# Data Element Sharing in Convergence Media Ecology Based on Evolutionary Game
## 4 Results and Discussion
### Evolutionary Stable Strategy
On the basis of Formula (27), we can obtain the local equilibrium point, eigenvalue distribution and stability conditions of the model, as shown in the following Table 3.  
According to the judgment of Table 3, we selected several special equilibrium points for sampling analysis in this paper: E1(0,0,0), E2(0,0,1), E7(1,1,0) and E8(1,1,1). Inference 1: Under condition a, \(I_{1}+F_{1}+G_{12}<G_{11}\), \(E_{2}+I_{2}\)\(<G_{2}\), \(F_{3}<G_{3}\), the replication dynamic system has stable points, E1(0,0,0). Under condition b, \(I_{1}+F_{1}+G_{12}<G_{11}\), \(E_{2}+I_{2}\)\(<G_{2}\), \(F_{3}>G_{3}\), the replication dynamic system has stable points, E2(0,0,1). Proof: According to the Lyapunov discriminant method, condition a and condition b, the eigenvalues \(\lambda_{1}\), \(\lambda_{2}\),\(\lambda_{3}\) of the Jacobian matrix corresponding to the replicated dynamic system at the equilibrium points E1(0,0,0), E2(0,0,1) are all less than 0, so the equilibrium points E1(0,0,0), E2(0,0,1) are the stable points of the system. It follows from Inference 1 that the cost of nodes participating in the sharing of ecological data elements or regulatory links plays an inhibitory role in the selection of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Equilibrium** & \multicolumn{4}{c}{**Eigenvalues**} & **Stability Conditions** \\ \cline{2-5}
**Points** & \(\lambda_{1}\) & \(\lambda_{2}\) & \(\lambda_{3}\) & \\ \hline \multirow{2}{*}{_E1(0,0,0)_} & \multirow{2}{*}{\(\mu_{1}\)} & \multirow{2}{*}{\(\mu_{2}\)} & \multirow{2}{*}{\(\pi_{3}\)} & \(I_{1}+F_{1}+G_{12}<G_{11}\) \\  & & & & \(F_{3}<G_{3}\) \\ \hline \multirow{2}{*}{_E2(0,0,1)_} & \multirow{2}{*}{\(\mu_{1}\)} & \multirow{2}{*}{\(\mu_{2}\)} & \multirow{2}{*}{\(-\pi_{3}\)} & \(I_{1}+F_{1}+G_{12}<G_{11}\) \\  & & & & \(F_{3}>G_{3}\) \\ \hline \multirow{2}{*}{_E3(0,1,0)_} & \multirow{2}{*}{\(\varphi_{1}+\mu_{1}\)} & \multirow{2}{*}{\(-\mu_{2}\)} & \multirow{2}{*}{\(\mu_{3}+\pi_{3}\)} & \(H+E_{11}+I_{1}+G_{12}<G_{11}\) \\  & & & & \(G_{11}+E_{12}<G_{2}\) \\  & & & & \(F_{3}>G_{3}\) \\ \hline \multirow{2}{*}{_E4(0,1,0)_} & \multirow{2}{*}{\(\varphi_{1}+\mu_{1}\)} & \multirow{2}{*}{\(-\mu_{2}\)} & \multirow{2}{*}{\(-\mu_{3}-\pi_{3}\)} & \(H+E_{11}+I_{1}+G_{12}<G_{12}\) \\  & & & & \(G_{11}+E_{12}\) \\  & & & & \(G_{2}+I_{2}>G_{2}\) \\  & & & & \(G*\beta+F_{3}>G_{3}\) \\ \hline \multirow{2}{*}{_E5(1,0,0)_} & \multirow{2}{*}{\(-\mu_{1}\)} & \multirow{2}{*}{\(H+\mu_{2}\)} & \multirow{2}{*}{\(\varphi_{3}+\pi_{3}\)} & \(I_{1}+F_{1}+G_{12}>G_{11}\) \\  & & & & \(G_{11}+E_{12}>G_{2}\) \\  & & & & \(G*\alpha+F_{3}<G_{3}\) \\ \hline \multirow{2}{*}{_E6(1,0,1)_} & \multirow{2}{*}{\(-\mu_{1}\)} & \multirow{2}{*}{\(H+\mu_{2}\)} & \multirow{2}{*}{\(-\varphi_{3}-\pi_{3}\)} & \(H+E_{2}+I_{2}<G_{2}\) \\  & & & & \(G_{11}+E_{12}\) \\  & & & & \(H+E_{2}+I_{2}>G_{2}\) \\  & & & & \(G*\alpha+F_{3}>G_{3}\) \\ \hline \multirow{2}{*}{_E7(1,1,0)_} & \multirow{2}{*}{\(-\varphi_{1}-\mu_{1}\)} & \multirow{2}{*}{\(-H-\mu_{2}\)} & \multirow{2}{*}{\(\varphi_{3}+\mu_{3}+\pi_{3}\)} & \(H+E_{2}+I_{2}>G_{2}\) \\  & & & & \(G*\alpha+F_{3}<G_{3}\) \\ \hline \multirow{2}{*}{_E8(1,1,1)_} & \multirow{2}{*}{\(-\varphi_{1}-\mu_{1}\)} & \multirow{2}{*}{\(-H-\mu_{2}\)} & \multirow{2}{*}{\(-\varphi_{3}-\mu_{3}-\pi_{3}\)} & \(H+E_{2}+I_{2}>G_{2}\) \\  & & & & \(G_{11}+E_{12}\) \\  & & & & \(G*\alpha+F_{3}>G_{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The equilibrium points correspond to eigenvalues and stability conditions. nodes participating in positive sharing, sharing or regulation. When the cost of participation is large enough, ecological nodes will choose negative sharing, not participate in sharing or not participate in regulation; therefore, controlling the cost of participation in sharing is an effective way to promote active sharing or regulation.