculate the mixed Nash equilibrium strategies for both attackers and defenders. Summary of the Invention

[0004] The present invention aims to address at least one of the technical problems existing in the prior art. To this end, the present invention discloses a node-based infrastructure network game strategy generation method. This method is based on a two-player zero-sum game, taking into account the attack and defense costs of each player and the success rate of the attack. The model is converted into a linear programming problem and solved, resulting in a mixed-strategy Nash equilibrium solution for both the attacker and defender.

[0005] The object of the present invention is achieved through the following technical solution: a node-based infrastructure network game strategy generation method, the method comprising:

[0006] Step 1: Obtain the topology of the real infrastructure network and construct a fake network by randomly adding and deleting edges and randomly adding and deleting nodes to build a fake network corresponding to the real network.

[0007] Step 2: Considering the different importance of different nodes in the network topology, the attacker and defender allocate their own resources and establish cost constraints for the attacker and defender in the network attack and defense game model;

[0008] Step 3: Considering the uncertainty of attack success during the network attack and defense process, determine the attack success rate constraints under unprotected and protected conditions for each node in the infrastructure network;

[0009] Step 4: Obtain the strategy sets of the attacker and defender through cost constraints. Use the maximum connected slice size as the network performance evaluation indicator and calculate the benefits of the attacker and defender under their respective strategies under the constraint of attack success rate.

[0010] Step 5: Convert the network attack and defense game model into a linear programming model, solve the mixed strategy Nash equilibrium solution and project the result to the node;

[0011] The infrastructure network is represented as a simple undirected graph G(V,E), where V = [v1,v2,...,v N ] represents the set of all nodes in the infrastructure network, N = |V| represents the number of nodes in the infrastructure network; represents the connection set, and |E| represents the number of connection relationships in the network.

[0012] Specifically, the methods for constructing a fake network involve randomly adding and deleting nodes and randomly adding and deleting edges. The random addition and deletion of edges method involves randomly eliminating connections between pairs of real nodes on the original network, while randomly selecting unconnected pairs of nodes to establish connections. The random addition and deletion of nodes method involves randomly selecting nodes on the original network, eliminating all edges connected to them, and simultaneously generating new nodes that randomly establish connections with other nodes in the network. Let α be the noise level when constructing the fake network. The random addition and deletion of edges method involves eliminating α×|E| existing edges on the real network and randomly selecting α×|E| unconnected pairs of nodes to connect, thereby creating a fake network. The random addition and deletion of nodes method involves randomly deleting nodes with a sum of α×|E| edges on the real network, while simultaneously generating new nodes and establishing new edges with a sum of α×|E| edges. Both methods for constructing fake networks modify the real network, retaining some of the real network's topological characteristics. This makes it impossible for attackers to verify the authenticity of the network and thus trust the reliability of the fake network they have obtained. Generally, α∈[0,0.5] allows the fake network to confuse the victim while ensuring their trustworthiness. When α>0.5, the gap between the real network and the fake one is too large to guarantee network credibility, a reality that defenders often struggle to achieve. When α=0, the defender fails to disguise the network, allowing the attacker to gain full access to the network's information.

[0013] Specifically, the attack and defense game cost constraint means that when the attacker and defender formulate strategies for nodes, it is impossible to have unlimited resources for all nodes. It can be considered that node v iThe higher a certain topological index is, the more important the node is in the network, and more resources or costs are needed when attacking or defending the node v i The degree k i of the node v i usually reflects the importance of the node in the network. The attack cost of the node can be expressed as follows:

[0014] c i A = q A k i FN

[0015] The same defense cost is expressed as:

[0016] c i D = q D k i TN

[0017] where q ∈ [0, 1] represents the cost sensitivity coefficient, when q = 1, it represents that the attack or defense cost is linearly related to the degree index, and when q = 0, it represents that the attack or defense cost is completely unrelated to the degree index.

[0018] The available resources of the attacker and the defender are defined as and where θ A ∈ [0, 1] and θ D ∈ [0, 1] are the attack budget coefficient and the defense budget coefficient, representing the proportion of the attack budget of the attacker (defender) in the cost required to attack all network nodes.

[0019] Next, the attack strategy and the defense strategy are defined. The attack strategy X = [x1, x2, … x N ] ∈ S A , where S A is all the strategies of the attacker. In an attack strategy x, if the attacker attacks the i-th node, then x i = 1, and does not attack the j-th node, then x j = 0. The attack cost of this attack strategy is:

[0020]

[0021] Similarly, there is a defense strategy Y = [y1, y2, … y N ] ∈ S D , where S D is all the strategies of the defender. In a defense strategy y, if the defender defends the i-th node, then y i = 1, and does not defend the j-th node, then yj = 0. The defense cost of this defense strategy is:

[0022]

[0023] Because of the attack and defense cost constraints, the attack strategy cost constraint is:

[0024]

[0025] The same defensive strategy cost constraint is:

[0026]

[0027] Specifically, the attack success rate constraint means that node attacks are affected by various factors. In the case of information asymmetry, the success probability of the attack should be considered. Define P 1 It represents the probability of a node being successfully attacked under unprotected conditions, which is expressed as follows:

[0028]

[0029] and Represents node v i Resources allocated in the fake network and the real network. When a node is not protected, it may not be able to achieve 100% success in attacking the target node due to insufficient resources allocated. If the resources allocated to the node are too few, there is a risk of P 1 The possibility of a strike failing is very low, and when resources are very sufficient, the target can be successfully struck.

[0030] Similarly, define P 2 It represents the probability of a successful attack when the node is protected, as follows:

[0031]

[0032] and Represents node v i The resources allocated in the fake network and the real network. When a node is defended, it may not be able to successfully protect the target node 100% due to insufficient defense resources allocated. 2 The possibility of protection failure is very high, and when the defense resources are sufficient, the target can be successfully protected.

[0033] Specifically, the benefits of both attackers and defenders refer to the impact of network performance changes on both attackers and defenders. Since the strategies and goals of the attackers and defenders are different, the benefit functions are also different.

[0034] Definition U A(X, Y) is the attacker's profit function, where X is the attack strategy selected by the attacker and Y is the defense strategy selected by the defender. Γ is defined as the network performance evaluation function. Here, the maximum connected patch size is selected. The attacker's profit is calculated as follows:

[0035]

[0036] in, After the fake network game, the remaining network is deleted after the nodes that were successfully attacked in the original fake network. Because the attacker is concerned about destroying the network and reducing network performance, when The further away from the original network, The smaller it is, the greater the benefit to the attacker.

[0037] Similarly, define U D (X,Y) is the defender's payoff function, which is calculated as follows:

[0038]

[0039] in, After the real network game, the remaining network is deleted after the nodes that were successfully attacked in the original real network. Because the defender is committed to maintaining the performance of the network, when The closer to the original network, The larger , the greater the defender's gain. It's important to note that the network observed by the defender is the real network, while the network observed by the attacker is a fake network. The game under this condition is not a zero-sum game.

[0040] Specifically, the linear programming model in step 5 is:

[0041] min z

[0042]

[0043] max z

[0044]

[0045] Among them, S A represents the attacker's strategy set, S D represents the defensive strategy set. P=[p1,p2,…p m ] indicates that the attacker's Nash equilibrium contains m pure strategies and the probability distribution of each strategy. Q=[q1,q2,…q n ] indicates that the defender’s Nash equilibrium contains n pure strategies and the probability distribution of each strategy. ijrepresents the payoff when the attacker adopts strategy i and the defender adopts strategy j, and z represents the final payoff. By solving the Nash equilibrium of the asymmetric information game model, we can obtain the optimal equilibrium strategy for both the attacker and the defender.

[0046] Compared with existing methods, the present invention's approach offers the following advantages: it establishes an asymmetric information attack and defense game model for critical infrastructure networks under conditions of non-uniform costs and attack success probability. This model considers more realistic conditions, providing a better reference for relevant departments and expanding research on attack and defense game models for critical infrastructure networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A schematic diagram of a process flow of an embodiment of the present invention is shown;

[0048] Figure 2 A schematic diagram showing a network topology structure according to an embodiment of the present invention is shown;

[0049] Figure 3 The invention shows a method for constructing a false network by randomly adding and deleting edges.

[0050] Figure 4 The invention shows a method for constructing a false network by randomly adding and deleting nodes. DETAILED DESCRIPTION

[0051] To make the objectives, technical solutions, and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the embodiments described herein are merely some, rather than all, of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0052] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0053] In this embodiment, the infrastructure network is represented as a simple undirected graph G(V,E), where V = [v1, v2, ..., v N ] represents the set of all nodes in the infrastructure network, and N = |V| represents the number of nodes in the infrastructure network. Taking the railway network as an example, Figure 1 As shown, it can be abstracted into a simple undirected graph G(V,E), where represents the connection set, |E| represents the number of connection relationships in the network, A(G)=(aij) N×N Represents the adjacency matrix of graph G. If nodes Vi and V j If there is a railway line betweenij =a ji =1, if node V i and V j If there is no railway line between ij =a ji =0.

[0054] like Figure 1 As shown, a node-based infrastructure network game strategy generation method includes:

[0055] Step 1: Obtain the topology of the real infrastructure network, and construct a false network by randomly adding and deleting edges and randomly adding and deleting nodes, so as to construct a false network corresponding to the real network; Figure 2 As shown;

[0056] Step 2: Considering the different importance of different nodes in the network topology, the attacker and defender allocate their own resources and establish cost constraints for the attacker and defender in the network attack and defense game model;

[0057] Step 3: Considering the uncertainty of attack success during the network attack and defense process, determine the attack success rate constraints under unprotected and protected conditions for each node in the infrastructure network;

[0058] Step 4: Obtain the strategy sets of the attacker and defender through cost constraints. Use the maximum connected slice size as the network performance evaluation indicator and calculate the benefits of the attacker and defender under their respective strategies under the constraint of attack success rate.

[0059] Step 5: Convert the network attack and defense game model into a linear programming model, solve the mixed strategy Nash equilibrium solution and project the result to the node.

[0060] Specifically, the false network construction method refers to randomly adding and deleting nodes and randomly adding and deleting edges. Figure 3 As shown in , the random addition and deletion method refers to randomly eliminating the connections between real node pairs on the original network, and randomly selecting unconnected node pairs to establish connections. Figure 4As shown, the random addition and deletion method involves randomly selecting nodes on the original network, eliminating all edges connected to them, and simultaneously generating new nodes that randomly connect to other nodes in the network. Let α be the noise level when constructing the fake network. The random addition and deletion method requires eliminating α×|E| existing edges on the real network and randomly selecting α×|E| pairs of unconnected nodes to connect, thereby generating a fake network. The random addition and deletion method involves randomly deleting nodes with a sum of α×|E| edges on the real network, while simultaneously generating new nodes and establishing new edges with a sum of α×|E| edges. Both methods of constructing fake networks modify the real network, retaining some of the real network's topological characteristics. This makes it difficult for attackers to determine the authenticity of the network and makes them believe the reliability of the fake network. Generally, α∈[0,0.5] allows the fake network to confuse the attacker while ensuring the attacker's trustworthiness. When α>0.5, the gap between the real network and the fake network is too large to guarantee network credibility, which is also difficult for defenders in real life. When α=0, the defender does not disguise the network, and the attacker also has all the information of the network.

[0061] Specifically, the attack and defense game cost constraint means that when the attacker and defender formulate strategies for nodes, it is impossible to have unlimited resources for all nodes. It can be considered that node v i The higher the topology index is, the more important it is in the network. i More resources or costs are required to attack or defend. i degree k i It usually reflects its importance in the network. The attack cost of a node can be expressed as follows:

[0062] c i A =q A k i FN

[0063] The same defense cost is expressed as:

[0064] c i D =q D k i TN

[0065] Where q∈[0,1] represents the cost sensitivity coefficient. When q=1, it means that the attack or defense cost is linearly related to the degree index. When q=0, it means that the attack or defense cost is completely unrelated to the degree index.

[0066] The available resources of the attacker and defender are defined as and where θ A ∈[0,1] and θ D ∈[0,1] is the attack budget coefficient and defense budget coefficient, which represents the proportion of the attacker's (defender's) attack budget in the cost of attacking all network nodes.

[0067] Next, define the attack strategy and defense strategy, and define the attack strategy X = [x1, x2, ... x N ]∈S A , where S A For all strategies of the attacker, in an attack strategy x, if the attacker attacks the i-th node, then x i =1, do not attack the jth node, then x j = 0. The attack cost of this attack strategy is:

[0068]

[0069] There is also a defensive strategy Y = [y1,y2,…y N ]∈S D , where S D For all strategies of the defender, in a defense strategy y, if the defender defends the i-th node, then y i =1, do not defend the jth node, then y j = 0. The defense cost of this defense strategy is:

[0070]

[0071] Because of the attack and defense cost constraints, the attack strategy cost constraint is:

[0072]

[0073] The same defensive strategy cost constraint is:

[0074]

[0075] Specifically, the attack success rate constraint means that node attacks are affected by various factors. In the case of information asymmetry, the success probability of the attack should be considered. Define P 1 It represents the probability of a node being successfully attacked under unprotected conditions, which is expressed as follows:

[0076]

[0077] and Represents node v iResources allocated in the fake network and the real network. When a node is not protected, it may not be able to achieve 100% success in attacking the target node due to insufficient resources allocated. If the resources allocated to the node are too few, there is a risk of P 1 The possibility of a strike failing is very low, and when resources are very sufficient, the target can be successfully struck.

[0078] Similarly, define P 2 It represents the probability of a successful attack when the node is protected, as follows:

[0079]

[0080] and Represents node v i The resources allocated in the fake network and the real network. When a node is defended, it may not be able to successfully protect the target node 100% due to insufficient defense resources allocated. 2 The possibility of protection failure is very high, and when the defense resources are sufficient, the target can be successfully protected.

[0081] Specifically, the benefits of both attackers and defenders refer to the impact of network performance changes on both attackers and defenders. Since the strategies and goals of the attackers and defenders are different, the benefit functions are also different.

[0082] Definition U A (X, Y) is the attacker's profit function, where X is the attack strategy selected by the attacker and Y is the defense strategy selected by the defender. Γ is defined as the network performance evaluation function. Here, the maximum connected patch size is selected. The attacker's profit is calculated as follows:

[0083]

[0084] in, After the game, the remaining network is deleted after the nodes that were successfully attacked in the original network. Because the attacker is concerned about destroying the network and reducing network performance, when The further away from the original network, The smaller it is, the greater the benefit to the attacker.

[0085] Similarly, define U D (X,Y) is the defender's payoff function, which is calculated as follows:

[0086]

[0087] Because the defender is committed to maintaining the performance of the network, when The closer to the original network, The larger , the greater the defender's gain. It's important to note that the network observed by the defender is the real network, while the network observed by the attacker is a fake network. The game under this condition is not a zero-sum game.

[0088] Specifically, the linear programming model in step 5 is:

[0089] min z

[0090]

[0091] max z

[0092]

[0093] Among them, S A represents the attacker’s strategy set, S D represents the defensive strategy set. P=[p1,p2,…p m ] indicates that the attacker's Nash equilibrium contains m pure strategies and the probability distribution of each strategy. Q=[q1,q2,…q n ] indicates that the defender’s Nash equilibrium contains n pure strategies and the probability distribution of each strategy. ij represents the payoff when the attacker adopts strategy i and the defender adopts strategy j, and z represents the final payoff. By solving the Nash equilibrium of the asymmetric information game model, we can obtain the optimal equilibrium strategy for both the attacker and the defender.

[0094] First, we use the method of randomly adding and deleting edges to construct a false network, and after solving it, we get the results shown in the table.

[0095] Attack Strategy Probability Defensive Strategy Probability {4,6,7,9,10} 0.0754 {3,4,5,7,8} 0.0986 {4,5,8,9,10} 0.2786 {2,5,6,7,8} 0.1115 {3,6,7,9,10} 0.3189 {2,3,6,7,8} 0.0598 {2,3,7,9,10} 0.0957 {2,3,5,7,8} 0.0251 {1,4,8,9,10} 0.0764 {2,3,4,7,8} 0.1217 {1,3,4,5,10} 0.0944 {1,3,7,8,9} 0.2405 {1,2,7,9,10} 0.0448 {1,3,4,7,8} 0.0002 {1,2,4,8,10} 0.0158 random 0.3427 Probability and 1 1

[0096] Analysis revealed that the attacker's mixed strategy in the calculated hybrid equilibrium solution included eight pure strategies, with all other strategies eliminated. Among these eight strategies, the probabilities assigned to {4, 5, 8, 9, 10} and {3, 6, 7, 9, 10} were significantly higher. Both strategies included the node {9, 10}, which has a relatively high degree in the network. The defender had eight pure strategies with probabilities greater than 0 to choose from, of which the random strategy had the highest probability, reaching 0.34. The probability assigned to {1, 3, 7, 8, 9} was also higher, as most of these nodes had low degrees.

[0097] Using the method of randomly adding and deleting nodes to construct a false network, the results shown in the table are obtained after solving the problem.

[0098] Attack Strategy Probability Defensive Strategy Probability {3,5,6,7,8,10} 0.3248 {4,5,6,7,8,9,10} 0.1721 {3,4,5,7,8,10} 0.0758 {2,6,7,8,9,10} 0.0755 {3,4,5,6,8,9} 0.2971 {2,5,6,7,9,10} 0.0408 {1,3,4,8} 0.0070 {2,4,6,7,9,10} 0.3409 {1,3,4,7} 0.0086 {2,4,5,7,8,9} 0.0353 {1,3,4,5} 0.0063 {2,3,4,5,9,10} 0.0810 {1,2,7,9} 0.1920 {1,3,5,8,10} 0.1096 {1,2,4,10} 0.0884 {1,3,5,8,9} 0.1448 Probability and 1 1

[0099] Analysis revealed that the attacker's mixed strategy contained eight pure strategies in the calculated hybrid equilibrium solution, with all other strategies eliminated. Among these eight strategies, the probabilities assigned to strategies {3, 5, 6, 7, 8, 10} and {3, 4, 5, 6, 8, 9} were significantly higher. Both strategies contained the node {3, 5, 6, 8}, which has neither the highest nor the lowest degree. The defender's mixed strategy also contained eight pure strategies, with the probabilities assigned to {4, 5, 6, 7, 8, 9, 10} and {2, 4, 6, 7, 9, 10} significantly higher. Both strategies contained the node {4, 6, 7, 9, 10}, which also has neither the highest nor the lowest degree.

[0100] To further study how the attack and defense strategies reflect the preferences of specific nodes, we use the following formula to map the mixed strategy Nash equilibrium into a value that can reflect the allocation of attack and defense resources on nodes.

[0101]

[0102] in, represents the attack probability of each node projected by the mixed strategy of the game equilibrium solution, It represents the defense probability of each node projected by the mixed strategy of the game equilibrium solution. and The probability of each pure strategy in the mixed strategy that represents the equilibrium solution of the game.

[0103] First, the equilibrium solution of the false network construction method of randomly adding and deleting edges is mapped, and the results are as follows:

[0104]

[0105] The equilibrium solutions of the false network construction method with random additions and deletions of nodes are mapped, and the results are shown in the following table:

[0106]

[0107]

[0108] Experimental results show that under the condition of random addition and deletion of edges, both the attacker and defender, considering the other's decisions and seeking to increase their own profits, will not directly invest resources in the most important nodes in the network. Instead, they tend to invest resources in nodes with less prominent degrees in the network. Under the condition of random addition and deletion of nodes, the attacker still pays little attention to the most important nodes, and the node degrees they focus on are smaller than those under the random addition and deletion of edges method. This is because the defender adopts a more deterministic defense strategy, selecting nodes with higher defensive degrees rather than a random strategy. Both the random addition and deletion of edges and the random addition and deletion of nodes can confuse the attacker.

[0109] Those skilled in the art will appreciate that embodiments of the present application can be readily used as a method, a system or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer-readable program code thereon for use by a computer.

Claims

1. A node-based infrastructure network game strategy generation method, characterized in that: The method comprises: Step 1: Obtain the topology of the real infrastructure network and construct a fake network by randomly adding and deleting edges and randomly adding and deleting nodes to build a fake network corresponding to the real network. Step 2: Considering the different importance of different nodes in the network topology, the attacker and defender allocate their own resources and establish cost constraints for the attacker and defender in the network attack and defense game model; Step 3: Considering the uncertainty of attack success during the network attack and defense process, determine the attack success rate constraints under unprotected and protected conditions for each node in the infrastructure network; Step 4: Obtain the strategy sets of the attacker and defender through cost constraints. Use the maximum connected slice size as the network performance evaluation indicator and calculate the benefits of the attacker and defender under their respective strategies under the constraint of attack success rate. Step 5: Convert the network attack and defense game model into a linear programming model, solve the mixed strategy Nash equilibrium solution and project the result to the node; The infrastructure network is represented as a simple undirected graph G(V,E), where V = [v1,v2,...,v N ] represents the set of all nodes in the infrastructure network, N = |V| represents the number of nodes in the infrastructure network; represents the connection set, and |E| represents the number of connection relationships in the network.

2. The node-based infrastructure network game strategy generation method according to claim 1, characterized in that: The method for constructing a false network refers to randomly adding and deleting nodes and randomly adding and deleting edges. The method for randomly adding and deleting edges refers to randomly eliminating the connections between pairs of nodes that actually exist on the original network, and randomly selecting pairs of nodes that have no connection to establish connections. The method for randomly adding and deleting nodes refers to randomly selecting nodes on the original network, eliminating all edges connected to them, and generating new nodes, and randomly establishing connections with nodes in the network. Let α be the noise level when constructing a false network. The method for randomly adding and deleting edges requires eliminating α×|E| existing edges on the real network, and randomly selecting α×|E| pairs of nodes that have no connection to connect, thereby obtaining a false network. The method for randomly adding and deleting nodes refers to randomly deleting nodes with a sum of α×|E| edges on the real network, and generating new nodes to establish new edges with a sum of α×|E| edges.

3. The node-based infrastructure network game strategy generation method according to claim 1, characterized in that: In the cost constraint, the attack cost c of the node is i A It is expressed as follows: c i A =q A k i FN Defense cost c i D Expressed as: c i D =q D k i TN Among them, q A represents the cost sensitivity coefficient of the attacker, q D represents the cost sensitivity coefficient of the defender, k i FN represents the degree of the i-th node in the false network, k i TN represents the degree of the i-th node in the real network; The available resources of the attacker and defender are defined as and where θ A ∈[0,1] and θ D ∈[0,1] is the attack budget coefficient and defense budget coefficient, which represents the proportion of the attack budget of the attacker or defender in the cost of attacking all network nodes; Define attack strategy X = [x1, x2, ... x N ]∈S A , where S A For all strategies of the attacker, in an attack strategy x, if the attacker attacks the i-th node, then x i =1, do not attack the jth node, then x j =0, the attack cost C of the attack strategy X for: There is also a defensive strategy Y = [y1,y2,…y N ]∈S D , where S D For all strategies of the defender, in a defense strategy y, if the defender defends the i-th node, then y i =1, do not defend the jth node, then y j =0, the defensive cost C of the defensive strategy Y for: Because of the attack and defense cost constraints, the attack strategy cost constraint is: The same defensive strategy cost constraint is:

4. The node-based infrastructure network game strategy generation method according to claim 3, characterized in that: The attack success rate constraint mentioned above means that node attacks are affected by various factors. In the case of information asymmetry, the success probability of the attack should be considered. The definition of P 1 It represents the probability of a node being successfully attacked under unprotected conditions, which is expressed as follows: and Represents node v i Resources allocated in the fake network and the real network, P i 1 represents the probability of successful attack on the i-th node under unprotected conditions; Define P 2 It represents the probability of a successful attack when the node is protected, as follows: P i 2 It represents the probability that the i-th node is successfully attacked under the protected condition.

5. The node-based infrastructure network game strategy generation method according to claim 4, characterized in that: Definition U A (X, Y) is the attacker's profit function, where X is the attack strategy selected by the attacker and Y is the defense strategy selected by the defender. Γ is defined as the network performance evaluation function. The maximum connected slice size is selected. The attacker's profit is calculated as follows: Among them, G F Indicates a fake network, It represents the remaining network after deleting the nodes that were successfully attacked in the original fake network after the fake network game; Similarly, define U D (X,Y) is the defender's payoff function, which is calculated as follows: Among them, G T represents the real network, It represents the network remaining after deleting the nodes that were successfully attacked in the original real network after the real network game.

6. The node-based infrastructure network game strategy generation method according to claim 1, characterized in that: The linear programming model is: min z max z Among them, S A represents the attacker’s strategy set, S D represents the defensive strategy set, P = [p1, p2, ... p m ] indicates that the attacker’s Nash equilibrium contains m pure strategies and the probability distribution of each strategy, Q = [q1,q2,…q n ] indicates that the defender’s Nash equilibrium contains n pure strategies and the probability distribution of each strategy, u ij It represents the profit when the attacker adopts the i-th strategy and the defender adopts the j-th strategy, and z represents the final profit value. By solving the Nash equilibrium, the optimal equilibrium strategy of the attacker and the defender is obtained.

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