Evolutionary Game—Theoretic Approach for Analyzing User Privacy Disclosure Behavior in Online Health Communities

Abstract

Privacy disclosure is one of the most common user information behaviors in online health communities. Under the premise of implementing privacy protection strategies in online health communities, promoting user privacy disclosure behavior can result in a “win–win” scenario for users and online health communities. Combining the real situation and evolutionary game theory, in this study, we first constructed an evolutionary game model of privacy disclosure behavior with users and online health communities as the main participants. Then, we solved the replication dynamic equations for both parties and analyzed the evolutionary stable strategies (ESSs) in different scenarios. Finally, we adopted MATLAB for numerical simulations to verify the accuracy of the model. Studies show that: (1) factors such as medical service support and community rewards that users receive after disclosing their private personal information affect user game strategy; and (2) the additional costs of the online health communities implementing the “positive protection” strategy and the expected loss related to the privacy leakage risk affect the online health communities’ game strategy. In this regard, this paper puts forward the following suggestions in order to optimize the benefits of both sets of participants: the explicit benefits of users should be improved, the internal environment of the communities should be optimized, the additional costs of the “positive protection” strategy should be reduced, and penalties for privacy leakages should be increased.

1. Introduction

In recent years, with the acceleration of urbanization and industrialization, China’s economy has developed rapidly, and the living standards of Chinese residents have further improved. According to the data released by the National Bureau of Statistics, in 2021, the per capita disposable income of Chinese residents was 35,128 Renminbi (RMB), representing a year-on-year increase of 8.1%. Moreover, the per capita consumption expenditure was RMB 24,100, representing a year-on-year increase of 12.6%, of which per capita healthcare expenditure accounted for 8.8% [1]. On the one hand, it can be seen that, while material needs are constantly being satisfied, people begin to pay more attention to their own health problems, and people are eager to obtain more convenient and efficient online medical services [2]. On the other hand, China’s medical security system is facing a series of challenges, including the following: (1) A high rate of population aging—by 2020, China’s elderly population aged 65 years or older will be as high as 190 million, accounting for 13.5% of China’s total population [3]. In contrast, data published by the United Nations show that the average percentage of the world population aged 65 years or older in 2019 was only 9.1% [4]. (2) There are more patients with noninfectious chronic diseases (NCDs)—data show that the prevalence of NCDs in China was as high as 34.3% in 2018, with a prevalence rate of 52.3% for those aged 65 years or older [5]. Furthermore, the top four diseases in terms of mortality in China in 2020 were malignant tumors, heart disease, cerebrovascular disease, and respiratory diseases, all of which are NCDs [5]. Notably, they were also the top 10 causes of death in the world in 2019, resulting in approximately 33.2 million deaths [6]. It is evident that NCDs have a particularly harmful effect. (3) The proportion of health expenditure to gross domestic product (GDP) is low—in 2020, China’s health expenditure occupied 7.12% of the GDP, while those of developed countries such as the United States, the United Kingdom, Japan, and Australia generally exceeded 10% [7,8]. Therefore, the Chinese government has to being investigating how to build a new medical and health service system.

In this context, in order to meet the medical and health needs of more residents without reducing the quality of medical care, the Chinese government has decided to accelerate the construction of the “Internet medical system”. As a result, since 2018, the Chinese government has introduced a series of polices to promote the development of Internet medical services, such as “The Opinions on Promoting the Development of “Internet plus Medical Health””, “Guidance from National Healthcare Security Administration on improving the price of “Internet plus” medical services and medical insurance payment policies” [9,10]. Under the dual influence of market demand and national policy guidance, as products of the in-depth integration of “Internet” and “medical and health services”, Chinese online health communities, such as “Good Doctor Online”, “Chunyu Doctor”, and “We Doctor”, have developed rapidly. They are favored by many Chinese users and patients because of their low costs, the diversity of medical services available, and the convenience of the communication between doctors and patients [2,11,12]. In June 2021, the number of online medical users in China reached 239 million, accounting for 23.7% of the total number of netizens in China (Figure 1) [13].

Online Health Communities (OHCs) refer to the virtual communities whose main function is to exchange medical and health information or who have both online medical and online social functions. There are three types of OHCs: Patient to Doctor (P2D), Patient to Patient (P2P), and Doctor to Doctor (D2D). When using online health communities, users engage in various forms of information behavior, such as information searching, information adoption, and knowledge sharing [14,15,16]. Among these information behaviors, privacy disclosure behavior, also known as personal information disclosure or self-disclosure, refers to the scenario in which users actively disclose or share their occupation, past medical history, treatment experiences, or other private information to the health technicians or other ordinary users in the online health communities [17]. For users, disclosing private personal information can not only help them obtain more effective treatment plans, medical treatment experience, sympathy, and encouragement from others, but may also provide a reference for other users with the same disease. However, this behavior is also accompanied by the risk of privacy leakage (Figure 2) [18,19,20]. User privacy may be compromised if the online health communities’ cyber-security is compromised or if health technicians are not aware of privacy protection. This can lead to scenarios in which they receive sales pitches for drugs and healthcare products, and they may even fall victim of telecommunication scams online. For online health communities, the active disclosure of private personal information by users not only improves the operational efficiency of online medical services, but also encourages an atmosphere of community, promoting trustworthy relationships between doctors and patients or between other ordinary users. Hence, internal social networks can be formed, which can enhance the influence of the communities [21,22,23]. However, it is worth noting that, once a user’s private information is leaked, the online health community suffers both in terms of reputation and economic losses due to the negative news [23]. On the basis of the above analysis, it is not difficult to see that, there is a certain game relationship between users and the online health communities as regards personal privacy disclosure, and both parties are constantly adjusting their strategies according to their interests and the strategies adopted by the other party. In view of this, in this study, we adopted evolutionary game theory to analyze the gaming process between users and online health communities in order to establish an evolutionary game model and identify the optimal evolutionary stable strategies. On the basis of the research results, this paper puts forward suggestions on how to achieve optimal strategies with the aim of reaching a “win–win” scenario between the users and communities by strengthening privacy protection within the communities while promoting user privacy disclosure behaviors.

The main contributions of this study are listed as follows:

(1) We establish an evolutionary game model to explain the different strategies of users and online health communities in the game process in which privacy disclosure behavior occurs.

(2) We explore the evolutionary stable strategy of the game between users and online health communities in various scenarios and analyze the reasons for the results.

(3) We conduct numerical simulation experiments to simulate the evolutionary game process to prove that our proposed model is effective.

(4) We put forward some suggestions based on the development status of online health communities to facilitate the formation of optimal evolutionary stable strategies.

The rest of this paper is organized as follows: In Section 2, we review the related research on privacy disclosure intentions and behavior. In Section 3, we first describe the different decisions of users and online health communities for privacy disclosure; we then build an evolutionary game model based on the cost–benefit matrix of both sides in the game, and we finally analyze the evolutionary stable strategy (ESS point) in different scenarios. In Section 4, we validate the evolutionary game model using numerical simulation methods. In Section 5, we elaborate our findings and make recommendations from multiple perspectives with which to promote user privacy disclosure behaviors. In Section 5.3, a brief overview of the content and the weaknesses of the study are given, and various future research directions are provided.

2. Literature Review

In recent years, scholars in the fields of Information Science and Library Science and Medical Informatics in China and abroad have carried out a series of studies on privacy disclosure intentions and behavior, mainly focusing on mobile applications, social media, e-commerce, and Internet medical services.

(1) Mobile applications. The research in this scenario mainly focuses on analyzing the influencing factors of mobile application user privacy disclosure willingness and relevant information behaviors. From the perspective of emotional attitude, Tang et al. proposed the concept of “privacy fatigue” and believed that the privacy disclosure willingness of mobile application users is affected by a combination of privacy fatigue, privacy concerns, and user personal characteristics [24]. Scholars such as Mouakket found that user internal satisfaction (such as entertainment, escapism) and social satisfaction (such as social communication) also affected their willingness to disclose private information [25]. In addition, Brandtzaeg and other scholars investigated the privacy policy of mobile applications. Their research showed that certain mobile applications continue to track and share private user data when they are not in use, which clearly violates the privacy policy provided to users and would have a negative impact on user privacy disclosure behavior [26].

(2) Social media. Certain scholars analyzed the influencing factors of social media user privacy disclosure willingness and behavior from different perspectives. Wang et al. conducted research from the perspective of information systems and concluded that the system quality, service quality, and information quality of social networking sites have a positive impact on user willingness to disclose personal location-related information (PLRI) [27]. From the perspective of sociology, Lin et al., Liu et al., and other scholars analyzed the privacy disclosure willingness of social networking site users with social exchange theory and trust theory. Factors such as trust in social networking sites and other social networking site users, potential social rewards, and the “supportive atmosphere” constructed by online social support such as emotion, information, respect, etc., had a positive impact on user willingness to disclose private information [28,29]. Scholars such as Thompson and Brindley, Sun et al., and Ashuri et al. found that users’ perceived usefulness, perceived enjoyment, perceived risk, and platform rewards all affect social media user willingness to disclose private information [30,31,32]. On the other hand, scholars such as Li K et al. explored the behavior patterns and formation mechanism of the privacy disclosure behavior of social media users. They defined two behavioral modes, i.e., voluntary sharing and mandatory provision. Voluntary sharing refers to the active personal privacy disclosure behavior of users, which is mainly affected by positive factors such as perceived benefits, social network scale, and personalized services. Mandatory regulations refer to platforms that force users to disclose personal information, which is mainly affected by negative factors such as age, privacy policy, and perceived risk [33].

(3) E-commerce. Various scholars have attempted to develop technical solutions to resolve the contradiction between user data collection and user privacy protection in e-commerce companies. Liu et al. designed an information technology solution called the “negotiation, active-recommendation privacy policy application”, and confirmed, through experiments, that the program could help companies resolve the contradiction between user data collection and privacy protection, reduce user privacy concerns, and increase user willingness to disclose privacy and actual disclosure behavior [34]. Various scholars also analyzed the potential influencing factors of e-commerce user privacy disclosure behavior. Gomez-Barroso used an experimental method to demonstrate that, when users shop online, the platform gives appropriate monetary incentives, which can promote user privacy disclosure behavior [35].

(4) Internet medical treatment. Certain scholars attempted to optimize medical equipment to improve the probability of user privacy disclosure behavior. Alaqra et al. proposed a privacy-enhancing technology that enables a user to edit their personal information in a signed document while preserving the validity of the signature and the authenticity of the document [36]. The application of this technology in electronic health medical records can effectively protect the personal privacy of patients, thereby promoting their privacy disclosure behavior [36]. Various scholars also analyzed the influencing factors of health information exchange and health information disclosure willingness; for example, Robinson, Esmaeilzadeh, and other scholars demonstrated that the perceived transparency of privacy policies, trust in medical service providers, and the severity of users’ diseases all affect user privacy disclosure behavior [37,38]. Research by Zhang et al., Wang et al., Hur et al., and Zhou shows that many individuals use online health communities for information support and emotional support, in which emotional support, such as being listened to and receiving attention and encouragement from other users in the communities, can encourage users to voluntarily disclose or share their private personal information, such as their disease conditions and consultation experiences [39,40,41,42]. In other words, the emotional support received by users is one of the influencing factors of their privacy disclosure behavior.

Overall, the current research on privacy disclosure willingness and behavior provides a solid theoretical foundation and rich research results. Scholars in China and abroad have fully applied multidisciplinary theories such as privacy computing theory, social exchange theory, and social support theory to analyze the influencing factors of privacy disclosure willingness and behavior, and the related privacy protection technologies and privacy protection policies [37,43,44,45]. It is worth noting that, from the perspective of research objects, existing studies mainly focus on social media users or mobile application users, while relatively few studies have been carried out on online health community users. In fact, the online health communities have the dual attributes of online medical care and online social networking. The research on user privacy disclosure behavior in this context can provide theoretical references for various scenarios, such as the sharing of medical data, the construction of Internet hospitals, and the privacy protection of social media. In this regard, we should pay more attention to the privacy disclosure behavior of online health community users. From the perspective of research methods, structural equation modeling is the most common research method in existing research. Although this method can effectively verify the influencing factors of user privacy disclosure behavior, it cannot observe the changes in user behavior over time. Moreover, we believe that the key factors affecting the privacy disclosure behavior of users are still perceived risks and perceived benefits, and the evolutionary game model can be combined with the real situation to analyze the costs and benefits of both parties in the game, and to observe the strategic changes made by both sides over time. In recent years, evolutionary game models have been widely used in many scenarios, such as virtual product development on social networking sites, social media crisis communication, and privacy protection in mobile health systems, and have achieved good results [46,47,48]. In view of this, this research takes the users of online health communities as the research object and adopts an evolutionary game model to analyze their privacy disclosure behavior.

3. Evolutionary Game Theoretical Model

We analyzed the privacy disclosure behavior of online health community users in real life using evolutionary game theory, built an evolutionary game model with users and online health communities as the main participants, and solved the evolutionary stable strategies using the replication dynamic equation and Jacobian matrix.

3.1. Problem Description and Model Assumptions

We believe that the main players in the evolutionary game model of user privacy disclosure behavior in online health communities are users and the online health communities. Thus, we propose the following assumptions:

(1) The game strategy of users is “disclosure” or “non-disclosure”. When users choose to disclose their private personal information, although there may be a risk of privacy leakage, they can also obtain certain benefits. The specific benefits are as follows: Firstly, disclosing private personal information to health technicians who provide online medical services in the communities may lead to higher quality and more personalized online medical services; secondly, disclosing private personal information to ordinary users may lead to emotional support, information support, and rewards from the communities. When the users choose not to disclose private personal information, they cannot obtain any benefits, but also do not bear the risk of privacy leakage.

(2) The game strategy of online health communities is to implement the “positive protection” or “negative protection” strategy for user personal privacy. When a community implements the “positive protection” strategy, the community needs to strengthen the privacy protection of users, such as strengthening the network security of the information system, improving the privacy protection awareness of registered health technicians, etc. This requires extra costs; however, it can also significantly reduce the probability of user privacy leakage. When a community implements the “negative protection” strategy, the community only needs to implement basic user privacy protection in accordance with the relevant laws and regulations, and the investment cost is relatively low.

(3) Both users and online health communities are “economic people” with bounded rationality. They only act according to their own benefits and costs, they constantly adjust their strategies according to the benefits, and may eventually reach an evolutionary stable state.

On the basis of the above assumptions, in order to facilitate the construction and solution of the model, the following parameters were used for the calculation in this study, as shown in

Table 1. Notation and description.

Notation	Description
M	Medical service support obtained by users after disclosing their personal information, $M>0$
E	Emotional support obtained by users after disclosing their personal information, $E>0$
I	Information support obtained by users after disclosing their personal information, $I>0$
$L_u$	Loss of users after their privacy leaks, $L_u>0$
$L_c$	Loss of OHCs after users’ privacy leaks, $L_c>0$
$R$	Rewards from the OHCs after users disclose their personal information, $R>0$
$C_1$	Costs of implementing the “negative protection” strategy in the OHCs, $C_1>0$
$C_2$	Extra costs of implementing the “positive protection” strategy in the OHCs, $C_2>0$
B	Benefits of user disclosure of personal information for OHCs influence, $B>0$
a	Probability of users disclosing personal information to medical personnel, $0\le a\le 1\cap a+b\ne 0$
b	Probability of users disclosing personal information to other ordinary users, $0\le b\le 1\cap a+b\ne 0$
c	Probability of privacy leakage under the “positive protection” strategy, $0<c<1$
d	Probability of privacy leakage under the “negative protection” strategy, $0<c<d<1$

. Additionally, the relationship between online health communities and users in the game model is presented in Figure 3.

The evolutionary game focuses on the decision-making behavior of different groups. Therefore, it can be assumed that, in the game process, the proportion of users choosing “disclosure” is x, then the proportion of users choosing “non-disclosure” is (1 − x). As far as online health communities are concerned, the proportion of online health communities selecting “positive protection” is y, while the proportion of online health communities that choose “negative protection” is (1 − y). As shown in Figure 2, there are two types of user privacy disclosure behaviors, and their probabilities of occurrence are a and b. Therefore, when we assume that users adopt a “disclosure” strategy, in order to ensure that privacy disclosure behaviors must occur, we need to assume that $a+b\ne 0$. Hence, we obtain the payoff matrix for online health communities and users as follows in

Table 2. Payoff matrix for users and online health communities.

		Online Health Communities
		Positive Protection	Positive Protection
Users	Disclosure	$\begin{array}{c}(aM+b\left(E+I+R\right)-c{L}_u,\\ B-C_1-C_2-c{L}_c)\end{array}$	$\begin{array}{c}(aM+b\left(E+I+R\right)-d{L}_u,\\ B-C_1-d{L}_c)\end{array}$
	Non-disclosure	$(0,-C_1-C_2)$	$(0,-C_1)$

.

3.2. Model Calculation and Stability Analysis

We define the expected benefit of choosing to “disclose” their personal information for users as $P_1$, the expected benefit of choosing to “non-disclose” personal information as $P_2$, and the average expected benefit as $\overline{P}$. Therefore,

$$P_1=y\left[aM+b\left(E+I+R\right)-c{L}_u\right]+\left(1-y\right)\left[aM+b\left(E+I+R\right)-d{L}_u\right]$$

(1)

$$P_2=y\times 0+\left(1-y\right)\times 0=0$$

(2)

$$\overline{P}=x{P}_1+\left(1-x\right)P_2=aM+b\left(E+I+R\right)+\left(d-c\right)y{L}_u-d{L}_u$$

(3)

From Formulas (1)–(3), we obtain the replication dynamic equation of user game strategy as follows:

$$F\left(x\right)=\frac{dx}{dt}=x\left(P_1-\overline{P}\right)=x\left(1-x\right)\left[aM+b\left(E+I+R\right)+\left(d-c\right)y{L}_u-d{L}_u\right]$$

(4)

We define the expected benefit of choosing to implement the “positive protection” strategy for OHCs as $G_1$, the expected benefit of choosing to implement the “negative protection” strategy as $G_2$, and the average expected benefit as $\overline{G}$. Therefore,

$$G_1=x\left(B-C_1-C_2-c{L}_c\right)+\left(1-x\right)\left(-C_1-C_2\right)$$

(5)

$$G_2=x\left(B-C_1-d{L}_c\right)+\left(1-x\right)\left(-C_1\right)$$

(6)

$$\overline{G}=y{G}_1+\left(1-y\right)G_2=\left(B-d{L}_c\right)x+\left(d-c\right)yx{L}_2-C_1-y{C}_2$$

(7)

From Formulas (5)–(7), we obtain the replication dynamic equation of OHC game strategy as follows:

$$F\left(y\right)=\frac{dy}{dt}=y\left(G_1-\overline{G}\right)=y\left(1-y\right)\left[\left(d-c\right)x{L}_c-C_2\right]$$

(8)

To simplify the calculation, we let $\Delta =aM+b\left(E+I+R\right)$, and obtain the replication dynamic system equations of users and online health communities as shown in Formula (9):

$$\left\{\begin{array}{l}F\left(x\right)=x\left(1-x\right)\left[\Delta +\left(d-c\right)y{L}_u-d{L}_u\right]\\ F\left(y\right)=y\left(1-y\right)\left[\left(d-c\right)x{L}_c-C_2\right]\end{array}\right.$$

(9)

Let $F\left(x\right)=F\left(y\right)=0$; then, we obtain the following five potential equilibrium points: D₁ (0, 0), D₂ (1, 0), D₃ (0, 1), D₄ (1, 1), and D₅ (x*, y*). Among them,

$$x^{*}=\frac{-C_2}{\left(c-d\right)L_c},y^{*}=\frac{\Delta -d{L}_u}{\left(c-d\right)L_u}$$

Furthermore, the Jacobian matrix can be obtained by solving Formula (9), as shown in Formula (10):

$$J_{(x,y)}=\left[\begin{array}{cc}\frac{\partial F\left(x\right)}{\partial x}& \frac{\partial F\left(x\right)}{\partial y}\\ \frac{\partial F\left(y\right)}{\partial x}& \frac{\partial F\left(y\right)}{\partial y}\end{array}\right]=\left[\begin{array}{cc}\left(1-2x\right)\left[\Delta +\left(d-c\right)y{L}_u-d{L}_u\right]& x\left(1-x\right)\left(d-c\right)L_u\\ y\left(1-y\right)\left(d-c\right)L_c& \left(1-2y\right)\left[\left(d-c\right)x{L}_c-C_2\right]\end{array}\right]$$

(10)

We used the research method proposed by Friedman (1998) [49] to determine the stability of the above potential equilibrium points, in accordance with the methods of Chen et al. (2021) [50] and Lv et al. (2022) [51]. According to this method, we can obtain the calculation formulas of $detJ$ and $trJ$, as shown in Formulas (11) and (12). If the conditions $detJ>0$ and $trJ<0$ are met, then the potential equilibrium points can be considered as the stable strategy of the evolutionary game, i.e., the Evolutionary Stable Strategy (ESS).

$$detJ=\frac{\partial F\left(x\right)}{\partial x}\times \frac{\partial F\left(y\right)}{\partial y}-\frac{\partial F\left(y\right)}{\partial x}\times \frac{\partial F\left(x\right)}{\partial y}$$

(11)

$$trJ=\frac{\partial F\left(x\right)}{\partial x}+\frac{\partial F\left(y\right)}{\partial y}$$

(12)

After substituting the five potential equilibrium points into the Jacobian matrix,

Table 3. Determinant and trace of the Jacobian matrix.

Equilibrium Points	$detJ$	$trJ$
D1 (0, 0)	$\left(d{L}_u-\Delta \right)\times C_2$	$\left(\Delta -d{L}_u\right)-C_2$
D2 (1, 0)	$\left(d{L}_u-\Delta \right)\times \left[\left(d-c\right)L_c-C_2\right]$	$\left(d{L}_u-\Delta \right)+\left[\left(d-c\right)L_c-C_2\right]$
D3 (0, 1)	$\left(\Delta -c{L}_u\right)\times C_2$	$\left(\Delta -c{L}_u\right)+C_2$
D4 (1, 1)	$\left(\Delta -c{L}_u\right)\times \left[\left(d-c\right)L_c-C_2\right]$	$\left(c{L}_u-\Delta \right)+\left[C_2-\left(d-c\right)L_c\right]$
D5 (x*, y*)	$\frac{C_2\times \left(\Delta -d{L}_u\right)\times \left(\Delta -c{L}_u\right)\times \left[\left(c-d\right)L_c+C_2\right]}{{\left(c-d\right)}^2{L}_u{L}_c}$	0

was obtained.

We used the cost–benefit analysis method to discuss the stability of the game strategies of the two sides in different situations.

From the perspective of the users, $aM+b\left(E+I+R\right)$ or $\Delta$ represents the medical service support, emotional support, information support, and rewards given by the OHCs after users disclose their personal information, i.e., the total benefits of users. $c{L}_u$ and $d{L}_u$ are the expected loss of user privacy leakage under the “positive protection” strategy and “negative protection” strategy implemented by the OHCs, respectively, i.e., the total costs of users under the “positive protection” strategy and “negative protection” strategy, respectively. Therefore, there are three situations in the relationship between the total benefits and the total costs of users: $\Delta <c{L}_u$, $c{L}_u<\Delta <d{L}_u$, and $\Delta >d{L}_u$.

From the perspective of OHCs, $B$ is the increase in the influence and recognition of the communities and other benefits received by the OHCs after users disclose their personal information, i.e., the total benefits of the OHCs. $C_2+\left(c-d\right)L_c$ is the sum of all types of extra costs paid by the OHCs after implementing the “positive protection” strategy and the reduced expected loss of user privacy leakage, as compared with the “negative protection” strategy, i.e., the total costs of the OHCs. It is worth noting that $C_2+\left(c-d\right)L_c$ may be greater than 0 or less than 0, which needs to be discussed in terms of classification. Therefore, the relationship between the total benefits and the total costs of OHCs also exist in three situations: $B<C_2+\left(c-d\right)L_c$ and $C_2+\left(c-d\right)L_c>0$, $B>C_2+\left(c-d\right)L_c$ and $C_2+\left(c-d\right)L_c>0$, and $B>C_2+\left(c-d\right)L_c$ and $C_2+\left(c-d\right)L_c>0$.

On the basis of the above discussion, after analyzing the costs and benefits of both players, the following nine scenarios can be obtained, as shown in

Table 4. Determination of potential equilibrium points in different scenarios.

Scenario	Conditions	Determinant	Equilibrium Point
			(0, 0)	(1, 0)	(0, 1)	(1, 1)	(x*, y*)
1	$\begin{array}{c}\Delta <c{L}_u\\ B<C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c>0\end{array}$	$detJ$	$+$	$-$	$-$	$+$	$-$
		$trJ$	$-$	$\pm$	$\pm$	$+$	0
		Stability	ESS	Saddle point	Saddle point	Unstable point	Center point
2	$\begin{array}{c}\Delta <c{L}_u\\ B>C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c>0\end{array}$	$detJ$	$+$	$-$	$-$	$+$	$-$
		$trJ$	$-$	$\pm$	$\pm$	$+$	0
		Stability	ESS	Saddle point	Saddle point	Unstable point	Center point
3	$\begin{array}{c}\Delta <c{L}_u\\ B>C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c<0\end{array}$	$detJ$	$+$	$+$	$-$	$-$	$+$
		$trJ$	$-$	$+$	$\pm$	$\pm$	0
		Stability	ESS	Unstable point	Saddle point	Saddle point	Center point
4	$\begin{array}{c}c{L}_u<\Delta <d{L}_u\\ B<C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c>0\end{array}$	$detJ$	$+$	$-$	$+$	$-$	$+$
		$trJ$	$-$	$\pm$	$+$	$\pm$	0
		Stability	ESS	Saddle point	Unstable point	Saddle point	Center point
5	$\begin{array}{c}c{L}_u<\Delta <d{L}_u\\ B>C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c>0\end{array}$	$detJ$	$+$	$-$	$+$	$-$	$+$
		$trJ$	$-$	$\pm$	$+$	$\pm$	0
		Stability	ESS	Saddle point	Unstable point	Saddle point	Center point
6	$\begin{array}{c}c{L}_u<\Delta <d{L}_u\\ B>C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c<0\end{array}$	$detJ$	$+$	$+$	$+$	$+$	$-$
		$trJ$	$-$	$+$	$+$	$-$	0
		Stability	ESS	Unstable point	Unstable point	ESS	Center point
7	$\begin{array}{c}\Delta >d{L}_u\\ B<C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c>0\end{array}$	$detJ$	$-$	$+$	$+$	$-$	$-$
		$trJ$	$\pm$	$-$	$+$	$\pm$	0
		Stability	Saddle point	ESS	Unstable point	Saddle point	Center point
8	$\begin{array}{c}\Delta >d{L}_u\\ B>C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c>0\end{array}$	$detJ$	$-$	$+$	$+$	$-$	$-$
		$trJ$	$\pm$	$-$	$+$	$\pm$	0
		Stability	Saddle point	ESS	Unstable point	Saddle point	Center point
9	$\begin{array}{c}\Delta >d{L}_u\\ B>C_2+\left(c-d\right)L_c\\ C_2+\left(c-d\right)L_c<0\end{array}$	$detJ$	$-$	$-$	$+$	$+$	$+$
		$trJ$	$\pm$	$\pm$	$+$	$-$	0
		Stability	Saddle point	Saddle point	Unstable point	ESS	Center point

.

Proposition 1.

When the conditions are those in Scenarios 1 to 3, D₁ (0, 0) is an ESS, and users and OHCs will choose (non-disclosure, negative protection).

In these scenarios, since the sum of the benefits obtained by users for disclosing their private personal information is less than the sum of the costs under the “positive protection” strategy, i.e., $\Delta <c{L}_u$, users tend not to disclose private personal information $\left(x\to 0\right)$. On the other hand, for the OHCs, there is no benefit to their “positive protection” strategy as users gradually choose not to disclose their private information. For cost reasons, they will tend to choose to implement the “negative protection” strategy $\left(y\to 0\right)$. Therefore, the evolutionary game process will eventually converge to D₁ (0, 0), which can be seen in Figure 4a.

Proposition 2.

When the conditions are those in Scenarios 4 to 5, D₁ (0, 0) is an ESS, and users and OHCs will choose (non-disclosure, negative protection).

In these scenarios, since the sum of the benefits obtained by the users who disclose private personal information is between the sum of the costs of the “positive protection” strategy and that of the “negative protection” strategy, i.e., $c{L}_u<\Delta <d{L}_u$, some users will choose to disclose their personal information $\left(x\to 1\right)$, while other users will choose non-disclosure $\left(x\to 0\right)$. On the other hand, for the OHCs, the additional costs to the OHCs are greater than the reduced expected loss of the lowered privacy risk, i.e., $C_2+\left(c-d\right)L_c>0$, so the OHCs still tend to implement the “negative protection” strategy $\left(y\to 0\right)$. Over time, when all online health communities choose to implement the “negative protection” strategy, users will gradually shift to not disclosing their private personal information $\left(x\to 0\right)$ because the relationship between the sum of benefits and the sum of costs will become $\Delta <d{L}_u$. Therefore, the evolutionary game process will eventually converge to D₁ (0, 0), which can be seen in Figure 4a.

Proposition 3.

When the conditions are those in Scenario 6, D₁ (0, 0) and D₄ (1, 1) are ESSs, and users and OHCs will choose (non-disclosure, negative protection) or (disclosure, positive protection).

In this scenario, the sum of the benefits obtained by users for disclosing private personal information is between the sum of the costs of the “positive protection” strategy and that of the “negative protection” strategy. As a result, there are users who are willing to disclose privacy $\left(x\to 1\right)$ and users who are unwilling to disclose privacy $\left(x\to 0\right)$. When the users disclose personal information, the sum of the benefits obtained by the OHCs must be greater than the sum of its costs under the “positive protection” strategy, and the additional cost is less than the reduced expected loss of the lowered privacy risk, so the OHCs will tend to implement the “positive protection” strategy $\left(y\to 1\right)$. Moreover, when users do not disclose private personal information, the OHCs will tend to implement the “negative protection” strategy in order to reduce costs $\left(y\to 0\right)$. Therefore, the evolutionary game process will eventually form two ESS points: D₁ (0, 0) and D₄ (1, 1), see Figure 4c. Among them, the proportion of the population at D₁ (0, 0) and D₄ (1, 1) is related to the critical point D₅ (x*, y*).

Proposition 4.

When the conditions are those in Scenarios 7 to 8, D₂ (1, 0) is an ESS, and users and OHCs will choose (disclosure, negative protection).

In these scenarios, since the sum of the benefits obtained by the user disclosing private personal information is greater than the sum of the costs under the “negative protection” strategy, i.e., $\Delta >d{L}_u$, the users will tend to disclose personal information $\left(x\to 1\right)$. Moreover, no matter how much benefit users can bring to the OHCs by disclosing their private information, as long as the additional cost is greater than the reduced expected loss of the lowered privacy risk, i.e., $C_2+\left(c-d\right)L_c>0$, the OHCs will tend to choose to implement the “negative protection” strategy $\left(y\to 0\right)$. Therefore, the evolutionary game process will eventually converge to D₂ (1, 0), which can be seen in Figure 4b.

Proposition 5.

When the conditions are those in Scenario 9, D₄ (1, 1) is an ESS, and users and OHCs will choose (disclosure, positive protection).

In this scenario, since the sum of the benefits obtained by users for disclosing personal information is more than the sum of the costs under the “negative protection” strategy, the users will tend to disclose personal information $\left(x\to 1\right)$. On the other hand, the sum of the benefits received by the OHCs because of user disclosure behavior is greater than the sum of the costs of implementing the “positive protection” strategy for the OHCs, and the additional cost is less than the reduced expected loss of the lowered privacy risk, i.e., $C_2+\left(c-d\right)L_c<0$. As a result, in order to obtain higher returns, the community will tend to implement “positive protection” strategies $\left(y\to 1\right)$. Therefore, the evolutionary game process will eventually converge to D₄ (1, 1), as shown in Figure 4d.

4. Numerical Simulation Experiment

In the previous section, we described the construction of the evolutionary game model, concluded that there were nine different scenarios in the evolutionary game process, and finally obtained the ESS points in all scenarios through calculation. In this section, we use MATLAB (R2021a) to carry out numerical simulation experiments. This simulation is used to show that the final results of the evolutionary game process in all scenarios are consistent with our analysis results, so as to prove the accuracy of the model and obtain the decisive influencing factors.

The simulation process was as follows: (1) In terms of parameter value setting, we needed to ensure that the values of all parameters in each scenario met their constraints. Therefore, according to Table 4, we preset the following values as the initial values of each parameter in this study, as shown in

Table 5. Initial values of parameters in different scenarios.

Scenario	$M$	$E$	$I$	$R$	$a$	$b$	$\Delta$	$B$	$L_u$	$L_c$	$C_1$	$C_2$	$c$	$d$
1	5	2.5	1.5	1	0.6	0.4	5	5	20	20	10	15	0.3	0.7
2	5	2.5	1.5	1	0.6	0.4	5	5	20	20	10	10	0.3	0.7
3	5	2.5	1.5	1	0.6	0.4	5	5	20	20	10	5	0.3	0.7
4	10	5	3	2	0.6	0.4	10	5	20	20	10	15	0.3	0.7
5	10	5	3	2	0.6	0.4	10	5	20	20	10	10	0.3	0.7
6	10	5	3	2	0.6	0.4	10	5	20	20	10	5	0.3	0.7
7	20	10	6	4	0.6	0.4	20	5	20	20	10	15	0.3	0.7
8	20	10	6	4	0.6	0.4	20	5	20	20	10	10	0.3	0.7
9	20	10	6	4	0.6	0.4	20	5	20	20	10	5	0.3	0.7

. (2) In terms of setting the initial values of x and y, we interviewed various OHCs user groups in the early stage. The results showed that the probability of different user groups choosing to disclose their private personal information was different, ranging from 10% to 90%. Moreover, combined with the simulation method applied by Zhu et al. (2018) [52] and Li et al. (2022) [53], we set the initial values of x and y to simulate randomly from 0.1 to 0.9, with 0.1 as the starting point and 0.1 as the fixed step. (3) As regards setting the iteration times, we referred to the methods of Zhu et al. (2018) [52] and Li et al. (2022) [53] and set the evolutionary time to replace the number of iterations. After testing, in order to more intuitively show the evolutionary game process, we set the evolutionary time to 5.

(1) According to the data in Table 5, Figure 5a–e were obtained by simulating the evolutionary game trend of users and the online health communities in Scenarios 1 to 5, respectively. It can be seen from Figure 5a–e that the ESSs of these scenarios are all (0, 0), i.e., users and OHCs choose (non-disclosure and negative protection). The simulation results in the above scenarios are consistent with the evolutionary process calculated by Proposition 1 and Proposition 2. It can be obtained from a, b, and c in Figure 5 that, when the values of other parameters are constant, the value of C₂ is reduced from 15 to 10. Although there is a decrease in the evolutionary rate of both sides, it is not significant.

However, when the value of C₂ is reduced from 10 to 5, the evolution rate of both sides decreases significantly. It can be concluded that the influence of C₂ on the evolutionary rate of both sides presents a nonlinear correlation. On the other hand, it can be obtained from Figure 5d,e that, when the value of C₂ is reduced from 15 to 10, the evolutionary rate of both sides exhibited a significant decrease. We can conclude that the reduction in C₂ at this time will significantly reduce the evolutionary rate of both sides simultaneously. In addition, we can also see from Figure 5d,e that, when the values of other parameters are constant and the value of $\Delta$ increases from 5 to 10, the evolutionary rates of both parties in the game model exhibited a significant decrease.

(2) On the basis of the data in Table 5, Figure 5f was obtained by simulating the evolutionary trend of the game between users and the online health communities in Scenario 6. It can be seen from Figure 5f that the evolutionary results in this scenario are not unique, and there are two ESSs at the same time, namely, (0, 0) and (1, 1), i.e., users and OHCs choose (non-disclosure, negative protection) or (disclosure, positive protection). The simulation results in the above scenarios are consistent with the evolutionary process calculated by Proposition 3.

It can be seen from Figure 5f that, from the beginning of the game, there are some users or communities that tend to both 0 and 1. We can see that in the early stage of the game, both sides are in a state of swing. Neither the sum of the benefits $\Delta$ gained by users from disclosing private personal information nor the additional costs C₂ paid by the communities to implement the “positive protection” strategy provide sufficient motivation for users or the communities to form a unified choice. Over time, two different evolutionary stable strategies (0, 0) and (1, 1) will eventually be formed.

(3) On the basis of the data in Table 5, Figure 5g,h were obtained by simulating the evolutionary game trend of users and online health communities in Scenarios 7 and 8. It can be seen from Figure 5g,h that the ESSs of these scenarios are all (1, 0), i.e., users all choose to disclose private personal information and communities all choose to implement the “negative protection” strategy, which is consistent with the evolutionary process calculated by Proposition 4. Comparing g and h in Figure 5, it can be seen that, when $\Delta >d{L}_u$ and other parameters are constant and the value of C₂ decreases from 15 to 10, there is no significant difference in the evolutionary rate of users, while the evolutionary rate of the communities decreases significantly.

It can be concluded that, when the sum of the user benefits is greater than the sum of the costs under the “negative protection” strategy, the drop in C₂ has little effect on the users’ strategy choice, but has a more significant impact on the communities’ strategy.

(4) On the basis of the data in Table 5, Figure 5i was obtained by simulating the evolutionary game trend of users and online health communities in Scenario 9. It can be seen from Figure 5i that the ESS of Scenario 9 is (1, 1), i.e., users choose to disclose their personal information and the communities choose to implement the “positive protection” strategy, which is consistent with the evolutionary process calculated by Proposition 5.

In this scenario, users can obtain the rewards they want by disclosing their private personal information. Moreover, the communities can enhance the influence of the platform by implementing positive privacy protection strategies and reduce the losses caused by user privacy leakage. Consequently, this result is the optimal evolutionary stable strategy in all scenarios and it represents a “win–win” for both sides of the game simultaneously.

On the basis of the above analysis, we found that the numerical simulation of Scenario 1 to 9 is completely consistent with the results calculated by the model. Therefore, it can be concluded that the evolutionary game model constructed in our research is accurate and effective. This also shows that the parameters involved in Formula (9) are decisive factors that can affect the decisions of both parties, such as $\Delta$, Lu, Lc, C₂, c, and d. Correspondingly, the parameters not involved in Formula (9) will not affect the evolutionary process, such as B and C₁.

5. Conclusions, Policy Implications, and Future Research

In this section, we summarized our conclusion of research based on evolutionary game model. From this conclusions, we have put forward a series of policy implications, which may provide suggestions to the government in order to promote the progress of privacy protections in OHC. Finally, this research also has its limitations, so the direction of future research has been given in the end.

5.1. Conclusions

On the basis of the simulation results, the evolutionary game model constructed in this study exhibits good accuracy and accurately reflects the game behavior and evolutionary process of both participants in the model. In this regard, we were able to draw the following conclusions:

(1) The total benefits, such as medical service support, emotional support, information support, and community rewards, obtained by users disclosing private personal information in the communities are the central factors that affect whether users choose to disclose personal information. If the total benefits obtained by users are greater than the expected loss caused by privacy leakage in the worst case, even if the communities choose to implement negative privacy protection policies, users will still actively and firmly choose to disclose their private personal information.

(2) Although the active disclosure of private personal information by users can help to form a good atmosphere within the community, thereby enhancing the credibility and popularity of the community and bringing certain benefits to the development of the community, this benefit is not the decisive factor for the community to choose which privacy protection strategy to implement. The relationship between the extra cost that the community needs to pay to implement the “positive protection” strategy and the expected loss caused by the difference in privacy leakage risk between the “positive protection” and “negative protection” strategy is what affects the community’s choice of privacy protection strategy.

5.2. Policy Implications

On the basis of the above conclusions, in order to improve the privacy protection of the communities and promote user privacy disclosure behavior, this study proposes the following suggestions (Figure 6):

(1) Improve the users’ explicit benefits. On the basis of the actual situation, for users, the explicit benefits obtained from disclosing private personal information, such as higher-quality online medical services, rewards from the communities, etc., will lead them to disclose private personal information. Therefore, community managers should focus on the improvement of explicit benefits to users.

Specifically, this firstly involves improving the quality of online medical services. For communities with online medical functions, community managers should deepen cooperation with medical institutions, medical schools, medical research institutes, and other institutions, integrate multiple resources, and improve the quality of online medical services as much as possible. Thus, when users disclose personal information, they obtain more accurate, comprehensive, and personalized online medical services.

Secondly, a reasonable incentive mechanism should be developed. For communities with online social functions, community managers should formulate a reasonable reward mechanism to provide richer material or spiritual rewards for users who actively share their private personal information or experiences through leaving messages, comments, and posts, such as giving a certain amount of vouchers or “excellent user certification” for highly active users, etc., in order to promote user privacy disclosure behavior.

(2) The internal environment of the community should be optimized. A relaxing and comfortable social environment can enhance users’ sense of belonging, promote communication and interaction between users, and effectively increase user willingness to disclose and share personal information in the communities. Therefore, community managers not only need to pay attention to the explicit benefits that users might obtain, but also to the optimization of the internal environment of the community.

Specifically, this involves firstly strengthening daily management. Daily management has an important impact on the community environment. When the management is principally absent, a large number of conflicts and disputes, false information, marketing, and other violations can occur within the community. Therefore, community managers should consider selecting certain active users or opinion leaders from the community to form a special management team to assist them in daily management tasks, thereby improving the efficiency of handling violations.

Thereafter, rules and regulations should be formulated. Community managers should formulate corresponding rules and regulations based on the community environment, and clearly inform users of their behavioral norms and legitimate rights and interests. The establishment of this system not only reduces the probability of violations within the community, but also provides a basis for the community management team to deal with various violations.

(3) The additional costs of the “positive protection” strategy should be reduced. For the online health communities, implementing a negative privacy protection strategy only needs to meet the minimum requirements stipulated by national laws or local regulations, but implementing an active privacy protection strategy entails certain additional costs, which may be prohibitively high. Therefore, community managers should try to reduce the additional costs of the “positive protection” strategy in the following ways.

Firstly, information systems and network equipment should be procured in a centralized manner. The implementation of an active privacy protection strategy in the communities is inseparable from the improvement of information systems and network equipment. Therefore, when specific needs are identified, community managers should actively seek cooperation with other enterprises or entrust specialized agencies to carry out centralized procurement, in order to reduce procurement costs.

Thereafter, training on privacy security should be designed and undertaken. The training cost of personnel is one of the additional costs that the community needs to pay for implementing an active privacy protection strategy. Traditional training courses are expensive and cannot be reused. Therefore, community managers can seek professional privacy security training companies to develop relevant online courses and question banks for health technicians and staff in the community. Only after meeting the required learning time and passing the test can a person become a registered health technician or staff member in the community, so as to improve users’ understanding of privacy security knowledge and reduce personnel training costs.

(4) The penalties for privacy leakage should be increased. In actual situations, if there is a user privacy leakage incident in the online health community, the community’s reputation not only suffers due to the exposure, but there are also administrative penalties from government regulatory authorities. In order to avoid punishment as much as possible in situations in which the punishment is severe, the community will tend to implement active privacy protection strategies. Therefore, local governments can consider increasing the punishment in the following ways.

Specifically, local laws and regulations should be improved. Since November 2021, China has officially implemented the Personal Information Protection Law of the People’s Republic of China [54]. Although the law clearly stipulates the government’s punishment for enterprises, it does not involve the compensation from enterprises to users. As compared to the serious consequences of harassing marketing techniques and telecommunication fraud after user privacy leaks, the compensation from enterprises to users remains relatively limited at present. Therefore, local governments can improve the local laws and regulations to increase the compensation from enterprises.

Secondly, supervision should be strengthened. Government supervision departments can implement “integrated online and offline supervision”. On the one hand, they can hold online activities such as cyber-security offensive and defensive drills to test the level of network security of the community. On the other, they can use on-site inspections to ascertain the actual operation of the community, and urge the community to pay attention to user privacy protection through the improvement of supervision.

5.3. Future Research

This research focuses on the privacy disclosure behavior of online health community users, and combines evolutionary game theory with real scenarios to construct an evolutionary game model of privacy disclosure behavior. Herein, how the model was built, analyzed, and numerically simulated using MALTAB R2021a to verify the results is described. Finally, suggestions are put forward to promote user privacy disclosure behavior, which provides a theoretical reference for the development of online health communities.

The main limitations of this study are as follows: (1) Some parameters, such as emotional support, information support, etc., are abstract concepts, which are difficult to directly quantify; and (2) this study only considers the two-party game between users and the online health community and does not consider the intervention of the government as a third-party regulator.

In this regard, in the follow-up research, on the one hand, we will consider designing a series of scenario experiments based on relevant economic theories, so as to quantify the value of medical services, emotions, and the information obtained by users after disclosing their private personal information. On the other hand, we will consider conducting a privacy disclosure behavior game study involving the participation of users, online health communities, and the government.