## 3 Model Analysis under the Static Reward and Punishment Mechanism  
### Analysis of Supply Side Strategy Stability  
The value perception of \"quality improvement\" and \"no quality improvement\" in the supply side are \(T_{1p}\) and \(T_{2p}\), respectively. \[ \begin{array}{l}T_{1p}=T(\Delta\pi)w(\epsilon)=w(\epsilon)[w(g)(P(H_{a}+H_{b} +R)-C((1-K)C_{pl}))+w(1-g)\\ (P(H_{a}+H_{b})-C((1-K)C_{ph}))]+w(1-e)[w(g)(P(H_{a}+H_{b}+R)-\\ C(C_{ph}+\phi\psi Lw(q)))+w(1-g)(P(H_{a}+H_{b})-C(C_{ph}+\phi\psi Lw(q)))]\\ \end{array}  \tag{1}\]  
\[ \begin{array}{l}T_{2p}=T(\Delta\pi)w(\epsilon)=w(e)[w(g)(P(KC_{ph})-C(F+\psi Lw (q)))\\ +w(1-g)(P(KC_{ph})-C(\phi Lw(q)))]\\ +w(1-e)[w(g)(-C(F+Lw(q)))+w(1-g)(-C(Lw(q)))]\end{array}  \tag{2}\]  
The average value perception of supply side is \(\overline{T_{p}}\). \[\overline{T_{p}}=pT_{1p}+(1-p)T_{2p} \tag{3}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Shared Platform**} \\ \hline  & \multicolumn{2}{c}{Active regulation \(g\)} & Negative regulation \(1-g\) \\ \hline  & \multicolumn{2}{c}{demand side} & \(P(H_{a}+H_{b}+R)-C((1-K)C_{ph})\) & \(P(H_{a}+H_{b})-C((1-K)C_{ph})\) \\  & \multicolumn{2}{c}{cost sharing} & \(P(H_{d}(Q_{b}-Q_{a}))-C(K_{cp})\) & \(P(H_{d}(Q_{b}-Q_{a})-C(K_{cp})\) \\ Supply side & \(e\) & \(P(H_{c})-C(C_{ph}+R)\) & \\ quality improvement & \multicolumn{2}{c}{demand side} & \(P(H_{a}+H_{b}+R)-C(C_{ph}+\phi\psi Lw(q))\) & \(P(H_{a}+H_{b})-C(C_{ph}+\phi\psi Lw(q))\) \\ \(p\) & \multicolumn{2}{c}{not cost sharing} & \(P(H_{d}(Q_{b}-Q_{a}))-C(\psi Lw(q))\) & \(P(H_{d}(Q_{b}-Q_{a}))-C(\psi Lw(q))\) \\  & \multicolumn{2}{c}{\(1-e\)} & \(P(H_{c})-C(C_{gh}+\Delta L+R)\) & \(-C(\epsilon L)\) \\ \cline{2-3}  & \multicolumn{2}{c}{demand side} & \(P(KC_{ph})-C(F+\psi Lw(q))\) & \(P(KC_{ph})-C(\psi Lw(q))\) \\  & \multicolumn{2}{c}{cost sharing} & \(-C(KC_{ph}+H_{d}(Q_{a}-Q_{c})+\phi\psi Lw(q))\) & \(-C(KC_{ph}+H_{d}(Q_{b}-Q_{c})+\phi\psi Lw(q))\) \\ \(\epsilon\) & \(P(H_{c}+F)-C(C_{gh}+\Delta L)\) & \(-C(\Delta L)\) \\ \cline{2-3}  & \multicolumn{2}{c}{demand side} & \(-C(F+Lw(q))\) & \(-C(Lw(q))\) \\  & \multicolumn{2}{c}{not cost sharing} & \(-C(H(Q_{a}-Q_{c})+Lw(q))\) & \(-C(H_{d}(Q_{a}-Q_{c})+Lw(q))\) \\  & \multicolumn{2}{c}{\(1-e\)} & \(P(H_{c}+F)-C(C_{gh}+L)\) & \(-C(L)\) \\ \hline \hline \end{tabular} Note: \(C_{ph}\), \(C_{gh}\), \(C_{eb}\), \(C_{eb}\), \(C_{ep}\), \(L_{a}\), \(L_{b}\), \(F\), \(D\) represent cost perception and are listed in the cost account. \(H_{a}\), \(H_{b}\), \(H_{c}\), \(H_{d}\), \(R\) represent valence perception and are listed in the valence account.  
\end{table} 
Table 1: Benefit Perception Matrix. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline \(p\) & Probability of supply side quality improvement \\ \(e\) & Probability of demand side cost sharing \\ \(g\) & Probability of active regulation of shared platforms \\ \(C_{ph}\) & Labor cost perception of supply side quality improvement \\ \(K\) & Demand side cost allocation ratio \\ \(C_{ph}\) & Labor cost perception of active supervision of shared platforms \\ \(H_{a}\) & Perceived loss reduction from supply side quality improvement \\ \(H_{b}\) & Increased perceived benefit from supply-side quality improvements \\ \(H_{c}\) & Benefit perception of active regulation of sharing platforms \\ \(H_{d}\) & Demand side unit gain/loss \\ \(Q_{d}\) & Initial product quality level \\ \(Q_{b}\) & Product quality level after supply side quality improvement \\ \(Q_{c}\) & The quality level of the product after the quality improvement of the supply side \\ \(F\) & Perceived value of punishment by supply sides \\ \(R\) & Perceived value of rewards by supply sides \\ \(q\) & Probability of quality accidents \\ \(L\) & Quality accident risk \\ \(\phi\) & Quality risk transfer coefficient \\ \(\alpha\) & Quality risk spillover coefficient \\ \(\psi\) & quality risk factor \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter symbols and their meanings. The dynamic equation of supply side replication is \(F_{(p)}\). \[\left.