# 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
negative participation in sharing revenue \(E_{12}\) on the participation of business organization nodes in data element sharing are related to the values of expression \"\(G_{12}+I_{1}+F_{1}-G_{11}\)\". (2) Expected revenue function and replication dynamic equation of common user node The definition of the expected revenue of the \"participate in data element sharing\" strategy of the common user node is \(Q_{1}\), the expected revenue of the \"not participate in data element sharing\" strategy is \(Q_{2}\), the average expected revenue is \(\overline{Q}\), and the calculation formula is: \[ \begin{array}{c}Q_{1}=x*z*(E_{2}+I_{2}+H-G_{2})+x*(1-z)*(E_{2}+I_{2}+H-G_{2}) +(1-x)*z*(E_{2}+I_{2}-G_{2})+(1-x)*(1-z)*(E_{2}\\ +I_{2}-G_{2})=x*H+E_{2}+I_{2}-G_{2}\\ \\ Q_{2}=0\\ \\ \overline{Q}=y*Q_{1}+(1-y)*Q_{2}=y*(x*H+E_{2}+I_{2}-G_{2})\\ \\ \end{array} \] (10) \[Q_{2}=0\] (11) \[\overline{Q}=y*Q_{1}+(1-y)*Q_{2}=y*(x*H+E_{2}+I_{2}-G_{2})\] (12) The replication dynamic equation of the game strategy of the common user node is: \[ \begin{array}{c}F(y)=\frac{dy}{dt}=y*(Q_{1}-\overline{Q})=y*[x*H+E_{2}+I_{2}- G_{2}-y*(x*H+E_{2}+I_{2}-G_{2})]\\ =y*(1-y)*(x*H+E_{2}+I_{2}-G_{2})\\ \end{array} \] (13) The first derivative of the replication dynamic equation F(y) of the common user node node is: \[F^{\prime}(y)=\frac{dF(y)}{dy}=(1-2y)*(x*H+E_{2}+I_{2}-G_{2})\] (14) Let \(L(x)=x*H+E_{2}+I_{2}-G_{2}\), we can obtain \(L^{\prime}(x)=H>0\), so the function L(x) is increasing with respect to x. Let \(F(y)=0\), we can obtain: \(y=0\)_or_\(y=1\)_or_\(x=x^{*}=\frac{G_{2}-E_{2}-I_{2}}{H}\). 1. When \(x=x^{*}\), for any \(y(0\leq y\leq 1)\), we can obtain \(F(y)=0\), and it indicates that all the policies meeting the constraints of the common user node are in a stable state, and the common user node chooses to participate in the sharing probability y will not change over time. 2. When \(x\
eq x^{*}\), \(y=0\) or \(y=1\) are the two evolutionary stability strategies of common user node, the distribution values of \(F^{\prime}(y)\) should be discussed: 1. When \(\frac{G_{2}-E_{2}-I_{2}}{H}>1\), because \(0\leq x\leq 1\), so \(x<x^{*}\). According to the monotonicity of the function \(L(x)\), we obtain \(L(x)<0\), and then we can obtain \(F^{\prime}(0)<0\) and \(F^{\prime}(1)>0\), so \(y=0\) is an evolutionary stable point, which indicates that the increased revenue of the common user node is less than the increased cost of the participation in sharing, and the not participation in sharing of the common user node is the evolutionary stability strategy. 2. When \(\frac{G_{2}-E_{2}-I_{2}}{H}<0\), because \(0\leq x\leq 1\), so \(x>x^{*}\). According to the monotonicity of the function \(L(x)\), we can obtain \(F^{\prime}(0)>0\) and \(F^{\prime}(1)<0\), so \(y=1\) is an evolutionary stable point, which indicates that the increased revenue of the common user node is more than the increased cost of the participation in sharing, and the participation in sharing of the common user node is the evolutionary stability strategy. 3. When \(0<\frac{G_{2}-E_{2}-I_{2}}{H}<1\), it was also necessary to discuss the size relationship between \(x\) and \(x^{*}\): When \(x<x^{*}\), we can obtain \(F^{\prime}(0)<0\) and \(F^{\prime}(1)>0\), so \(y=0\) is an evolutionary stable point. When \(x>x^{*}\), we can obtain \(F^{\prime}(0)>0\) and \(F^{\prime}(1)<0\), so \(y=1\) is an evolutionary stable point. Phase diagram of common user node's strategy evolution is shown in Figure 6.  
According to the figure above, the probability of selecting not to participate in data element sharing is volume \(V_{1}\), and the probability of participation in data element sharing is volume \(V_{2}\). The projection interval of the surface \(x=\frac{\mathcal{G}_{2}-E_{2}-I_{2}}{H}\) onto the yoz plane is \(0\leq y\leq 1,0\leq z\leq 1\).