## 6 The Impact of the Subsidy Mechanism on the Evolution of the System
### The Impact of Subsidy Mechanism on System Evolution  
In order to further improve the decision-making model, this paper introduces a subsidy mechanism. The shared platform provides certain subsidies to the subjects who actively participate in quality synergy to achieve the effect of incentives. The subsidy variable is represented by \(He\).  
Based on this, a shared manufacturing decision model under the reputation mechanism is constructed. The value perception function of each game subject and the replica dynamic equation of strategy selection are as follows:  
The value perception of \"quality improvement\" and \"no quality improvement\" in the supply side are \(T_{1p}\) and \(T_{2p}\), respectively.  
\[\begin{array}{l}T_{1p}=T(\Delta\pi)w(\epsilon)=w(e)[w(g)(P(H_{a}+H_{b}+R)-C((1 -K)C_{ph}))\\ +w(1-g)(P(H_{a}+H_{b})-C((1-K)C_{ph}-H_{e}))]+\\ w(1-e)[w(g)(P(H_{a}+H_{b}+R)-C(C_{ph}-H_{e}+\phi\psi Lw(q)))+\\ w(1-g)(P(H_{a}+H_{b})-C(C_{ph}-H_{e}+\phi\psi Lw(q)))]\end{array} \tag{26}\]  
\[\begin{array}{l}T_{2p}=T(\Delta\pi)w(\epsilon)=w(e)[w(g)(P(KC_{ph})-C(F+ \psi Lw(q)))+w(1-g)\\ (P(KC_{ph})-C(\phi Lw(q)))]+w(1-e)[w(g)(-C(F+Lw(q)))+w(1-g)(-C(Lw(q)))]\end{array} \tag{27}\]  
The average value perception of supply side is \(\overline{T_{p}}\).  
\[\begin{array}{l}T_{p}=pT_{1p}+(1-p)T_{2p}\end{array} \tag{28}\]  
The dynamic equation of supply side replication is \(F(p)\).  
\[\begin{array}{l}F(p)=dp/dt=p(T_{1p}-\overline{T_{p}})=p(1-p)(T_{1p}-T_{2p} )=p(1-p)\\ \left\{\begin{array}{l}w(e)[w(g)(P(H_{a}+H_{b}+R)-C((1-K)C_{ph}-H_{e}))+w(1 -g)(P(H_{a}+H_{b})-C((1-K)C_{ph}-H_{e}))]\\ -w(e)[w(g)(P(KC_{ph})-C(F+\psi Lw(q)))+w(1-g)(P(KC_{ph})-C(\psi Lw(q)))]\\ +w(1-e)[w(g)(P(H_{a}+H_{b}+R)-C(C_{ph}-H_{e}+\phi\psi Lw(q)))+w(1-g)(P(H_{a}+H _{b})\\ -C(C_{ph}-H_{e}+\phi\psi Lw(q)))]-w(1-e)[w(g)(-C(F+Lw(q)))+w(1-g)(-C(Lw(q)))] \end{array}\right\}\end{array} \tag{29}\]  
The value perception of \"cost sharing\" and \"no cost sharing\" in the demand side are \(T_{1e}\) and \(T_{2e}\), respectively.  
\[\begin{array}{l}T_{1e}=T(\Delta\pi)w(\epsilon)\\ =w(p)[P(H_{d}(Q_{b}-Q_{a}))-C(KC_{ph})]+w(1-p)[-C(KC_{ph}+H_{d}(Q_{a}-Q_{c})+ \phi\psi Lw(q))]\end{array} \tag{30}\]  
\[\begin{array}{l}T_{2e}=T(\Delta\pi)w(\epsilon)\\ =w(p)[P(H_{d}(Q_{b}-Q_{a}))-C(\psi Lw(q))]+w(1-p)[-C(H_{d}(Q_{a}-Q_{c})+Lw(q))] \end{array} \tag{31}\]  
The average value perception of demand side is \(\overline{T_{e}}\).  
\[\overline{T_{e}}=eT_{1e}+(1-e)T_{2e} \tag{32}\]  
The dynamic equation of demand side replication is \(F(e)\).  
\[\begin{array}{l}F(e)=de/dt=e(T_{1e}-\overline{T_{e}})=e(1-e)(T_{1e}-T_{2e} )=e(1-e)\\ \left\{\begin{array}{l}w(p)[P(H_{d}(Q_{b}-Q_{a}))-C(KC_{ph})]-w(p)[P(H_{d} (Q_{b}-Q_{a}))-C(\psi Lw(q))]+w(1-p)\\ [-C(kC_{ph}+H_{d}(Q_{a}-Q_{c})+\phi\psi Lw(q))]-w(1-p)[-C(H_{d}(Q_{a}-Q_{c})+ Lw(q))]\end{array}\right\}\end{array} \tag{33}\]The value perception of \"positive regulation\" and \"negative regulation\" in the shared platform are \(T_{1g}\) and \(T_{2g}\), respectively.  
\[\begin{array}{l}T_{1g}==T(\Delta\pi)w(\epsilon)=w(p)[w(e)(P(H_{c})-C(C_{gh}+R) )+w(1-e)(P(H_{c})-C(C_{gh}+\alpha L+R))]\\ +w(1-p)[w(e)(P(H_{c}+F)-C(C_{gh}+\alpha L))+w(1-e)(P(H_{c}+F)-C(C_{gh}+L))]\\ \\ T_{2g}=T(\Delta\pi)w(\epsilon)=\\ w(p)[w(1-e)(-C(\alpha L))]+w(1-p)[w(e)(-C(\alpha L))+w(1-e)(-C(L))]\end{array} \tag{34}\]  
The average value perception of shared platform is \(\overline{T_{g}}\).  
\[\overline{T_{g}}=gT_{1g}+(1-g)T_{2g} \tag{36}\]  
The dynamic equation of shared platform replication is \(F(g)\).  
\[\begin{array}{l}F(g)=dg/dt=g(T_{1g}-\overline{T_{g}})=g(1-g)(T_{1g}-T_{2g})= g(1-g)\\ \left\{\begin{array}{l}w(p)[w(e)(P(H_{c})-C(C_{gh}+R))+w(1-e)(P(H_{c})-C(C_{ gh}+\alpha L+R))]-\\ w(p)[w(1-e)(-C(\alpha L))]+w(1-p)[w(e)(P(H_{c}+F)-C(C_{gh}+\alpha L))+\\ w(1-e)(P(H_{c}+F)-C(C_{gh}+L))]-w(1-p)[w(e)(-C(\alpha L))+w(1-e)(-C(L))]\\ \end{array}\right\}\end{array} \tag{37}\]