In the context of global support for green and sustainable development, the EV car industry is emerging as a pivotal force in achieving energy savings and emission reductions in the transportation sector, as well as promoting energy structure optimization. This transformation is significantly influenced by the extensive application of digital technology, leading to a profound change in both developmental methodologies and ecological patterns within the industry. Utilizing game theory, we develop a behavioral evolution model involving the government, digital technology suppliers, and EV car enterprises. The aim is to elucidate the dynamic game process and its stable equilibrium point under the varying strategic choices of the three parties. This will provide more precise theoretical support and recommendations for the high-quality progression of the EV car industry.
We focus on the unique “policy-driven + technology iteration + market game” triad characteristics of the EV car industry, construct the strategy combinations and game payment matrices of the government, digital technology suppliers, and EV car enterprises, and then obtain the Jacobi matrix by partial derivation of the replicated dynamic equations. Through the replicated dynamic equations and numerical simulation, the evolution mechanism of the strategies of technology adoption, policy incentives, and market response is revealed, and the influence of the changes of each parameter on the evolution results is analyzed comparatively. The integration of digital technologies, such as AI and IoT, into EV cars is reshaping how stakeholders interact, necessitating a balanced approach to decision-making.
The literature on digital technology empowerment in industrial transformation highlights several key mechanisms. Dynamic capability theory suggests that firms reconfigure resources through digitalization to adapt to technological changes, while value co-creation theory reveals how digital technologies reshape value networks among producers, consumers, and complementors. In terms of applications, digital technologies enhance industrial upgrading by reconfiguring production factor allocation efficiency and reshaping industrial value chains. However, existing studies often focus on macro-mechanisms, with limited attention to how technological characteristics micro-level alter behavioral rules of actors. In the EV car sector, research indicates that digital technologies drive innovation and efficiency; for instance, provincial panel data show that the digital economy empowers the industry through technical efficiency improvements, resource optimization, and R&D innovation. Additionally, digital technologies enhance supply chain resilience, with key players like ecosystem leaders playing a crucial role. International studies emphasize technology integration, such as digital twins and blockchain in EV cars, yet they lack systematic modeling of how digital technologies change the interactive rules and coordination mechanisms among multiple stakeholders, including technology providers, users, and regulators.
Regarding interest conflicts and equilibria in the EV car industry, under carbon neutrality goals and policy incentives, multiple stakeholders like manufacturers, suppliers, consumers, and governments engage in complex games. Scholars have examined policy tools, such as subsidies and dual-credit systems, and their impact on industrial development. Market behavior research focuses on consumer preferences and corporate strategy evolution, while supply chain coordination uses multi-agent game models to provide diverse solutions. Methods like evolutionary game theory, Stackelberg games, and numerical simulations are commonly employed. Despite these advances, there is a gap in studying the tripartite behavioral evolution of government, digital technology suppliers, and EV car enterprises under digital technology empowerment. This paper addresses this by constructing a dynamic game framework to analyze the effects of policy incentives, strategy costs, and revenue changes on strategic choices.
To model the tripartite evolutionary game, we begin with basic assumptions. First, all actors—government, digital technology suppliers, and EV car enterprises—are boundedly rational decision-makers. They learn and adjust strategies through trial and error in the game process, gradually approaching optimal choices. Second, the strategy sets are defined as follows: government strategies are {Encourage, Not Encourage}, digital technology supplier strategies are {Provide, Not Provide}, and EV car enterprise strategies are {Adopt, Not Adopt}. “Encourage” includes fiscal subsidies and industrial policy support, while “Not Encourage” relies on market self-regulation. “Provide” involves investing in R&D and adaptation for EV cars, and “Not Provide” means maintaining the status quo. “Adopt” refers to EV car enterprises introducing digital technologies into production and R&D, whereas “Not Adopt” implies continuing traditional methods. Third, the probabilities of strategy selection are assigned: let \( x \) (0 ≤ x ≤ 1) be the probability of government choosing “Encourage”, \( y \) (0 ≤ y ≤ 1) for suppliers choosing “Provide”, and \( z \) (0 ≤ z ≤ 1) for EV car enterprises choosing “Adopt”. Fourth, we define the payoffs and costs: the government gains comprehensive benefits \( E_1 \) (e.g., industrial upgrading, economic growth) from “Encourage” but incurs cost \( C_1 \) (e.g., subsidies, administrative costs), with \( E_1 > C_1 > 0 \). Digital technology suppliers earn \( E_2 \) (e.g., technology transfer income, market expansion) from “Provide” with cost \( C_2 \) (e.g., R&D investment, market adaptation), where \( E_2 > C_2 > 0 \). EV car enterprises obtain \( E_3 \) (e.g., production efficiency gains, product premium) from “Adopt” with cost \( C_3 \) (e.g., technology procurement, line upgrades), and \( E_3 > C_3 > 0 \). If they “Not Adopt”, they get traditional收益 \( E_4 \) with \( E_3 > E_4 > 0 \) and cost \( C_4 \) where \( C_4 > C_3 > 0 \) and \( E_3 – C_3 > E_4 – C_4 > 0 \). Fifth, potential benefits and costs are considered: when the government “Encourages”, it subsidizes suppliers with \( mG_1 \) and EV car enterprises with \( nG_2 \) (where \( m \) and \( n \) are subsidy willingness coefficients). Suppliers “Provide” creates potential benefits \( S_1 \) for the government and external benefits \( S_2 \) for EV car enterprises. EV car enterprises “Adopt” contributes \( M_1 \) to the government and \( M_2 \) to suppliers. The government’s benefits exceed its costs and subsidies, so \( 0 < mG_1 + nG_2 + C_1 < E_1 \). If the government “Not Encourages”, it adds external costs \( G_3 \) to suppliers and overrun costs \( G_4 \) to EV car enterprises. If suppliers “Not Provide”, it increases government administrative cost \( S_3 \) and EV car enterprise production cost \( S_4 \). If EV car enterprises “Not Adopt”, it raises government governance cost \( M_3 \) and supplier market opportunity loss \( M_4 \).
Based on these assumptions, we construct the tripartite game payoff matrix as shown in Table 1. This matrix outlines the payoffs for each combination of strategies, considering the interactions among the government, digital technology suppliers, and EV car enterprises. The evolution of EV cars heavily relies on such strategic alignments.
| EV Car Enterprise Strategy | Government Strategy | Digital Technology Supplier Strategy | Government Payoff | Supplier Payoff | EV Car Enterprise Payoff |
|---|---|---|---|---|---|
| Adopt (z) | Encourage (x) | Provide (y) | \( E_1 – C_1 – mG_1 – nG_2 + S_1 + M_1 \) | \( E_2 – C_2 + mG_1 + M_2 \) | \( E_3 – C_3 + nG_2 + S_2 \) |
| Not Provide (1-y) | \( E_1 – C_1 – nG_2 + M_1 – S_3 \) | \( -M_4 \) | \( E_3 – C_3 + nG_2 – S_4 \) | ||
| Not Encourage (1-x) | Provide (y) | \( S_1 + M_1 \) | \( E_2 – C_2 + M_2 – G_3 \) | \( E_3 – C_3 + S_2 – G_4 \) | |
| Not Provide (1-y) | \( M_1 – S_3 \) | \( -G_3 – M_4 \) | \( E_4 – C_4 – G_4 – S_4 \) | ||
| Not Adopt (1-z) | Encourage (x) | Provide (y) | \( E_1 – C_1 – mG_1 + S_1 – M_3 \) | \( E_2 – C_2 + mG_1 – M_4 \) | \( E_4 – C_4 \) |
| Not Provide (1-y) | \( E_1 – C_1 – S_3 – M_3 \) | \( -M_4 \) | \( E_4 – C_4 – S_4 \) | ||
| Not Encourage (1-x) | Provide (y) | \( S_1 – M_3 \) | \( E_2 – C_2 – G_3 – M_4 \) | \( E_4 – C_4 – G_4 \) | |
| Not Provide (1-y) | \( -S_3 – M_3 \) | \( -G_3 – M_4 \) | \( E_4 – C_4 – G_4 – S_4 \) |
From this payoff matrix, we derive the replicated dynamic equations for each party. For the government, the expected payoff for “Encourage” is \( E_{a1} \) and for “Not Encourage” is \( E_{a2} \). The replication dynamic equation is:
$$
F(x) = \frac{dx}{dt} = x(1 – x)(E_{a1} – E_{a2}) = x(1 – x)(C_1 – E_1 + y m G_1 + z n G_2)
$$
For digital technology suppliers, the expected payoff for “Provide” is \( E_{b1} \) and for “Not Provide” is \( E_{b2} \). The equation is:
$$
F(y) = \frac{dy}{dt} = y(1 – y)(E_{b1} – E_{b2}) = y(1 – y)(E_2 – C_2 + x m G_1 + z M_2 + z M_4)
$$
For EV car enterprises, the expected payoff for “Adopt” is \( E_{c1} \) and for “Not Adopt” is \( E_{c2} \). The equation is:
$$
F(z) = \frac{dz}{dt} = z(1 – z)(E_{c1} – E_{c2}) = z(1 – z)(x C_4 – x C_3 – y C_3 + y C_4 + x n G_2 + x E_3 – x E_4 + y E_3 – y E_4 + y S_2 + x y C_3 – x y C_4 – x y E_3 + x y E_4)
$$
These equations capture the evolutionary dynamics of strategy adoption in the EV car industry, highlighting how digital technology integration influences decision-making.
Next, we analyze the stability of the equilibrium points. For the government, when \( y = y^* = \frac{E_1 – C_1 – z n G_2}{m G_1} \), \( F(x) = 0 \), indicating any strategy is stable. If \( y > y^* \), \( x = 0 \) is stable; if \( y < y^* \), \( x = 1 \) is stable. For digital technology suppliers, when \( z = z^* = \frac{C_2 – E_2 – x m G_1}{M_2 + M_4} \), \( F(y) = 0 \). If \( z > z^* \), \( y = 1 \) is stable; if \( z < z^* \), \( y = 0 \) is stable. For EV car enterprises, when \( x = x^* = \frac{y(C_4 – C_3 + E_3 – E_4 + S_2)}{(C_4 – C_3 + n G_2 + E_3 – E_4) + y(C_3 – C_4 – E_3 + E_4)} \), \( F(z) = 0 \). If \( x > x^* \), \( z = 1 \) is stable; if \( x < x^* \), \( z = 0 \) is stable.
To further investigate stability, we use the Jacobian matrix and Lyapunov stability theory. The Jacobian matrix J is derived by taking partial derivatives of the replicated dynamic equations:
$$
J = \begin{bmatrix}
\frac{\partial F(x)}{\partial x} & \frac{\partial F(x)}{\partial y} & \frac{\partial F(x)}{\partial z} \\
\frac{\partial F(y)}{\partial x} & \frac{\partial F(y)}{\partial y} & \frac{\partial F(y)}{\partial z} \\
\frac{\partial F(z)}{\partial x} & \frac{\partial F(z)}{\partial y} & \frac{\partial F(z)}{\partial z}
\end{bmatrix}
$$
After substituting the pure strategy equilibrium points, we analyze the eigenvalues. Under the assumptions \( 0 < E_4 < E_3 \), \( 0 < C_1 < E_1 \), \( 0 < C_2 < E_2 \), \( 0 < C_3 < C_4 \), \( 0 < E_4 – C_4 < E_3 – C_3 \), and \( 0 < m G_1 + n G_2 + C_1 < E_1 \), the point (1,1,1) is asymptotically stable if \( E_1 > C_1 + m G_1 + n G_2 \), \( E_2 > C_2 \), and \( E_3 – C_3 > E_4 – C_4 \). This means the government encourages, suppliers provide, and EV car enterprises adopt digital technologies, forming a stable strategy combination. Other equilibrium points are unstable due to positive eigenvalues, as summarized in Table 2.
| Equilibrium Point | Eigenvalue 1 | Eigenvalue 2 | Eigenvalue 3 |
|---|---|---|---|
| (0,0,0) | 0 | \( E_1 – C_1 \) | \( E_2 – C_2 \) |
| (1,0,0) | \( C_1 – E_1 \) | \( m G_1 – C_2 + E_2 \) | \( C_4 – C_3 + n G_2 + E_3 – E_4 \) |
| (0,1,0) | \( C_2 – E_2 \) | \( E_1 – m G_1 – C_1 \) | \( C_4 – C_3 + E_3 – E_4 + S_2 \) |
| (0,0,1) | 0 | \( E_1 – n G_2 – C_1 \) | \( M_2 – C_2 + M_4 + E_2 \) |
| (1,1,0) | \( C_2 – m G_1 – E_2 \) | \( C_1 + m G_1 – E_1 \) | \( C_4 – C_3 + n G_2 + E_3 – E_4 + S_2 \) |
| (1,0,1) | \( C_1 + n G_2 – E_1 \) | \( C_3 – C_4 – n G_2 – E_3 + E_4 \) | \( m G_1 – C_2 + M_2 + M_4 + E_2 \) |
| (0,1,1) | \( E_1 – m G_1 – n G_2 – C_1 \) | \( C_2 – M_2 – M_4 – E_2 \) | \( C_3 – C_4 – E_3 + E_4 – S_2 \) |
| (1,1,1) | \( C_1 + m G_1 + n G_2 – E_1 \) | \( C_2 – m G_1 – M_2 – M_4 – E_2 \) | \( C_3 – C_4 – n G_2 – E_3 + E_4 – S_2 \) |
For numerical simulation, we assign parameter values based on initial constraints to verify the evolutionary stability. We set initial probabilities for {Encourage, Provide, Adopt} as low (0.2), medium (0.5), and high (0.8) to test sensitivity. Referring to relevant studies, the parameters are: \( E_1 = 18 \), \( E_2 = 6 \), \( E_3 = 6 \), \( E_4 = 4 \), \( C_1 = 1 \), \( C_2 = 1 \), \( C_3 = 1 \), \( C_4 = 2 \), \( G_1 = 2 \), \( G_2 = 2 \), \( S_1 = 2 \), \( S_2 = 2 \), \( S_3 = 1 \), \( S_4 = 1 \), \( M_1 = 2 \), \( M_2 = 2 \), \( M_3 = 1 \), \( M_4 = 1 \), \( m = 0.7 \), \( n = 0.7 \). We use MATLAB 2022b for simulations, focusing on how government subsidies, costs, and revenues affect strategic decisions for EV cars.
First, we examine the impact of government subsidies by varying \( G_1 = G_2 = \{2, 4, 6\} \). The results show that subsidies significantly promote convergence to {Encourage, Provide, Adopt}. As subsidies increase from 2 to 6, the time to reach stable states shortens, and probability values rise faster, indicating that subsidies reduce the risk or cost expectations for actors. Initial willingness affects convergence speed: low initial probability (0.2) leads to slow response, medium (0.5) shows more积极性, and high (0.8) amplifies incentive effects, demonstrating strong synergy between high willingness and positive incentives. This underscores the role of subsidies in accelerating the adoption of digital technologies in EV cars.
Second, we analyze subsidy coefficients by setting \( m = n = \{0.3, 0.5, 0.7\} \). Higher coefficients enhance the guiding effect on evolutionary paths. At \( m = n = 0.3 \), the government lacks motivation to encourage, suppliers have low enthusiasm due to limited \( m G_1 \), and EV car enterprises face prolonged adjustment periods as \( n G_2 \) may not cover costs. At \( m = n = 0.5 \), policy guidance aligns better with market demand; suppliers are driven by reduced R&D costs from \( m G_1 \), and EV car enterprises benefit from cost coverage and technical support, accelerating convergence. At \( m = n = 0.7 \), suppliers experience lower R&D risks, and EV car enterprises gain clear advantages from digital transformation, leading to efficient evolution. Thus, policymakers should dynamically adjust subsidy coefficients based on industrial stages to foster ideal equilibria for EV cars.
Third, we investigate cost changes by setting \( C_1 = C_2 = C_3 = \{1, 3, 5\} \). Rising costs inhibit evolution toward equilibrium. As costs increase, the slopes of strategy evolution curves decrease, slowing adjustment speeds and delaying equilibrium attainment. Initial willingness influences convergence; for example, for EV car enterprises, increasing initial probability from 0.2 to 0.8 reduces equilibrium time from over 1 unit to 0.4-0.6 units, indicating that higher initial willingness speeds up convergence. Therefore, stakeholders should focus on reducing the costs of proactive strategies to accelerate evolution in the EV car sector.
Fourth, we explore revenue effects by varying \( E_1 = \{18, 12, 9\} \), \( E_2 = \{6, 4, 3\} \), and \( E_3 = \{6, 4, 3\} \). Higher revenues激励 actors to converge to equilibrium faster. As E values rise, the slopes of evolution curves increase, boosting government policy推进, supplier R&D积极性, and EV car enterprise expansion主动性. Initial willingness plays a key role; for EV car enterprises, raising initial probability from 0.2 to 0.8 cuts convergence time from over 1 unit to 0.4-0.6 units. This highlights the need to enhance the benefits of proactive strategies to synchronize personal development with industry progress for EV cars.
In conclusion, our study reveals that in the evolutionary game framework, the strategies of the government, digital technology suppliers, and EV car enterprises exhibit interactive influence and coordinated evolution, with the stable strategy being {Encourage, Provide, Adopt}. Government subsidies and revenue increases have significant positive incentive effects, while rising strategy costs notably inhibit evolution. Initial strategy probabilities affect convergence speed, showing path-dependent characteristics in system evolution. For management implications, we recommend building a dynamic cooperation system integrating government, enterprises, and commerce; for instance, a 10% increase in subsidies can shorten evolution cycles by about 10%. EV car enterprises should actively seek subsidies and collaborate with suppliers to deploy technologies like AI and IoT, enhancing productivity and user experience. Additionally, a strategy optimization system focused on “precise cost reduction and diversified value enhancement” is essential, as cost increases by one level can prolong evolution cycles by 10%. Enterprises should analyze cost structures, engage in reasonable collaborations, and leverage digital services to add value. Finally, establishing a dynamic assessment and flexible adjustment mechanism is crucial, as low initial probabilities (0.2) double convergence time compared to high probabilities (0.8). EV car firms should start with pilot projects, accumulate experience, and adapt to external changes like government policies and supplier strategies. This approach ensures sustainable development and high-quality growth in the EV car industry, empowered by digital technology.