# A Game Theory-Based Model for the Dissemination of Privacy Information in Online Social Networks
## 3 A Game-Based Model for Privacy Information Dissemination
### Decision on the Recipients of Privacy Information
\(J\)_income_dist_ : This is the benefit to the receiver when the receiver adopts strategy \"do not like privacy information\" and the sender adopts strategy \"do not send privacy information. The benefit can be viewed in the way that the receiver does not receive the message that he/she does not like. Now, we need to analyze the game matrix in Table 2. From the perspective of the receiver, when the sender chooses the strategy \"send privacy information \", adopting the strategy \"like privacy information\" by the receiver can bring greater benefits, i.e., \(J\)_income_send_ \(>-\)_J_loss_send_. When the sender chooses strategy \"do not send privacy information\", adopting strategy \"do not like privacy information\" by the receiver can bring greater benefits, i.e., \(J\)_income_dist_ \(>-\)_J_loss_send_. From the perspective of the sender, when the receiver chooses strategy \"like privacy information\", adopting strategy \"send privacy information\" by the sender can bring greater benefits, i.e., \(F\)_income_send_ \(>-\)_F_loss_ind_. When the receiver chooses strategy \"do not like privacy information\", adopting strategy \"send privacy information\" brings less benefits than adopting strategy \"do not send privacy information\" by the sender, i.e., \(-\)_F_loss_send_ \(<\)_F_income_ \(\_dist\)_. From the above analysis, we can see that there is no pure strategy Nash equilibrium in the game matrix, so we need to calculate its mixed strategy Nash equilibrium. \(P_{F}\) and \(P_{J}\) is set as the income matrix of the sender and the receiver, respectively. Assuming that the probability that the sender chooses strategy \"send privacy information\" is x, then the probability that the sender chooses strategy \"do not send privacy information\" is \(1-\)x and the mixed strategy probability of the sender is \(P_{f}=(\)x\(1-\)x\()\). Similarly, assuming that the probability that the receiver chooses strategy \"like privacy information\" is y, then the probability that the receiver chooses strategy \"do not like privacy information\" is \(1-\)y and the mixed strategy probability of the receiver is \(P_{j}=(\)y\(,1-\)y\()\). The sender's revenue function can be calculated by Equation (4):  
Our experiment aims to both evaluate and validate the proposed privacy information dissemination model. The strategy of the experiment is to use the constructed BA scale-free network to evaluate our model through examining how privacy information is disseminated in the network and the Facebook network data to validate our model through comparing the results of the BA scale-free network and the Facebook network. In the experiment, we divided intimacy into four levels: family affection, friendship, acquaintance, and stranger relationship, whose intervals and the proportion of users are shown in Table 3.  
Figure 4: Range of privacy dissemination vs. intimacy and popularity. Figure 3: Degree distribution in the constructed BA network. Figure 2: Degree distribution in the Facebook network. In our experiment, we divided popularity into three levels: high popularity, middle popularity, and low popularity. According to formula (1), we can calculate each user's popularity in the network. We found after repeated experiment that the average value of the popularity of three types of users is around 0.8, 0.5, and 0.3, respectively. Considering that in a real situation, the degree of awareness of a user to a particular user is not the same, the popularity of other users in the network is set according to the normal distribution of their popularity to better reflect the reality as shown in Table 4.