## 5 Simulation Analysis and Discussion
### Pricing and Impact of Subsidies  
In order to study the importance of current policy support for the development of electric vehicle sharing, this paper sets up two scenarios for case study. Scenario 1 considers the trilateral game among the government, operator and users with the government's financial subsidies. Scenario 2 cancels the subsidy support. Only considering the environmental and social benefits of the government, a trilateral game among the same three players is built. The results are shown in Table 2. The environmental benefits include the benefits of energy-saving and emission reduction. The social benefits take the reduction of urban land pressure and delaying of the construction of ancillary service facility in the power grid into account. Their mathematical expressions are as follows:  
\[U_{e}=\sum_{n=1}^{n_{t}}(x_{n}^{1}s_{n})DW_{100}P_{e}l_{es}/100+\sum_{n=1}^{n _{t}}(x_{n}^{1}s_{n})\frac{DC_{100}P_{e}l_{os}}{100}, \tag{20}\]  
\[U_{s}=\frac{\sum_{n=1}^{n_{t}}(x_{n}^{1})}{n_{0}}P_{p}S_{p}\frac{i(1+i)^{k_{p}} }{(1+i)^{k_{p}}-1}+k_{1}m, \tag{21}\]  
In the unsubsidized scenario, the operator increases the prices to ensure the income level. The average daily number of sharing decreases and then the scale of operation also decreased. The reduced spending leads to higher revenue. Meanwhile, the decline in the enthusiasm of the users causes a decrease in the government benefits, resulting in a reduction in environmental and social benefits, which is not worth the loss for the government. This shows that subsidie  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(W_{100}(kWh)\) & 76. 662 & \(k_{2}\) & 1.3 \\ \(P_{e}(CNY/kWh)\) & 0.81 & \(W_{100}(kWh)\) & 35. 001 \\ \(\eta_{es}\) & 50.5\% & \(i\) & 10\% \\ \(\eta_{cs}\) & 28.7\% & \(k_{c}\) & 4 \\ \(C_{100}(kg)\) & 14.955 & \(k_{i}\) & 20 \\ \(P_{c}(CNY/kg)\) & 0.15 & \(k_{p}\) & 10 \\ \(n_{0}\) & 2 & \(\theta_{1}(CNY/min)\) & 1/6 \\ \(P_{p}\big{(}CNY/m^{2}\big{)}\) & 2500 & \(\theta_{2}(CNY/min)\) & 5/6 \\ \(S_{p}\big{(}m^{2}\big{)}\) & 30 & \(\theta_{3}(min)\) & 5 \\ \(C_{1}(CNY)\) & 134800 & \(\theta_{4}(min)\) & 15 \\ \(C_{2}(CNY)\) & 30000 & \(p_{p}(CNY/km)\) & 2.63 \\ \(C_{3}(CNY)\) & 150 & \(COM_{e}\) & 0.3 \\ \(D\) & 365 & \(COM_{p}\) & 0.09 \\ \(k_{1}\) & 1277.5 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter value for game solving.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Scenario 1 (with Subsidies)** & **Scenario 2 (no Subsidies)** \\ \hline Price per kilometer (CNY) & 1.683 & 1.7823 \\ Price per minute (CNY) & 0.175 & 0.1883 \\ Subsidy rate for electric vehicles & 0.1444 & / \\ Subsidy rate for infrastructure & 0.3835 & / \\ The number of sharing travel daily & 2008 & 1650 \\ Sharing travel ratio & 40.16\% & 33.00\% \\ Operator benefit (million CNY) & 16.30 & 18.14 \\ Government benefit (million CNY) & 17.73 & 16.22 \\ Environmental benefit (million CNY) & 6.57 & 6.13 \\ Social benefit (million CNY) & 12.46 & 10.24 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Equilibrium solution and the benefits of each participant in two scenarios.  
the early development of electric vehicle sharing. Comparing to the current mathematical models discussed about electric vehicle sharing, we take the influence of the government into account [13; 14]. The analysis of this paper shows that the subsidies can give operators and consumers a positive signal, reduce the burden of initial investment by operators, support their development and operation and bring more social and environmental benefits, which can satisfy the interests of all the players in the game.