# 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
When \(\frac{G_{3}-F_{3}-R-y*R*\beta}{R*\alpha}<0\)(\(\frac{G_{3}-F_{3}-R-x*R*\alpha}{R*\beta}<0\)), because \(0\leq z\leq 1\), so we can obtain: \(x>x^{*}(y>y^{*})\). According to the monotonicity of the function \(L(x,y)\), we obtain \(L(x,\,y)>0\), and then we can obtain \(F^{\prime}(0)>0\) and \(F^{\prime}(1)<0\), so \(z=1\) is an evolutionary stable point, which indicates that the increased revenue of the regulator node is more than the increased cost of the participation in regulation, and the not participation in regulation of the regulator node is the evolutionary stability strategy. 3. When \(0<\frac{G_{3}-F_{3}-R-y*R*\beta}{R*\alpha}<1(0<\frac{G_{3}-F_{3}-R-x*R*\alpha}{ R*\beta}<1)\), it was also necessary to discuss the size relationship between x and \(x^{*}(y\) and \(y^{*})\): When \(0<\frac{G_{3}-F_{3}-R-y*R*\beta}{R*\alpha}<1\): If \(x<x^{*}\), we can obtain: \(F^{\prime}(0)<0\) and \(F^{\prime}(1)>0\), so \(z=0\) is an evolutionary stable point. If \(x>x^{*}\), we can obtain: \(F^{\prime}(1)<0\) and \(F^{\prime}(0)>0\), so \(z=1\) is an evolutionary stable point. When \(0<\frac{G_{3}-F_{3}-R-x*R*\alpha}{R*\beta}<1\): If \(y<y^{*}\), we can obtain: \(F^{\prime}(0)<0\) and \(F^{\prime}(1)>0\), so \(z=0\) is an evolutionary stable point. If \(y>y^{*}\), we can obtain: \(F^{\prime}(1)<0\) and \(F^{\prime}(0)>0\), so \(z=1\) is an evolutionary stable point. Phase diagram of regulator node's strategy evolution is shown in Figure 7.  
According to the figure above, the probability of selecting not to participate in data element sharing regulation is volume \(V_{1}\), and the probability of participating in data element sharing regulation is volume \(V_{2}\). The projection interval of the surface \(\mathrm{x}=\tau(y)=\frac{G_{2}-F_{3}-R-y*R*\beta}{R*\alpha}\) onto the yoz plane is \(0\leq z\leq 1,\rho\leq y\leq\delta(\rho<\delta,0\leq\rho\leq 1,0\leq \delta\leq 1)\). Set \(y=\tau^{-1}(x)\) is the inverse function of \(x=\tau(y)\), then \(\delta\) and \(\rho\) satisfy the following conditions:  
\[\rho= \begin{cases}\tau^{-1}(1)&\tau(0)\geq 1\\ 0&\tau(0)<1\end{cases}  \tag{22}\]  
\[\delta= \begin{cases}1&\tau^{-1}(0)\geq 1\\ \tau^{-1}(0)&\tau^{-1}(0)<1\end{cases}  \tag{23}\]  
The volume \(V_{1}\) calculation formula is as follows:  
\[ \begin{split}& V_{1}=\int_{0}^{1}\int_{\rho}^{\delta}\frac{G_{3} -F_{3}-R-y*R*\beta}{R*\alpha}dydz\\ &=\int_{0}^{1}\left[\frac{-(F_{3}+R+\beta*R*\beta-G_{3})^{2}}{2* \alpha*\beta*R^{2}}+C\right]\bigg{|}_{\rho}^{\delta}dz\\ &=\frac{(F_{3}+R+\beta*R*\rho-G_{3})^{2}-(F_{3}+R+\beta*R*\delta-G_{3})^{2}} {2*\alpha*\beta*R^{2}}\end{split}  \tag{24}\]  
where \(C\) is the integral constant. \[V_{2}=1-V_{1}-V_{3}=1+\frac{(F_{3}+R+\beta*R*\delta-G_{3})^{2}-(F_{3}+R+\beta* R*\rho-G_{3})^{2}}{2*\alpha*\beta*R^{2}}-V_{3} \tag{25}\]  
where \(V_{3}\) is the constant of \(\rho\) and \(\delta\). Figure 7: Phase diagram of regulator node’s strategy evolution. According to the expression of the volume \(V_{2}\) and the way of calculating the partial derivatives of the parameters, it is concluded that the punishment of regulator nodes not participating in sharing regulation \(F_{3}\) promoted the participation of regulator nodes in data element sharing regulation; the cost of regulator nodes participating in the sharing regulation \(G_{3}\) restricts the participation in the regulation of regulator nodes; the effect of regulation revenue \(R\) on the participation of regulator nodes in data element sharing regulation is related to the values of the expression \"\(F_{3}-G_{3}\)\".