The rapid global adoption of the electric vehicle car represents a pivotal shift in sustainable transportation. However, the development of a ubiquitous and reliable charging infrastructure remains a critical bottleneck. For electric vehicle car manufacturers, the decision to invest in building their own charging networks is complex, especially within competitive markets. This paper investigates the strategic investment decisions of competing electric vehicle car manufacturers regarding charging station deployment, explicitly accounting for the indirect network effects that link the value of an electric vehicle car to the availability of its compatible charging infrastructure. We develop a game-theoretic model to analyze how these effects, coupled with product quality differentiation and market competition, influence optimal pricing, infrastructure investment levels, and overall profitability for firms producing electric vehicle cars.
1. Introduction and Model Framework
The market for the electric vehicle car is characterized by significant indirect network effects. The utility a consumer derives from purchasing an electric vehicle car increases with the number of compatible charging stations available (the hardware side), and conversely, the incentive to build charging stations increases with the number of compatible electric vehicle cars on the road (the software side). This two-sided market dynamic creates strategic interdependence between electric vehicle car manufacturers.
We consider a market with two competing electric vehicle car manufacturers, Firm A and Firm B. Firm B produces a higher-quality electric vehicle car compared to Firm A. The quality differential is denoted by $\\theta > 0$. Consumers are uniformly distributed along a Hotelling line of unit length, with Firm A located at 0 and Firm B at 1. A consumer at location $x$ has the following utility functions:
$$u_A = v – p_A – t x + \\phi(n_A)$$
$$u_B = v + \\theta – p_B – t(1 – x) + \\phi(n_B)$$
where $v$ is the base valuation, $p_i$ is the price of firm $i$’s electric vehicle car, $t$ is the transportation cost parameter representing market competition intensity, and $\\phi(n_i)$ captures the indirect network benefit from the charging network size $n_i$ of firm $i$. We model this benefit as $\\phi(n_i) = e \\cdot n_i$, where $e > 0$ is the strength of the indirect network effect. The cost for a manufacturer to build $n_i$ charging stations is given by $C_i = \\frac{k}{2} n_i^2 + f_i$, where $k$ is a cost scaling parameter and $f_i$ is a fixed entry cost.
We analyze four pure-strategy scenarios based on the investment decisions of the two electric vehicle car manufacturers:
- Strategy NN: Neither firm invests in charging stations.
- Strategy NC: Only Firm B (the high-quality firm) invests.
- Strategy CN: Only Firm A (the low-quality firm) invests.
- Strategy CC: Both firms invest in their own charging networks.
Using backward induction, we solve for the subgame perfect Nash equilibrium in each scenario, determining optimal prices ($p_i^*$), optimal charging station deployment ($n_i^*$), market shares ($d_i^*$), and profits ($\\pi_i^*$).
2. Equilibrium Analysis and Key Propositions
The following table summarizes the key equilibrium outcomes under the four strategies, providing a basis for comparative analysis.
| Variable | Strategy NN | Strategy NC | Strategy CN | Strategy CC |
|---|---|---|---|---|
| $p_A^*$ | $t – \\frac{\\theta}{3}$ | $\frac{2t[3k(3t-\\theta)-e^2]}{18kt – e^2}$ | $\frac{6kt(3t-\\theta)}{18kt – e^2}$ | $t + \frac{3kt\\theta}{e^2 – 9kt}$ |
| $p_B^*$ | $t + \\frac{\\theta}{3}$ | $\frac{6kt(3t+\\theta)}{18kt – e^2}$ | $\frac{2t[3k(3t+\\theta)-e^2]}{18kt – e^2}$ | $t – \frac{3kt\\theta}{e^2 – 9kt}$ |
| $d_A^*$ | $\frac{1}{2} – \frac{\\theta}{6t}$ | $\frac{9kt – e^2 – 3k\\theta}{18kt – e^2}$ | $\frac{3k(3t-\\theta)}{18kt – e^2}$ | $\frac{9kt – e^2 – 3k\\theta}{2(9kt – e^2)}$ |
| $d_B^*$ | $\frac{1}{2} + \frac{\\theta}{6t}$ | $\frac{3k(3t+\\theta)}{18kt – e^2}$ | $\frac{9kt – e^2 + 3k\\theta}{18kt – e^2}$ | $\frac{9kt – e^2 + 3k\\theta}{2(9kt – e^2)}$ |
| $n_A^*$ | 0 | 0 | $\frac{e(3t-\\theta)}{18kt – e^2}$ | $\frac{e}{6}\left( \frac{1}{k} + \frac{3\\theta}{e^2 – 9kt} \right)$ |
| $n_B^*$ | 0 | $\frac{e(3t+\\theta)}{18kt – e^2}$ | 0 | $\frac{e}{6}\left( \frac{1}{k} – \frac{3\\theta}{e^2 – 9kt} \right)$ |
| $\\pi_A^*$ | $\frac{(3t-\\theta)^2}{18t}$ | $\frac{2t[3k(3t-\\theta)-e^2]^2}{(18kt-e^2)^2}$ | $\frac{k(3t-\\theta)^2}{18kt-e^2} – f_A$ | $\frac{(18kt-e^2)[e^2+(3k(\\theta-3t))^2]}{36k(e^2-9kt)^2} – f_A$ |
| $\\pi_B^*$ | $\frac{(3t+\\theta)^2}{18t}$ | $\frac{k(3t+\\theta)^2}{18kt-e^2} – f_B$ | $\frac{2t[3k(3t+\\theta)-e^2]^2}{(18kt-e^2)^2}$ | $\frac{(18kt-e^2)[e^2-(3k(\\theta-3t))^2]}{36k(e^2-9kt)^2} – f_B$ |
From these equilibrium results, we derive several important propositions that illuminate the strategic interactions in the electric vehicle car market.
Proposition 1 (Baseline without Investment). Under Strategy NN (no investment):
1. The high-quality electric vehicle car manufacturer (B) sets a higher price, achieves a larger market share, and earns higher profit than the low-quality one (A): $p_B^{NN} > p_A^{NN}$, $d_B^{NN} > d_A^{NN}$, $\\pi_B^{NN} > \\pi_A^{NN}$.
2. A larger quality gap $\\theta$ benefits Firm B ($\\partial p_B^{NN}/\\partial \\theta > 0$, $\\partial \\pi_B^{NN}/\\partial \\theta > 0$) but harms Firm A ($\\partial p_A^{NN}/\\partial \\theta < 0$, $\\partial \\pi_A^{NN}/\\partial \\theta < 0$).
3. Intense market competition (high $t$) allows both firms to increase prices and profits, as consumer loyalty increases.
Proposition 2 (Asymmetric Investment – Only High-Quality Firm Invests). Under Strategy NC:
1. The investing firm (B) can leverage the indirect network effect to potentially earn more than the non-investing firm (A), i.e., $\\pi_B^{NC} > \\pi_A^{NC}$, if its fixed cost $f_B$ is sufficiently low and the network effect $e$ is strong enough.
2. Stronger network effects ($e$) increase Firm B’s price, market share, and charging network size ($\\partial p_B^{NC}/\\partial e > 0$, $\\partial d_B^{NC}/\\partial e > 0$, $\\partial n_B^{NC}/\\partial e > 0$), while having the opposite effect on Firm A.
3. The network effect amplifies Firm B’s quality advantage.
Proposition 3 (Asymmetric Investment – Only Low-Quality Firm Invests). Under Strategy CN:
1. Investment by the low-quality electric vehicle car manufacturer can be a powerful tool to counteract its quality disadvantage. When network effects are moderate and fixed costs are low ($f_A$ is small), Firm A’s profit can surpass Firm B’s ($\\pi_A^{CN} > \\pi_B^{CN}$).
2. A stronger network effect $e$ directly benefits the investing Firm A, increasing its price, market share, and profit ($\\partial p_A^{CN}/\\partial e > 0$, $\\partial \\pi_A^{CN}/\\partial e > 0$), while harming the non-investing Firm B.
3. This strategy demonstrates how charging infrastructure investment can serve as a strategic equalizer for a lower-quality electric vehicle car brand.
Proposition 4 (Symmetric Investment). Under Strategy CC:
1. The high-quality firm (B) still commands a higher price, market share, and builds a larger charging network than the low-quality firm (A): $p_B^{CC} > p_A^{CC}$, $d_B^{CC} > d_A^{CC}$, $n_B^{CC} > n_A^{CC}$.
2. The impact of stronger network effects ($e$) on profits is nuanced. It always benefits the high-quality firm B ($\\partial \\pi_B^{CC}/\\partial e > 0$) but can hurt the low-quality firm A if the quality gap $\\theta$ is small ($\\partial \\pi_A^{CC}/\\partial e < 0$ under certain conditions). Intuitively, when products are similar, intensified network competition primarily benefits the firm with the initial quality edge.
3. The profit difference $\\pi_B^{CC} – \\pi_A^{CC}$ increases with the network effect strength $e$ and the fixed cost disparity $(f_B – f_A)$.
3. Strategic Equilibrium and Managerial Insights
Comparing profits across all four strategy profiles leads to the central equilibrium characterization for the electric vehicle car manufacturers.
Proposition 5 (Market Equilibrium). The Nash equilibrium of the investment game is determined by the fixed costs of investment ($f_A, f_B$) and the strength of the network effect ($e$).
1. No-Investment Equilibrium (NN): Occurs when both fixed costs are high $(f_A > \\bar{f}_A, f_B > \\bar{f}_B)$. Investment is too expensive for either electric vehicle car manufacturer.
2. Asymmetric Investment Equilibrium (NC or CN): Occurs when one firm’s fixed cost is low and the other’s is high. For instance, if $f_A$ is high and $f_B$ is low, only the high-quality electric vehicle car manufacturer (B) invests (Equilibrium NC).
3. Symmetric Investment Equilibrium (CC): Occurs when both fixed costs are sufficiently low $(f_A < \\bar{f}_A, f_B < \\bar{f}_B)$. The intense competition in both the electric vehicle car and charging network markets makes mutual investment the dominant strategy. The threshold fixed costs $\\bar{f}_A$ and $\\bar{f}_B$ are decreasing functions of the network effect strength $e$, meaning stronger network effects lower the barrier for investment by electric vehicle car manufacturers.
The following threshold functions characterize the equilibrium regions, where $F_1(e,t,\\theta,k)$ and $F_2(e,t,\\theta,k)$ are specific functions derived from profit comparisons:
$$\\bar{f}_A = F_1(e, t, \\theta, k), \\quad \\frac{\\partial \\bar{f}_A}{\\partial e} < 0$$
$$\\bar{f}_B = F_2(e, t, \\theta, k), \\quad \\frac{\\partial \\bar{f}_B}{\\partial e} < 0$$
These results yield critical managerial insights for executives in the electric vehicle car industry:
Insight 1: The Dual Role of Network Effects. While indirect network effects generally expand the total market for the electric vehicle car, they do not benefit all manufacturers equally. A stronger network effect ($e$) can paradoxically reduce profits for both firms if the quality differential ($\\theta$) is small, as it triggers a fierce and costly infrastructure war without significantly altering market shares.
Insight 2: Investment as a Strategic Weapon and Shield. For a low-quality electric vehicle car manufacturer, investing in charging stations (Strategy CN) can be an effective offensive strategy to erode the rival’s quality advantage and capture market share, provided the fixed costs are manageable. For a high-quality manufacturer, investment (Strategy NC) acts as a defensive strategy to solidify its premium position and exploit the network effect, but it must carefully weigh the substantial fixed costs against the incremental benefits.
Insight 3: The Free-Riding Dilemma. Under asymmetric strategies (NC or CN), the non-investing electric vehicle car manufacturer free-rides on the market expansion created by the investor’s charging network but suffers from a competitive disadvantage in product attractiveness. The investing firm must ensure its network’s quality and exclusivity benefits are not easily appropriated by competitors, possibly through proprietary connectors or software integration specific to its electric vehicle car models.
4. Extensions: Charging Compatibility and Heterogeneous Costs
The base model assumes proprietary, incompatible charging networks. In reality, partial compatibility (e.g., through adapters or industry standards) is emerging. We extend the model by introducing a compatibility parameter $\\beta \\in [0,1]$. When $\\beta=0$, networks are proprietary; when $\\beta=1$, they are fully compatible. A consumer of firm $i$’s electric vehicle car now gets network benefit $e(n_i + \\beta n_j)$.
Proposition 6 (Effect of Compatibility).
1. Increased compatibility ($\\beta$) typically benefits the firm with the smaller proprietary network (often the low-quality electric vehicle car manufacturer) by allowing its customers access to a larger combined network. It harms the firm with the larger proprietary network by diluting its competitive advantage.
2. Specifically, $\\partial \\pi_A^{GG} / \\partial \\beta > 0$ and $\\partial \\pi_B^{GG} / \\partial \\beta < 0$ under certain conditions, where $GG$ denotes both firms investing with compatibility.
3. High compatibility can reduce the incentive for individual electric vehicle car manufacturers to over-invest in infrastructure, potentially leading to a more efficient industry-wide outcome but also softening differentiation.
Furthermore, manufacturers may have heterogeneous capabilities in building charging stations. We modify the cost function to $C_i = \\frac{k_i}{2} n_i^2 + f_i$, where $k_A \\ne k_B$.
Proposition 7 (Heterogeneous Building Costs).
1. A decrease in a firm’s own cost parameter $k_i$ (higher efficiency) naturally increases its profit and incentive to invest.
2. Interestingly, a decrease in the rival’s cost parameter $k_j$ can sometimes benefit firm $i$. For example, in the HH scenario, $\\partial \\pi_A^{HH} / \\partial k_B > 0$. The intuition is that if the rival becomes much more efficient at building stations, it may expand the total network effect significantly, which firm A’s electric vehicle car customers can partially benefit from if some compatibility exists, and the intensified network competition may force the rival to lower its electric vehicle car price.
5. Conclusion
This analysis demonstrates that the decision for an electric vehicle car manufacturer to invest in charging infrastructure is a complex strategic maneuver deeply intertwined with product market positioning, competitive dynamics, and the powerful force of indirect network effects. Key findings indicate that:
- Indirect network effects are a double-edged sword. They can motivate infrastructure investment and grow the electric vehicle car pie but can also trigger profit-destroying arms races when competitors are closely matched.
- The optimal investment strategy for an electric vehicle car manufacturer is highly contingent on its quality position, its rival’s strategy, the fixed costs of network deployment, and the strength of network effects. There is no one-size-fits-all answer.
- Asymmetric equilibria, where only one electric vehicle car manufacturer invests, are common and can be stable, especially when fixed costs are significant. This mirrors observed market states where certain brands lead in fast-charging deployment.
- The move towards charging compatibility, while beneficial for consumers and overall electric vehicle car adoption, alters competitive dynamics by reducing the strategic value of an exclusive, proprietary network and can shift profits between manufacturers.
For policymakers aiming to accelerate electric vehicle car adoption, these results suggest that subsidies should be carefully designed. Broad subsidies for charging infrastructure that lower $f_i$ for all manufacturers may lead to a symmetric investment equilibrium (CC) which maximizes total charging availability but may not always maximize consumer welfare or industry profits due to potential overinvestment. Targeted subsidies or support for standardization that increases compatibility ($\\beta$) could be efficient alternatives to stimulate the market for the electric vehicle car. Ultimately, the evolution of the electric vehicle car charging ecosystem will be shaped by the strategic interactions analyzed here, as manufacturers balance the imperative to assure customers against the costs of building the hardware that makes the electric vehicle car a fully viable product.