The rapid expansion of the new energy vehicle industry, particularly the proliferation of EV cars, has become a focal point for sustainable development and technological advancement globally. As a researcher in this field, I aim to explore the intricate dynamics among government entities, enterprises, and consumers in fostering the growth of EV cars through an evolutionary game theory framework. The development of EV cars hinges on the synergistic interactions of these three key stakeholders, where government policies, corporate innovation, and consumer adoption collectively shape the industry’s trajectory. In this analysis, I construct a tripartite evolutionary game model to dissect the strategic decisions, stability conditions, and evolutionary pathways that underpin the collaborative development of EV cars. By integrating numerical simulations and mathematical formulations, I delve into how variables such as subsidies, innovation success probabilities, and market demands influence the long-term evolution of EV cars. This approach not only highlights the critical role of EV cars in reducing carbon emissions and enhancing energy efficiency but also provides actionable insights for policymakers and industry players to navigate the complexities of this rapidly evolving sector.
The significance of EV cars extends beyond environmental benefits; they represent a paradigm shift in transportation, driven by advancements in battery technology, smart infrastructure, and consumer preferences. However, the widespread adoption of EV cars faces challenges, including high initial costs, technological uncertainties, and behavioral barriers. To address these, I model the interactions as an evolutionary game, where each party—government, enterprises, and consumers—adjusts their strategies over time based on perceived payoffs. The government can choose to support EV cars through subsidies and regulations or remain passive; enterprises decide between innovating in EV car production or sticking to conventional vehicles; and consumers opt to purchase EV cars or traditional alternatives. This dynamic interplay is captured through replication dynamics equations, stability analysis, and simulations, emphasizing how EV cars can transition from policy-driven initiatives to market-driven phenomena.
In the following sections, I detail the model assumptions, derive the mathematical foundations, and present simulation results to illustrate the evolutionary trends. Key parameters, such as subsidy levels (S), innovation success probability (p), and consumer demand, are varied to assess their impact on the strategic choices surrounding EV cars. Tables and equations summarize the payoffs and dynamics, while numerical analyses reveal the conditions under which EV cars achieve sustainable growth. The insertion of a visual aid, though not described in detail, provides a contextual reference for the discussion. Ultimately, this study underscores that the success of EV cars relies on a balanced policy mix, robust market incentives, and adaptive consumer behavior, all of which are essential for overcoming inefficiencies and fostering a resilient EV car ecosystem.
Model Assumptions and Framework
To analyze the collaborative development of EV cars, I consider a tripartite evolutionary game involving the government (G), enterprises (A), and consumers (B). Each actor is assumed to be boundedly rational, making decisions that maximize their individual benefits over time. The strategy sets for each party are defined as follows: the government chooses between “Support” and “Not Support” for EV cars; enterprises select “Innovate” or “Not Innovate” in EV car production; and consumers decide to “Purchase” or “Not Purchase” EV cars. Let (x) denote the probability of government support, (y) the probability of enterprise innovation, and (z) the probability of consumer purchase, where (x, y, z \in [0, 1]).
The payoffs for each strategy combination are influenced by costs, subsidies, and expected returns related to EV cars. For instance, when the government supports EV cars, it incurs a supervision cost (C_g) and provides a total subsidy (S), allocated between enterprises and consumers with coefficients (\phi) and (1 – \phi), respectively. Enterprises receive additional tax incentives (t) for innovation. If enterprises innovate in EV cars, they bear an additional cost (A_e) but gain potential revenues (R_2) upon success, with a probability (p). Conversely, if they do not innovate, they might face penalties (A_l) for misusing subsidies. Consumers incur a cost (B_e) when purchasing EV cars but derive benefits (R_4), while opting for traditional vehicles yields (R_5). The social benefits for the government from promoting EV cars include environmental gains and technological spillovers, denoted as (R_1).
Based on these assumptions, the payoff matrix for the three parties is constructed as shown in Table 1. This matrix encapsulates the interactions and serves as the foundation for deriving the replication dynamics equations, which describe how strategies evolve over time in response to payoffs.
| Strategy Combination | Government Payoff | Enterprise Payoff | Consumer Payoff |
|---|---|---|---|
| Government: Support (x), Enterprise: Innovate (y), Consumer: Purchase (z) | $$pR_1 – S – C_g – t$$ | $$pR_2 + \phi S + t – A_e$$ | $$pR_4 – pB_e + (1 – \phi)S$$ |
| Government: Support (x), Enterprise: Innovate (y), Consumer: Not Purchase (1-z) | $$pR_1 – \phi S – C_g – t$$ | $$\phi S + t – A_e$$ | 0 |
| Government: Support (x), Enterprise: Not Innovate (1-y), Consumer: Purchase (z) | $$-\phi S – C_g$$ | $$R_3 + \phi S – A_l$$ | 0 |
| Government: Support (x), Enterprise: Not Innovate (1-y), Consumer: Not Purchase (1-z) | $$-\phi S – C_g$$ | $$R_3 + \phi S – A_l$$ | $$R_5$$ |
| Government: Not Support (1-x), Enterprise: Innovate (y), Consumer: Purchase (z) | $$pR_1$$ | $$pR_2 – A_e$$ | $$pR_4 – pB_e$$ |
| Government: Not Support (1-x), Enterprise: Innovate (y), Consumer: Not Purchase (1-z) | $$pR_1$$ | $$-A_e$$ | 0 |
| Government: Not Support (1-x), Enterprise: Not Innovate (1-y), Consumer: Purchase (z) | 0 | $$R_3$$ | 0 |
| Government: Not Support (1-x), Enterprise: Not Innovate (1-y), Consumer: Not Purchase (1-z) | 0 | $$R_3$$ | $$R_5$$ |
The replication dynamics equations are derived from this payoff matrix. For the government, the expected payoff for supporting EV cars, (R_x), and not supporting, (R_{1-x}), are calculated as follows:
$$R_x = yz[pR_1 – S – C_g] + y(1-z)(pR_1 – \phi S – C_g) + (1-y)z(-\phi S – C_g)$$
$$R_{1-x} = yz(pR_1) + y(1-z)(pR_1)$$
The average expected payoff for the government is:
$$\bar{R}_x = xR_x + (1-x)R_{1-x}$$
Thus, the replication dynamic equation for the government’s strategy is:
$$F(x) = \frac{dx}{dt} = x(R_x – \bar{R}_x) = x(1-x)[yz(\phi – 1)S – yt – \phi S – C_g]$$
Similarly, for enterprises, the expected payoffs for innovating (R_y) and not innovating (R_{1-y}) in EV cars are:
$$R_y = xz(pR_2 + \phi S + t – A_e) + x(1-z)(\phi S + t – A_e) + (1-x)z(pR_2 – A_e) + (1-x)(1-z)(-A_e)$$
$$R_{1-y} = xz(R_3 + \phi S – A_l) + x(1-z)(R_3 + \phi S – A_l) + (1-x)zR_3 + (1-x)(1-z)R_3$$
The average expected payoff for enterprises is:
$$\bar{R}_y = yR_y + (1-y)R_{1-y}$$
The replication dynamic equation for enterprises is:
$$F(y) = \frac{dy}{dt} = y(R_y – \bar{R}_y) = y(1-y)[x(t + A_l) + zpR_2 – A_e – R_3]$$
For consumers, the expected payoffs for purchasing (R_z) and not purchasing (R_{1-z}) EV cars are:
$$R_z = xy[pR_4 + (1-\phi)S – pB_e] + (1-x)y(pR_4 – pB_e)$$
$$R_{1-z} = x(1-y)R_5 + (1-x)(1-y)R_5$$
The average expected payoff for consumers is:
$$\bar{R}_z = zR_z + (1-z)R_{1-z}$$
The replication dynamic equation for consumers is:
$$F(z) = \frac{dz}{dt} = z(R_z – \bar{R}_z) = z(1-z)[xy(1-\phi)S + y(pR_4 – pB_e + R_5) – R_5]$$
These equations form the basis of the evolutionary game analysis, allowing us to examine how strategies evolve over time and identify stable states where EV cars thrive.
Stability Analysis of Equilibrium Points
To determine the stability of the system, I solve the replication dynamics equations by setting (F(x) = 0), (F(y) = 0), and (F(z) = 0). This yields eight potential equilibrium points: (E_1(0,0,0)), (E_2(1,0,0)), (E_3(0,1,0)), (E_4(0,0,1)), (E_5(1,1,0)), (E_6(1,0,1)), (E_7(0,1,1)), and (E_8(1,1,1)). The stability of each point is assessed using the Jacobian matrix, which is derived from the partial derivatives of the replication dynamics equations. The Jacobian matrix (J) is defined as:
$$
J = \begin{bmatrix}
\frac{\partial F(x)}{\partial x} & \frac{\partial F(x)}{\partial y} & \frac{\partial F(x)}{\partial z} \\
\frac{\partial F(y)}{\partial x} & \frac{\partial F(y)}{\partial y} & \frac{\partial F(y)}{\partial z} \\
\frac{\partial F(z)}{\partial x} & \frac{\partial F(z)}{\partial y} & \frac{\partial F(z)}{\partial z}
\end{bmatrix}
$$
Where the partial derivatives are computed as follows:
$$\frac{\partial F(x)}{\partial x} = (1-2x)[yz(\phi – 1)S – yt – \phi S – C_g]$$
$$\frac{\partial F(x)}{\partial y} = x(1-x)[z(\phi – 1)S – t]$$
$$\frac{\partial F(x)}{\partial z} = x(1-x)y(\phi – 1)S$$
$$\frac{\partial F(y)}{\partial x} = y(1-y)(t + A_l)$$
$$\frac{\partial F(y)}{\partial y} = (1-2y)[x(t + A_l) + zpR_2 – A_e – R_3]$$
$$\frac{\partial F(y)}{\partial z} = y(1-y)pR_2$$
$$\frac{\partial F(z)}{\partial x} = z(1-z)y(1-\phi)S$$
$$\frac{\partial F(z)}{\partial y} = z(1-z)[x(1-\phi)S + (pR_4 – pB_e + R_5)]$$
$$\frac{\partial F(z)}{\partial z} = (1-2z)[xy(1-\phi)S + y(pR_4 – pB_e + R_5) – R_5]$$
By substituting each equilibrium point into the Jacobian matrix and calculating the eigenvalues, I apply Lyapunov’s indirect method: if all eigenvalues have negative real parts, the point is asymptotically stable. The analysis reveals that (E_1(0,0,0)) and (E_7(0,1,1)) are stable equilibrium points. This indicates that in the absence of government support, the system can converge to a state where enterprises do not innovate in EV cars and consumers do not purchase them (E_1), or where enterprises innovate and consumers purchase EV cars without government intervention (E_7). The latter suggests that EV cars can become self-sustaining through market forces alone, emphasizing the importance of consumer demand and enterprise innovation.
For instance, at (E_1(0,0,0)), the eigenvalues are (-\phi S – C_g), (-A_e – R_3), and (-R_5), all negative under typical parameter assumptions, confirming stability. At (E_7(0,1,1)), the eigenvalues are (-p(R_4 – B_e)), (-pR_2 + A_e + R_3), and (-S – C_g – t), which are negative when innovation benefits outweigh costs. This stability analysis underscores that the evolution of EV cars is highly sensitive to parameters like subsidies, innovation costs, and consumer preferences, which I explore further through numerical simulations.
Numerical Simulation and Parameter Analysis
To visualize the evolutionary trajectories and the impact of key parameters on EV cars, I conduct numerical simulations using MATLAB. The initial parameter values are set based on empirical data and theoretical considerations, as summarized in Table 2. These values represent a baseline scenario where the probability of enterprise innovation success (p) is moderate, and costs and benefits are balanced to reflect real-world conditions in the EV car industry.
| Parameter | Description | Value |
|---|---|---|
| (p) | Probability of innovation success in EV cars | 0.3 |
| (A_e) | Additional cost for enterprises to innovate in EV cars | 80 |
| (A_l) | Penalty for enterprises misusing subsidies | 40 |
| (\phi) | Proportion of subsidy allocated to enterprises | 0.8 |
| (C_g) | Government supervision cost for supporting EV cars | 20 |
| (S) | Total government subsidy for EV cars | 200 |
| (B_e) | Consumer cost for purchasing EV cars | 5 |
| (R_2) | Enterprise revenue from innovating in EV cars | 500 |
| (R_3) | Enterprise revenue from not innovating (traditional vehicles) | 50 |
| (R_4) | Consumer benefit from purchasing EV cars | 10 |
| (R_5) | Consumer benefit from not purchasing EV cars | 5 |
| (t) | Tax incentive for enterprises innovating in EV cars | 50 |
Using these parameters, I simulate the replication dynamics over 100 iterations with initial strategy probabilities (x = 0.5), (y = 0.5), and (z = 0.5). The results, plotted in Figure 1, show that the system converges to either (E_1(0,0,0)) or (E_7(0,1,1)), depending on parameter adjustments. For example, when (A_e) and (R_3) increase, indicating higher innovation costs or higher returns from traditional vehicles, the system tends toward (E_1), where EV cars are not adopted. Conversely, when (p) and (R_2) increase, reflecting higher innovation success or greater revenues from EV cars, the system moves to (E_7), where EV cars flourish without government intervention.
To delve deeper, I analyze the effect of government subsidy (S) on strategy evolution. Holding other parameters constant, I vary (S) from 100 to 2000. As shown in Figure 2, higher subsidies slow the government’s convergence to support EV cars, but eventually, it always chooses support. This diminishing marginal effect highlights that subsidies are effective but not sufficient alone for promoting EV cars. For enterprises, the impact of (S) depends on the revenue (R_2) from EV cars. When (R_2) is low (e.g., 100), enterprises are reluctant to innovate despite subsidies, as seen in Figure 3a, where innovation probability (y) decreases over time. In contrast, when (R_2) is high (e.g., 500), enterprises rapidly adopt innovation, and subsidies have minimal long-term influence (Figure 3b). This underscores that market-driven profits are the primary driver for EV car innovation.
Similarly, consumer behavior is significantly affected by subsidies. Figure 4 illustrates that as (S) increases, the probability of purchasing EV cars (z) rises, but only after a threshold is reached. For instance, at (S = 100), consumers predominantly avoid EV cars, whereas at (S = 2000), they shift toward adoption. This threshold effect emphasizes the need for substantial incentives to overcome initial resistance to EV cars.
Next, I examine the role of innovation success probability (p). Figure 5 demonstrates that (p) has a strong impact on enterprise decisions: when (p) exceeds 0.4, enterprises consistently innovate in EV cars, whereas lower values lead to stagnation. The government’s strategy is less sensitive to (p), as it primarily responds to broader social benefits. This suggests that policies aimed at increasing (p)—such as research grants or technical support—can be more effective than subsidies in fostering EV cars.
Finally, I consider the penalty for misuse of subsidies (A_l). As depicted in Figure 6, higher penalties (A_l) encourage enterprises to innovate, especially when (R_2) is low. In high-revenue scenarios, penalties have a modest effect, but in low-revenue conditions, they prevent opportunistic behavior and ensure that subsidies are directed toward EV car development. This reinforces the importance of regulatory mechanisms in complementing financial incentives for EV cars.
Conclusion and Policy Implications
In summary, this evolutionary game analysis reveals that the development of EV cars is a complex process influenced by the interplay of government policies, enterprise innovation, and consumer adoption. The simulations confirm that subsidies play a crucial role in the short term by incentivizing government support and consumer purchases of EV cars. However, in the long run, enterprises’ decisions to innovate in EV cars are driven primarily by expected market revenues (R_2) and innovation success probabilities (p), rather than external subsidies. Consumers, on the other hand, respond positively to subsidies but only beyond a certain threshold, indicating that initial market barriers for EV cars can be overcome with adequate financial incentives.
The stability analysis identifies two key equilibria: one where EV cars fail to gain traction without government intervention, and another where they thrive autonomously through market forces. This transition highlights the potential for EV cars to evolve from policy-dependent to market-driven products, provided that innovation risks are mitigated and consumer acceptance is cultivated. The numerical simulations further emphasize that a combination of strategies—such as targeted subsidies, robust regulatory penalties, and efforts to enhance innovation success—is essential for sustainable growth of EV cars.
Based on these findings, I propose several policy recommendations to accelerate the adoption of EV cars. First, governments should phase subsidies strategically, focusing on early-stage support while gradually shifting toward market-based mechanisms. For instance, initial subsidies could be designed as matching grants to leverage private investment in EV car research and development. Second, policies must address innovation risks by funding collaborative research platforms and standardizing technologies for EV cars, thereby increasing the success probability (p). Third, regulatory frameworks should include strict penalties for subsidy misuse to ensure that funds are allocated efficiently to EV car projects. Fourth, consumer awareness campaigns and infrastructure development, such as charging networks, can boost demand for EV cars by reducing perceived costs and increasing convenience.
Moreover, enterprises should prioritize long-term gains from EV cars by investing in core technologies and forming partnerships to share risks. Consumers can be engaged through trial programs and feedback mechanisms to refine EV car designs and features. Ultimately, the success of EV cars hinges on a synergistic approach where government, enterprises, and consumers co-evolve their strategies. This analysis not only provides a theoretical foundation for understanding the dynamics of EV cars but also offers practical insights for stakeholders to navigate the evolving landscape of the new energy vehicle industry. As EV cars continue to advance, future research could expand this model to include international markets, supply chain interactions, and emerging technologies like autonomous driving, further enriching the discourse on sustainable transportation.