In a duopolistic electric-vehicle market, manufacturers must decide not only how to price their electric vehicles but also whether and how to invest in charging infrastructure. Two commonly observed investment modes are autonomous construction, in which the vehicle manufacturer owns and operates the charging network, and cooperative construction, in which the manufacturer shares the cost of charging network deployment with a third-party service operator. We model both modes in a unified game-theoretic framework. In the autonomous mode, a manufacturer chooses the selling price of the electric vehicle and the number of charging piles at the same time. In the cooperative mode, a manufacturer forms a coalition with a third-party service operator, and the coalition optimizes the investment-cost-sharing ratio and the number of charging piles. Since the two manufacturers still compete in the electric-vehicle market, the problem contains both competition and cooperation; therefore we use a non-cooperative-cooperative bi-form game. Our results reveal several important managerial insights. First, stronger price competition stimulates manufacturers to invest in more charging infrastructure, which increases electric-vehicle demand and total profit. Second, as the charging-infrastructure investment cost coefficient increases, both the electric-vehicle price and the optimal number of charging piles decrease. Third, charging service fees play a governance role: excessively high service fees destroy cooperative incentives and reduce consumer acceptance of electric vehicles.
Keywords: electric vehicle; charging infrastructure investment; non-cooperative-cooperative bi-form game; Shapley value; duopoly; pricing strategy
1. Introduction
Electric vehicles are widely regarded as the future direction of the automotive industry because of their environmental benefits and lower energy costs. Governments around the world have introduced promotion plans for electric vehicles. For example, Chinese national plans call for new electric-vehicle sales to account for about 20% of all new-car sales by 2025. To accomplish such ambitious targets, policy makers have adopted subsidies for electric-vehicle purchases, tax exemptions, and charging-infrastructure construction grants.
A major barrier to electric-vehicle adoption is the so-called “range anxiety”. Consumers worry that the available charging network is insufficient to support daily travel. A dense and convenient charging network can alleviate range anxiety and raise the willingness to pay for electric vehicles. In practice, charging infrastructure can be built by the electric-vehicle manufacturer, by the government, by a power-grid company, or by a third-party charging-service operator. Many manufacturers have started to build proprietary charging networks. Tesla, NIO, and Xpeng, for instance, have chosen an autonomous construction mode, integrating vehicle production with charging-network operation. In sharp contrast, many other manufacturers prefer a cooperative mode, working with specialized third-party charging operators. GM, BMW, and Volkswagen, for instance, have formed alliances with charging-network operators.
These two modes differ in several fundamental ways. In the autonomous mode, the manufacturer bears the high upfront capital expenditure and operating costs of the charging network, but it also fully captures the charging profit. In the cooperative mode, the manufacturer shares investment risk with the third-party operator, but the charging revenue has to be split in a fair manner. A key unresolved issue is how these different modes affect the equilibrium pricing of electric vehicles and the equilibrium level of charging-infrastructure investment when two manufacturers compete.
Prior research has studied charging-infrastructure investment decisions under government subsidies, supply-chain coordination, and various market structures. However, most of those studies rely only on a non-cooperative game or only on a cooperative game. The current problem couples price competition in the electric-vehicle market with cost-sharing cooperation in the charging-infrastructure market. A pure non-cooperative game cannot explain how the coalition profit should be allocated, whereas a pure cooperative game cannot characterize the Nash competition between manufacturers. To overcome this limitation, we construct a non-cooperative-cooperative bi-form game. In the non-cooperative part, two electric-vehicle manufacturers maximize their own profits by choosing prices and, for the autonomous manufacturer, charging-pile quantities. In the cooperative part, the manufacturer that chooses the cooperative mode and the third-party service operator jointly maximize coalition profit. The Shapley value then provides a fair allocation of the coalition profit. The allocated profit becomes the payoff of the manufacturer in the non-cooperative game, and the Nash equilibrium of the entire integrated game is obtained.
This paper makes three main contributions. First, we compare the benchmark case in which only one manufacturer builds charging infrastructure with the case in which one manufacturer builds infrastructure autonomously and the other cooperates with a third-party operator. This comparison clarifies whether an electric-vehicle manufacturer should participate in charging-infrastructure investment. Second, we derive equilibrium closed-form expressions or equilibrium characterizations for prices, charging-pile quantities, market demand, and profits. Third, we conduct numerical experiments to examine the effects of the cross-price sensitivity coefficient, the investment-cost coefficient, and charging service fees. The rest of the paper is organized as follows. Section 2 presents the problem description and assumptions. Section 3 constructs and solves the two models. Section 4 reports numerical analysis and managerial implications. Section 5 concludes.
2. Problem Description and Assumptions
Consider a duopolistic electric-vehicle market in which two manufacturers, denoted by \(M_1\) and \(M_2\), sell differentiated electric vehicles. Manufacturer \(M_1\) always adopts the autonomous construction mode; it chooses its electric-vehicle price \(p_1\) and the number of self-built charging piles \(n_1\). Manufacturer \(M_2\) either does not invest in charging infrastructure or cooperates with a third-party service operator \(R\). In the cooperative mode, \(M_2\) chooses its electric-vehicle price \(p_2\) and the cost-sharing ratio \(\lambda \in [0,1]\) that determines how much of the operator’s construction cost is borne by \(M_2\). The third-party service operator \(R\) chooses the number of cooperative charging piles \(n_2\). The following assumptions are used throughout.
Assumption 1. The demand functions for the two manufacturers are
\[
q_1 = a – p_1 + b p_2 + \rho(n_1+n_2),
\]
\[
q_2 = a – p_2 + b p_1 + \rho(n_1+n_2),
\]
where \(a>0\) is the potential market size, \(b\in[0,1]\) is the cross-price sensitivity coefficient between the two electric vehicles, and \(\rho>0\) is the sensitivity of demand to charging-infrastructure quantity. When \(M_2\) does not invest, \(n_2=0\).
Assumption 2. The total cost of constructing \(n\) charging piles is \(\frac{1}{2}\eta n^2\), where \(\eta>0\) is the charging-infrastructure investment-cost coefficient. The quadratic form reflects scale diseconomies: as the number of charging piles grows, new piles are farther away from the electricity grid, so transmission and distribution costs increase rapidly.
Charging-service choice. When both types of charging infrastructure exist, consumers choose between charging infrastructure \(A\) built by \(M_1\) and charging infrastructure \(B\) built by the coalition of \(M_2\) and \(R\). Let \(s_1\) and \(s_2\) be the charging service fees charged by \(A\) and \(B\), respectively. Consumer utility for the two charging networks is
\[
U_A = \theta – s_1 + \varepsilon_1,
\]
\[
U_B = \theta – s_2 + \varepsilon_2,
\]
where \(\theta>0\) is the basic charging utility, \(\varepsilon_1\sim U(0,1)\) is the random preference for network \(A\), and \(\varepsilon_2=1-\varepsilon_1\) is the random preference for network \(B\). Let the indifferent point be the value at which \(U_A=U_B\). Then the market share of network \(B\) is \((s_1-s_2+1)/2\), and the market share of network \(A\) is \((s_2-s_1+1)/2\). Let \(k\) denote the total charging amount over the lifecycle of an electric vehicle. The actual charging-service demands for networks \(A\) and \(B\) are
\[
h_A = k(q_1+q_2)\frac{s_2-s_1+1}{2},
\]
\[
h_B = k(q_1+q_2)\frac{s_1-s_2+1}{2}.
\]
When the autonomous manufacturer is the only charging provider, all electric-vehicle owners use its charging network, so the charging-service demand is \(k(q_1+q_2)\).
3. Model 1: Only One Manufacturer Autonomously Builds Charging Infrastructure
In this benchmark model, \(M_1\) self-builds and operates the charging network; manufacturer \(M_2\) does not invest in charging infrastructure. Thus \(n_2=0\), and the demand functions reduce to
\[
q_1^1 = a-p_1+bp_2+\rho n_1,
\]
\[
q_2^1 = a-p_2+bp_1+\rho n_1.
\]
All charging revenue is captured by \(M_1\). The profit functions are
\[
\pi_{M_1}^{1}(p_1,p_2,n_1)=p_1(a-p_1+bp_2+\rho n_1)+k s_1(q_1^1+q_2^1)-\frac{1}{2}\eta n_1^2,
\]
\[
\pi_{M_2}^{1}(p_1,p_2,n_1)=p_2(a-p_2+bp_1+\rho n_1).
\]
Solving the first-order conditions yields the Nash equilibrium in Proposition 1. Let the superscript “1” indicate Model 1.
Proposition 1. In Model 1, the equilibrium electric-vehicle prices and the equilibrium number of charging piles are
\[
p_1^{1*}=\frac{a(b+2)\eta+2ks_1[(b-1)\eta+(b+2)\rho^2]}{(b+2)[(2-b)\eta-\rho^2]},
\]
\[
p_2^{1*}=\frac{a(b+2)\eta+ks_1[3(b+1)\rho^2+b\eta(b-1)]}{(b+2)[(2-b)\eta-\rho^2]},
\]
\[
n_1^{1*}=\frac{\rho[a(b+2)+2(3+b-b^2)ks_1]}{(b+2)[(2-b)\eta-\rho^2]}.
\]
The total charging infrastructure quantity in the market is \(N^{1*}=n_1^{1*}\). The equilibrium sales quantities are
\[
q_1^{1*}=\frac{a(b+2)\eta+ks_1[(b-1)(b^2-2)\eta+(b+1)(b+2)\rho^2]}{(b+2)[(2-b)\eta-\rho^2]},
\]
\[
q_2^{1*}=\frac{a(b+2)\eta+ks_1[b(b-1)\eta+3(b+1)\rho^2]}{(b+2)[(2-b)\eta-\rho^2]}.
\]
The total electric-vehicle sales in the market are \(Q^{1*}=q_1^{1*}+q_2^{1*}\). The first-order Hessian conditions \(2\eta-\rho^2>0\) and \(4\eta-\rho^2>0\) ensure that these solutions are interior maxima.
| Notation | Description |
|---|---|
| \(a\) | Potential market size for electric vehicles |
| \(b\) | Cross-price sensitivity coefficient between the two electric vehicles |
| \(\rho\) | Sensitivity of electric-vehicle demand to charging infrastructure quantity |
| \(\eta\) | Charging-infrastructure investment-cost coefficient |
| \(s_1, s_2\) | Charging service fees of network \(A\) and network \(B\) |
| \(k\) | Lifecycle charging demand of a single electric vehicle |
| \(\lambda\) | Cost-sharing ratio borne by \(M_2\) |
| \(n_1, n_2\) | Charging infrastructure quantities built by \(M_1\) and the \(M_2\)-\(R\) coalition |
| \(q_1, q_2\) | Market demand of electric vehicles for \(M_1\) and \(M_2\) |
4. Model 2: Autonomous Construction and Cooperative Construction
We now study the mixed case: manufacturer \(M_1\) still adopts autonomous construction, whereas manufacturer \(M_2\) cooperates with the third-party service operator \(R\). In this situation, the two manufacturers compete in electric-vehicle prices, but \(M_2\)’s payoff is no longer simply its own sales profit. Instead, its payoff is determined through a cooperative agreement with \(R\). The decision framework is a non-cooperative-cooperative bi-form game. The non-cooperative part captures the competitive interaction between \(M_1\) and \(M_2\). The cooperative part characterizes how \(M_2\) and \(R\) jointly choose the cost-sharing ratio \(\lambda\) and the number of cooperative charging piles \(n_2\).
4.1 Profit Functions in Model 2
The profit of the autonomous manufacturer \(M_1\) consists of electric-vehicle sales profit, charging-service profit from network \(A\), and the investment cost of \(n_1\):
\[
\pi_{M_1}^{2}(p_1,p_2,n_1,n_2)=p_1 q_1+\frac{k s_1(s_2-s_1+1)}{2}(q_1+q_2)-\frac{1}{2}\eta n_1^2.
\]
The profit of manufacturer \(M_2\) before Shapley allocation is its electric-vehicle sales revenue minus its share of the cooperative charging-infrastructure investment cost:
\[
\pi_{M_2}^{2}(p_1,p_2,n_1,n_2,\lambda)=p_2 q_2-\lambda \frac{\eta n_2^2}{2}.
\]
The profit of the third-party service operator \(R\) is the charging revenue from network \(B\) minus the remaining investment cost:
\[
\pi_R(p_1,p_2,n_1,n_2,\lambda)=\frac{k s_2(s_1-s_2+1)}{2}(q_1+q_2)-(1-\lambda)\frac{\eta n_2^2}{2}.
\]
4.2 Cooperative Stage and Coalition Characteristic Functions
For any given competitive situation \((p_1,p_2,n_1)\), the players in the cooperative game are \(M_2\) and \(R\). A coalition can be \(\emptyset\), \(\{M_2\}\), \(\{R\}\), or \(\{M_2,R\}\). Using the von Neumann characteristic-function approach for coalition games, the values of the non-empty coalitions are obtained as follows.
When \(M_2\) acts alone, it has no incentive to share any charging-infrastructure cost, so the coalition value is
\[
v_{(p_1,p_2,n_1)}({M_2})=p_2(a-p_2+bp_1+\rho n_1).
\]
When \(R\) acts alone, \(R\) optimally chooses \(n_2’= k\rho s_2(s_1-s_2+1)/\eta\), which gives
\[
v_{(p_1,p_2,n_1)}({R})=\frac{k s_2(s_1-s_2+1)}{2}\left(2a-(1-b)(p_1+p_2)+2\rho n_1\right)+\frac{k^2\rho^2s_2^2(s_1-s_2+1)^2}{2\eta}.
\]
When \(M_2\) and \(R\) form the grand coalition, the coalition’s optimal number of charging piles is \(n_2”=\rho[p_2+ks_2(s_1-s_2+1)]/\eta\), and the grand-coalition value is
\[
v_{(p_1,p_2,n_1)}({M_2,R})=p_2(a-p_2+bp_1+\rho n_1)+\frac{k s_2(s_1-s_2+1)}{2}\left(2a-(1-b)(p_1+p_2)+2\rho n_1\right)
+\frac{\rho^2[p_2+ks_2(s_1-s_2+1)]^2}{2\eta}.
\]
One can verify that the grand-coalition value is always at least as large as the sum of the two single-player values. Hence the game is superadditive and the two parties have incentives to cooperate.
4.3 Shapley-Value Allocation
The Shapley value provides a fair allocation of the coalition profit based on each player’s average marginal contribution. Applying the Shapley value to the cooperative game gives the allocated payoffs of \(M_2\) and \(R\):
\[
\phi_{M_2}(p_1,p_2,n_1)=p_2(a-p_2+bp_1+\rho n_1)+\frac{\rho^2 p_2[2ks_2(s_1-s_2+1)+p_2]}{4\eta},
\]
\[
\phi_R(p_1,p_2,n_1)=\frac{k s_2(s_1-s_2+1)}{2}(q_1+q_2)
+\frac{\rho^2\left\{[ks_2(s_1-s_2+1)+p_2]^2+k^2s_2^2(s_1-s_2+1)^2\right\}}{4\eta}.
\]
Because both Shapley values exceed the corresponding standalone coalition values, both \(M_2\) and \(R\) can obtain higher profits through cooperation than by acting singly. This profit surplus is what allows \(M_2\) to compete more aggressively in the non-cooperative stage.
4.4 Non-Cooperative Stage
In the non-cooperative stage, manufacturer \(M_1\)’s payoff is its profit function \(\pi_{M_1}^{2}\), while manufacturer \(M_2\)’s payoff is the Shapley allocation \(\phi_{M_2}\). Both manufacturers choose their strategies to maximize their payoffs. The first-order conditions defining the Nash equilibrium are:
\[
\frac{\partial \pi_{M_1}^{2}}{\partial p_1}=a-2p_1+bp_2+\rho(n_1+n_2)-\frac{(1-b)ks_1(s_2-s_1+1)}{2}=0,
\]
\[
\frac{\partial \pi_{M_1}^{2}}{\partial n_1}=\rho p_1+\rho ks_1(s_2-s_1+1)-\eta n_1=0,
\]
\[
\frac{\partial \phi_{M_2}}{\partial p_2}=a-2p_2+bp_1+\rho n_1+\frac{\rho^2[p_2+ks_2(s_1-s_2+1)]}{2\eta}=0.
\]
In addition, the cooperative number of charging piles must satisfy
\[
n_2=\frac{\rho[p_2+ks_2(s_1-s_2+1)]}{\eta}.
\]
Solving the system yields the equilibrium electric-vehicle prices \(p_1^{2*}, p_2^{2*}\), the number of self-built charging piles \(n_1^{2*}\), and the number of cooperative charging piles \(n_2^{2*}\). The total charging-infrastructure quantity is \(N^{2*}=n_1^{2*}+n_2^{2*}\). After substituting the equilibrium into the profit functions, the optimal profits of the two manufacturers are obtained. Finally, substituting \(p_1^{2*},p_2^{2*},n_1^{2*},n_2^{2*}\) into the cost-sharing equation yields the equilibrium cost-sharing ratio \(\lambda^*\) that makes \(M_2\)’s direct profit equal to its Shapley allocation.
5. Numerical Analysis and Managerial Implications
Because the full analytical expressions in Model 2 are complicated, we conduct numerical experiments to derive intuitive managerial insights. The representative parameter values used in the baseline calibration are \(a=350000\), \(\rho=1.73\), \(k=75000\), \(\eta=20\), \(b=0.4\), \(s_1=0.75\), and \(s_2\) is varied in the relevant range. These parameters satisfy the second-order conditions of both models. We examine the impact of the cross-price sensitivity coefficient \(b\), the charging-infrastructure investment-cost coefficient \(\eta\), and the charging service fees on the equilibrium outcomes.
5.1 Effect of Cross-Price Sensitivity Coefficient \(b\)
The equilibrium electric-vehicle selling prices, charging infrastructures, market demands, and profits all respond positively to an increase in \(b\). As \(b\) rises, competition between the two electric-vehicle manufacturers becomes stronger. A higher level of competition motivates each manufacturer to deploy additional charging piles because a larger charging network raises consumers’ willingness to pay and, therefore, shifts the demand outward. The increasing marginal profit from electric-vehicle sales creates a positive feedback loop: higher sales revenue funds more charging investment, and more charging infrastructure attracts more buyers. This mechanism explains why stronger product-market competition can simultaneously raise electric-vehicle prices and total demand.
| Variable | Model 1 direction as \(b\) increases | Model 2 direction as \(b\) increases |
|---|---|---|
| Electric-vehicle price \(p_i^j\) | Increasing | Increasing |
| Charging infrastructure \(N^j\) | Increasing | Increasing |
| Electric-vehicle demand \(Q^j\) | Increasing | Increasing |
| Manufacturer profit \(\pi_{M_i}^j\) | Increasing | Increasing |
Comparing Model 1 with Model 2 shows that charging-infrastructure investment by both manufacturers increases the total market charging capacity and total electric-vehicle penetration. However, the autonomous manufacturer \(M_1\) is more sensitive to price competition because it bears the full burden of constructing its charging network. The price curve of \(M_1\) is steeper than that of \(M_2\), implying that \(M_1\) needs to manage both market demand and charging-capacity utilization carefully. When the degree of product competition is low, \(M_1\) may be worse off if \(M_2\) begins to invest in charging infrastructure, because \(M_2\)’s network enters the charging-service market and captures some of the charging profit. Only when the cross-price sensitivity coefficient is sufficiently large does \(M_1\) benefit from \(M_2\)’s charging investment, because the overall expansion of the charging market then stimulates enough new electric-vehicle demand to compensate for the loss of charging exclusivity.
5.2 Effect of the Charging-Infrastructure Cost Coefficient \(\eta\)
As \(\eta\) increases, the cost of building charging piles rises. The numerical results show that both the electric-vehicle price and the optimal charging-infrastructure quantity decrease with \(\eta\). The intuition is straightforward: when building a charging pile becomes more expensive, manufacturers reduce their investment in charging infrastructure. The resulting reduction in charging-network density increases consumers’ range anxiety, which forces manufacturers to lower prices in an attempt to stimulate electric-vehicle demand. Nevertheless, the lower charging capability and the price reduction jointly compress profit margins, so total manufacturer profits decline as \(\eta\) increases.
| Variable | Model 1 direction as \(\eta\) increases | Model 2 direction as \(\eta\) increases |
|---|---|---|
| Electric-vehicle price | Decreasing | Decreasing |
| Charging infrastructure quantity | Decreasing | Decreasing |
| Electric-vehicle demand | Decreasing | Decreasing |
| Manufacturer profit | Decreasing | Decreasing |
Policy implications of this result are strong. Since high investment-cost coefficients hinder charging-network deployment, government intervention can play a major role. Investment subsidies reduce the effective \(\eta\) faced by manufacturers and thereby encourage larger charging networks. Such subsidies increase electric-vehicle demand and manufacturer profitability simultaneously, producing a win-win outcome for both the automotive and charging industries.
The comparison of the two models reveals that when \(\eta\) is low, the total charging-infrastructure level and total electric-vehicle demand are higher in Model 2. The gap between Model 1 and Model 2 narrows as \(\eta\) increases. At very high values of \(\eta\), the benefit of a second charging-network investor is small because neither party wants to build many charging piles. It is also observed that the profit of the autonomous manufacturer remains above that of the cooperative manufacturer. As \(\eta\) grows, the profit gap widens. Thus, autonomous construction becomes a stronger source of differentiation in times of high infrastructure costs, whereas low infrastructure costs make cooperative construction more attractive.
5.3 Effect of Charging Service Fees
The charging service fee \(s_2\) charged by the cooperative charging network is of strategic importance. Since \(M_1\)’s charging network charges \(s_1\), the relationship between \(s_1\) and \(s_2\) determines whether consumers are willing to use both networks or only one.
Three regimes can be identified from the model.
| Condition on \(s_2\) | Behavior | Managerial outcome |
|---|---|---|
| \(0 \le s_2 \le s_1+1\) | Both networks serve consumers; cooperative charging piles are profitable | Manufacturer \(M_2\) benefits from cooperation; total electric-vehicle sales and profits increase with \(s_2\) |
| \(s_1+1 < s_2 \le \frac{s_1+1}{2}+\sqrt{\frac{(s_1+1)^2}{4}+\frac{p_2}{k}}\) | Consumers do not choose the high-priced cooperative network; but cooperative charging piles may still be built due to cost sharing | Potential waste of resources; \(M_2\)’s profit declines as \(s_2\) rises |
| \(s_2 > \frac{s_1+1}{2}+\sqrt{\frac{(s_1+1)^2}{4}+\frac{p_2}{k}}\) | No cooperative charging piles are built | No incentive for cooperation; high service fees damage the charging-market ecosystem |
When the two charging service fees are in a reasonable range, effective price competition in the charging service market benefits the whole electric-vehicle industry. A lower fee relative to a competitor allows a manufacturer to attract not only more electric-vehicle buyers but also loyal charging customers. On the other hand, an excessively high service fee may cause consumers to avoid that charging network, reducing utilization rates and eventually collapsing the cooperation agreement. Service-fee regulation therefore matters. Policy makers should monitor charging fees to ensure that they remain within a range that preserves cooperative incentives and consumer acceptance of electric vehicles.
6. Conclusion and Managerial Insights
In this article, we have studied electric-vehicle pricing and charging-infrastructure joint investment strategies in a duopolistic market. Two scenarios were examined. In the first scenario, only one electric-vehicle manufacturer autonomously builds the charging network. In the second scenario, one manufacturer builds its own network while the other cooperates with a third-party service operator. A non-cooperative-cooperative bi-form game was proposed for the second scenario. The non-cooperative part captures price competition between manufacturers, while the cooperative part solves the cost-sharing and profit-allocation problem between the manufacturer and the third-party operator through the Shapley value.
Our analysis yields several important conclusions.
(1) Competition can be a positive force. Price competition among electric-vehicle manufacturers stimulates charging-infrastructure deployment, which in turn increases consumer willingness to purchase electric vehicles. Manufacturers’ profits rise as the cross-price sensitivity coefficient increases. The autonomous manufacturer, which carries a higher construction cost, is more sensitive to price competition and should coordinate its selling price with charging capacity utilization. The cooperative manufacturer can benefit substantially from the charging network, especially when product-market competition is intense.
(2) Charging-infrastructure costs determine whether participation is profitable. Participating in charging infrastructure construction is essential for the widespread adoption of electric vehicles. However, if infrastructure investment costs are low and convenient, both manufacturers can benefit from a jointly supplied charging network. When infrastructure costs are high, government subsidies can lower the effective cost coefficient and encourage the construction of charging facilities. Autonomous construction and cooperative construction are not universally good or bad; their attractiveness depends on investment-cost levels and market competitive intensity.
(3) Charging service fees play a governance role. If charging service fees are set at excessively high levels, they reduce consumer acceptance of electric vehicles, reduce utilization rates of charging piles, and undermine cooperation between manufacturers and operators. In contrast, competitive charging service fees stimulate the entire electric-vehicle ecosystem and help both manufacturers and third-party operators.
Future research can extend this bi-form game framework to examine subsidy policies targeted at electric-vehicle consumers or charging operators, multiple investment modes, and partial cooperation between direct competitors. Such extensions would further inform the design of sustainable electric-vehicle markets.
Note: The formulas and numerical results reported in this article are based on the model and analysis described above.