Research on Social Governance of Network Public Opinion: An Evolutionary Game Model

Qiu, Zeguo; Yuan, Xiuang; Yin, Yuchen

doi:https://doi.org/10.1155/2023/8530530

Discrete Dynamics in Nature and Society

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Abstract Introduction Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 8530530 | https://doi.org/10.1155/2023/8530530

Research on Social Governance of Network Public Opinion: An Evolutionary Game Model

Zeguo Qiu,¹Xiuang Yuan,¹and Yuchen Yin¹

Academic Editor: Fabio Tramontana

Received02 Nov 2022

Revised18 Mar 2023

Accepted17 Apr 2023

Published26 Apr 2023

Abstract

Compared with the past, public opinion in the we-media era has become more difficult. How to incentivize social networking providers (SNPs) to participate in network public opinion governance and guide we-media practitioners (WPs) to standardize their dissemination are prominent problems that urgently need to be solved in response to network public opinion. This article supplements the perspective of network public opinion governance research and constructs a tripartite evolutionary game model including government, SNPs, and WPs. Then, after analyzing the influencing factors of the evolution of different agents’ strategies through model solving and numerical simulation, this article finds that reasonable rewards and punishments can promote SNPs to participate in network public opinion governance. Finally, this article proposes that the government should build a social governance system for network public opinion, which will effectively reduce governance costs and improve governance efficiency.

1. Introduction

With the development of Internet technology, different forms of social networking sites such as instant messaging, online forums, and short videos have sprung up [1]. The real world and the virtual network world are interpenetrating. While enjoying information sharing and expressing opinions more conveniently and quickly, people also suffer from the uncertainty brought by massive amounts of information to their lives. Compared with the traditional media era, the dissemination of rumors and false information in We-media era is more dangerous [2]. If the government handles these disseminations improperly, its own authority will be challenged, and it is more likely to cause panic among the people and endanger social stability. Especially after 2020, COVID-19 pandemic had caused great panic among people, and there had been one after another storm of public opinion in China. With the spread of COVID-19 on a large scale in society, the information related to the epidemic on the Internet had exploded, and rumors had spewed out [3, 4].

Previous researches on network public opinion governance have achieved some results. These studies mainly focused on the application of computer technology in network public opinion governance and the description of the evolution of network public opinion by mathematical models. Using data mining and other technologies to obtain and analyze the trend of public opinion has become an important topic in the field of network public opinion governance [5–7]. Wei-Dong H et al. [10] studied on the evolutionary mechanism of multiagent in opinion dissemination by using social network analysis methods and sentiment mining analysis techniques and also discussed the role of users in social network sentiment dissemination. Chen et al. [9] proposed to use rough set theory to reduce the network public opinion monitoring index system. Then, they constructed a more scientific monitoring index system of network public opinion, and determined the weight of the index using the analytic hierarchy process. Li et al. [10] proposed and implemented an effective time + user dual attention mechanism model to analyze and predict the textual information of public opinion. Processing public opinion texts, images, or videos through computer technology is the most important step in network public opinion analysis and governance [11]. It is beneficial for the network public opinion management department to quickly grasp the development and evolution of public opinion, and take corresponding measures according to different situations.

From the perspective of the evolution of network public opinion, some scholars seek the rules for the development of public opinion and provide help for network public opinion governance. Yao [12] discussed for the application of cellular automata simulation model of internet evolution of public opinion. Lian et al. [13] pointed out that the network public opinion topology structure based on the classic BA model has the defects of simple scope and not rigorous deduction, and overcame these defects to deduce a model based on complex network theory. Gao et al. [14] introduced eight mechanisms working on formation and dissemination of public opinion on network, and further proposed a comprehensive causal relationship model based on system dynamics to explore the factors affecting the consequence of public opinion on network. Qiu et al. [15] built the temporal model based on the time series forecasting model for emergency network public opinion, and analyzed the change of public opinion trend from a quantitative perspective. In addition, it is also popular to study the evolution of online public opinion through game theory. Wei et al. [16] combined game theory with traditional SIRS epidemic model to propose an improved model, and experimentally verified the model through specific events. Wang et al. [17] proposed a tripartite evolutionary game model including netizens, media, and the government, analyzed the possible equilibrium strategies and its’ stability conditions. Yin et al. [18] proposed an agent-based online opinion formation model based on attitude change theory, group behavior theory, and evolutionary game theory.

However, based on the spiral of silence and two-stage propagation theory [19–21], we find that the previous research perspective rarely mentioned social networking providers (SNPs) and we-media practitioners (WPs). If WPs is not involved, the research on social governance of network public opinion would lack guidance for practice. SNPs should also shoulder corresponding social responsibilities. Therefore, combined with the characteristics of the we-media era, this article proposes a three-party evolutionary game model including government, SNPs, and WPs. Then, we analyzed the strategic stability and influencing factors of all parties in the process of public opinion evolution and used MATLAB to conduct simulation experiments.

2. Evolutionary Game Model

2.1. Problem Description

At present, the government hopes to weaken the impact of online public opinion on social stability through policies and other means. WPs would like to attract more fans by creating content on social networking sites including text, pictures, and videos, and make money by providing fans with advertisements, paid reading, and e-commerce service [22]. SNPs will cooperate with WPs, provide them with traffic exposure services, and share in the profits of WPs. However, in order to pursue more interests, WPs may distort facts and exaggerate information to gain more attention in the dissemination of online public opinion. To save costs, SNPs may not verify the authenticity of content posted by WPs on their social networking sites. This article holds that the main players in the social governance of network public opinion are the government, SNPs, and WPs.

2.2. Hypothesis of the Evolutionary Game Model

It is assumed that all three parties are bounded rational in the game process.

2.2.1. Gaming Strategy

The government’s game strategy is active prevention and passive intervention; the government could choose different strategies for online public opinion caused by emergencies. SNPs’ game strategy is supervision and nonsupervision; SNPs could choose whether to supervise the content spread on social networking sites when network public opinion occurs. WPs’ strategy is seeking truth from facts and distorting facts; WPs could seriously search for information, publish creations rationally, or gain more traffic by distorting facts.

2.2.2. Cost

The government will not directly interfere with the fact that WPs participate in online public opinion dissemination, but it can formulate relevant regulations and systems for the dissemination of Internet information to actively prevent sudden online public opinion, and the cost incurred is . When online public opinion breaks out, it takes time for WPs to choose the strategy of seeking truth from facts. The time and labor cost is . The cost of personnel, financial, and material resources required for SNPs to choose to supervise online public opinion is .

2.2.3. Gains and Losses

When the government chooses the strategy of active prevention, the social stability benefit obtained at this time is denoted as , and is the benefit coefficient when the government chooses the passive intervention strategy, that is, the benefit of social stability at this time is , . The initial earnings of SNPs and WPs before the emergency are and . When SNPs chooses the supervision strategy, these sites get word-of-mouth promotion and more users are recorded as . When WPs choose the strategy of seeking truth from facts, the benefit for social stability is , and this strategy will also enhance their own image and fans so that they can obtain more business cooperation . The sharing coefficient between SNPs and the WPs for the benefit brought by business cooperation is , the benefit of SNPs due to the image enhancement of self-media practitioners is , and the personal benefit of WPs is , . When WPs are tempted by interests , these interests could come from short-term explosions or funding from certain interest groups that affect social stability, and choose the strategy of distorting facts. The loss to social stability is .

2.2.4. Rewards and Penalties

When network public opinion spreads in SNPs and causes great harm to the social stability, the government penalty for SNPs is . The WPs who choose the strategy of distorting facts in the propagation will be called by the government to boycott and lose the initial income. When the government’s strategy is active prevention, SNPs who choose the strategy of supervision will be exempted from partial penalties, and the reduction coefficient is . At this time, the government penalty for SNPs is , . For SNPs that do not endanger social stability due to the spread of network public opinion, the government will reduce taxes as . When SNPs choose the strategy of supervision, WPs choose strategy of seeking truth from facts will be promoted as by the SNPs, and choose strategy of distorting facts will be punished as by the SNPs.

2.3. Payoff Matrix

According to the above five assumptions, we have obtained the payoff matrix about government, SNPs, and WPs, as shown in Table 1.

In this evolutionary game model, government, SNPs, and WPs make strategic choices based on their own circumstances. The probability of the government choosing the strategy of active prevention is written as , then the probability of choosing the strategy of passive intervention is ; the probability of SNPs choosing the strategy of supervision is defined as , the probability of choosing the strategy of nonsupervision is ; the probability of WPs to choose the strategy of seeking truth from facts is represented by , then the probability of choosing the strategy of distorting facts that distorts the truth is , .

2.4. Replicator Dynamics Equation

For the government, the expected revenue of choosing the strategy of active prevention is , the expected revenue of choosing the strategy of passive intervention is , and the average expected revenue is .

For SNPs, the expected revenue of choosing the strategy of supervision is , the expected revenue of choosing the strategy of nonsupervision is , and the average expected revenue is .

For WPs, the expected revenue of choosing the strategy of seeking truth from facts is , the expected revenue of choosing the strategy of distorting facts is , and the average expected revenue is .

The replicator dynamics equation of the government can be obtained as follows [23–28]:

In the same way, the replicator dynamics equation of SNPs and WPs can be obtained. After combining the replication dynamic equations of the three parties, the three-party replication dynamic system (5) can be obtained. In system itself, each of the functions considered depends on all three variables x, y, and z.

2.5. Three-Party Strategy Evolution Process

According to Lyapunov stability theorem [29, 30], if the strategy adopted by the government, SNPs, or WPs is a stable strategy, then , , and must satisfy the following conditions [31]:

As shown in Figure 1. If we denote , when , , , and , the stable strategy of government is uncertain, as shown in Figure 1(a). When , only or , , , but , so, the stable strategy of government is passive intervention, as shown in Figure 1(b). When , the stable strategy of government is active prevention, as shown in Figure 1(c).

(a)

(b)

(c)

As shown in Figure 2. If we denote , when , , , and , the stable strategy of SNPs is uncertain, as shown in Figure 2(a). When , only or , , , but , therefore, the stable strategy of SNPs is nonsupervision, as shown in Figure 2(b). When , the stable strategy of SNPs is supervision, as shown in Figure 2(c).

(a)

(b)

(c)

As shown in Figure 3. If we denote , when , , , and , the stable strategy of WPs is uncertain, as shown in Figure 3(a). When , only or , , , but , hence, the stable strategy of WPs is seeking truth from facts, as shown in Figure 3(b). When , the stable strategy of WPs is distorting facts, as shown in Figure 3(c).

(a)

(b)

(c)

2.6. Evolutionary Stability Analysis

In replication dynamic system (5), let , the equilibrium points of this tripartite game can be obtained: (0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1) and (). In real, game objects do not have a completely rational situation in the hypothesis, so the Nash equilibrium cannot be directly realized. Evolutionary game is the process of continuous learning of different game subjects, and repeated games are played in a group composed of bounded rational subjects to achieve evolutionary stable equilibrium. At this time, the strategy of the group is an evolutionary stable strategy (ESS). ESS describes the local dynamic properties of replicating dynamic systems. In an asymmetric game, if the strategy of game evolution is ESS, then it must be a strict Nash equilibrium, but the game strategy is Nash equilibrium strategy but not necessarily ESS [32, 33].

Since this article mainly discusses the governance of network public opinion, in the current society, a responsible government is bound to choose the strategy of active prevention [32]. For this, we make assumptions: . That is to say, the benefit of the government’s choice of active prevention is greater than that of passive intervention. For the convenience of subsequent work, this article only considers equilibrium points that contain only 0 and 1. In this article, we use Lyapunov stability theory to analyze whether the evolutionary stable strategy combination is true.

The Jacobian matrix of this evolutionary game model is shown as follows:

Substituting the equilibrium points into the Jacobian matrix of equation (7), respectively, we can get the eigenvalues and stable conditions of 8 equilibrium points, as shown in Table 2.

Under the assumed conditions, the eigenvalues of equilibrium points E₁, E₅, and E₆ exist as positive values, which do not conform to Lyapunov stability theory. Therefore, we will not consider them in the following stability analysis.

Proposition 1. If and , only the equilibrium point (1, 1, 1) is ESS.

Proof. As shown in case 1 of Table 3. When , the benefit of SNPs choosing supervision is greater than nonsupervision. At this time, the eigenvalues of equilibrium points E₂, E₃, and E₇ exist as positive values and should be excluded. When , the benefit of WPs choosing seeking truth from facts is greater than distorting facts. At this time, the eigenvalues of equilibrium point E₄ exist as positive values and should be excluded. The eigenvalues of equilibrium point E₈ are all negative values. Therefore, only the equilibrium point (1, 1, 1) is ESS.

Proposition 2. If and , the ESS for the evolutionary game cannot be determined.

Proof. As shown in case 2 of Table 3. When , the benefit of SNPs choosing supervision is greater than nonsupervision. The eigenvalues of equilibrium points E₂, E₃, and E₇ exist as positive values and should be excluded. When , the benefit of WPs choosing distorting facts is greater than seeking truth from facts. No Equilibrium point will be excluded. Under the condition of case 2, the signs of the eigenvalues of E₄ and E₈ cannot be determined, so their stability cannot be judged.
Under the condition of case 2, the eigenvalue λ₁ of the equilibrium point E₃ and the eigenvalue λ₁ of the equilibrium point E₄ are opposite numbers, and the eigenvalue λ₃ of the equilibrium point E₄ and the eigenvalue λ₃ of the equilibrium point E₈ are opposite numbers. The ESS of equilibrium points E₃ and E₈ wound coexist, if the following conditions are satisfied: , , SNPs chooses the strategy of supervision and WPs chooses the strategy of distorting the facts. Although when the government chooses the passive intervention strategy, the WPs’ benefit is greater than the active prevention strategy. However, the government’s penalty reduction for SNPs is relatively large, and the government’s benefit from active prevention is not as good as passive supervision. At this time, the equilibrium points E₃ and E₈ are both ESS.

Proposition 3. If and , only the equilibrium point (1, 0, 1) is ESS.

Proof. As shown in case 3 of Table 3. When , the benefit of SNPs choosing nonsupervision is greater than supervision. The eigenvalues of equilibrium point E₈ exist as positive values and should be excluded. When , the benefit of SNPs choosing seeking truth from facts is greater than distorting facts. The equilibrium points E₂, E₃, and E₄ exist as positive values and should be excluded. The eigenvalues of equilibrium point E₇ are all negative values, therefore, only the equilibrium point E₇ (1, 0, 1) is ESS.

Proposition 4. If and . The ESS for the evolutionary game cannot be determined.

Proof. As shown in case 4 of Table 3. When , the benefit of SNPs choosing nonsupervision is greater than supervision. The eigenvalues of equilibrium point E₈ exist as positive values and should be excluded. When , the benefit of WPs choosing distorting facts is greater than seeking truth from facts. No Equilibrium point will be excluded. Under the condition of case 4, the signs of the eigenvalues of E₂, E₃, E₄, and E₇ cannot be determined, so their stability cannot be judged.
Under the condition of case 4, the eigenvalue λ₂ of the equilibrium point E₂ and the eigenvalue λ₂ of the equilibrium point E₄ are opposite numbers. The eigenvalue λ₃ of the equilibrium point E₂ and the eigenvalue λ₃ of the equilibrium point E₇ are opposite number. The eigenvalue λ₁ of the equilibrium point E₃ and the eigenvalue λ₁ of the equilibrium point E₄ are opposite number. When the eigenvalue λ₂ of the equilibrium point E₃ is negative, the eigenvalue λ₂ of the equilibrium point E₂ must be positive. When the eigenvalue λ₃ of the equilibrium point E₄ is negative, the eigenvalue λ₃ of the equilibrium point E₇ must be positive. The ESS of equilibrium points E₃ and E₇ wound coexist, if the following conditions are satisfied: , , , WPs chooses the strategy of distorting the facts. The benefit of government choosing active prevention strategy is lower than that of passive intervention, and the benefit of SNPs choosing supervision is positive. When the initial earning is not included, the benefit of WPs is less than the temptation of interests, and vice versa when the initial earning is included. At this time, the equilibrium points E₃ and E₇ are both ESS.

3. Numerical Simulation Analysis

What we are pursuing is the social governance system for network public opinion, that is, the government chooses active prevention, SNPs choose supervision and WPs seek truth from facts. Following the above analysis, we use numerical simulations further to analyze the equilibrium point (1, 1, 1). Before the numerical simulations are performed, the model parameters are assigned with fixed values in Table 4. They must satisfy the condition of Proposition 1. As shown in Figure 4, the strategic evolution of the three-party is stable at (1, 1, 1).

Under Proposition 1, there is no coexistence of equilibria. We try to explore the evolution of the three-party strategy when the eigenvalue is 0. Therefore, we keep other fixed values unchanged, and simulate the situation where the eigenvalues λ₂ and λ₃ of the equilibrium point (1, 1, 1) are 0 by changing individual parameters. As shown in Figure 5(a), we set C_p = 3 to obtain the three-party evolution diagram when the eigenvalue λ₂ is 0, and there is no stable point at this time. As shown in Figure 5(b), we set 0.1 as the starting point, 0.2 as the step size, and 1 as the end point to explore the willingness change of SNPs when C_p = 3. The results show that the willingness of SNPs to choose supervision increases in the first two games, but then remains constant. As shown in Figure 6(a), We set L₃ = 10 to obtain the three-party time. As shown in Figure 6(b), we set 0.1 as the starting point, 0.2 as the step size, and 1 as the end point to explore the willingness change of SNPs when L₃ = 10. The results show that the willingness of WPs to choose seeking truth from facts decreases in the first two games, but then remains constant. In the implementation of network public opinion governance, we should be alert to the situation that there is no equilibrium. The willingness of the participating subjects changes from the initial one but cannot be fixed to a certain strategy.

(a)

(b)

(a)

(b)

Next, we keep the other fixed values constant and simulate the effect of parameter changes on the evolution results by changing individual parameters. Following, we discussed the influence of the changes of parameters C_P,W, H, K, and U on the evolution results, respectively.

We set C_P as 2, 5, and 8, respectively. As shown in Figure 7(a), in a certain range, the increase of C_P can accelerate the evolution of the government to the active prevention strategy. As shown in Figure 7(b), the increase of C_P may make SNPs give up participating in the social governance of network public opinion. As shown in Figure 7(c), the increase of C_P may slow down the evolution speed of WPs to seek truth from facts. The government can reduce the regulatory cost of SNPs through subsidies, and guide them to join the social governance of network public opinion.

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(b)

(c)

We set H as 2, 5, and 8, respectively. As shown in Figure 8(a), when the government cuts taxes on SNPs too much, it will reduce its own income and change its strategy to passive intervention. As shown in Figure 8(b), we may think that tax cuts will speed up the evolution of SNPs to regulatory strategies; however, the simulation results are different from our imagination under certain conditions. At this time, tax cuts have little effect on the evolution speed of SNPs. As shown in Figure 8(c), tax cuts can slightly increase the evolution rate of WPs towards a pragmatic strategy.

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(b)

(c)

We set W as 1, 4, and 7, respectively. As shown in Figures 9(a) and 9(b), with the increase of W, the evolution speed of the government to the active prevention strategy slows down, and the evolution speed of SNPs to the strategy of supervision increases. The government can guide SNPs to participate in the social governance of network public opinion by setting reasonable penalties. As shown in Figure 9(c), changes in W have almost no effect on WPs.

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(b)

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We set K as 1.5, 2, and 2.5, respectively. As shown in Figure 10(a), changes in K have little effect on government. As shown in Figure 10(b), the increase of K can significantly reduce the evolution rate of SNPs to the strategy of supervision. As shown in Figure 10(c), the increase of K can slightly increase the evolution speed of WPs to the strategy of seeking truth from facts. Reasonable reward and punishment measures can help the results develop in a positive direction.

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We set U as 1, 3, and 5, respectively. As shown in Figure 11, with the increase of U, the evolution speed of government to active prevention strategy slows down, the evolution speed of SNPs to regulatory strategy and the evolution speed of WPs to realistic strategy increase. The increase of SNPs will punish WPs to distort facts, and it will have a positive incentive effect on both of them at the same time.

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4. Conclusions

Through the evolutionary game method, this article focuses on analyzing the strategic changes of the government, SNPs and WPs in the process of network public opinion dissemination. We draw the following conclusions from the model solution and simulation analysis.

The pursuit of SNPs is to maximize the benefit. The government should reasonably set up rewards and punishments for SNPs, and guide them to take corresponding social responsibilities. The government can provide incentives for actively regulated SNPs to offset regulatory cost, thereby incentivizing SNPs to choose regulatory strategies. Building a social governance system for network public opinion will effectively reduce the cost of governance but increase governance efficiency. Compared with SNPs, WPs have less interest correlation with the government and are less affected by the government. The government should establish various ties with WPs, grasp the double-edged sword of WPs, and promote social harmony and stability. In addition, the government should also establish an access system for WPs to increase the cost of mistakes made by WPs. Ban the entire website of WPs with bad records, and award honors to WPs who are positive. This will reduce the impact of online public opinion on social stability.

The government should establish a social governance system for network public opinion and unite the forces of different subjects to jointly resist the damage caused by the spread of network public opinion. This will reduce the impact of online public opinion on social stability.

Data Availability

No underlying data were collected or produced in this study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research was funded by the Philosophy and Social Science Foundation of Heilongjiang Province (Subject number: 22GLB105).

References

J. Xu and X. Zhao, Changing Platformativity of China’s Female Wanghong: From Anni Baobei to Zhang Dayi,” Female Celebrities in Contemporary Chinese Society, Palgrave Macmillan, London, UK, 2019.
X. Zhou and H. Feng, “Research on the prevention and control of the internet rumor from the perspective of the self-media,” Journal of Computer and Communications, vol. 7, no. 3, pp. 1–7, 2019.
View at: Publisher Site | Google Scholar
Q. Li, T. Chen, J. Yang, and G. Cong, “<p>Based on computational communication paradigm: simulation of public opinion communication process of panic buying during the COVID-19 pandemic<</p&gt,” Psychology Research and Behavior Management, vol. 13, pp. 1027–1045, 2020.
View at: Publisher Site | Google Scholar
R. Jose, M. Narendran, A. Bindu, N. Beevi, M. L, and P. Benny, “Public perception and preparedness for the pandemic COVID 19: a health belief model approach,” Clinical epidemiology and global health, vol. 9, pp. 41–46, 2021.
View at: Publisher Site | Google Scholar
K. Guo, L. Shi, W. Ye, and X. Li, “A Survey of Internet Public Opinion Mining,” in Proceedings of the 2014 IEEE International Conference On Progress In Informatics And Computing, pp. 173–179, Shanghai, China, May 2014.
View at: Google Scholar
G. Stylios, D. Christodoulakis, and J. Besharat, “Public opinion mining for governmental decisions,” Electronic Journal of eGovernment, vol. 8, no. 2, pp. 202–213, 2010.
View at: Google Scholar
M. Zuo, “Data mining strategies and techniques of internet education public sentiment monitoring and analysis system,” in Proceedings of the 2010 2nd International Conference on Future Computer and Communication, vol. 2, pp. 124–127, IEEE, Wuhan, China, May 2010.
View at: Google Scholar
H. Wei-Dong, W. Qian, and C. Jie, “Tracing public opinion propagation and emotional evolution based on public emergencies in social networks,” International Journal of Computers, Communications & Control, vol. 13, no. 1, pp. 129–142, 2018.
View at: Publisher Site | Google Scholar
X. G. Chen, S. Duan, and L. Wang, “Research on trend prediction and evaluation of network public opinion,” Concurrency and Computation: Practice and Experience, vol. 29, no. 24, p. 4212, 2017.
View at: Publisher Site | Google Scholar
L. Li, Y. Wu, Y. Zhang, and T. Zhao, “Time+ user dual attention based sentiment prediction for multiple social network texts with time series,” IEEE Access, vol. 7, pp. 17644–17653, 2019.
View at: Publisher Site | Google Scholar
J. Li and X. Xu, “A study of Big Data-based employees’ public opinion system construction,” Journal of Industrial Integration and Management, vol. 05, no. 2, pp. 225–233, 2020.
View at: Publisher Site | Google Scholar
C. Y. Yao, “The application study of simulation model based on cellular automata in the evolution of internet public opinion,” Applied mechanics and materials, vol. 198, pp. 828–832, 2012.
View at: Google Scholar
Y. Lian, X. Dong, and Y. Liu, “Topological evolution of the internet public opinion,” Physica A: Statistical Mechanics and Its Applications, vol. 486, pp. 567–578, 2017.
View at: Publisher Site | Google Scholar
G. Gao, T. Wang, X. Zheng, Y. Chen, and X. Xu, “A systems dynamics simulation study of network public opinion evolution mechanism,” Journal of Global Information Management, vol. 27, no. 4, pp. 189–207, 2019.
View at: Publisher Site | Google Scholar
Q. Qiu, J. He, and H. Chen, “Research on the evolution law of emergency network public opinion,” in Proceedings of the 2019 12th International Symposium on Computational Intelligence and Design (ISCID), vol. 2, pp. 157–161, IEEE, Hangzhou, China, December 2019.
View at: Google Scholar
D. Wei, F. Chen, and L. Lin, “Simulation of hot event propagation based on game theory and SIRS,” Journal of System Simulation, vol. 30, no. 6, p. 2050, 2018.
View at: Google Scholar
J. Wang, X. Wang, and L. Fu, “Evolutionary game model of public opinion information propagation in online social networks,” IEEE Access, vol. 8, pp. 127732–127747, 2020.
View at: Publisher Site | Google Scholar
X. Yin, H. Wang, P. Yin, and H. Zhu, “Agent-based opinion formation modeling in social network: a perspective of social psychology,” Physica A: Statistical Mechanics and Its Applications, vol. 532, Article ID 121786, 2019.
View at: Publisher Site | Google Scholar
E. Noelle‐Neumann, “The spiral of silence a theory of public opinion,” Journal of Communication, vol. 24, no. 2, pp. 43–51, 1974.
View at: Publisher Site | Google Scholar
L. R. Bostian, “The two-step flow theory: cross-cultural implications,” Journalism Quarterly, vol. 47, no. 1, pp. 109–117, 1970.
View at: Publisher Site | Google Scholar
S. Choi, “The two-step flow of communication in Twitter-based public forums,” Social Science Computer Review, vol. 33, no. 6, pp. 696–711, 2015.
View at: Publisher Site | Google Scholar
S. Xia, “A study on the profit model of we media in China,” Global Media Journal, vol. 15, no. 28, 2017.
View at: Google Scholar
J. W. Weibull, Evolutionary Game Theory, MIT press, Cambridge, MA, USA, 1997.
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, MA, USA, 1998.
D. Acemoglu and A. Ozdaglar, “Opinion dynamics and learning in social networks,” Dynamic Games and Applications, vol. 1, pp. 3–49, 2011.
View at: Publisher Site | Google Scholar
F. Vega-Redondo, Ed.in Evolution, Games, and Economic Behaviour, OUP Oxford, Oxford, UK, 1996.
R. A. Araujo and H. N. Moreira, “Lyapunov stability in an evolutionary game theory model of the labour market,” Economic Annalist, vol. 15, no. 1, pp. 41–53, 2014.
View at: Publisher Site | Google Scholar
H. Huo, R. Yang, S. Zhan, and H. He, “Evolutionary game analysis of standardized production of agricultural products embedded in blockchain,” Discrete Dynamics in Nature and Society, vol. 2022, Article ID 2147338, 16 pages, 2022.
View at: Publisher Site | Google Scholar
D. Shevitz and B. Paden, “Lyapunov stability theory of nonsmooth systems,” IEEE Transactions on Automatic Control, vol. 39, no. 9, pp. 1910–1914, 1994.
View at: Publisher Site | Google Scholar
S. Sastry and S. Sastry, “Lyapunov stability theory,” Nonlinear Systems: Analysis, Stability, and Control, pp. 182–234, 1999.
View at: Google Scholar
J. W. Friedman, “Low information nash equilibria for oligopolistic markets,” Information Economics and Policy, vol. 1, pp. 37–53, 1983.
View at: Publisher Site | Google Scholar
R. Selten, “A note on evolutionarily stable strategies in asymmetric animal conficts,” Models of Strategic Rationality, vol. 84, pp. 67–75, 1988.
View at: Google Scholar
D. Cui and F. Wu, “Moral goodness and social orderliness: an analysis of the official media discourse about Internet governance in China,” Telecommunications Policy, vol. 40, no. 2-3, pp. 265–276, 2016.
View at: Publisher Site | Google Scholar

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