## 3 The Stackelberg Game Models
### A-model: A Stackelberg Game Model with Advertiser as Leader
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Decision Variables** & **P-Model** & **A-Model** & **Comparisons** \\ \hline \(\lambda^{*}\) & 0.1082 & 0.0325 & \(\lambda^{p*}>\lambda^{a*}\) \\ \(p_{a}{}^{*}\) & 118.5665 & 112.5000 & \(p_{a}{}^{p*}>p_{a}{}^{a*}\) \\ \(p_{a}{}^{*}\) & 118.5665 & 112.5000 & \(p_{a}{}^{p*}>p_{a}{}^{a*}\) \\ \(B_{p}{}^{*}\) & 3633.2000 & 1114.6000 & \(B_{p}{}^{p*}>B_{a}{}^{a*}\) \\ \(B_{a}{}^{*}\) & 1089.9000 & 5975.9000 & \(B_{a}{}^{p*}<B_{a}{}^{a*}\) \\ \(\Pi_{p}{}^{*}\) & 9167.9000 & 7801.9000 & \(\Pi_{p}{}^{p*}>\Pi_{p}{}^{a*}\) \\ \(\Pi_{a}{}^{*}\) & 4634.8000 & 15,584.0000 & \(\Pi_{p}{}^{p*}<\Pi_{a}{}^{a*}\) \\ \(\Pi^{*}\) & 13,803.0000 & 23,386.0000 & \(\Pi{}^{p*}<\Pi^{a*}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimal equilibriums and profits of the platform and the advertiser in two models in Exp. 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Decision Variables** & **P-Model** & **A-Model** & **Comparisons** \\ \hline \(\lambda^{*}\) & 0.1082 & 0.0321 & \(\lambda^{p*}>\lambda^{a*}\) \\ \(p_{a}{}^{*}\) & 237.1331 & 225.0000 & \(p_{a}{}^{p*}>p_{a}{}^{a*}\) \\ \(B_{p}{}^{*}\) & 14,533.0000 & 4354.4000 & \(B_{p}{}^{p*}>B_{a}{}^{a*}\) \\ \(B_{p}{}^{*}\) & 4359.8000 & 24,700.0000 & \(B_{p}{}^{p*}<B_{a}{}^{a*}\) \\ \(\Pi_{p}{}^{*}\) & 35,351.0000 & 30,480.0000 & \(\Pi_{p}{}^{p*}>\Pi_{p}{}^{a*}\) \\ \(\Pi_{a}{}^{*}\) & 17,949.0000 & 60,941.0000 & \(\Pi_{p}{}^{p*}<\Pi_{a}{}^{a*}\) \\ \(\Pi^{*}\) & 53,300.0000 & 91,421.0000 & \(\Pi^{p*}<\Pi^{a*}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal equilibriums and profits of the platform and the advertiser in two models in Exp. 3. 3. The e-commerce platform and the advertiser invest more in their own brand effect in their respective dominant model than the other side's investment. Because both intend to pay more cost on building their own brand image to enhance their own brand effect when they are respectively taking the leadership in the game model. 4. The profit of the platform is greater in the P-model than that in the A-model. Because the platform is in the dominant position in the stackelberg P-model, he aims at maximizing his own profit. The platform would increase the decision variables: the proportion of advertiser's income commission and the cost of advertising effort of the platform brand which could help to obtain much higher profit than that in the A-model. 5. The profit of advertiser is greater in the A-model than that in the P-model. Since the advertiser plays a leading role in the stackelberg A-model, it would make the optimal decision variables: the advertising product price and the cost of advertising effort of the advertiser brand, to achieve his own optimal income, which is better than that in the P-model when the platform as the leader. 6. The total profit is greater in the A-model than that in the P-model. Because both parties are benefited by the advertiser's large income in e-commerce transaction and the profit of the advertiser accounts for a larger proportion of the total profit, so the total profit is much greater in the A-model than that in the P-model.