# An Evolutionary Game Analysis on Public Information Communication between the Government and the Public in China

Authors: Hongsen Luo; Ying Gao; Fulei Shi
Journal: Complexity
 (2021)

---

## Abstract

Public information is a social resource that connects all aspects of social life, regulates social activities and public behaviors, and plays a very important role in influencing public trust. Based on the perspective of communication, we divide the government into two ways to release public information, that is, mass communication and personalized recommendation. Moreover, the public can choose to acquire or not acquire a strategy. Then, this study conducts an evolutionary game between the government and the public to analyze the influence of public information on the public in China. Our objective is to find how the evolutionary path changes between the two players when strategies are changing. Then, a simulation analysis is presented in six scenarios to illustrate the results. The results show that the two players can converge to different stable statuses under different situations.


---

## Body

## 1. Introduction

Public information plays a very important role in influencing public trust in recent years. However, in 2015, the General Office of the State Council pointed out that there were “not in time, inaccurate, unresponsive, and impractical” problems in the construction of Chinese government websites, and the public even had a certain trust crisis on some public information services provided by the government, such as food safety information disclosure. Therefore, how to improve the accessibility and transmissibility of public information and improve the public’s overall satisfaction with public information service is an urgent problem to be solved in China.In the past few decades, many scholars focused on the studies of the social value of public information [1–4]. For example, Cornand and Heinemann [1] argued that public information should always be provided with maximum precision. James and Lawler [2] concluded that better public information is unambiguously beneficial. However, the public’s overall satisfaction with public information services is not high in recent years in China. How to solve this kind of problem? It is actually a decision-making problem, which is a special field of game theory.There are two ways for the government to release public information. The first way is mass communication which is often discussed in these years [5–9]. For example, as Flanagin [5] proposed, mass communication has traditionally been conceptualized as the one-way transmission of messages from a central organizational source to a large and largely anonymous audience. Hume [6] argued that mass communication is a meaningful way to understand the past. Moreover, the second way is the personalized recommendation which is very popular to be studied by the scholars [10–18]. For example, as Chaney et al. [10] proposed, the goal of recommendation is to suggest a set of unobserved items that she will like; personalized recommendation has become a core component in our online experience. With the fast development of the Internet, Lin et al. [11] argued that personalized news recommendation has become a promising research direction. From the above analyses, we find that this literature has made some contributions to their special field; however, our objective in this paper is to explore how the strategies change between the government and the public. When do the government adopt these two ways to release public information, and what is the best choice? Therefore, it is actually a decision-making problem between the government and the public which is a special field of game theory.In recent years, mounting attention has been paid to the evolutionary game; it has been applied to lots of areas, such as supply chain, environmental pollution, and economics [19–23]. For example, Tian [19] established an evolutionary game to study the industrial pollution problem between the government and enterprises. Friedman [22] introduced the applications of the evolutionary game on economics. In our study, from the former analyses, we can see that how the evolutionary path changes on public information communication problem between the government and the public is actually a field of game theory. Therefore, it is very suitable to use this method to handle this problem in our study.To the best of our knowledge, how the strategies of the evolutionary path between the government and the public are rarely discussed for public information. Moreover, there is little research on studying the influence of public information on the public in China. Therefore, in this paper, our contributions can be summarized as follows: (1) we present a dynamic strategy analysis on the influence of public information on the public in China based on the perspective of communication in an evolutionary game. (2) A numerical simulation is given to illustrate the results.The rest of this paper is organized as follows: in Section2, we describe in detail the evolutionary game model between the government and the public. In Section 3, we explore the stability of the evolutionary game. In Section 4, a numerical simulation is presented to illustrate the results. Finally, in Section 5, the conclusions and the future work of this paper are proposed.


## 2. Model

### 2.1. Research Assumptions

Before establishing the evolutionary game model, some assumptions are shown as follows:Assumption 1.
Public information plays an important role in modern society. The government is responsible for releasing public information and the public can choose whether or not to acquire public information. Therefore, the agents in this evolutionary game are the government and the public. The government is the first player, marked as (G), and the public is the second player, marked as (P). Moreover, we assume that both of these two agents are bounded rational.Assumption 2.
On the one hand, the government can choose different communication modes to release the public information to the public. They can choose a mass communication strategy or personalized recommendation strategy. Then, we assume that the strategy set of the government is {mass communication, personalized recommendation}. On the other hand, the public can adopt whether or not to acquire public information. Then, we assume that the strategy set of the public is {acquire, not acquire}.Assumption 3.
We assume that the probability of government with mass communication strategy isx, so the probability of the government with personalized recommendation strategy is 1−x. x,1−x∈0,1. In addition, we assume that the probability of the public with the acquire strategy is y, so the probability of the public with the not acquire strategy is 1−y. y,1−y∈0,1. The basic variables symbol and descriptions are shown in Table 1 and the strategy matrix of two agents is shown in Table 2.Table 1
Variables symbol and descriptions.
VariablesDescriptionsValue rangexProbability of the government with mass communication strategy0≤x≤1yProbability of the public with the acquire strategy0≤y≤1GThe government—PThe public—Table 2
The strategy matrix of two agents.
The public (P)The government (G)Mass communication, acquireMass communication, not acquirePersonalized recommendation, acquirePersonalized recommendation, not acquire


### 2.2. Parameters

①
In order to establish the payoff matrix of the evolutionary game model between the government and the public, firstly, the costs of the government are presented as follows:We assume that the government hasnn∈N+ pieces of public information in a certain time t. Then, we assume that the value of information of piece ii=1,2,3,…,n is Vii=1,2,3,…,n. Moreover, in Section 2.1, we have assumed that the government can adopt two kinds of communication modes to release the public information. When the government chooses the mass communication strategy, it will spend a certain cost, and we assume that the cost is CG1CG1>0. When the government adopts the personalized recommendation strategy, we assume that the cost is CG2CG2>0. As an emerging mode, the personalized recommendation strategy needs to make statistics of users’ browsing records, mine users’ preference for public information according to their previous browsing records, and then classify users’ hobbies. Based on data mining, recommend public information content, which requires a high cost. Therefore, CG2>CG1. Furthermore, we assume that the arrival rate of public information to the public is k1k1∈0,1 when the government chooses the mass communication strategy. Also, we assume that the arrival rate of public information to the public is k2k2∈0,1 when the government chooses the personalized recommendation strategy. Here, we assume that the public could acquire more pieces of public information when the government adopts the personalized recommendation strategy. Thus, k1<k2.②
Secondly, the costs of the public are shown as follows:If the government adopts the personalized recommendation strategy, it is easier for the public to acquire public information. In this situation, we assume that the cost of the public isCP3CP3∈0,+∞. In addition, if the government adopts the mass communication strategy, it is harder for the public to acquire information. In this situation, we assume that the cost of the public is CP4CP4∈0,+∞. Thus, CP3>CP4. Moreover, if the public chooses the not acquire strategy, we assume that the cost is 0.③
Thirdly, the benefits of the government and the public are listed as follows:Firstly, when the government adopts the mass communication strategy and the public chooses the acquire strategy, we assume that the revenue of the public isRP3, RP3=k1∑i=1nVi. On the contrary, when the government adopts the personalized recommendation strategy and the public chooses the acquire strategy, we assume that the revenue of the public is RP4, RP4=k2∑i=1nVi. Moreover, if the public chooses the not acquire strategy, the revenue of the public is 0. Secondly, if the public acquires the public information, we assume that the government could also get revenues which are regarded as the increases of the social welfare. Then, if the government adopts the mass communication strategy, we assume that the revenue of the government is RG1, RG1=αRP3=αk1∑i=1nVi, αα>1 is the conversion rate for the revenue of the public. Moreover, if the government adopts the personalized recommendation strategy, we assume that the revenue of the government is RG2, RG2=αRP4=αk2∑i=1nVi.Based on the above assumptions, all parameters in this model are presented in Table3. Moreover, the logical framework of this paper is presented in Figure 1.Table 3
All parameters and their descriptions.
ParametersDescriptionsValueCG1The cost of the government with mass communication strategyCG1∈0,+∞CG2The cost of the government with personalized recommendation strategyCG2∈0,+∞CP3The cost of the acquire strategy when the government adopts the mass communication strategyCP3∈0,+∞CP4The cost of the acquire strategy when the government adopts the personalized recommendation strategyCP4∈0,+∞k1Arrival rate when the government chooses the mass communication strategyk1∈0,+∞k2Arrival rate when the government chooses the personalized recommendation strategyk2∈0,+∞αThe conversion rate for the revenue of the publicα∈0,+∞ViThe value of information of pieceiVi∈0,+∞RG1The revenue of the government with mass communication strategyRG1∈0,+∞RG2The revenue of the government with personalized recommendation strategyRG2∈0,+∞RP3The revenue of the acquire strategy when the government adopts mass communication strategyRP3∈0,+∞RP4The revenue of the acquire strategy when the government adopts the personalized recommendation strategyRP4∈0,+∞Figure 1
The logical framework of this paper.


### 2.3. Payoffs of Two Players

(1)
When the government adopts the mass communication strategy and the public chooses the acquire strategy, the payoff of the government is presented as follows:(1)αk1∑i=1nVi−CG1.The payoff of the public is presented as follows:(2)k1∑i=1nVi−CP3.(2)
When the government adopts the mass communication strategy and the public chooses the not acquire strategy, then the payoff of the public is 0. Moreover, the payoff of the government is−CG1.(3)
When the government adopts the personalized recommendation strategy and the public chooses the acquire strategy, the payoff of the government is presented as follows:(3)αk2∑i=1nVi−CG2.The payoff of the public is presented as follows:(4)k2∑i=1nVi−CP4.(4)
When the government adopts the mass communication strategy and the public chooses the not acquire strategy, then the payoff of the public is 0. Moreover, the payoff of the government is−CG2.Based on the above analyses, the payoff matrix of the model is presented in Table4.Table 4
The payoff matrix of the model.
The public (G)The government (E)AcquireyNot acquire1−yMass communicationxαk1∑i=1nVi−CG1,k1∑i=1nVi−CP3−CG1,0Personalized recommendation1−xαk2∑i=1nVi−CG2,k2∑i=1nVi−CP4−CG2,0


### 2.4. The Evolutionary Game Model

In order to study the evolutionary path between the government and the public, the evolutionary game model is established as follows.Firstly, the expected returnπG1 of the government with mass communication strategy is given by(5)πG1=yαk1∑i=1nVi−CG1+1−y−CG1.On the contrary, the expected returnπG2 of the government with the personalized recommendation strategy is given by(6)πG2=yαk2∑i=1nVi−CG2+1−y−CG2.Besides, the expected returnπ¯G of the government is given by(7)π¯G=xπG1+1−xπG2.Then, combining equations (5)–(7), the replicated dynamic equation πGx of the government can be obtained as follows:(8)πGx=dxdt=x1−xyαk1−k2∑i=1nVi−CG1−CG2.Secondly, the expected returnπP1 of the public with the acquire strategy is given by(9)πP1=xk1∑i=1nVi−CP3+1−xk2∑i=1nVi−CP4.On the contrary, the expected returnπP2 of the public with the not acquire strategy is given by(10)πP2=x×0+1−x×0=0.Besides, the expected returnπ¯P of the public is given by(11)π¯P=yπP1+1−yπP2.Then, combining equations (9)–(11), the replicated dynamic equation πPy of the public can be obtained as follows:(12)πPy=dydt=y1−yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.Thus, according to equations (12) and (21), a dynamic system S1 is given by(13)πGx=dxdt=x1−xyαk1−k2∑i=1nVi−CG1−CG2,πPy=dydt=y1−yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.Then, lettingπGx=0 and πPy=0, Theorem 1 can be obtained as follows:Theorem 1.
(0, 0), (0, 1), (1, 0), (1, 1) must be four Nash equilibrium points of systemS1. Moreover, if(14)|CP4−k2∑i=1nVi|−|k1−k2∑i=1nVi−CP3−CP4|<0,CP4−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4>0.|CG1−CG2|−|αk1−k2∑i=1nVi|<0,CG1−CG2αk1−k2∑i=1nVi>0,then the point x∗,y∗ with x∗=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4,y∗=CG1−CG2/αk1−k2∑i=1nVi could be a mixed strategy Nash equilibrium point of system S1.Proof.
According to equation (13), let πGx=0 and πPy=0; then, it is obvious that (0, 0), (0, 1), (1, 0), (1, 1) must be four Nash equilibrium points of system S1. Moreover, letting(15)yαk1−k2∑i=1nVi−CG1−CG2=0,xk1+1−xk2∑i=1nVi−xCP3−CP4−CP4=0,we can obtain that x∗,y∗ with x∗=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4,y∗=CG1−CG2/αk1−k2∑i=1nVi could be a potential mixed strategy Nash equilibrium point of system S1. Furthermore, if(16)|CP4−k2∑i=1nVi|−|k1−k2∑i=1nVi−CP3−CP4|<0,CP4−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4>0,|CG1−CG2|−|αk1−k2∑i=1nVi|<0,CG1−CG2αk1−k2∑i=1nVi>0,then we can obtain that(17)0<CP4−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4<1,0<CG1−CG2αk1−k2∑i=1nVi<1.
Therefore, under this condition, we can obtain thatx∗,y∗ is also a mixed strategy Nash equilibrium point of system S1.
From Theorem1, we can obtain that the government and the public will adopt different strategies under different situations. Therefore, we should divide it into different cases to explore the stability of the evolutionary game.


## 2.1. Research Assumptions

Before establishing the evolutionary game model, some assumptions are shown as follows:Assumption 1.
Public information plays an important role in modern society. The government is responsible for releasing public information and the public can choose whether or not to acquire public information. Therefore, the agents in this evolutionary game are the government and the public. The government is the first player, marked as (G), and the public is the second player, marked as (P). Moreover, we assume that both of these two agents are bounded rational.Assumption 2.
On the one hand, the government can choose different communication modes to release the public information to the public. They can choose a mass communication strategy or personalized recommendation strategy. Then, we assume that the strategy set of the government is {mass communication, personalized recommendation}. On the other hand, the public can adopt whether or not to acquire public information. Then, we assume that the strategy set of the public is {acquire, not acquire}.Assumption 3.
We assume that the probability of government with mass communication strategy isx, so the probability of the government with personalized recommendation strategy is 1−x. x,1−x∈0,1. In addition, we assume that the probability of the public with the acquire strategy is y, so the probability of the public with the not acquire strategy is 1−y. y,1−y∈0,1. The basic variables symbol and descriptions are shown in Table 1 and the strategy matrix of two agents is shown in Table 2.Table 1
Variables symbol and descriptions.
VariablesDescriptionsValue rangexProbability of the government with mass communication strategy0≤x≤1yProbability of the public with the acquire strategy0≤y≤1GThe government—PThe public—Table 2
The strategy matrix of two agents.
The public (P)The government (G)Mass communication, acquireMass communication, not acquirePersonalized recommendation, acquirePersonalized recommendation, not acquire


## 2.2. Parameters

①
In order to establish the payoff matrix of the evolutionary game model between the government and the public, firstly, the costs of the government are presented as follows:We assume that the government hasnn∈N+ pieces of public information in a certain time t. Then, we assume that the value of information of piece ii=1,2,3,…,n is Vii=1,2,3,…,n. Moreover, in Section 2.1, we have assumed that the government can adopt two kinds of communication modes to release the public information. When the government chooses the mass communication strategy, it will spend a certain cost, and we assume that the cost is CG1CG1>0. When the government adopts the personalized recommendation strategy, we assume that the cost is CG2CG2>0. As an emerging mode, the personalized recommendation strategy needs to make statistics of users’ browsing records, mine users’ preference for public information according to their previous browsing records, and then classify users’ hobbies. Based on data mining, recommend public information content, which requires a high cost. Therefore, CG2>CG1. Furthermore, we assume that the arrival rate of public information to the public is k1k1∈0,1 when the government chooses the mass communication strategy. Also, we assume that the arrival rate of public information to the public is k2k2∈0,1 when the government chooses the personalized recommendation strategy. Here, we assume that the public could acquire more pieces of public information when the government adopts the personalized recommendation strategy. Thus, k1<k2.②
Secondly, the costs of the public are shown as follows:If the government adopts the personalized recommendation strategy, it is easier for the public to acquire public information. In this situation, we assume that the cost of the public isCP3CP3∈0,+∞. In addition, if the government adopts the mass communication strategy, it is harder for the public to acquire information. In this situation, we assume that the cost of the public is CP4CP4∈0,+∞. Thus, CP3>CP4. Moreover, if the public chooses the not acquire strategy, we assume that the cost is 0.③
Thirdly, the benefits of the government and the public are listed as follows:Firstly, when the government adopts the mass communication strategy and the public chooses the acquire strategy, we assume that the revenue of the public isRP3, RP3=k1∑i=1nVi. On the contrary, when the government adopts the personalized recommendation strategy and the public chooses the acquire strategy, we assume that the revenue of the public is RP4, RP4=k2∑i=1nVi. Moreover, if the public chooses the not acquire strategy, the revenue of the public is 0. Secondly, if the public acquires the public information, we assume that the government could also get revenues which are regarded as the increases of the social welfare. Then, if the government adopts the mass communication strategy, we assume that the revenue of the government is RG1, RG1=αRP3=αk1∑i=1nVi, αα>1 is the conversion rate for the revenue of the public. Moreover, if the government adopts the personalized recommendation strategy, we assume that the revenue of the government is RG2, RG2=αRP4=αk2∑i=1nVi.Based on the above assumptions, all parameters in this model are presented in Table3. Moreover, the logical framework of this paper is presented in Figure 1.Table 3
All parameters and their descriptions.
ParametersDescriptionsValueCG1The cost of the government with mass communication strategyCG1∈0,+∞CG2The cost of the government with personalized recommendation strategyCG2∈0,+∞CP3The cost of the acquire strategy when the government adopts the mass communication strategyCP3∈0,+∞CP4The cost of the acquire strategy when the government adopts the personalized recommendation strategyCP4∈0,+∞k1Arrival rate when the government chooses the mass communication strategyk1∈0,+∞k2Arrival rate when the government chooses the personalized recommendation strategyk2∈0,+∞αThe conversion rate for the revenue of the publicα∈0,+∞ViThe value of information of pieceiVi∈0,+∞RG1The revenue of the government with mass communication strategyRG1∈0,+∞RG2The revenue of the government with personalized recommendation strategyRG2∈0,+∞RP3The revenue of the acquire strategy when the government adopts mass communication strategyRP3∈0,+∞RP4The revenue of the acquire strategy when the government adopts the personalized recommendation strategyRP4∈0,+∞Figure 1
The logical framework of this paper.


## 2.3. Payoffs of Two Players

(1)
When the government adopts the mass communication strategy and the public chooses the acquire strategy, the payoff of the government is presented as follows:(1)αk1∑i=1nVi−CG1.The payoff of the public is presented as follows:(2)k1∑i=1nVi−CP3.(2)
When the government adopts the mass communication strategy and the public chooses the not acquire strategy, then the payoff of the public is 0. Moreover, the payoff of the government is−CG1.(3)
When the government adopts the personalized recommendation strategy and the public chooses the acquire strategy, the payoff of the government is presented as follows:(3)αk2∑i=1nVi−CG2.The payoff of the public is presented as follows:(4)k2∑i=1nVi−CP4.(4)
When the government adopts the mass communication strategy and the public chooses the not acquire strategy, then the payoff of the public is 0. Moreover, the payoff of the government is−CG2.Based on the above analyses, the payoff matrix of the model is presented in Table4.Table 4
The payoff matrix of the model.
The public (G)The government (E)AcquireyNot acquire1−yMass communicationxαk1∑i=1nVi−CG1,k1∑i=1nVi−CP3−CG1,0Personalized recommendation1−xαk2∑i=1nVi−CG2,k2∑i=1nVi−CP4−CG2,0


## 2.4. The Evolutionary Game Model

In order to study the evolutionary path between the government and the public, the evolutionary game model is established as follows.Firstly, the expected returnπG1 of the government with mass communication strategy is given by(5)πG1=yαk1∑i=1nVi−CG1+1−y−CG1.On the contrary, the expected returnπG2 of the government with the personalized recommendation strategy is given by(6)πG2=yαk2∑i=1nVi−CG2+1−y−CG2.Besides, the expected returnπ¯G of the government is given by(7)π¯G=xπG1+1−xπG2.Then, combining equations (5)–(7), the replicated dynamic equation πGx of the government can be obtained as follows:(8)πGx=dxdt=x1−xyαk1−k2∑i=1nVi−CG1−CG2.Secondly, the expected returnπP1 of the public with the acquire strategy is given by(9)πP1=xk1∑i=1nVi−CP3+1−xk2∑i=1nVi−CP4.On the contrary, the expected returnπP2 of the public with the not acquire strategy is given by(10)πP2=x×0+1−x×0=0.Besides, the expected returnπ¯P of the public is given by(11)π¯P=yπP1+1−yπP2.Then, combining equations (9)–(11), the replicated dynamic equation πPy of the public can be obtained as follows:(12)πPy=dydt=y1−yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.Thus, according to equations (12) and (21), a dynamic system S1 is given by(13)πGx=dxdt=x1−xyαk1−k2∑i=1nVi−CG1−CG2,πPy=dydt=y1−yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.Then, lettingπGx=0 and πPy=0, Theorem 1 can be obtained as follows:Theorem 1.
(0, 0), (0, 1), (1, 0), (1, 1) must be four Nash equilibrium points of systemS1. Moreover, if(14)|CP4−k2∑i=1nVi|−|k1−k2∑i=1nVi−CP3−CP4|<0,CP4−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4>0.|CG1−CG2|−|αk1−k2∑i=1nVi|<0,CG1−CG2αk1−k2∑i=1nVi>0,then the point x∗,y∗ with x∗=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4,y∗=CG1−CG2/αk1−k2∑i=1nVi could be a mixed strategy Nash equilibrium point of system S1.Proof.
According to equation (13), let πGx=0 and πPy=0; then, it is obvious that (0, 0), (0, 1), (1, 0), (1, 1) must be four Nash equilibrium points of system S1. Moreover, letting(15)yαk1−k2∑i=1nVi−CG1−CG2=0,xk1+1−xk2∑i=1nVi−xCP3−CP4−CP4=0,we can obtain that x∗,y∗ with x∗=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4,y∗=CG1−CG2/αk1−k2∑i=1nVi could be a potential mixed strategy Nash equilibrium point of system S1. Furthermore, if(16)|CP4−k2∑i=1nVi|−|k1−k2∑i=1nVi−CP3−CP4|<0,CP4−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4>0,|CG1−CG2|−|αk1−k2∑i=1nVi|<0,CG1−CG2αk1−k2∑i=1nVi>0,then we can obtain that(17)0<CP4−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4<1,0<CG1−CG2αk1−k2∑i=1nVi<1.
Therefore, under this condition, we can obtain thatx∗,y∗ is also a mixed strategy Nash equilibrium point of system S1.
From Theorem1, we can obtain that the government and the public will adopt different strategies under different situations. Therefore, we should divide it into different cases to explore the stability of the evolutionary game.


## 3. The Stability Analysis of the Evolutionary Game

### 3.1. Basic Analysis of the Two Single Players in the Evolutionary Game

Proposition 1.
In terms of the public, it will achieve stable status in the following three cases:①
Whenx=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, the evolutionary strategy is always in equilibrium②
Whenx>CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then y=1 is an evolutionary equilibrium point③
Whenx<CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then y=0 is an evolutionary equilibrium pointProof.
According to the work proposed by Friedman [],πGx=0 and πG′x<0 are required in order to achieve the “evolutionary stable strategy” (ESS); this is similar for πPy to meet the same condition. According to equation (13), we can obtain the following equation:(18)πG′x=dxdt=1−2xyαk1−k2∑i=1nVi−CG1−CG2,πP′y=dydt=1−2yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.①
Whenx=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, there is always πPy≡0. Thus, whatever the value of y is, the evolutionary strategy is always in equilibrium.②
Whenx>CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then there are πP′0>0 and πP′1<0. Therefore, y=1 is an evolutionary equilibrium point, and the public will choose the not acquire strategy.③
Whenx<CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then there are πP′0<0 and πP′1>0. Thus, in this situation, y=0 is an evolutionary equilibrium point, and the public will choose the acquire strategy.Proposition 2.
In terms of the government, it will achieve stable status in the following three cases:①
Wheny=CG1−CG2/αk1−k2∑i=1nVi, the evolutionary strategy is always in equilibrium②
Wheny>CG1−CG2/αk1−k2∑i=1nVi, then x=1 is an evolutionary equilibrium point③
Wheny<CG1−CG2/αk1−k2∑i=1nVi, then x=0 is an evolutionary equilibrium pointProof.
Similar to the proof of Proposition1, we can obtain the following:①
Wheny=CG1−CG2/αk1−k2∑i=1nVi, there is always πGx≡0. Thus, whatever the value of x is, the evolutionary strategy is always in equilibrium.②
Wheny>CG1−CG2/αk1−k2∑i=1nVi, then there are πG′0>0 and πG′1<0. Therefore, x=1 is an evolutionary equilibrium point, and the government will choose the personalized recommendation strategy.③
Wheny<CG1−CG2/αk1−k2∑i=1nVi, then there are πG′0<0 and πG′1>0. Thus, in this situation, x=0 is an evolutionary equilibrium point, and the government will choose the mass communication strategy.


### 3.2. Analysis of Stability of the Evolutionary Game

According to the method of the Jacobi matrix proposed by Friedman [18], we assume that the Jacobi matrix of system S1 is J. Then, the corresponding Jacobi matrix is(19)J=M11M12M21M22,where(20)M11=∂πGx∂x=1−2xyαk1−k2∑i=1nVi−CG1−CG2,M12=∂πGx∂y=x1−xk1−k2α∑i=1nVi,M21=∂πPy∂x=y1−yk1−k2∑i=1nVi−CP3−CP4,M22=∂πPy∂y=1−2yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.Based on the analysis of the Jacobi matrix, we can get the local stability of the equilibrium points; then, Theorem2 can be obtained as follows.Theorem 2.
The ESS point may be achieved at (0, 0), (0, 1), (1, 0), (1, 1); however,x∗,y∗ must be the central point. Moreover, the following six cases are presented:①
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 1) is the ESS point②
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then (0, 1) is the ESS point③
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 0) is the ESS point④
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then the ESS point may be achieved at (0, 1) or (1, 0)⑤
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 0) is the ESS point⑥
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4<0, and αk1−k2∑i=1nVi−CG1−CG2<0, then (1, 0) is the ESS pointProof.
According to equation (19), we can obtain that the determinant of J as follows:(21)detJ=1−2x1−2yyαk1−k2∑i=1nVi−CG1−CG2xk1+1−xk2∑i=1nVi−xCP3−CP4−xy1−x1−yαk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4.
The trace of the matrixJ is(22)trJ=1−2xyαk1−k2∑i=1nVi−CG1−CG2+1−2yxk1+1−xk2∑i=1nVi−xCP3−CP4.
Then, from equations (21) and (22) and the point x∗,y∗, we can obtain(23)ψ1:detJ|x∗,y∗=1−2x∗1−2y∗y∗αk1−k2∑i=1nVi−CG1−CG2x∗k1+1−x∗k2∑i=1nVi−x∗CP3−CP4−x∗y∗1−x∗1−y∗αk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4=k1∑i=1nVi−CP3k2∑i=1nVi−CP4CG1−CG2αk1−k2∑i=1nVi−CG1−CG2αk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4,ψ2:trJ|x∗,y∗=1−2x∗y∗αk1−k2∑i=1nVi−CG1−CG2+1−2y∗x∗k1+1−x∗k2∑i=1nVi−x∗CP3−CP4=0.
According to equation (23), we know that trJ|x∗,y∗=0; therefore, the trace of the matrix under different situations must be 0. Thus, x∗,y∗ must be the central point. Moreover, we can obtain that the expressions of five points as shown in Table 5.
Moreover, according to the work proposed by Friedman [], the corresponding evolutionary strategy will become the ESS point ifdetJ>0 and trJ<0. In Section 2.2, we assume that the parameters in this model are all positive; in addition, CG2>CG1, CP3>CP4, and k1<k2. Thus, there must be CG1−CG2<0, CP3−CP4>0, and k1−k2<0. Then, we can obtain that αk1−k2∑i=1nVi<0 and k1−k2∑i=1nVi−CP3−CP4<0. Therefore, we just need to discuss the following three cases:
Whenk1∑i=1nVi−CP3>0, due to CP3>CP4 and k1<k2, there must be k2∑i=1nVi−CP4>0. Therefore, the following two cases are discussed:①
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then we have detJ|1,1=αk1−k2∑i=1nVi−CG1−CG2k1∑i=1nVi−CP3>0 and trJ|1,1=−αk1−k2∑i=1nVi−CG1−CG2−k1∑i=1nVi−CP3<0. Therefore, (1, 1) is the ESS point.②
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then we have detJ|0,1=−αk1−k2∑i=1nVi−CG1−CG2k2∑i=1nVi−CP4>0 and trJ|0,1=αk1−k2∑i=1nVi−CG1−CG2−k2∑i=1nVi−CP4<0. Therefore, (0, 1) is the ESS point.
Whenk1∑i=1nVi−CP3<0, the following four cases are shown in Table 6.Table 5
The expressions of five points.
Equilibrium pointExpression(0, 0)detJ−CG1−CG2k2∑i=1nVi−CP4trJ−CG1−CG2+k2∑i=1nVi−CP4(0, 1)detJ−αk1−k2∑i=1nVi−CG1−CG2k2∑i=1nVi−CP4trJαk1−k2∑i=1nVi−CG1−CG2−k2∑i=1nVi−CP4(1, 0)detJCG1−CG2k1∑i=1nVi−CP3trJCG1−CG2+k1∑i=1nVi−CP3(1, 1)detJαk1−k2∑i=1nVi−CG1−CG2k1∑i=1nVi−CP3trJ−αk1−k2∑i=1nVi−CG1−CG2−k1∑i=1nVi−CP3x∗,y∗detJk1∑i=1nVi−CP3k2∑i=1nVi−CP4CG1−CG2αk1−k2∑i=1nVi−CG1−CG2/αk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4trJ0Table 6
The evolutionary stability of local equilibrium points under four cases.
CaseConditionEquilibrium pointdetJtrJResultsCase 1k1∑i=1nVi−CP3<0(0, 0)++Unstable point③k2∑i=1nVi−CP4>0(0, 1)−±Saddle pointαk1−k2∑i=1nVi−CG1−CG2>0(1, 0)+−ESS(1, 1)−±Saddle pointx∗,y∗+0Central pointCase 2k1∑i=1nVi−CP3<0(0, 0)++Unstable point④k2∑i=1nVi−CP4>0(0, 1)+−ESSαk1−k2∑i=1nVi−CG1−CG2<0(1, 0)+−ESS(1, 1)++Unstable pointx∗,y∗−0Central pointCase 3k1∑i=1nVi−CP3<0(0, 0)−±Saddle point⑤k2∑i=1nVi−CP4<0(0, 1)−±Saddle pointαk1−k2∑i=1nVi−CG1−CG2>0(1, 0)+−ESS(1, 1)−±Saddle pointx∗,y∗−0Central pointCase 4k1∑i=1nVi−CP3<0(0, 0)−±Saddle point⑥k2∑i=1nVi−CP4<0(0, 1)−±Saddle pointαk1−k2∑i=1nVi−CG1−CG2<0(1, 0)+−ESS(1, 1)++Unstable pointx∗,y∗+0Central pointFrom Table6, we can obtain the cases in ③∼⑥.


## 3.1. Basic Analysis of the Two Single Players in the Evolutionary Game

Proposition 1.
In terms of the public, it will achieve stable status in the following three cases:①
Whenx=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, the evolutionary strategy is always in equilibrium②
Whenx>CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then y=1 is an evolutionary equilibrium point③
Whenx<CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then y=0 is an evolutionary equilibrium pointProof.
According to the work proposed by Friedman [],πGx=0 and πG′x<0 are required in order to achieve the “evolutionary stable strategy” (ESS); this is similar for πPy to meet the same condition. According to equation (13), we can obtain the following equation:(18)πG′x=dxdt=1−2xyαk1−k2∑i=1nVi−CG1−CG2,πP′y=dydt=1−2yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.①
Whenx=CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, there is always πPy≡0. Thus, whatever the value of y is, the evolutionary strategy is always in equilibrium.②
Whenx>CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then there are πP′0>0 and πP′1<0. Therefore, y=1 is an evolutionary equilibrium point, and the public will choose the not acquire strategy.③
Whenx<CP4−k2∑i=1nVi/k1−k2∑i=1nVi−CP3−CP4, then there are πP′0<0 and πP′1>0. Thus, in this situation, y=0 is an evolutionary equilibrium point, and the public will choose the acquire strategy.Proposition 2.
In terms of the government, it will achieve stable status in the following three cases:①
Wheny=CG1−CG2/αk1−k2∑i=1nVi, the evolutionary strategy is always in equilibrium②
Wheny>CG1−CG2/αk1−k2∑i=1nVi, then x=1 is an evolutionary equilibrium point③
Wheny<CG1−CG2/αk1−k2∑i=1nVi, then x=0 is an evolutionary equilibrium pointProof.
Similar to the proof of Proposition1, we can obtain the following:①
Wheny=CG1−CG2/αk1−k2∑i=1nVi, there is always πGx≡0. Thus, whatever the value of x is, the evolutionary strategy is always in equilibrium.②
Wheny>CG1−CG2/αk1−k2∑i=1nVi, then there are πG′0>0 and πG′1<0. Therefore, x=1 is an evolutionary equilibrium point, and the government will choose the personalized recommendation strategy.③
Wheny<CG1−CG2/αk1−k2∑i=1nVi, then there are πG′0<0 and πG′1>0. Thus, in this situation, x=0 is an evolutionary equilibrium point, and the government will choose the mass communication strategy.


## 3.2. Analysis of Stability of the Evolutionary Game

According to the method of the Jacobi matrix proposed by Friedman [18], we assume that the Jacobi matrix of system S1 is J. Then, the corresponding Jacobi matrix is(19)J=M11M12M21M22,where(20)M11=∂πGx∂x=1−2xyαk1−k2∑i=1nVi−CG1−CG2,M12=∂πGx∂y=x1−xk1−k2α∑i=1nVi,M21=∂πPy∂x=y1−yk1−k2∑i=1nVi−CP3−CP4,M22=∂πPy∂y=1−2yxk1+1−xk2∑i=1nVi−xCP3−CP4−CP4.Based on the analysis of the Jacobi matrix, we can get the local stability of the equilibrium points; then, Theorem2 can be obtained as follows.Theorem 2.
The ESS point may be achieved at (0, 0), (0, 1), (1, 0), (1, 1); however,x∗,y∗ must be the central point. Moreover, the following six cases are presented:①
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 1) is the ESS point②
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then (0, 1) is the ESS point③
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 0) is the ESS point④
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then the ESS point may be achieved at (0, 1) or (1, 0)⑤
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 0) is the ESS point⑥
Whenk1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4<0, and αk1−k2∑i=1nVi−CG1−CG2<0, then (1, 0) is the ESS pointProof.
According to equation (19), we can obtain that the determinant of J as follows:(21)detJ=1−2x1−2yyαk1−k2∑i=1nVi−CG1−CG2xk1+1−xk2∑i=1nVi−xCP3−CP4−xy1−x1−yαk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4.
The trace of the matrixJ is(22)trJ=1−2xyαk1−k2∑i=1nVi−CG1−CG2+1−2yxk1+1−xk2∑i=1nVi−xCP3−CP4.
Then, from equations (21) and (22) and the point x∗,y∗, we can obtain(23)ψ1:detJ|x∗,y∗=1−2x∗1−2y∗y∗αk1−k2∑i=1nVi−CG1−CG2x∗k1+1−x∗k2∑i=1nVi−x∗CP3−CP4−x∗y∗1−x∗1−y∗αk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4=k1∑i=1nVi−CP3k2∑i=1nVi−CP4CG1−CG2αk1−k2∑i=1nVi−CG1−CG2αk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4,ψ2:trJ|x∗,y∗=1−2x∗y∗αk1−k2∑i=1nVi−CG1−CG2+1−2y∗x∗k1+1−x∗k2∑i=1nVi−x∗CP3−CP4=0.
According to equation (23), we know that trJ|x∗,y∗=0; therefore, the trace of the matrix under different situations must be 0. Thus, x∗,y∗ must be the central point. Moreover, we can obtain that the expressions of five points as shown in Table 5.
Moreover, according to the work proposed by Friedman [], the corresponding evolutionary strategy will become the ESS point ifdetJ>0 and trJ<0. In Section 2.2, we assume that the parameters in this model are all positive; in addition, CG2>CG1, CP3>CP4, and k1<k2. Thus, there must be CG1−CG2<0, CP3−CP4>0, and k1−k2<0. Then, we can obtain that αk1−k2∑i=1nVi<0 and k1−k2∑i=1nVi−CP3−CP4<0. Therefore, we just need to discuss the following three cases:
Whenk1∑i=1nVi−CP3>0, due to CP3>CP4 and k1<k2, there must be k2∑i=1nVi−CP4>0. Therefore, the following two cases are discussed:①
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then we have detJ|1,1=αk1−k2∑i=1nVi−CG1−CG2k1∑i=1nVi−CP3>0 and trJ|1,1=−αk1−k2∑i=1nVi−CG1−CG2−k1∑i=1nVi−CP3<0. Therefore, (1, 1) is the ESS point.②
Whenk1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then we have detJ|0,1=−αk1−k2∑i=1nVi−CG1−CG2k2∑i=1nVi−CP4>0 and trJ|0,1=αk1−k2∑i=1nVi−CG1−CG2−k2∑i=1nVi−CP4<0. Therefore, (0, 1) is the ESS point.
Whenk1∑i=1nVi−CP3<0, the following four cases are shown in Table 6.Table 5
The expressions of five points.
Equilibrium pointExpression(0, 0)detJ−CG1−CG2k2∑i=1nVi−CP4trJ−CG1−CG2+k2∑i=1nVi−CP4(0, 1)detJ−αk1−k2∑i=1nVi−CG1−CG2k2∑i=1nVi−CP4trJαk1−k2∑i=1nVi−CG1−CG2−k2∑i=1nVi−CP4(1, 0)detJCG1−CG2k1∑i=1nVi−CP3trJCG1−CG2+k1∑i=1nVi−CP3(1, 1)detJαk1−k2∑i=1nVi−CG1−CG2k1∑i=1nVi−CP3trJ−αk1−k2∑i=1nVi−CG1−CG2−k1∑i=1nVi−CP3x∗,y∗detJk1∑i=1nVi−CP3k2∑i=1nVi−CP4CG1−CG2αk1−k2∑i=1nVi−CG1−CG2/αk1−k2∑i=1nVik1−k2∑i=1nVi−CP3−CP4trJ0Table 6
The evolutionary stability of local equilibrium points under four cases.
CaseConditionEquilibrium pointdetJtrJResultsCase 1k1∑i=1nVi−CP3<0(0, 0)++Unstable point③k2∑i=1nVi−CP4>0(0, 1)−±Saddle pointαk1−k2∑i=1nVi−CG1−CG2>0(1, 0)+−ESS(1, 1)−±Saddle pointx∗,y∗+0Central pointCase 2k1∑i=1nVi−CP3<0(0, 0)++Unstable point④k2∑i=1nVi−CP4>0(0, 1)+−ESSαk1−k2∑i=1nVi−CG1−CG2<0(1, 0)+−ESS(1, 1)++Unstable pointx∗,y∗−0Central pointCase 3k1∑i=1nVi−CP3<0(0, 0)−±Saddle point⑤k2∑i=1nVi−CP4<0(0, 1)−±Saddle pointαk1−k2∑i=1nVi−CG1−CG2>0(1, 0)+−ESS(1, 1)−±Saddle pointx∗,y∗−0Central pointCase 4k1∑i=1nVi−CP3<0(0, 0)−±Saddle point⑥k2∑i=1nVi−CP4<0(0, 1)−±Saddle pointαk1−k2∑i=1nVi−CG1−CG2<0(1, 0)+−ESS(1, 1)++Unstable pointx∗,y∗+0Central pointFrom Table6, we can obtain the cases in ③∼⑥.


## 4. Simulation Analysis

### 4.1. The Evolutionary Path between the Government and the Public

In order to observe the evolutionary path between the government and the public, simulation analyses are used. Then, according to Theorem2, the assumed values of the parameters under the six scenarios are presented in Table 7.Table 7
The assumed values of the parameters under the six scenarios.
The scenariosScenario ①Scenario ②Scenario ③Scenario ④Scenario ⑤Scenario ⑥k10.30.30.30.30.30.3k20.70.70.70.70.70.7n333333Vi555555CP333551515CP422221212CG1222222CG2151015101510α222222x(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)y(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)To simplify the analysis, we assume thatα=2, n=3, and Vi=5 in six scenarios. Moreover, in order to fully discuss the influence of different initial values of probabilities to the stability of the model, we assume that x=y=0.1:0.2:0.9. For example, if x=0.1,y=0.1, it means that the government will adopt a weak willingness to choose the mass communication strategy while the enterprises will also adopt a weak willingness to choose the acquire strategy. If x=0.1,y=0.9, it means that the government will adopt a weak willingness to choose the mass communication strategy while the enterprises will also adopt a high willingness to choose the acquire strategy. Then, the simulation results of six scenarios are presented in Figure 2.Figure 2
The simulation results of six scenarios.
(a)(b)(c)(d)(e)(f)From Figure2 and combined with Theorem 2, we can obtain the following conclusions.Conclusion 1.
Combined with Figures2(a) and 2(b) and Theorem 2, we can see that when k1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 1) is the ESS point. Therefore, in this situation, the government will fully adopt the mass communication strategy and the public will fully adopt the acquire strategy. When k1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then (0, 1) is the ESS point. In this situation, the government will adopt the personalized recommendation strategy while the public adopts the acquire strategy. These two scenarios are very similar because the public will choose the acquire strategy. This is mainly due to the condition that k1∑i=1nVi−CP3>0; thus, the revenue of the public with the acquire strategy is higher than the cost.Conclusion 2.
Combined with Figures2(c) and 2(f) and Theorem 2, we can see that when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0; when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4<0, and αk1−k2∑i=1nVi−CG1−CG2>0; or when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4<0, and αk1−k2∑i=1nVi−CG1−CG2<0, the ESS point is always (0, 0). That is to say, in these three situations, the government will choose the personalized recommendation strategy and the public will choose the not acquire strategy. Moreover, when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then three are two ESS points, (0, 1) and (1, 0). In this case, the strategies can be different between the government and the public.Conclusion 3.
Combined with the above six scenarios, we can obtain that the time to convergence is different; in Scenario ③, it will spend more time to converge to a stable status.


## 4.1. The Evolutionary Path between the Government and the Public

In order to observe the evolutionary path between the government and the public, simulation analyses are used. Then, according to Theorem2, the assumed values of the parameters under the six scenarios are presented in Table 7.Table 7
The assumed values of the parameters under the six scenarios.
The scenariosScenario ①Scenario ②Scenario ③Scenario ④Scenario ⑤Scenario ⑥k10.30.30.30.30.30.3k20.70.70.70.70.70.7n333333Vi555555CP333551515CP422221212CG1222222CG2151015101510α222222x(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)y(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)(0.1 : 0.2 : 0.9)To simplify the analysis, we assume thatα=2, n=3, and Vi=5 in six scenarios. Moreover, in order to fully discuss the influence of different initial values of probabilities to the stability of the model, we assume that x=y=0.1:0.2:0.9. For example, if x=0.1,y=0.1, it means that the government will adopt a weak willingness to choose the mass communication strategy while the enterprises will also adopt a weak willingness to choose the acquire strategy. If x=0.1,y=0.9, it means that the government will adopt a weak willingness to choose the mass communication strategy while the enterprises will also adopt a high willingness to choose the acquire strategy. Then, the simulation results of six scenarios are presented in Figure 2.Figure 2
The simulation results of six scenarios.
(a)(b)(c)(d)(e)(f)From Figure2 and combined with Theorem 2, we can obtain the following conclusions.Conclusion 1.
Combined with Figures2(a) and 2(b) and Theorem 2, we can see that when k1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0, then (1, 1) is the ESS point. Therefore, in this situation, the government will fully adopt the mass communication strategy and the public will fully adopt the acquire strategy. When k1∑i=1nVi−CP3>0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then (0, 1) is the ESS point. In this situation, the government will adopt the personalized recommendation strategy while the public adopts the acquire strategy. These two scenarios are very similar because the public will choose the acquire strategy. This is mainly due to the condition that k1∑i=1nVi−CP3>0; thus, the revenue of the public with the acquire strategy is higher than the cost.Conclusion 2.
Combined with Figures2(c) and 2(f) and Theorem 2, we can see that when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2>0; when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4<0, and αk1−k2∑i=1nVi−CG1−CG2>0; or when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4<0, and αk1−k2∑i=1nVi−CG1−CG2<0, the ESS point is always (0, 0). That is to say, in these three situations, the government will choose the personalized recommendation strategy and the public will choose the not acquire strategy. Moreover, when k1∑i=1nVi−CP3<0, k2∑i=1nVi−CP4>0, and αk1−k2∑i=1nVi−CG1−CG2<0, then three are two ESS points, (0, 1) and (1, 0). In this case, the strategies can be different between the government and the public.Conclusion 3.
Combined with the above six scenarios, we can obtain that the time to convergence is different; in Scenario ③, it will spend more time to converge to a stable status.


## 5. Conclusions and Policy Recommendations

This paper conducts an evolutionary game on public information communication between the government and the public. Then, the stability of the evolutionary under different cases is explored. Moreover, the simulation analysis is presented to illustrate the results. The results can be affected by differential situations. The strategies selected by the government and the public are mainly influenced by their cost and revenue. Reducing the cost of different communication strategies of the government will help to improve the arrival rate of public information and improve the efficiency of public access. Furthermore, the evolutionary path under different scenarios can converge to different stable statuses.With the rapid development of the Internet, the dissemination of public information has become more convenient. It requires the joint efforts of all parties in the system to improve the public’s overall satisfaction with public information services, makes targeted personalized recommendations on public information, and improves the effectiveness and arrival rate of communication. Based on the above analyses results, several policies suggestions are proposed as follows: reducing the cost of the “personalized recommendation” of public information and mining the information required by users can avoid resource waste, improve the efficiency of public access, and thus enhance the overall satisfaction of the public on public information dissemination. Moreover, on the one hand, we can establish a good user information feedback mechanism which is called “the user access, personalized recommendation, and customer satisfaction.” On the other hand, the dissemination of public information should be regulated reasonably, and the release of public information should be subject to a strict review mechanism, so as to reduce or even eliminate the release of inferior public information, to improve the dissemination quality of public information and meet the public demand for public information in a real sense.


## 6. Limitations and Future Work

There are also some limitations to our study due to the fact that the data we used in our paper is the simulated data. Therefore, in future work, we can use real cases to explore the evolutionary path on public information communication between the government and the public.



---

*Source: 8956704-2021-02-03.xml*