# Data Element Sharing in Convergence Media Ecology Based on Evolutionary Game
## 4 Results and Discussion  
### Evolutionary Stable Strategy  
The evolutionary stable strategy was proposed by [PERSON] in 1973 based on the principle of natural selection in [PERSON]'s theory of biological evolution. In detail, it means that when all individuals in a population adopt the same behavior strategy, under the influence of natural selection, this population can resist any mutation strategy invading the population from inside or outside, that is to say, in an evolutionary game system, any individual in the system, under the limited payoff information, through repeated games, constantly adjust their strategy selection according to their existing interests, so as to maximize their own interests. Finally, in order to maintain their own interests, a dynamic equilibrium state is reached. In this dynamic equilibrium state, every individual in the system is no longer willing to change their strategy, and the strategy formed in this state is an evolutionary, stable strategy [59]. Based on the stability analysis of the single agent strategy, the stability of the equilibrium point of the tripartite subject evolutionary game system is further analyzed. According to the stability theorem of the differential equation of the evolutionary game, in order to keep a strategy in a stable state, the probability of the game party choosing the strategy must meet the replication dynamic equation equal to 0, and the first derivative is less than 0. The point that meets such a condition is the equilibrium point of the evolutionary game. When the equilibrium point satisfies certain conditions, then the equilibrium point is the evolutionary stability strategy of the dynamic evolutionary game. According to the Lyapunov discrimination method, when the eigenvalue \(\lambda\) surpasses zero, the equilibrium point is unstable, and the point is the source point; when the eigenvalue \(\lambda\) encompasses both positive and negative values, the equilibrium point is unstable, and the point is the saddle point; when the eigenvalue \(\lambda\) falls below zero, the equilibrium point maintains stability and functions as a junction point, which also signifies the point's stability in terms of evolution. [33, 60]. To simplify the operation, we set \(H+E_{11}-E_{12}=\varphi_{1}\); \(I_{1}+F_{1}+G_{12}-G_{11}=\mu_{1}\); \(E_{2}+I_{2}-G_{2}=\mu_{2}\); \(R*\alpha=\varphi_{3}\); \(R*\beta=\mu_{3}\); \(F_{3}-G_{3}=\pi_{3}\). Then, the replication dynamic equation of the evolutionary game is simplified as follows:  
\[\left\{ \begin{array}{c}F(x)=x*(1-x)*(y*\varphi_{1}+\mu_{1})\\ F(y)=y*(1-y)*(x*H+\mu_{2})\\ F(z)=z*(1-z)*(x*\varphi_{3}+y*\mu_{3}+\pi_{3})\end{array} \right. \tag{26}\]  
The corresponding Jacobian matrix [61] ) is as follows:  
\[J=\left[ \begin{array}{ccc}\frac{\partial F(x)}{\partial x}&\frac{\partial F (x)}{\partial y}&\frac{\partial F(x)}{\partial z}\\ \frac{\partial F(y)}{\partial x}&\frac{\partial F(y)}{\partial y}&\frac{ \partial F(y)}{\partial z}\\ \frac{\partial F(z)}{\partial x}&\frac{\partial F(z)}{\partial y}&\frac{ \partial F(z)}{\partial z}\\ \end{array} \right]= \tag{27}\] \[\left[ \begin{array}{ccc}\lambda_{1}(x,y,z)&x*(1-x)*\varphi_{1}&0\\ y*(1-y)*H&\lambda_{2}(x,y,z)&0\\ z*(1-z)*\varphi_{3}&z*(1-z)*\mu_{3}&\lambda_{3}(x,y,z)\end{array} \right]\]  
where \(\lambda_{1}(x,y,z)=(1-2x)*(y*\varphi_{1}+\mu_{1})\), \(\lambda_{2}(x,y,z)=(1-2y)*(x*H+\mu_{2})\), \(\lambda_{3}(x,y,z)=(1-2z)*(x*\varphi_{3}+y*\mu_{3}+\pi_{3})\). The equilibrium point is solved according to the replication dynamic equation:  
\[ \begin{cases}F(x)=0\\ F(y)=0\\ F(z)=0\end{cases}  \tag{28}\]  
On the basis of Formula (26), we can obtain the equilibrium points for the system: E1(0,0,0), E2(0,0,1), E3(0,1,0), E4(0,1,1), E5(1,0,0), E6(1,0,1), E7(1,1,0), E8(1,1,1).