# 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
So the volume \(V_{1}\) calculation formula is as follows:  
\[V_{1}=\int_{0}^{1}\int_{0}^{1}\frac{G_{2}-E_{2}-I_{2}}{H}dxdy=\int_{0}^{1}( \frac{G_{2}-E_{2}-I_{2}}{H})dy=\frac{G_{2}-E_{2}-I_{2}}{H} \tag{15}\]  
\[V_{2}=1-V_{1}=1+\frac{E_{2}+I_{2}-G_{2}}{H} \tag{16}\]  
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 revenue of common user nodes participating in sharing \(E_{2}\) and the incentive revenue of the system \(I_{2}\) promoted the participation of common user nodes in data element sharing; the cost of common user nodes participating in the sharing of data elements \(G_{2}\) restricts the participation of common user nodes; the effect of collaborative revenue \(H\) on the participation of common user nodes in data element sharing is related to the values of the expression \"\(E_{2}+I_{2}-G_{2}\)\". (3) Expected revenue function and replication dynamic equation of regulator node. The definition of the expected revenue of the \"participating in data element sharing regulation\" strategy of the regulator node is \(R_{1}\), the expected revenue of the \"not participating in data element sharing regulation\" strategy is \(R_{2}\), the average expected revenue is \(\overline{R}\), and the calculation formula is:  
\[ \begin{split} R_{1}=x*y*[R*(1+\alpha+\beta)-G_{3}]+x*(1-y)*[R*(1+ \alpha)-G_{3}]+(1-x)*y*[R\\ *(1+\beta)-G_{3}]+(1-x)*(1-y)*(R-G_{3})\\ =x*R*\alpha+y*R*\beta+R-G_{3}\end{split}  \tag{17}\]  
Figure 6: Phase diagram of common user node’s strategy evolution. \[ \begin{array}{l}R_{2}=x*y*(-F_{3})+x*(1-y)*(-F_{3})+(1-x)*y*(-F_{3})+(1-x)*(1-y)\\ *(-F_{3})\\ =-F_{3}\\ \end{array}  \tag{18}\]  
\[ \begin{array}{l}\overline{R}=z*R_{1}+(1-z)*R_{2}\\ =z*(x*R*\alpha+y*R*\beta+R-G_{3})-(1-z)*F_{3}\\ \end{array}  \tag{19}\]  
The replication dynamic equation of the game strategy of the regulator node is:  
\[ \begin{array}{l}F(z)=\frac{dz}{dt}=z*(R_{1}-\overline{R})\\ =z*(x*R*\alpha+y*R*\beta+R-G_{3})-z*[z*(x*R*\alpha+y*R*\beta+R-G_{3})-\\ (1-z)*F_{3}]\\ =z*(1-z)*(x*R*\alpha+y*R*\beta+R-G_{3}+F_{3})\\ \end{array}  \tag{20}\]  
The first derivative of the replication dynamic equation F(z) of the regulator node is:  
\[F^{\prime}(z)=\frac{dF(z)}{dz}=(1-2z)*(x*R*\alpha+y*R*\beta+R-G_{3}+F_{3}) \tag{21}\]  
Let \(L(x,y)=x*R*\alpha+y*R*\beta+R-G_{3}+F_{3}\), then \(\frac{\partial L}{\partial x}=R*\alpha\), we can obtain \(\frac{\partial L}{\partial x}>0\), so the function \(L(x,y)\) is increasing with respect to \(x\); \(\frac{\partial L}{\partial y}=R*\beta\), we can obtain \(\frac{\partial L}{\partial y}>0\), so the function \(L(x,y)\) is increasing with respect to y. Let \(F(z)=0\), then we can obtain: \(z=0\) or \(z=1\) or \(x=x^{*}=\frac{G_{3}-F_{3}-R-y*R*\beta}{R*\alpha}(y=y^{*}=\frac{G_{3}-F_{3}-R- x*R*\alpha}{R*\beta})\). 1. When \(x=x^{*}\) or \(y=y^{*}\), for any \(z(0\leq z\leq 1)\), we can obtain: \(F(z)=0\), which indicates that all the policies meeting the constraints of the regulator node are in a stable state, and the regulator node chooses to participate in the sharing regulation probability z will not change over time. 2. When \(x\
eq x^{*}\) and \(y\
eq y^{*}\), \(z=0\) or \(z=1\) are the two evolutionary stability strategies of the regulator node, and the distribution values of \(F^{\prime}(z)\) should be discussed: 1. When \(\frac{G_{3}-F_{3}-R-y*R*\beta}{R*\alpha}>1\)(\(\frac{G_{3}-F_{3}-R-x*R*\alpha}{R*\beta}>1\)), 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 \(z=0\) is an evolutionary stable point, which indicates that the increased revenue of the regulator node is less than the increased cost of the participation in regulation, and the not participation in regulation of the regulator node is the evolutionary stability strategy. 2.