As the global automotive industry shifts towards sustainability, electric vehicles (EVs) have emerged as a pivotal solution to reduce carbon emissions and dependence on fossil fuels. In China, the government has implemented aggressive policies, such as the “New Energy Vehicle Industry Development Plan (2021–2035)”, aiming for a 20% market penetration of new energy vehicles by 2025. Despite these efforts, range anxiety—stemming from limited driving range and inadequate charging infrastructure—remains a significant barrier to EV adoption. To address this, EV manufacturers are increasingly investing in charging infrastructure, either independently or through collaborations with third-party service operators. This article explores the joint investment strategies for EV pricing and charging infrastructure in a duopoly market, where manufacturers choose between self-building and cooperative building modes. By developing a non-cooperative-cooperative bi-form game model, we analyze optimal pricing, infrastructure investment levels, and profit distribution. Numerical simulations reveal how key parameters, such as cross-price sensitivity, infrastructure cost coefficients, and charging service fees, influence equilibrium strategies. The findings provide actionable insights for manufacturers and policymakers to foster a robust EV ecosystem in China.
The rapid growth of China’s electric vehicle market is driven by environmental concerns and government incentives, including subsidies and tax breaks. However, the lack of a comprehensive charging network hampers consumer confidence. EV manufacturers, such as Tesla and NIO, have adopted self-building strategies, while others, like BMW and Volkswagen, partner with third-party operators to share costs and risks. This study examines two scenarios: one where only one manufacturer self-builds charging infrastructure, and another where manufacturers adopt different modes—self-building and cooperative building. The non-cooperative-cooperative bi-form game model integrates competitive pricing decisions with collaborative infrastructure investments, using the Shapley value for fair profit allocation. Key parameters, including cross-price sensitivity ($b$), infrastructure cost coefficient ($\eta$), and charging service fees ($s_1$ and $s_2$), are analyzed to determine their impact on EV demand, infrastructure deployment, and profitability. The results highlight that price competition stimulates infrastructure investment, but high costs can deter collaboration. Effective management of charging service fees is crucial to avoid consumer dissatisfaction and ensure sustainable growth of China’s EV industry.
Problem Description and Model Framework
Consider a duopoly market for electric vehicles in China, where two manufacturers, $M_1$ and $M_2$, compete in pricing and charging infrastructure investment. Manufacturer $M_1$ adopts a self-building mode, determining its EV price $p_1$ and charging station quantity $n_1$. Manufacturer $M_2$ either does not invest in infrastructure or collaborates with a third-party service operator $R$ under a cost-sharing agreement, where $M_2$ sets its EV price $p_2$ and cost-sharing ratio $\lambda \in (0,1)$, while $R$ decides the charging station quantity $n_2$. The demand functions for EVs are based on linear models, incorporating price competition and infrastructure sensitivity. For instance, the demand for $M_1$’s EVs is $q_1 = a – p_1 + b p_2 + \rho (n_1 + n_2)$, and for $M_2$’s EVs is $q_2 = a – p_2 + b p_1 + \rho (n_1 + n_2)$, where $a > 0$ is the potential market size, $b \in (0,1)$ is the cross-price sensitivity coefficient, and $\rho > 0$ is the sensitivity to charging infrastructure. The total cost for building $n$ charging stations is $\frac{1}{2} \eta n^2$, with $\eta > 0$ representing the infrastructure cost coefficient.
Consumers choose between two types of charging stations: $A$ (built by $M_1$) and $B$ (built by $M_2$ and $R$), with utility functions $U_A = \theta – s_1 + \varepsilon_1$ and $U_B = \theta – s_2 + \varepsilon_2$, where $\theta > 0$ is the base utility, $s_1$ and $s_2$ are charging service fees, and $\varepsilon_1, \varepsilon_2$ are random preferences. Assuming $\varepsilon_1 \sim U(0,1)$ and $\varepsilon_2 = 1 – \varepsilon_1$, the market share for station $A$ is $\tau = \frac{s_1 – s_2 + 1}{2}$, and for station $B$ is $1 – \tau$. The actual charging demand is $h_A = k (q_1 + q_2) \tau$ and $h_B = k (q_1 + q_2) (1 – \tau)$, where $k$ is the lifetime charging volume per EV.
The profit functions for the manufacturers and operator are as follows. For $M_1$ in self-building mode: $$\pi_{M_1} = p_1 q_1 + s_1 h_A – \frac{\eta n_1^2}{2}.$$ For $M_2$ in cooperative mode: $$\pi_{M_2} = p_2 q_2 – \lambda \frac{\eta n_2^2}{2}.$$ For $R$: $$\pi_R = s_2 h_B – (1 – \lambda) \frac{\eta n_2^2}{2}.$$ The non-cooperative-cooperative bi-form game involves two stages: first, manufacturers engage in a Nash game over prices and infrastructure; second, $M_2$ and $R$ form a coalition to optimize $\lambda$ and $n_2$, with profits allocated via the Shapley value.
Model 1: Self-Building Mode Only
In this scenario, only manufacturer $M_1$ invests in charging infrastructure ($n_2 = 0$). The demand functions simplify to $q_1 = a – p_1 + b p_2 + \rho n_1$ and $q_2 = a – p_2 + b p_1 + \rho n_1$. All charging services are provided by $M_1$, generating additional revenue. The profit maximization problems are:
$$\max_{p_1, n_1} \pi_{M_1} = p_1 (a – p_1 + b p_2 + \rho n_1) + k s_1 (2a – (1-b)(p_1 + p_2) + 2\rho n_1) – \frac{\eta n_1^2}{2},$$
$$\max_{p_2} \pi_{M_2} = p_2 (a – p_2 + b p_1 + \rho n_1).$$
Solving the first-order conditions yields the Nash equilibrium. The optimal EV prices and infrastructure quantity are:
$$p_1^* = \frac{a(b+2)\eta + 2k s_1 [(b-1)\eta + (b+2)\rho^2]}{(b+2)[(2-b)\eta – \rho^2]},$$
$$p_2^* = \frac{a(b+2)\eta + k s_1 [3(b+1)\rho^2 + b(b-1)\eta]}{(b+2)[(2-b)\eta – \rho^2]},$$
$$n_1^* = \frac{\rho [a(b+2) + 2k s_1 (3 + b – b^2)]}{(b+2)[(2-b)\eta – \rho^2]}.$$
The total charging infrastructure is $N^* = n_1^*$, and the total EV demand is $Q^* = q_1^* + q_2^*$. The profits are derived by substituting these values into the profit functions. This model highlights how a single manufacturer’s infrastructure investment can influence market dynamics, but it may lead to suboptimal outcomes due to high costs and limited competition.
| Variable | Expression |
|---|---|
| $p_1^*$ | $\frac{a(b+2)\eta + 2k s_1 [(b-1)\eta + (b+2)\rho^2]}{(b+2)[(2-b)\eta – \rho^2]}$ |
| $p_2^*$ | $\frac{a(b+2)\eta + k s_1 [3(b+1)\rho^2 + b(b-1)\eta]}{(b+2)[(2-b)\eta – \rho^2]}$ |
| $n_1^*$ | $\frac{\rho [a(b+2) + 2k s_1 (3 + b – b^2)]}{(b+2)[(2-b)\eta – \rho^2]}$ |
| $Q^*$ | $\frac{2a(b+2)\eta + k s_1 [(b^3 – 3b + 2)\eta + (b+1)(b+5)\rho^2]}{(b+2)[(2-b)\eta – \rho^2]}$ |
Model 2: Self-Building and Cooperative Building Modes
In this model, manufacturer $M_1$ self-builds infrastructure, while $M_2$ collaborates with operator $R$. The non-cooperative-cooperative bi-form game is used to analyze this scenario. The game sequence is as follows: manufacturers $M_1$ and $M_2$ compete in a Nash game over $p_1$, $p_2$, and $n_1$; then, $M_2$ and $R$ form a coalition to optimize $\lambda$ and $n_2$, with profits allocated via the Shapley value. The payoff functions in the non-cooperative part are $f_{M_1} = \pi_{M_1}$ for $M_1$ and $f_{M_2} = \phi_{M_2}$ for $M_2$, where $\phi_{M_2}$ is the Shapley value allocation.
The coalition characteristic functions for the cooperative part are computed for all subsets of $\{M_2, R\}$. For example, the characteristic function for the grand coalition $\{M_2, R\}$ is:
$$v(\{M_2, R\}) = \max_{\lambda, n_2} \left[ p_2 (a – p_2 + b p_1 + \rho(n_1 + n_2)) – \lambda \frac{\eta n_2^2}{2} + s_2 h_B – (1-\lambda) \frac{\eta n_2^2}{2} \right].$$
Simplifying, the optimal infrastructure quantity for the coalition is $n_2^{**} = \frac{\rho [p_2 + k s_2 (s_1 – s_2 + 1)]}{\eta}$, and the characteristic function is:
$$v(\{M_2, R\}) = p_2 (a – p_2 + b p_1 + \rho n_1) + \frac{s_2 (s_1 – s_2 + 1)}{2} k (2a – (1-b)(p_1 + p_2) + 2\rho n_1) + \frac{\rho^2 [k s_2 (s_1 – s_2 + 1) + p_2]^2}{2\eta}.$$
The Shapley value allocations for $M_2$ and $R$ are:
$$\phi_{M_2} = p_2 (a – p_2 + b p_1 + \rho n_1) + \frac{\rho^2 p_2 [2 k s_2 (s_1 – s_2 + 1) + p_2]}{4\eta},$$
$$\phi_R = \frac{s_2 (s_1 – s_2 + 1)}{2} k (2a – (1-b)(p_1 + p_2) + 2\rho n_1) + \frac{\rho^2 \left[ (k s_2 (s_1 – s_2 + 1) + p_2)^2 + k^2 s_2^2 (s_1 – s_2 + 1)^2 \right]}{4\eta}.$$
In the non-cooperative part, solving the first-order conditions for $p_1$, $p_2$, and $n_1$ yields the Nash equilibrium. The optimal strategies are:
$$p_1^* = \frac{(b-1)(4\eta – \rho^2) – 2[2(2+b)\eta + \rho^2](a\eta + F_1 \rho^2) – F_2 (4+b)\eta \rho}{2[2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4]},$$
$$p_2^* = \frac{-4a(2+b)\eta^2 – 4F_1 \eta [b(b-1)\eta + \rho^2(2b+1)] – F_2 [2(b+1)\eta + \rho^2] \rho}{2[2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4]},$$
$$n_1^* = \frac{\rho \left\{ -a[2(b+2)\eta + \rho^2] + F_1 [2\eta(b(b-2)-2) + \rho^2(3b+1)] – \rho(b+4) F_2 \right\}}{2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4},$$
where $F_1 = k s_1 (s_2 – s_1 + 1)$ and $F_2 = 2\rho k s_2 (s_1 – s_2 + 1)$. The optimal cost-sharing ratio $\lambda^*$ is derived from $\pi_{M_2} = \phi_{M_2}$ at equilibrium.
| Variable | Expression |
|---|---|
| $p_1^*$ | $\frac{(b-1)(4\eta – \rho^2) – 2[2(2+b)\eta + \rho^2](a\eta + F_1 \rho^2) – F_2 (4+b)\eta \rho}{2[2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4]}$ |
| $p_2^*$ | $\frac{-4a(2+b)\eta^2 – 4F_1 \eta [b(b-1)\eta + \rho^2(2b+1)] – F_2 [2(b+1)\eta + \rho^2] \rho}{2[2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4]}$ |
| $n_1^*$ | $\frac{\rho \left\{ -a[2(b+2)\eta + \rho^2] + F_1 [2\eta(b(b-2)-2) + \rho^2(3b+1)] – \rho(b+4) F_2 \right\}}{2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4}$ |
| $n_2^*$ | $\frac{-2a\rho(b+2)\eta – 2F_1 \rho [b(b-1)\eta + \rho^2(2b+1)] + (b+2) F_2 [(b-2)\eta + \rho^2]}{2(b^2-4)\eta^2 + 2(3+2b)\eta \rho^2 + \rho^4}$ |
Numerical Analysis and Insights
To validate the theoretical models, numerical simulations are conducted using parameters based on the Chinese electric vehicle market: $a = 350000$, $\rho = 1.53$, $s_1 = 0.75$, $k = 75000$, $\eta = 20$, $s_2 = 0.5$, and $b = 0.4$. These values ensure feasibility and align with industry data. The analysis focuses on how cross-price sensitivity ($b$), infrastructure cost coefficient ($\eta$), and charging service fees ($s_2$) impact optimal strategies and profits.
Impact of Cross-Price Sensitivity
As $b$ increases, price competition intensifies, leading to higher EV prices and increased infrastructure investment. For example, in Model 1, $p_1^*$ and $p_2^*$ rise with $b$, as manufacturers leverage infrastructure to differentiate products and capture market share. The total infrastructure $N^*$ and EV demand $Q^*$ also increase, boosting profits for both manufacturers. In Model 2, the cooperative mode enables $M_2$ to achieve higher profits than in Model 1, especially at high $b$ values. However, $M_1$ benefits only when $b$ is sufficiently large, as competition drives mutual infrastructure expansion. The results underscore that price competition in China’s EV market can stimulate infrastructure deployment, but manufacturers must balance pricing and investment to maximize returns.
Key equations include the demand functions: $$q_1 = a – p_1 + b p_2 + \rho(n_1 + n_2),$$ $$q_2 = a – p_2 + b p_1 + \rho(n_1 + n_2).$$ The sensitivity of profits to $b$ is shown by the derivative $\frac{\partial \pi}{\partial b} > 0$ under equilibrium conditions.
Impact of Infrastructure Cost Coefficient
Higher infrastructure costs ($\eta$) reduce optimal EV prices, infrastructure quantity, and profits. In Model 1, $n_1^*$ decreases as $\eta$ increases, due to diminishing returns on investment. Similarly, in Model 2, both $n_1^*$ and $n_2^*$ decline, but the cooperative mode mitigates profit losses for $M_2$ through cost-sharing. When $\eta$ is low, both manufacturers benefit from collaborative infrastructure; however, at high $\eta$, $M_1$’s profits may suffer due to reduced charging revenue. This highlights the importance of government subsidies in China to lower infrastructure costs and encourage investment. For instance, subsidies covering 30% of infrastructure costs can make collaboration more viable, promoting EV adoption.
The cost function is $\frac{1}{2} \eta n^2$, and the optimal infrastructure satisfies $\frac{\partial \pi}{\partial n} = \rho p + \rho k s – \eta n = 0$.
Impact of Charging Service Fees
Charging service fees ($s_1$ and $s_2$) influence consumer behavior and collaboration viability. When $s_2 \leq s_1 + 1$, consumers use both charging stations, and cooperation between $M_2$ and $R$ is beneficial. If $s_2 > s_1 + 1$, consumers avoid station $B$, reducing infrastructure utilization and potentially breaking the coalition. Numerical results show that moderate $s_2$ values maximize profits, while high fees lead to consumer dissatisfaction and lost opportunities. In China’s EV market, regulating service fees is essential to maintain competition and ensure affordable charging access.
The utility functions $U_A = \theta – s_1 + \varepsilon_1$ and $U_B = \theta – s_2 + \varepsilon_2$ determine market shares, and the optimal $s_2$ balances revenue and demand.
| Parameter | Effect on EV Price | Effect on Infrastructure | Effect on Profit |
|---|---|---|---|
| Cross-price sensitivity ($b$) | Increases | Increases | Increases |
| Cost coefficient ($\eta$) | Decreases | Decreases | Decreases |
| Charging fee ($s_2$) | Mixed | Decreases if high | Decreases if high |
Conclusion and Managerial Implications
This study analyzes joint investment strategies for electric vehicle pricing and charging infrastructure in China’s duopoly market. The non-cooperative-cooperative bi-form game model provides a framework to optimize decisions under competition and collaboration. Key findings indicate that price competition drives infrastructure investment, but cost-sharing is crucial for sustainability. Manufacturers should adopt cooperative modes to reduce risks and enhance market coverage. Policymakers can support this through subsidies and fee regulations. For China’s EV industry, these strategies can accelerate adoption and achieve environmental goals. Future research could explore dynamic pricing, consumer heterogeneity, and multi-period models to refine these insights.
The proliferation of electric vehicles in China depends on robust charging networks. By aligning pricing and infrastructure investments, stakeholders can overcome range anxiety and foster a green transportation ecosystem. The models presented here offer a foundation for strategic decision-making in the rapidly evolving EV market.