# Data Element Sharing in Convergence Media Ecology Based on Evolutionary Game
## 3 Data Element Sharing Model Based on Evolutionary Game
### Model Construction and Evolutionary Path Analysis  
Let the payoff function of the participating data element sharing nodes in the system be S, then the payoff matrix of the data element sharing is shown in the following Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & \multicolumn{2}{c}{**Parameter Description**} \\ \hline \(E_{11}\) & The revenue of business organization nodes positively participate in data element sharing. \\ \hline \(E_{12}\) & The revenue of business organization nodes negatively participate in data element sharing. \\ \hline \(G_{11}\) & The cost of business organization nodes positively participate in data element sharing. \\ \hline \(G_{12}\) & The cost of business organization nodes negatively participate in data element sharing. \\ \hline \(I_{1}\) & The dynamic incentive revenue of business organization nodes positively participate in data element sharing. \\ \hline \(F_{1}\) & The system punishment for business organization nodes negatively participate in data element sharing. \\ \hline \(E_{2}\) & The revenue of common user nodes’ participation in data element sharing. \\ \hline \(G_{2}\) & The cost of common user nodes’ participation in data element sharing. \\ \hline \(I_{2}\) & The system dynamic incentive revenue of common user nodes participating in data element sharing. \\ \hline \(R\) & The revenue of regulator nodes participating in data element sharing regulation. \\ \hline \(G_{3}\) & The cost of regulator nodes participating in the regulation of data element sharing. \\ \hline \(\alpha\) & The additional revenue coefficient obtained from the successful urging business organization nodes to positively participate in sharing. \\ \hline \(\beta\) & The additional revenue coefficient obtained from the successful urging of common user nodes to participate in sharing. \\ \hline \(F_{3}\) & The system punishment of regulator nodes does not participate in data element sharing regulation. \\ \hline \(H\) & The revenue received by the parties participating in the sharing. When the business organization node actively participates in sharing and the common user node participates in sharing. \\ \hline \(x\) & The probability of the business organization nodes to positively participate in data element sharing. \\ \hline \(y\) & The probability of the common user nodes to participate in data element sharing. \\ \hline \(z\) & The probability of regulator nodes participating in data element sharing regulation. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting and symbol description. \begin{table}
\begin{tabular}{c c c c} \hline \hline  
The expected revenue of the \"positive data element sharing\" strategy of the business organization node is defined as \(P_{1}\), the expected revenue of the \"negative data element sharing\" strategy is \(P_{2}\), the average expected revenue is \(\overline{P}\), and the calculation formula is:  
\[P_{1}=y*z*(E_{11}+I_{1}+H-G_{11})+y*(1-z)*(E_{11}+I_{1}+H-G_{11})+(1-y)*z*(I_{1}- G_{11})+(1-y)*(1-z)* \tag{1}\] \[(I_{1}-G_{11})=y*H+y*E_{11}+I_{1}-G_{11}\] (2) \[P_{2}=y*z*(E_{12}-G_{12}-F_{1})+y*(1-z)*(E_{12}-G_{12}-F_{1})+(1-y)* z*(-G_{12}-F_{1})+(1-y)*(1-z)*\] (3) \[(-G_{12}-F_{1})=y*E_{12}-G_{12}-F_{1}\]  
The replication dynamic equation of the game strategy of the business organization node is:  
\[F(x)=\frac{dx}{dt}=x*(P_{1}-\overline{P})=x*(1-x)(P_{1}-P_{2})=x*(1-x)*(y*H+y*E _{11}-y*E_{12}+I_{1}+F_{1}+G_{12}-G_{11}) \tag{4}\]  
The first derivative of the replication dynamic equation F(x) of the business organization node is as follows:  
\[F^{\prime}(x)=(1-2x)*(y*H+y*E_{11}-y*E_{12}+I_{1}+F_{1}+G_{12}-G_{11}) \tag{5}\]  
According to the evolutionary game theory, the equilibrium point of the evolutionary game is obtained when the result of the replication dynamic equation is 0, and the first derivative is less than 0 [58], and it can be expressed as follows: \(\mathrm{F(x)}=0\) and \(\frac{dF(x)}{dx}<0\).