# A Game Theory-Based Model for the Dissemination of Privacy Information in Online Social Networks
## 3 A Game-Based Model for Privacy Information Dissemination
### Validation of the Model  
Figure 9 shows the dissemination of privacy information in the BA network and in the Facebook network. As the Nash equilibrium continues to improve, the two models display the same downward trend and the final coverage is almost the same. When categorizing the popularity of privacy subjects as high popularity users, meddle popularity users, and low popularity users, the current number of hops in the BA network and Facebook network to receive information and the total number of users receiving the information change with the number of hops are shown in Figures 10 and 11, respectively. Figure 8: Range of dissemination vs. popularity under different Nash equilibrium thresholds. Figure 10: The dissemination process of the privacy information of high popularity users in the BA and the Facebook networks. Figure 9: Range of privacy dissemination under different Nash equilibrium thresholds in the BA and the Facebook networks. Figure 12 shows that the final coverage, the speed and the dissemination trend are highly consistent. Thus, our proposed model can be used to simulate the process of privacy information dissemination in OSNs such as Facebook reasonably and effectively. Additional model verification was done based on the classification of users in which the Xinbang data platform ([[https://data.newrank.cn/](https://data.newrank.cn/)]([https://data.newrank.cn/](https://data.newrank.cn/))) was crawled to get the data for the experiment. The Xinbang platform focuses on analyzing data and predicting future trends based on data provided by third-party platforms that have a large number of users, such as Tencent's WeChat, ByteDance's Douyin (TikTok China), etc. It analyzes business and user data and predicts future trends for industries and enterprises by collaborating with large companies. Powered with proprietary analytical software, the Xinbang platform has been one of the major prediction platforms in China for many years with the partnership with WeChat and Douyin that have accumulated 1.2 billion and 920 million users, respectively. In the experiment, Xinbang was searched using several keywords to obtain the privacy information of three types of users as well as the spreading of the privacy information of these users during the period of dissemination. The keywords used in the search for the three different types of users are shown in Table 5.  
Figure 11: The dissemination process of the privacy information of middle popularity users on the BA network and the Facebook network. Figure 12: The dissemination process of the privacy information of low popularity users on the BA network and the Facebook network. As shown in Figures 13-15, for user with different level of popularity, the model's simulation data and the real statistical data are highly consistent in terms of the change and the overall trend. Although there is a slight difference in terms of the time that it takes to reach the peak, the overall performance is similar, which can be used to simulate the privacy information dissemination process of different types of users in OSNs. These results suggest that the model proposed in this paper can largely reflect the dissemination of privacy information of various privacy subjects in OSNs and the experimental results can provide a valuable reference for understanding the dissemination of privacy information by social network users. Figure 14: Dissemination of the privacy information of a medium popular user between simulated data and real data. Figure 13: Dissemination of the privacy information of a highly popular user between simulated data and real data. \begin{table}
\begin{tabular}{c c} \hline \hline
**Types of Popularity** & **Search Keyword** \\ \hline High popularity users & [PERSON] sex scandal \\ Middle popularity users & Anchor B was bursting in love \\ Low popularity users & Husband C Domestic Violence Wife \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Types of selected users and search keywords.