Research on the Optimization Management of Cloud Privacy Strategy Based on Evolution Game

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Introduction
With the development of information technology, the scale of the network is becoming more and more complex, and the serious privacy leak events cause tremendous harm to cloud computing [1].To protect privacy of network service, firewalls, intrusion detection, and antivirus software technologies have been widely used.However, invaders can only be detected after the event, which often causes serious losses.
Advanced persistent threat attackers use a variety of complex methods to steal information continuously and secretly from the cloud storage system, such as spear phishing and waterhole attack.ey can even induce the cloud storage system to apply specific defense strategies and attack them, which is a great threat to cloud computing.erefore, it is necessary to research the new privacy protection technologies [2].An ideal protection system should protect all weak points or attacks.However, considering the limitation of organizational resources, we must consider the concept of "moderate security" to find a balance between information privacy security risk and investment and make the most reasonable decision with limited resources.Whether the strategy of protector is effective should depend not only on its own behavior, but also on the strategies of the attacker and the system.erefore, the game theory can be used to study the information security problems such as the conflict of attack and protect and the optimal protection decision.
e basic characteristics of game theory are the opposition of objectives; both the dependence of strategies and the noncooperation of relationships are in the process of privacy protection.In the process of the game, because of the learning mechanism, low-payoff participants constantly learn the strategies of high-payoff participants and improve their behaviors [3].
Based on bounded rationality, the evolutionary game continuously improves the intrinsic driving force of behavior strategy through learning mechanism, which can effectively enhance the accuracy and reliability of the game model [3,4].
is paper constructs an evolutionary game model of attack and protect and analyzes the rules of stability and equilibrium evolution.So, the main contributions of our paper are as follows: (i) We propose a quantitative weight model of privacy information, construct an evolutionary game model of attack-protect, make an evolutionary stable strategy solution method, achieve the optimal privacy strategy selection, and analyze the different evolutionary stable equilibrium (ii) To express the strategic dependence, we propose improving the accuracy of the replication dynamic equation by incentive coefficients, construct an improved evolutionary game model of cloud computing privacy protection, and give the detailed process of equilibrium solution (iii) We use the Jacobian matrix method to analyze the stability of the game equilibrium point and the evolutionary trend of the game and obtain the optimal protect strategy e structure of this paper is as follows.In Section 2, the related research work is introduced.In Section 3, this paper constructs an evolutionary game model of attack and protect and analyzes the different evolutionary equilibrium.In Section 4, this paper proposes an improved evolutionary game model by incentive coefficients and analyzes the stability of the evolutionary game.In Section 5, this paper designs relevant experiments.In Section 6, this paper summarizes the work and future research directions.To understand this article, a framework is given in Figure 1.

Related Work
e main security privacy strategy technologies for cloud system can be classified into three categories: attack defense game, evolution game, and strategy selection.
2.1.Attack Defense Game Approach.Neupane et al. [5] proposed a new defense system based on the camouflage theory, which can prevent the attackers from the analysis of attack characteristics and can reduce the impact of the target attack on the high-value services hosted in the cloud platform by "isolating virtual machine" and strategy coordination.Xiao et al. [6,7] described the interaction between defenders and attackers in the cloud storage system, studied a mixed strategy in storage defense game, and proved that the view of the attackers can improve the effectiveness of defenders.Li et al. [8] proposed an attack-defend game model, which was a twoperson zero-sum static game with complete information.When the price parameter exceeded the threshold, the defender will switch to the protection mode.Lv et al. [9] proposed a dynamic defense model based on the mixed strategy game, which optimized the allocation of the limited security resources of the target network, and allocated the dynamic optimal defense strategy for each node at different times.Based on the game between the data owner and data requester, Sfar et al. [10] proposed a solution to protect privacy in the context, which used incentives for privacy concessions or active attacks to describe game elements and found a balance between privacy concessions and incentives.Min et al. [11] derived the Nash equilibrium of symmetric and asymmetric allocation game between the attacker and the defender, initialized the quality value by using the experience in similar scenarios, and obtained the optimal defense performance.Hota and Sundaram [12] studied the influence of node's behavior probability weight and the distribution of security risk and described the graph topology of the average attack probability under the Nash equilibrium in the weakest game.
Stackelberg games are very useful for decision making in attack and defense scenario.Xiao et al. [6] deduced the Nash equilibrium of detection game and proposed a detection scheme based on strategy hill-climbing, which increased the uncertainty of strategy to deceive attacker in dynamic game.So Jakóbik et al. [13] defined a Stackelberg game model, which allowed the automatic selection of provider level security decisions and maximized the benefits of defenders.Wahab et al. [14] proposed a repeated Bayesian Stackelberg game, which provided the optimal distribution of detection for virtual machines, increased the detection ability of attack, and greatly reduced the number of attacks.

Evolutionary Game
Approach.Khalifa et al. [15] proposed a new tool to simulate the evolution of several populations, defined three different stable levels, strong, weak, and medium, which improved the accuracy and adaptability of the evolutionary game.Jiang et al. [16] studied the information reliability of a series of cooperative networks and proposed an evolutionary game model based on closed expression and reinforcement assistant method.Tan et al. [17] studied the strategy selection problem of evolutionary game dynamics with group interaction and obtained the cooperative conditions of public goods game and volunteer dilemma game.Based on the bounded rationality of the players, Hu et al. [18] established a game model of attack and defense under incomplete information, which extended the game strategy in the game structure.Du et al. [19] used the evolutionary game theory framework of community to analyze the privacy protection behavior of the social network and designed incentives based on cost performance.Based on the analytic hierarchy process, Zhang et al. [20] comprehensively analyzed the impact of mobile target defense technology, proposed an effective strategy selection algorithm based on joint defense, and selected many variation elements to defend different attack.

Game Strategy Selection
Approach.Various game methods have been developed to study the privacy strategy selection between proctors and adversaries.Kamhoua et al. [21] studied the security of cloud computing participants and internal interdependence, analyzed many possible Nash equilibria, and described the adversary's motivation more accurately.In order to study heterogeneous network system and provide the optimal security detection strategy, Wu et al. [22] gave the analysis of Bayesian equilibrium and robust Nash equilibrium with incomplete information and proposed a verification and calculation method for continuous kernels.
Tan et al. [17] studied the strategy selection problem of evolutionary game dynamics with group interaction and obtained the cooperative conditions of public goods game 2 Security and Communication Networks and volunteer dilemma game.Cheng et al. [23] established a mobile target defense game model based on incomplete information and designed an optimal strategy algorithm to prevent the selection strategy from deviating from the actual network conditions.After synthetically analyzing the influence of defense cost and benefit on strategy selection, Cheng et al. [24] designed an optimal strategy selection algorithm, which corrected the deviation between the selected strategy and the actual network conditions, thus ensuring the correctness of the optimal strategy selection.Zhang et al. [25] emphasized the applicability and advantages of multiobjective in network security, proposed a multiobjective game model, and introduced and demonstrated the set strategy selection technology.Armstrong et al. [26] proposed a threat specific risk assessment method, which allowed administrators to make fine-grained decisions for the selection of mitigation strategies.

Discussion and Features of Our Research.
In the attack defense game approach, the existing research is mainly to explore deterministic strategies, so we need to study the application of stochastic strategies in practice.In the evolutionary game behavior, the current research is mainly to calculate the equilibrium through the income matrix and focuses on the optimization of the calculation process, rarely summarizing the dynamic process of strategic evolution.In terms of application scenarios, both the behavior analysis of cloud computing networks and the dynamic research of privacy security are based on strategy selection, which makes the research on strategy selection more universal.e game is a continuous process, different strategies in the same group have a great impact on the game results, but there are few researches in these above articles.
Our research is more general in network security protection, because the strategy set of our model can be extended to N, and both attackers and defenders can choose any strategy, which can be applied to general protection strategy choice.On the basis of bounded rationality, we consider and quantitatively describe the influence of similar strategies, introduce the influence factors, establish the evolutionary game model of attack and protect based on the improved dynamic replication equation, provide the detailed stability analysis, and improve the accuracy of the model.

A Game Model of Attack-Protect
In this section, we propose a quantitative weight model of privacy information, construct a game model of privacy protection, and analyze the evolution of the strategy selection mechanism to realize the optimal protect strategy.To read this article, some parameters are given in Table 1.Security and Communication Networks

Privacy Metric Space.
To make the expression of privacy information, this paper proposes a measurement model and proposes the distance between any elements in the metric space.
Definition 1. Suppose that R is a nonempty set metric space; for two elements x, y in the R, Φ(x, y) represents the distance between two elements, which has two characters: (1) Φ(x, y) ≥ 0, Φ(x, y) � 0, and x � y (2) If z ∈ R, Φ(x, y) < Φ(x, z) + Φ(y, z) Φ(x, y) is the distance between two points x, y. (R, Φ) is called as metric space according to the distance.
According to the definition of metric space, the following properties can be obtained: Norm is a basic concept in performance analysis, which is often used to measure the length or size of each element in the metric space.
Let n(n 1 , n 2 , . . ., n k ) be a vector, and Η � (h i,j ) m×n is a matrix.
Vector 1-norm is Vector 2-norm is Matrix F-norm is In this paper, the privacy vector is considered as an index in the measurement space, 2-norm is used to represent the size of the privacy value.
Assuming that a piece of privacy information is PI i � (g 1 , g 2 , . . ., g i , . . ., g n ), w i represents the privacy factor related to the user's privacy; then the privacy value |PI i | of PI i can be expressed as

􏽶 􏽴
, i � 1, 2, . . ., n. ( w i is the weight coefficient of the influence factor g i .e correlation coefficient is an objective weight method to eliminate the influence of duplicate information on the comprehensive evaluation results.Calculate the correlation coefficient matrix; the original data contains n factors.en the correlation coefficient matrix is After standardization, it can be simplified as Calculate the sum value of (1 − r ij ) in the jth column as follows: e result of (1 − e ij ) row vector is larger, the influence in the comprehensive evaluation system is greater, and the weight is more.Both privacy variability and conflict factor need to be considered in weight.In the paper, the objective weight method is adopted, and factor variability is represented by the standard deviation to show the difference between evaluation schemes of a factor.e larger the standard deviation is, the larger the value is.
Assume that I i is the information quantity of ith factor; the various results of indicators can be considered by selecting the standard deviation σ i .e conflict characteristics between the ith standard and other standards are measured by (1 − e ij ).e ij represents the correlation coefficient between the ith and the jth factors, and I i can be expressed as follows: Security and Communication Networks e result of I i is larger, the amount of data in the ith criterion is larger, and the importance is more.erefore, the weight w i of the ith factor is as follows: 3.2.Attack-Protect Evolutionary Game Model.In order to protect privacy information PI(s) � PI 1 , PI 2 , . . ., PI n  , we propose an attack-protect game model (Figure 2).

Definition 2. An attack-protect evolutionary game model can be defined as a 4-tuple APEGM � (G, S, T, U).
G � (GP, GA) is the participant space of evolutionary game, GP is the protector, and GA is the adversary.
S � (PS, AS) is game action strategy space, PS � PS 1 , PS 2 , . . ., PS n   represents an optional strategy set for the protector, and AS � AS 1 , AS 2 , . . ., AS m   represents an optional strategy set for the adversary.Both adversary and protector have multiple strategies.
T � (p i , q i ) is a set of game beliefs, q i represents the probability set that the protector chooses a strategy PS i , and p i represents the probability set that the adversaries choose a strategy AS i .
U � (UP, UA) is a set of game payoff functions, UP represents the game payoffs of protectors, and UA expresses the game payoffs of adversaries.
In the game, both protector and adversary have PS � PS 1 , PS 2 , . . ., PS n   and AS � AS 1 , AS 2 , . . ., AS m  , respectively, m, n ∈ N, m, n ≥ 2. When different strategies are used in the attack-protect game, both a ij and b ij represent the payoffs of adversary and protector when they adopt AS i and PS i .We can get the following formula: In the PS � PS 1 , PS 2 , . . ., PS n  , the player chooses PS i with q i , and Further, we can get the expected payoff UPS i and average payoff UP of different protection strategies: In strategy set PS � PS 1 , PS 2 , . . ., PS n  , because of the learning mechanism, we use q i (t) to show the proportion of people who choose a strategy PS i with time, and  n i�1 q i (t) � 1. q i (t) is a time constant, for the first derivation, and the dynamic replication rate can be expressed as the following formula: Similarly, the expected payoff UAS i and average payoff UA of different protect strategy are calculated: In the strategy set AS 1 , AS 2 , . . ., AS m  , p i (t) is the proportion of people who choose the attack strategy AS i , and For a strategy AS i , p i (t) is a time constant, according to the expected payoff UAS i and average payoff UA, and we can get the dynamic replication equation of attack strategy: By combining formulas ( 14) and ( 17), we can get the following formula: Adversary Protector Protector Protector ...

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When , we can get the equilibrium point of evolutionary game and thus realize the analysis and prediction of strategy selection.
According to the basic theory of game theory, pure strategy can be regarded as the mixed strategy with the choice probability 1 and the choice probability 0 of other strategies.Because the attack and protect game of cloud network system is a limited game, there must be a mixed strategy (p * i , q * j ) to form the Nash equilibrium, and (p * i , q * j ) meets the following conditions:

Protect Strategy Selection Algorithm.
Both adversary and protector choose different strategy with different probabilities.We design an optimal privacy strategy selection algorithm (Algorithm 1).
From the analysis of Section 3, the time complexity of the algorithm is O(m + n) 2 , and the storage space complexity is O(mn).According to this algorithm, not only the payoff value of each strategy can be obtained, but also the state change rate of strategy selection can be obtained.

Improvement of the Game Model
e evolutionary game originates from the idea of biological evolution, and replication dynamic application is the most widely used in many ways.However, in the actual process of network attack and protection, not only the strategy groups of the attacker and the protector are dependent on each other, but also the protect strategy and the attack strategy are dependent on each other.erefore, it is necessary to study the interaction among the same strategy group.In this section, we introduce the relation function to express the strategy dependence to improve the traditional replication dynamic equation and the accuracy of the replication dynamic rate.

Improvement of the Replication Dynamic Model.
Based on Section 3, in the strategy PS � PS 1 , PS 2 , . . ., PS n  , assume that the number of strategy PS i is x i (t) at t; the proportion of the number of protect strategy is q i (t), and we can get the following formula: With the advance of the game process, the number x i (t) of players selecting strategy PS i changes with time, and the replication dynamic rate is proportional to the number of selection strategy PS i , which is related to the adaptability of strategy PS i .e expected payoff of protect strategy PS i is UPS i , and the average payoff of protect strategy is UP.We can construct the following formula: α i (α i > 0) is the influence factor, which indicates the impact of protect strategy PS i .e greater the value of α i , the stronger the influence of PS i on the other protect strategy.Based on formula (21), we can obtain formula (22) of PS i : Similarly, assume that the number of AS i is y i (t) at time t. e proportion of the number of adversary is p i (t), the expected payoff is UAS i , and the average payoff is UA.We can get the following formula to express the p i (t): With the advance of the attack-protect game, the number of adversary who chooses the strategy AS i changes with time, and the dynamic replication rate is proportional to the number of players, so we can get the following formula: is the strategy influence factor, which is determined by the strategy AS i .e larger the value of β i , the stronger the influence of AS i on other attack strategies.
Furthermore, we can get the replication dynamics of AS i : 6 Security and Communication Networks By combining formulas ( 22) and ( 25), we obtain an improved replicated dynamic differential equation: When a i � a j � 1 and β i � β j � 1, we can obtain the following dynamic replication equations: We define an incentive coefficient θ ij � (a i /a j ) to represent incentive relationship between PS i and PS j , θ ij < 1 indicates that protect strategy PS i can promote PS j , and θ ij > 1 indicates that protect strategy PS i can suppress PS i .
Similarly, we define an incentive coefficient Δ ij � (β i /β j ) to represent incentive relationship between AS i and AS i .
rough further deduction, we can get the following formula: , we can get the equilibrium solution of attack-protect evolutionary game to realize the analysis and prediction of strategy selection.  (4) According to the strategy selection of the adversary, a reasonable protect strategy PS i is selected by probability q i (1 ≤ i ≤ m), and  m i�1 q i (t) � 1 (5) For attack -protect strategy AS i , PS j  , we get the payoff value b ij of protect strategy.(6)

Evolutionary Game
of the protect strategy.(7) Calculating the average payoffs of the protector UP �  n i�1 q i UPS i .(8) Establishing protector's dynamic replication equation UP(q) � (dq i (t)/dt) � q(UPS i − UP).(9) Computing equilibrium solution of UP(q) � 0. (10) Output privacy protect strategy.ALGORITHM 1: Optimal privacy strategy selection.
Security and Communication Networks an adversary has an optional strategy set AS 1 , AS 2  , where AS 1 represents that the adversary implements attack and AS 2 represents the idea that the adversary does not implement an attack.p 1 denotes the selection probability of attack strategy AS 1 , p 2 denotes the selection probability of attack strategy AS 2 , and p 1 + p 2 � 1; q 1 denotes the selection probability of strategy AS 1 and q 2 denotes the selection probability of strategy AS 2 , and q 1 + q 2 � 1.

Evolutionary Game Solution of Attack-Protect.
Based on the attack-protect model of Section 3, similarly, we can construct the following formula: According to q 1 (t) + q 2 (t) � 1, p 1 (t) + p 2 (t) � 1, by first derivative of time t, we can get the following formula: According to formulas ( 28) and (30), we can further obtain the dynamic replication equation of PS 1 and AS 2 : , we can get five solutions: , and ( When det J > 0 and trJ > 0, the equilibrium point is unstable; when det J < 0 and trJ is an arbitrary value, the equilibrium point is a saddle point.Because the value of D(p * , q * ) cannot be determined, we give several discussion of different values of q * and p * :   ) is a stable point, both O(0, 0) and B(1, 1) are saddle points, C(0, 1) is an unstable point, and D(p * , q * ) is a center point 4.5.Further Discussion and Analysis.According to the above analysis, when the parameters in the income matrix satisfy Conditions 1-3, the system has four equilibrium points, O(0, 0), C(0, 1) A(1, 0), and B(1, 1).Under these conditions, the game system has a unique evolutionary stable state, which is related to the incentive coefficients θ ij and Δ ij .When the payoff function of attack-protect satisfies Condition 4, there are five equilibrium points: O(0, 0), A(1, 0), B(1, 1), C(0, 1), and D(p * , q * ).Next, we analyze Case 1 of situation 5 in Condition 4, and other cases are similar.
Based on geometry knowledge, the area S of the quadrilateral region by O(0, 0), A(1, 0), B(1, 1), and D(p * , q * ) is shown as follows: 2 )<0, when θ 21 increases, S will decrease and the equilibrium strategy is q 1 (t)�0.So the stable state of the system tends to the equilibrium point A(1,0); on the contrary, the stable state of the system tends to the equilibrium point C(0,1).
is paper extends the framework of evolutionary game theory by incentive coefficient, analyzes the evolutionary stability of two players when they adopt different strategies, and reflects the influence of incentive coefficient on game decision making.Further analysis shows that the incentive coefficient can affect the optimal behavior of the players in multiple stable states and affect the evolution trend of the stable state of the dynamic system.

Experiment Simulation and Analysis
Based on the evolution of dynamic privacy protection game in this paper, a simple network system is deployed for simulation experiments to verify the validity of our research.e system's topology environment is shown in Figure 4, which is mainly composed of cloud computing protection device, web server, file server, data server, and client.e access control rules are that the remote host can only access the web server in the system, and the local host can access the data server.
We set the duration time of the game of attack and protect for 35 minutes, t ∈ [0, 35], and we can realize the optimal protect strategy selection algorithm and obtain the optimal game strategy.in four kinds of situations.Next, we will simulate the different states of p and q.By observing their evolution trend, we can get the final stable state of evolution, and we can realize the prediction of attack strategy and select the optimal protect strategy: (1) When the initial states are p � 0 and q � 0, the adversary chooses a strategy AS 2 , and the protector chooses a strategy PS 2 .From the evolution of the system, the choice of strategies between the adversary and the protector will be consistent.PS 2 is the optimal protect strategy in Figure 5.
(2) When the initial states are p � 1 and q � 1, the adversary chooses a strategy AS 2 , and the protector chooses a strategy PS 2 .From the evolution of the system, it can be seen that the choice of strategies between the adversary and the protector will be consistent.PS 1 is the optimal protect strategy in Figure 6.(3) When the initial state is p � 0.3 and q � 0.4, the adversary chooses AS 1 , AS 2   with the probability (0.3, 0.7) and the protector chooses PS 1 , PS 2   with the probability (0.4, 0.6).After continuous evolution, the protector finally does not choose strategy PS 1 and chooses PS 2 to reach equilibrium state.Y 1 � 0 0   is one of the evolutionary equilibrium points, and PS 2 is the optimal protect strategy in Figure 7. (4) When the initial state is p � 0.6 and q � 0.4, the adversary chooses AS 1 , AS 2   with the probability (0.6, 0.4), and the protector chooses PS 1 , PS 2   with the probability (0.4, 0.6).After continuous evolution, the protector finally chooses PS 2 instead of PS 1 .
Y 1 � 0 1   is the equilibrium point, PS 2 is the optimal protect strategy in Figure 8 at this time, (investment protection, no attack) is the evolution stable strategy of attack protect, and investment protection is the optimal selection of the protector.
(5) When the initial state is p � 0.3 and q � 0.7, the adversary chooses AS 2 , and the protector chooses a strategy PS 1 .After continuous evolution, the protector finally chooses PS 1 to reach an equilibrium state, the value of q tends to be 1, and the value of p tends to be 0. Y 3 � 1 0   is the equilibrium point, and PS 1 is the optimal protect strategy in Figure 9. (6) When the initial states are p � 0.8 and q � 0.7, after continuous evolution, the adversary chooses AS 2 , and the protector chooses strategy PS 1 .e values of  12 Security and Communication Networks p and q tend to be 1, Y 4 � 1 1   is the evolutionary equilibrium point, and PS 1 is the optimal protect strategy in Figure 10.
When q is adjusted from 0.91 to 0.86 and p is adjusted from 0.44 to 0.38, the simulation evolution trend of the game has no obvious change in Figure 11, which indicates that the game has good robustness.erefore, the game model has good adaptability and can be applied to complex and changeable network environment.
From the above simulation results, we can see that the evolutionary system will eventually evolve to a stable state under the initial state of different strategies.By observation and comparison, we can find that the simulation results of the system are consistent with the theoretical analysis of the model, which shows that the evolutionary game model is consistent with the evolutionary law of the real system.
e influence of parameter variation on system behavior is studied by parameter sensitivity test.If the parameters change slightly, the evolutionary behavior curve changes greatly, which indicates that the game model is sensitive, and it is difficult to maintain stability and robustness in the the network environment, and vice versa.

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By setting different values of incentive coefficients, we verify the influence of the dependence between different strategies on the evolution process of the game, and we highlight the superiority of the improved replicated dynamic evolutionary game model.e greater the incentive coefficient, the greater the influence among the strategies; otherwise, the smaller the influence among the strategies.In the cloud computing system, there are 200 players, according to the different values of the incentive coefficients (Table 5), the initial parameters in the experiment are (q 1 , p 1 ) � (0.3, 0.4) and (q 1 , p 1 ) � (0.7, 0.6), and the role of different incentive coefficients in the evolution process of the game can be obtained.
(1) Under the conditions θ 21 � 1 and Δ 21 � 1, there is no dependency between protect strategy and attack strategy.e evolution process belongs to the classical replication dynamics.e state evolution trend of the game system is shown in Figure 12.When the initial state is (q 1 , p 1 ) � (0.   15.When the initial state is (q 1 , p 1 ) � (0.2, 0.3), strategy PS 1 achieves stability at time t � 10, strategy AS 1 achieves stability at time t � 2. When the initial state is (q 1 , p 1 ) � (0.6, 0.7), strategy PS 1 achieves stability at time t � 11 and strategy AS 1 achieves stability at time t � 4. Compared with Figure 12, when θ 21 � 1.5, the strategy PS 2 can suppress PS 1 and reduce the convergence speed.When Δ 21 � 0.5, the strategy AS 2 can promote AS 1 and accelerate the convergence speed.
(5) Under the conditions θ 21 � 0.5 and Δ 21 � 1.5, the strategy PS 2 can promote PS 1 and the strategy AS 2 can suppress AS 1 .e state evolution trend is shown in Figure 16.When the initial state is (q 1 , p 1 ) � (0.3, 0.4), PS 1 achieves stability at time t � 2 and AS 1 achieves stability at time t � 10.When the initial state is (q 1 , p 1 ) � (0.7, 0.6), PS 1 achieves stability at time t � 3 and AS 1 achieves stability at time t � 12. Compared with Figure 12, when Δ 21 � 1.5, AS 2 can suppress AS 1 and reduce the convergence speed.When θ 21 � 0.5, PS 2 can promote PS 1 and accelerate the convergence speed.

Comparison of Several Models.
According to the experimental parameters in Table 5 and formulas (29) and (31), we compare this paper with [11,14,18] to enhance credibility, and we show the results with several experimental graphs.
According to Figure 17(a), with the increase of experiments, the average attack rate is stable at 0.141, 0.135, 0.125, and 0.114, respectively.Our scheme is lower than [11,14,18], because our scheme can moderately adjust the relationship between attack strategy and protection strategy, and has better adaptability.
According to Figure 17(b), in terms of the average attack detection rate, alarm rate, and survived service rate, our Security and Communication Networks scheme performs better than [11,14,18].According to Figures 17(c) and 17(d), compared with [11,14,18], in our scheme, the protector can get more benefits and the attacker can get fewer benefits.rough observation and comparison, different incentive coefficients have different effects on the convergence speed of game system evolution.
is shows that our research improves the evolution process of the game and can be used to guide cloud computing privacy protection.

Performance Comparison.
To further show the characteristics and advantages of our study, the related results of comparison with other works of literature are shown in Table 6.16

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In [8,21], the participants are completely rational, but because of the participants' incomplete rationality in the implementation, the feasibility of the model is reduced.Literature [17] and literature [18] are evolutionary game models, but the process of solving the model is simple.e universality of a model is mainly reflected in whether the type and strategy set are well extended to n. Paper [27] is only applicable to two game objects, and its universality is poor, which indicates that the model can only be applied to special cases.Moreover, our model has good generality by extending the optional strategy to n and can be applied to the common selection strategy.

Conclusion
Privacy protection has always been a hotpot in the field of cloud computing.Based on the assumption of bounded rationality, this paper proposes an attack protection game model for privacy strategy selection.Firstly, the dynamic replication equation is used to analyze the strategy process of the attack-protect and the formation mechanism of the evolution stable state.Secondly, the solution method of the evolution stable strategy is proposed, and the optimal privacy strategy selection algorithm is designed.
irdly, aiming at the problem of strategy dependence, we construct an improved replication dynamic attack-protect evolutionary game model by incentive coefficients, and we use the Jacobian matrix to analyze the stability of the equilibrium point and get the optimal protect strategies under different conditions.Finally, the effectiveness of our research is validated by simulation experiments under several game parameters.
Our research expands the evolutionary game theory and has important significance for cloud computing privacy protection [25].Although this paper is limited to analyzing the situation of two players of two strategies, for the stable state of multiple strategies of multiple players, the same theory can be studied; only the amount of calculation is relatively complex.
is will play an important role in guiding the use of evolutionary game theory to solve practical problems.Besides, there are still some shortcomings, such as the determination of attack-protect strategy set, lack of credible third-party supervision, and the quantification of incentive coefficient, which will become the future research [28,29].

5. 1 .
Experiment 1. Aiming at the above conventional attackprotect model, system dynamics is used to simulate and analyze the selection of the optimal protect strategy in the Security and Communication Networks evolutionary game model.Section 3 shows that the evolutionary stable states analyses of this attack-protect game model are Y 1 �

Table 1 :
Parameters and meanings.
: cloud computing attack-protect game tree.Output: optimal privacy protect strategy.(1)Initialization APEGM � (G, S, T, U) (2) Constructing protector's space set UP � PS i , i ≥ 1   (3) Constructing an optional strategy space set for protectors PS � PS 1 , PS 2 , . . ., PS n Description.Assume that the protector has an optional strategy set PS 1 , PS 2  , where PS 1 represents investment privacy protection and PS 2 represents noninvestment privacy protection.Similarly, Input

Table 4 .
2. During this experiment, the game strategies consist of attack strategy AS i � r 1 , r 2 , . . ., r k   and protect strategy PS i � b 1 , b 2 , . . ., b l  . e atomic attack strategies are shown in Table 3 and the atomic protect strategy is shown in In the experiment, we design these related attack strategies for AS 1 � r 1 , r 2 , r 5   and AS 2 � r 3 , r 4 , r 6   and protect strategy for PS 1 � b 3 , b 4 , b 6   and PS 2 � b 1 , b 2 , b 5  .
3, 0.4), PS 1 achieves stability at the time t � 7 and AS 1 achieves stability at time t � 8.When the initial state is (q 1 , p 1 ) � (0.7, 0.6), PS 1 achieves stability at time t � 8 and AS 1 achieves stability at time t � 9.(2) Under the conditions θ 21 � 0.5 and Δ 21 � 0.5, the protect strategy PS 2 promotes PS 1 and the attack strategy AS 2 promotes AS 1 .estateevolutiontrend of the game system is shown in Figure13.When the initial state is (q 1 , p 1 ) � (0.3, 0.4), PS 1 achieves stability at time t � 2 and AS 1 achieves stability at time t � 2. When the initial state is (q 1 , p 1 ) � (0.7, 0.6), PS 1 achieves stability at time t � 3 and AS 1 achieves stability at time t � 5. (3) Under the conditions θ 21 � 1.5 and Δ 21 � 1.5, the protect strategy PS 2 promotes PS 1 and the attack strategy AS 2 promotes AS 1 .estateevolution trend of the game system is shown in Figure14.When the initial state is (q 1 , p 1 ) � (0.3, 0.4), strategy PS 1 achieves stability at time t � 8 and strategy AS 1 achieves stability at time t � 10.When the initial state is (q 1 , p 1 ) � (0.7, 0.6), strategy PS 1 achieves stability at time t � 10 and strategy AS 1 achieves stability at time t � 12. Compared with Figure12, when θ 21 � 1.5 and Δ 21 � 1.5, different strategies in the same group have a suppression effect, which reduces the convergence speed of the protective strategy.is can lead to better performance.

Table 3 :
Atomic attack strategy description.

Table 4 :
Description of atomic protect strategy.

Table 5 :
e value of related game parameters.Figure 11: Sensitivity test of game parameter.(a)q � 0.91, q � 0.86 and p � 0.7.(b) p � 0.44, p � 0.38, q � 0.7.Under the conditions θ 21 � 1.5 and Δ 21 � 0.5, the protect strategy PS 2 can suppress PS 1 and the attack strategy AS 2 can promote AS 1 .estate evolution trend is shown in Figure