The global imperative to combat climate change has positioned the electrification of transportation as a critical pathway toward sustainability. The electric vehicle car market has experienced explosive growth, with sales penetration reaching unprecedented levels. However, the parallel development of charging infrastructure—particularly the public charging network—has often lagged, presenting a significant bottleneck to widespread electric vehicle car adoption. Key challenges include not just an aggregate shortage of charging points but also severe structural imbalances: a predominance of low-to-medium power chargers and a stark geographical unevenness in distribution. This mismatch between supply and demand undermines user convenience, operational efficiency, and ultimately, consumer confidence in transitioning to an electric vehicle car.
In response, governments have deployed various subsidy schemes aimed at accelerating the build-out of charging infrastructure. These policies primarily fall into two categories: construction subsidies and operational subsidies. While existing research confirms the positive impact of subsidies, there is a need for a more nuanced analysis that considers the heterogeneity of charging equipment—specifically the power disparity between Direct Current (DC) fast chargers and Alternating Current (AC) slow chargers—and the dynamic interplay between different subsidy types. This article constructs a tripartite game-theoretic model involving the government, charging infrastructure operators, and consumers to systematically analyze and compare the effects of various subsidy strategies on electric vehicle car adoption rates and socio-environmental benefits.
1. Methodology and Model Framework
To accurately assess the welfare effects of different subsidy policies, we model a market scenario with a monopolistic charging infrastructure operator, a government policymaker, and a pool of potential electric vehicle car consumers. This setting allows for a clear analysis of strategic interactions. The decision-making sequence follows a Stackelberg game structure:
- Government (Leader): Decides the subsidy policy type and its parameters to maximize socio-environmental benefits.
- Operator (Follower): Observes the government’s policy and decides the construction levels of DC and AC charging piles.
- Consumers: Observe the available charging infrastructure and decide whether to purchase an electric vehicle car based on convenience and cost.
The model is solved using backward induction. The key variables and parameters are defined in Table 1.
| Symbol | Definition |
|---|---|
| $a$ | Potential base demand for electric vehicle cars. |
| $d$ | Realized demand (quantity) for electric vehicle cars. |
| $\beta_f, \beta_s$ | Marginal impact on demand from one additional DC or AC charger, respectively ($\beta_f > \beta_s$). |
| $n_f, n_s$ | Number of DC and AC chargers built by the operator. |
| $k_f, k_s$ | Power rating of DC and AC chargers ($k_f > k_s$). |
| $\eta_f, \eta_s$ | Cost coefficient for building and operating DC and AC chargers ($\eta_f > \eta_s$). |
| $\gamma$ | Consumers’ sensitivity to the charging service fee. |
| $p$ | Annual charging service fee per electric vehicle car (exogenous). |
| $e$ | Annual environmental benefit generated per electric vehicle car. |
| $c_n, c_k, m$ | Subsidy rates: per-charger construction, per-power-unit construction, and per-demand operational subsidy. |
The demand function for electric vehicle cars is formulated as:
$$ d = a + \beta_f n_f + \beta_s n_s – \gamma p $$
This captures the positive influence of infrastructure availability (with a stronger effect from DC chargers due to consumer preference for fast charging) and the negative influence of the service fee.
The operator’s profit is revenue from service fees minus the convex cost of infrastructure construction and operation:
$$ \pi = p d – \frac{\eta_f n_f^2}{2} – \frac{\eta_s n_s^2}{2} $$
The government’s objective is to maximize net environmental benefit, defined as total environmental benefit minus total subsidy expenditure:
$$ E = e \cdot d – \text{Subsidy Outlay} $$
2. Analysis of Subsidy Strategies
2.1 Benchmark Case (No Subsidy)
Without government intervention, the operator maximizes profit, leading to optimal charger quantities:
$$ n_{f,O}^* = \frac{p\beta_f}{\eta_f}, \quad n_{s,O}^* = \frac{p\beta_s}{\eta_s} $$
The resulting demand and government net benefit are:
$$ d_O^* = a – \gamma p + p\left(\frac{\beta_f^2}{\eta_f} + \frac{\beta_s^2}{\eta_s}\right), \quad E_O^* = e \cdot d_O^* $$
This outcome shows a natural bias towards building more AC chargers due to their lower cost, potentially leading to a power structure misaligned with the needs of the electric vehicle car market.
2.2 Construction Subsidy: Uniform vs. Power-Differentiated
Uniform Per-Unit Subsidy (Strategy Z): The government provides a flat subsidy $c_n$ for each charger built, regardless of power. The optimal subsidy and outcomes are derived as:
$$ c_{n,Z}^* = \frac{(e-p)(\beta_s \eta_f + \beta_f \eta_s)}{2(\eta_f + \eta_s)} $$
$$ n_{f,Z}^* = \frac{p\beta_f}{\eta_f} + \frac{(e-p)(\beta_s \eta_f + \beta_f \eta_s)}{2\eta_f(\eta_f+\eta_s)}, \quad n_{s,Z}^* = \frac{p\beta_s}{\eta_s} + \frac{(e-p)(\beta_s \eta_f + \beta_f \eta_s)}{2\eta_s(\eta_f+\eta_s)} $$
$$ d_Z^* = a – \gamma p + \frac{(e+p)(\beta_s \eta_f + \beta_f \eta_s)^2}{4\eta_f\eta_s(\eta_f+\eta_s)} + \frac{p(\beta_f – \beta_s)^2}{\eta_f+\eta_s} $$
Power-Differentiated Subsidy (Strategy G): The government provides a subsidy $c_k$ per unit of power installed. This directly lowers the effective cost burden of high-power DC chargers. The optimal solutions are:
$$ c_{k,G}^* = \frac{(e-p)(k_s \beta_s \eta_f + k_f \beta_f \eta_s)}{2(k_s^2 \eta_f + k_f^2 \eta_s)} $$
$$ n_{f,G}^* = \frac{p\beta_f}{\eta_f} + \frac{k_f (e-p)(k_s \beta_s \eta_f + k_f \beta_f \eta_s)}{2\eta_f(k_s^2 \eta_f + k_f^2 \eta_s)}, \quad n_{s,G}^* = \frac{p\beta_s}{\eta_s} + \frac{k_s (e-p)(k_s \beta_s \eta_f + k_f \beta_f \eta_s)}{2\eta_s(k_s^2 \eta_f + k_f^2 \eta_s)} $$
$$ d_G^* = a – \gamma p + \frac{(e+p)(\beta_s k_s \eta_f + \beta_f k_f \eta_s)^2}{4\eta_f\eta_s(k_s^2 \eta_f + k_f^2 \eta_s)} + \frac{p(\beta_f k_s – \beta_s k_f)^2}{2(k_s^2 \eta_f + k_f^2 \eta_s)} $$
Proposition 1: For public areas with strong fast-charging demand ($\beta_f \gg \beta_s$), a power-differentiated construction subsidy (Strategy G) is more effective in promoting electric vehicle car adoption and social welfare. For residential areas where fast-charging preference is weak ($\beta_f \approx \beta_s$), a uniform per-unit construction subsidy (Strategy Z) is superior for expanding the electric vehicle car user base.
2.3 Operational Subsidy (Strategy Y)
Instead of subsidizing infrastructure build-out, the government provides a subsidy $m$ per unit of realized electric vehicle car demand (e.g., linked to charging volume). The operator’s effective revenue per electric vehicle car becomes $(p+m)$. The optimal operational subsidy is:
$$ m_Y^* = \frac{e-p}{2} – \frac{(a-\gamma p)\eta_f \eta_s}{2(\beta_s^2 \eta_f + \beta_f^2 \eta_s)} $$
The resulting demand under this optimal subsidy is:
$$ d_Y^* = \frac{1}{2}(a – \gamma p) + \frac{(e+p)(\beta_s^2 \eta_f + \beta_f^2 \eta_s)}{4\eta_f\eta_s} $$
A key finding is that the threshold for implementing an operational subsidy is higher than for construction subsidies. It requires the environmental benefit $e$ to be significantly greater than the service fee $p$. However, once this threshold is crossed, the operational subsidy can be highly effective, especially as consumer preference for fast charging ($\beta_f$) increases or infrastructure costs ($\eta_f, \eta_s$) decrease.
2.4 Hybrid Subsidy Strategy (Strategy GY)
This strategy combines the power-differentiated construction subsidy ($c_k$) and the operational subsidy ($m$). The optimal subsidy rates are:
$$ c_{k,GY}^* = \frac{(a-\gamma p)(k_s \beta_s \eta_f + k_f \beta_f \eta_s)}{2(k_s \beta_f – k_f \beta_s)^2} $$
$$ m_{GY}^* = \frac{e-p}{2} – \frac{(a-\gamma p)(k_s^2 \eta_f + k_f^2 \eta_s)}{2(k_s \beta_f – k_f \beta_s)^2} $$
Notably, the optimal charger quantities and final electric vehicle car demand under this hybrid strategy lead to the same demand level as the standalone optimal operational subsidy: $d_{GY}^* = d_Y^*$. However, the hybrid strategy achieves this demand level with a strictly higher net environmental benefit for the government than any standalone subsidy strategy, making it the most efficient approach from a public welfare perspective when the goal is to maximize both adoption and net benefit.
3. Numerical Simulations and Policy Insights
To validate the theoretical findings and explore the impact of key market evolutions, numerical simulations are conducted based on data from typical Chinese cities. The baseline parameters are summarized in Table 2.
| Parameter | Symbol | Baseline Value |
|---|---|---|
| Potential Demand | $a$ | 10 million vehicles/year |
| DC Charger Impact | $\beta_f$ | 15 vehicles/charger |
| AC Charger Impact | $\beta_s$ | 2 vehicles/charger |
| DC Charger Power | $k_f$ | 80 kW |
| AC Charger Power | $k_s$ | 20 kW |
| DC Cost Coefficient | $\eta_f$ | 3500 |
| AC Cost Coefficient | $\eta_s$ | 750 |
| Price Sensitivity | $\gamma$ | 0.3 |
| Service Fee | $p$ | 3200 CNY/vehicle/year |
| Environmental Benefit | $e$ | 20,000 CNY/vehicle/year |
The analysis focuses on three critical dynamic factors: the greenification level of the electric vehicle car industry (proxied by $e$), the strength of consumer fast-charging preference (proxied by $\beta_f$), and the reduction in DC charger costs (proxied by $\eta_f$).
3.1 Impact of Increasing Environmental Benefit ($e$)
As the per-vehicle environmental benefit rises from 10,000 to 30,000 CNY/year, all subsidy strategies improve in performance. The ranking of strategies, however, shifts dynamically:
- Electric Vehicle Car Promotion ($d$): For $e < 16,000$, the power-differentiated construction subsidy (G) is most effective. For $e > 16,000$, the operational (Y) and hybrid (GY) subsidies become dominant and provide identical demand uplift, significantly outperforming construction-only subsidies.
- Operator Profit ($\pi$): The operational subsidy (Y) consistently provides the highest profit increase for the operator, followed by the hybrid (GY) and then the construction (G) subsidies.
- Government Net Benefit ($E$): The hybrid subsidy (GY) is universally optimal. The second-best strategy transitions from the construction subsidy (G) to the operational subsidy (Y) as $e$ exceeds approximately 28,000.
This underscores that as the societal value of each electric vehicle car increases, the policy focus should shift from building infrastructure to stimulating its usage.
3.2 Impact of Strengthening Fast-Charging Preference ($\beta_f$)
As $\beta_f$ increases from 15 to 20, the advantage of usage-oriented subsidies (Y and GY) over the construction subsidy (G) in promoting electric vehicle car demand widens. The operational subsidy (Y) remains the most profitable strategy for the operator. The hybrid subsidy (GY) maintains its position as the strategy yielding the highest net environmental benefit, regardless of the change in $\beta_f$.
3.3 Impact of Decreasing DC Charger Cost ($\eta_f$)
Reducing $\eta_f$ from 4000 to 3000 enhances the performance of all strategies but does not alter their relative rankings. The operational (Y) and hybrid (GY) subsidies retain their lead in promoting electric vehicle car adoption, and their advantage over the construction subsidy (G) actually grows larger. This indicates that technological progress that lowers infrastructure costs amplifies the effectiveness of usage-based incentives.
| Policy Objective / Market Condition | Early Stage (Low $e$, High $\eta_f$) | Maturing Stage (High $e$, Low $\eta_f$, High $\beta_f$) |
|---|---|---|
| Maximize Electric Vehicle Car Adoption | Power-Differentiated Construction Subsidy (G) | Operational Subsidy (Y) / Hybrid Subsidy (GY) |
| Maximize Operator Profit | Operational Subsidy (Y) | Operational Subsidy (Y) |
| Maximize Government Net Benefit | Hybrid Subsidy (GY) | Hybrid Subsidy (GY) |
| Recommended Focus for Public Areas | Construction subsidy to build network coverage and fast-charging capability. | Shift subsidy weight from construction to operation; use hybrid schemes for efficiency. |
| Recommended Focus for Residential Areas | Uniform per-unit construction subsidy to achieve wide, basic coverage. | Maintain uniform construction subsidy to support mass electric vehicle car ownership. |
4. Conclusions and Policy Recommendations
The transition to electric vehicle car transportation is critically dependent on a well-planned and efficiently subsidized charging infrastructure ecosystem. This analysis provides a framework for designing dynamic and context-specific subsidy policies:
- Implement Differentiated Subsidies Based on Location and Use Case: In public areas and corridors with high fast-charging demand, power-differentiated construction subsidies are initially more effective for guiding a balanced DC/AC infrastructure mix. In residential areas, uniform per-unit construction subsidies are better suited for achieving widespread coverage to support the electric vehicle car owner base.
- Dynamically Transition from Construction to Operational Support: Policymakers must account for the evolving market. As the electric vehicle car industry’s greenification level rises (e.g., when the annual environmental benefit per vehicle exceeds 16,000 CNY), consumer fast-charging preference strengthens, and infrastructure costs fall, the optimal policy for public areas should progressively shift from construction-focused subsidies towards operational subsidies or hybrid strategies. This transition helps prevent inefficient overbuilding and encourages high utilization of the charging network.
- Prioritize Hybrid Strategies for Maximum Social Welfare: While standalone operational subsidies are powerful for boosting electric vehicle car adoption and operator profits, a hybrid strategy combining targeted construction support with operational incentives consistently yields the highest net environmental benefit for the government. This approach efficiently aligns public spending with long-term social gains.
- Establish Clear Subsidy Phase-Out Mechanisms: As the charging infrastructure industry moves from a rapid growth phase to a stage of high-quality development, governments should plan for a gradual reduction in the scale of broad construction subsidies. Concurrently, the strategic use of operational and hybrid subsidies can be strengthened to refine network efficiency, service quality, and interoperability, ensuring the sustainable development of the electric vehicle car ecosystem.
Future research could extend this model by incorporating competition among multiple charging operators, integrating the spatial dimension of infrastructure deployment, and conducting empirical validation with city-specific policy and market data to further refine these strategic insights.