## 3 Evolutionary Game Theoretical Model
### 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. 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 \(a+b\
eq 0\). Hence, we obtain the payoff matrix for online health communities and users as follows in Table 2.