Evolutionary Game Analysis of New Energy Transition Among Government, Traditional Automobile Enterprises, and Research Institutions Under the Dual Carbon Goals

Abstract

This paper delves into the evolutionary dynamics of dynamic games among governments, traditional automotive enterprises, and scientific research institutions during the new energy transition process by establishing a stochastic evolutionary game model. The research focuses on exploring the conditions for the formation of system stability and the key factors influencing strategic choices. MATLAB R2021a software is employed to simulate the game process, visually demonstrating the dynamic changes in the behaviors of each participant. The results indicate that research and development (R&D) costs are a crucial consideration for scientific research institutions when deciding whether to collaborate with traditional automotive enterprises. Traditional automotive enterprises exhibit significantly higher sensitivity to government incentives for cooperation than to potential penalties for non-cooperation. Furthermore, an increase in government support costs notably dampens its enthusiasm for promoting the development of the new energy transition. Reducing government support costs and R&D costs for scientific research institutions, as well as enhancing rewards for cooperative behavior and penalties for non-cooperative behavior, can effectively facilitate the formation of evolutionarily stable strategies among governments, traditional automotive enterprises, and scientific research institutions.

1. Introduction

In the context of the urgent demands for global climate change mitigation and environmental protection, the dual carbon targets (i.e., carbon peaking and carbon neutrality) have emerged as significant issues of universal concern in the international community. As the largest automobile producer and consumer in the world, China faces immense pressure for energy transition. With the continuous advancement of new energy vehicle (NEV) technology and the gradual expansion of the market, the high-quality development of the NEV industry is regarded as one of the key pathways to achieving the dual carbon targets [1,2]. However, the transformation of the NEV industry has not been smooth sailing, as it faces multiple challenges, including technological innovation, infrastructure construction, market acceptance, and policy support. Against this backdrop, the cooperation and game relationships among governments, traditional automotive enterprises, and research institutions have become particularly complex and crucial.

This study focuses on the evolutionary game analysis of the new energy transition among governments, traditional automotive enterprises, and research institutions under dual carbon targets. We aim to provide theoretical support and policy recommendations for the coordinated development of the NEV industry by deeply analyzing the strategic choices, evolutionary paths, and mutual influences of these three entities during the NEV transformation process.

Firstly, from the perspective of energy transition, the development of the NEV industry is of great significance for reducing carbon emissions and promoting green and low-carbon development [3]. According to data from the International Energy Agency (IEA), carbon emissions from the global transportation sector account for approximately 25% of total global emissions, with the automobile industry being a major contributor. Therefore, promoting the development of the NEV industry is not only one of the key measures to achieve national dual carbon targets but also a common requirement globally for addressing climate change and fostering sustainable development. On a global scale, the development of the NEV industry has exhibited a vigorous trend. In Europe, numerous governments have introduced a series of policy measures to encourage the development of NEVs, such as providing purchase subsidies and constructing charging infrastructure networks. These initiatives have greatly promoted the expansion of the NEV market. Meanwhile, Europe has also made significant progress in NEV technology research and development, providing robust support for the sustained development of the industry. In the United States, although the development of the NEV market is relatively late, it has shown a trend of rapid growth in recent years. With the rise of NEV companies such as Tesla and increasing government support for the NEV industry, the American NEV industry has gradually become an important component of the global NEV market. In China, with the continuous advancement of NEV technology and the sustained promotion of policies, the production and sales of NEVs have shown a rapid growth trend. However, at the same time, the NEV industry also faces numerous challenges, such as inadequate technological innovation and lagging infrastructure construction, which restrict the further popularization and application of NEVs [4,5].

In the development process of the NEV industry, governments, traditional automotive enterprises, and research institutions play vital roles. Governments promote the development of the NEV industry through policy formulation, financial support, and infrastructure construction. Traditional automotive enterprises need to actively adjust their strategies, increase investments and research and development in the NEV field, and achieve transformation and upgrading [6,7]. Research institutions provide technical support and an impetus for industrial upgrading through technological innovation and research and development for the development of the NEV industry. However, the game relationships among these three entities are complex and dynamic, and their strategic choices and evolutionary paths have a significant impact on the coordinated development of the NEV industry.

To date, numerous studies have conducted in-depth research on the development of the NEV industry and the challenges it faces. For example, some studies have focused on the innovation and development trends of NEV technology [8,9], while others have explored the driving effect of the NEV industry on economic growth [10,11]. Additionally, studies have analyzed the guiding and supporting roles of governments in the development of the NEV industry and the opportunities and challenges faced by traditional automotive enterprises in the NEV transformation [12,13,14]. However, most of these studies have focused on the behavioral analysis of a single entity, neglecting game relationships and mutual influences among governments, traditional automotive enterprises, and research institutions.

To address this research gap, this study introduces the method of evolutionary game analysis. Evolutionary game analysis is an effective method for studying the strategic choices and evolutionary processes of boundedly rational individuals in dynamic environments. In the NEV transformation, game relationships among governments, traditional automotive enterprises, and research institutions are complex and dynamic, making evolutionary game analysis a suitable tool for studying this process. By constructing an evolutionary game model, we can analyze the strategic choices and benefits of these three entities in different scenarios, thereby revealing their evolutionary paths and stable strategies.

Compared with the existing literature, the main contributions of this study are as follows: Firstly, we are the first to apply evolutionary game analysis to the study of the NEV transformation, revealing the game relationships and strategic choices among governments, traditional automotive enterprises, and research institutions. Secondly, by constructing an evolutionary game model, we analyze the strategic choices and benefits of these three entities in different scenarios, providing theoretical support for the coordinated development of the NEV industry. Finally, based on the research results, we propose targeted policy recommendations, providing practical guidance for the cooperation and game among governments, traditional automotive enterprises, and research institutions in the NEV transformation.

2. Literature Review

The research in this paper focuses on four aspects: (1) the significance of high-quality development of the NEV industry under the dual carbon goals; (2) challenges faced by the NEV industry under the dual carbon goals; (3) the roles of governments, traditional automobile firms, and research institutions in the transition to NEVs; and (4) the application of evolutionary game analysis in the transition to NEVs.

2.1. The Significance of High-Quality Development of the NEV Industry Under the Dual Carbon Goals

As an important direction for green and low-carbon development, the high-quality development of the NEV industry holds significant strategic importance [15,16,17]. Firstly, NEVs can significantly reduce carbon emissions and promote green and low-carbon development [18,19]. Traditional fuel vehicles produce a large amount of carbon dioxide emissions during use, while NEVs rely on electric power, reducing dependence on fossil fuels and thus lowering carbon emissions. With the continuous advancement and popularization of NEV technology, their emission reduction effects will become more apparent.

Secondly, the development of the NEV industry will drive the development of related industrial chains, such as batteries, motors, and charging facilities, thereby promoting economic growth [20]. The NEV industrial chain covers multiple links from raw material supply and component manufacturing to vehicle assembly, sales, and after-sales service, and its development will drive the synergistic development of related industries and form new economic growth points [21,22].

Furthermore, the development of the NEV industry will improve energy utilization efficiency and reduce dependence on traditional energy sources [23]. NEVs, powered by electricity, can achieve efficient energy utilization and reduce energy consumption. Meanwhile, with the continuous development of renewable energy, the power sources for NEVs will become cleaner and more sustainable, further reducing dependence on traditional energy sources.

Lastly, the development of the NEV industry will drive the upgrading and transformation of the traditional automobile industry [24]. As NEV technology continues to advance, and as the market expands, traditional automobile firms need to actively adjust their strategies to achieve transformation and upgrading. This will not only enhance their competitiveness but also promote the upgrading and development of the entire automobile industry [25,26].

2.2. Challenges Faced by the NEV Industry Under the Dual Carbon Goals

Despite the huge development potential of the NEV industry, it still faces numerous challenges in its actual development process.

(1)

Insufficient Technological Innovation: The technological innovation of the NEV industry is still insufficient, especially in battery technology, charging technology, and other areas that require further breakthroughs. Currently, NEVs face bottlenecks in battery endurance, charging speed, and safety, which restrict their popularization and application [27,28].

(2)

Lagging Infrastructure Construction: NEVs require a large number of charging facilities and after-sales service networks, but the current infrastructure construction lags behind, hindering the industry’s development. Insufficient charging facilities and uneven distribution lead to issues such as charging difficulties and range anxiety for NEV users [29].

(3)

Low Market Acceptance: The prices of NEVs are relatively high, and consumer awareness and acceptance of these products are still relatively low. Despite government policies such as purchase subsidies and tax incentives for NEVs, consumers still have concerns about the performance, reliability, and resale value of NEVs [30,31].

(4)

Inadequate Policy Support: Although the government has issued a series of policies to support the development of the NEV industry, the level of policy support is still insufficient, and the policy system needs further improvement. For example, issues such as the reduction in purchase subsidies and inadequate funding support for charging facility construction hinder the development of the NEV industry [32,33].

2.3. Roles of Governments, Traditional Automobile Firms, and Research Institutions in the Transition to NEVs

Governments, traditional automobile firms, and research institutions play crucial roles in the transition to NEVs.

(1)

Role of Governments

Governments play a guiding and supporting role in the transition to NEVs. They promote the development of the NEV industry through policy formulation, financial support, and infrastructure construction [34]. For example, governments have issued policies such as purchase subsidies, tax incentives, and charging facility construction subsidies, reducing the cost of consumers purchasing NEVs. Additionally, governments actively promote the construction and optimized layout of charging facilities, improving the convenience of NEVs.

Furthermore, governments guide the healthy development of the NEV industry through the formulation of development plans and standard systems. By formulating development plans, governments clarify the development direction and goals of the NEV industry. By formulating standard systems, they regulate the design and production processes of NEV products, improving product quality and technological level [35,36].

(2)

Role of Traditional Automobile Firms

Traditional automobile firms face significant challenges and opportunities in the transition to NEVs. On the one hand, they need to actively adjust their strategies, increase investment and research and development in the NEV field, and achieve transformation and upgrading. Traditional automobile firms need to strengthen research and innovation in core technologies such as batteries, motors, and electronic controls to improve the performance and competitiveness of NEVs. Additionally, they need to strengthen technological innovation in intelligence and connectivity, promoting the integration and development of NEVs with intelligent transportation and smart cities [37].

On the other hand, traditional automobile firms also need to strengthen cooperation and synergy with governments, research institutions, and upstream and downstream enterprises in the industry chain. Through cooperation with governments, they can obtain more policy support and financial assistance. Through cooperation with research institutions, they can obtain more technological support and innovation resources. Through cooperation with upstream and downstream enterprises in the industry chain, they can achieve resource sharing and complementary advantages, promoting the synergistic development of the NEV industry [38].

(3)

Role of Research Institutions

Research institutions play an important role in technological innovation and research and development in the transition to NEVs. They drive technological progress and industrial upgrading in the NEV industry through enhanced technological innovation and research and development [39]. For example, research institutions have made breakthroughs in battery technology, charging technology, intelligent technology, and other areas, providing powerful technological support for the development of the NEV industry.

Additionally, research institutions promote the industrial application of NEV technologies through cooperation and synergy with governments, traditional automobile firms, and upstream and downstream enterprises in the industry chain [40,41,42]. Through cooperation with governments, they can obtain more financial and policy support. Through cooperation with traditional automobile firms, they can convert research results into actual products. Through cooperation with upstream and downstream enterprises in the industry chain, they can achieve the industrial application of technology and market expansion.

2.4. Application of Evolutionary Game Analysis in the Transition to NEVs

Evolutionary game analysis is a method for studying the strategy selection and evolutionary process of bounded rational individuals in dynamic environments [43]. In the transition to NEVs, the game relationships among governments, traditional automobile firms, and research institutions are complex and dynamic, making evolutionary game analysis suitable for studying this process. Evolutionary game analysis can reveal the strategy selection and evolutionary paths of governments, traditional automobile firms, and research institutions in the transition to NEVs. By constructing evolutionary game models, it can analyze the strategy choices and benefits of these three entities in different scenarios, thereby revealing their evolutionary paths and stable strategies. Additionally, evolutionary game analysis can provide policy recommendations for the synergistic development of the NEV industry. By analyzing the game relationships and strategy choices among governments, traditional automobile firms, and research institutions, it can provide targeted policy recommendations for policymakers, promoting the synergistic development of the NEV industry [44].

3. Materials and Methods

3.1. Model Variables and Hypotheses

Under the dual carbon targets, governments, traditional automobile enterprises, and scientific research institutions exhibit obvious bounded rationality characteristics during the transition to new energy vehicles. The tripartite game is conducted under conditions of incomplete information, meaning that governments, traditional automobile enterprises, and scientific research institutions choose their strategies without knowing the strategies of other players. Therefore, a tripartite evolutionary game model is constructed based on the bounded rationality of governments, traditional automobile enterprises, and scientific research institutions. The basic hypotheses of the asymmetric evolutionary game model are as follows:

Hypothesis 1.

During the new energy transition, scientific research institutions, as important participants, face various influencing factors when deciding whether to collaborate with traditional automobile enterprises to achieve the new energy transition. Let x ($0\le x\le 1$) represent the probability of scientific research institutions choosing to collaborate with traditional automobile enterprises, and let $1-x$ represent the probability of not collaborating. The human and material resources invested by scientific research institutions during the research and development (R&D) stage constitute the R&D cost W. Under this hypothesis, the magnitude of W is positively related to the expected research output benefits, meaning that higher costs imply higher potential benefits.

Hypothesis 2.

Traditional automobile enterprises, as another key entity in the new energy transition process, base their decisions on the trade-off between new energy transition costs R and expected benefits (N). Let y ($0\le y\le 1$) represent the probability of traditional automobile enterprises choosing to collaborate with scientific research institutions, and let $1-y$ represent the probability of not collaborating. This decision-making process reflects the rational choice of traditional automobile enterprises after assessing resource investment and expected market returns.

Hypothesis 3.

Governments play a crucial role in the new energy transition, and their decisions are based on considerations of social interests, regulatory costs, and other aspects. Let z ($0\le z\le 1$) represent the probability of governments choosing to support the collaboration between scientific research institutions and traditional automobile enterprises, and let $1-z$ represent the probability of not supporting. Governments aim to promote the deep integration of new energy technologies and the economy by guiding policies and optimizing resource allocation to improve the new energy transition environment.

Hypothesis 4.

When governments adopt a supportive strategy, they will achieve social benefits (S) while incurring certain costs (G). To actively promote collaboration between scientific research institutions and traditional automobile enterprises in the new energy transition, governments provide certain rewards (A) to both parties as incentives. In addition, to ensure the seriousness and effectiveness of the collaboration process, governments establish corresponding punishment mechanisms, meaning that any party that defaults during the new energy transition collaboration process will face fines (B), with B explicitly set higher than A to constrain collaborative behavior. On the other hand, if governments choose not to support this strategy, social benefits will correspondingly decrease to T, and the condition $S-G>T$ is satisfied, reflecting the superiority of the net benefits (i.e., social benefits minus costs) when governments adopt a supportive strategy compared to when they do not.

Hypothesis 5.

Regarding the distribution of benefits from new energy transition outcomes, we assume that scientific research institutions receive a proportion F of the benefits, specifically expressed as NF. Correspondingly, traditional automobile enterprises receive a proportion of 1 − F, with their benefits being $N(1-F)$. It is worth noting that when discussing and deciding whether to collaborate on the new energy transition, the new energy transition outcomes held by scientific research institutions and the related resources possessed by traditional automobile enterprises already have certain values, which can be directly or indirectly converted into tangible or intangible benefits. For the convenience of subsequent analysis and discussion, we define these benefits as the general benefits (D) of scientific research institutions and the general benefits (C) of traditional automobile enterprises, respectively.

The notations and parameter meanings related to the tripartite evolutionary game are presented in

Table 1. Model parameters and definitions.

Parameters	Definitions
S	The benefit when the government chooses to support the strategy
T	The benefit when the government chooses not to support the strategy
A	The reward to the cooperating party when the government chooses to support the strategy
B	The penalty to the non-cooperating party when the government chooses to support the strategy
D	The general benefit of scientific research institutions
C	The general benefit of traditional automobile enterprises
N	The benefit from the outcome of new energy transformation
F	The proportion of the benefit obtained by scientific research institutions in the outcome benefit
W	The research and development cost incurred when scientific research institutions choose to cooperate
R	The operating cost incurred when traditional automobile enterprises choose to cooperate
G	The cost incurred when the government chooses to support the strategy

.

3.2. Model Construction

Based on the above hypotheses, we obtain the payoff matrix for the evolutionary game model among governments, traditional automobile enterprises, and scientific research institutions during the new energy transition, as shown in

Table 2. Payoff matrix for the evolutionary game among governments, traditional automobile enterprises, and scientific research institutions.

Government			Scientific Research Institution
			Collaboration x	Non-Collaboration 1 − x
Traditional automobile enterprise	collaboration y	support z	$D+NF+A-W,$ $C+N\left(1-F\right)+A-R,S-G-2A$	$D-B,$ $C+A-R,$ $S-G-A+B$
		non-support $1-z$	$D+NF+A-W,$ $C+N(1-F)-R,T$	$D,$ $C-R,T$
	non-collaboration $1-y$	support z	$D+A-W,C-B,$ $S-G-A+B$	$D-B,C-B,$ $S-G+2B$
		non-support $1-z$	$D-W,C,T$	$D,C,T$

.

3.3. Model Analysis

Based on the aforementioned payoff matrix, the expected benefits for research institutions choosing the collaboration strategy are as follows:

$$E_{11}=yz\left(D+NF+A-W\right)+z\left(1-y\right)\left(D+A-W\right)+y\left(1-z\right)\left(D+NF-W\right)+\left(1-y\right)\left(1-z\right)(D-W)$$

(1)

The expected benefits for research institutions choosing the non-collaboration strategy are as follows:

$$E_{12}=yz\left(D-B\right)+z\left(1-y\right)\left(D-B\right)+y\left(1-z\right)D+\left(1-y\right)\left(1-z\right)D$$

(2)

During the transition to renewable energy, the average expected benefits for research institutions are as follows:

$$E_1=x{E}_{11}+(1-x)E_{12}$$

(3)

The expected benefits for traditional automotive enterprises choosing the collaboration strategy are as follows:

$$E_{21}=xz\left[C+N\left(1-F\right)+A-R\right]+z\left(1-x\right)\left(C+A-R\right)+x\left(1-z\right)[C+N\left(1-F\right)-R]+(1-x)(1-z)(C-R)$$

(4)

The expected benefits for traditional automotive enterprises choosing the non-collaboration strategy are as follows:

$$E_{22}=xz\left(C-B\right)+z\left(1-x\right)\left(C-B\right)+x\left(1-z\right)C+\left(1-x\right)\left(1-z\right)C$$

(5)

During the transition to renewable energy, the average expected benefits for traditional automotive enterprises are as follows:

$$E_2=y{E}_{21}+\left(1-y\right)E_{22}$$

(6)

The expected benefits for the government choosing the support strategy are as follows:

$$E_{31}=xy\left(S-G-2A\right)+x\left(1-y\right)\left(S-G-A+B\right)+y\left(1-x\right)\left(S-G-A+B\right)+(1-x)(1-y)(S-G+2B)$$

(7)

The expected benefits for the government choosing the non-support strategy are as follows:

$$E_{32}=xyT+x\left(1-y\right)T+\left(1-x\right)yT+\left(1-x\right)\left(1-y\right)T$$

(8)

During the transition to renewable energy, the average expected benefits for the government are as follows:

$$E_3=z{E}_{31}+(1-z)E_{32}$$

(9)

Based on the above analysis, the replicator dynamic equation for research institutions choosing the collaboration strategy can be expressed as follows:

$$H\left(x\right)={\displaystyle \frac{dx}{dt}}=x\left(E_{11}-E_1\right)=x\left(1-x\right)\left(E_{11}-E_{12}\right)=x\left(1-x\right)\left[z\left(A+B\right)+yNF-W\right]$$

(10)

The replicator dynamic equation for traditional automotive enterprises choosing the collaboration strategy is as follows:

$$H\left(y\right)={\displaystyle \frac{dy}{dt}}=y\left(E_{21}-E_2\right)=y\left(1-y\right)\left(E_{21}-E_{22}\right)=y\left(1-y\right)\left[z\left(A+B\right)+xN\left(1-F\right)-R\right]$$

(11)

The replicator dynamic equation for the government choosing the support strategy is as follows:

$$H\left(z\right)={\displaystyle \frac{dz}{dt}}=z\left(E_{31}-E_3\right)=z\left(1-z\right)\left(E_{31}-E_{32}\right)=z\left(1-z\right)\left[S-G+2B-T-\left(A+B\right)\left(x+y\right)\right]$$

(12)

According to Equations (10)–(12), we obtain the replicator dynamic system for the government, traditional automotive enterprises, and research institutions:

$$\left\{\begin{array}{l}H\left(x\right)=x\left(1-x\right)[z\left(A+B\right)+yNEF-W]\\ H\left(y\right)=y\left(1-y\right)[z\left(A+B\right)+xNE\left(1-F\right)-R]\\ H\left(z\right)=z\left(1-z\right)[S-G+2B-T-\left(A+B\right)\left(x+y\right)]\end{array}\right.$$

According to the theorem stated by Friedman, the evolutionarily stable strategy (ESS) of the replicator dynamic system can be obtained through the local stability analysis of its Jacobian matrix. By setting $H\left(x\right)=0,H\left(y\right)=0$, and $H\left(z\right)=0$, we obtain eight pure strategy solutions within the replicator dynamic system: $E_1(0,0,0),E_2(1,0,0),E_3(0,1,0),E_4(0,0,1),E_5(1,1,0),E_6(0,1,1),E_7(1,0,1),$ and $E_8(1,1,1)$. The Jacobian matrix for the evolutionary game is as follows:

$$J=\left[\begin{array}{ccc}{\displaystyle \frac{dH\left(x\right)}{dx}}& {\displaystyle \frac{dH\left(x\right)}{dy}}& {\displaystyle \frac{dH\left(x\right)}{dz}}\\ {\displaystyle \frac{dH\left(y\right)}{dx}}& {\displaystyle \frac{dH\left(y\right)}{dy}}& {\displaystyle \frac{dH\left(y\right)}{dz}}\\ {\displaystyle \frac{dH\left(z\right)}{dx}}& {\displaystyle \frac{dH\left(z\right)}{dy}}& {\displaystyle \frac{dH\left(z\right)}{dz}}\end{array}\right]$$

$$=\left[\begin{array}{ccc}[z\left(A+B\right)+yNF-W]\left(1-2x\right)& NFx\left(1-x\right)& (A+B)x(1-x)\\ N(1-F)y\left(1-y\right)& [z\left(A+B\right)+xN\left(1-F\right)-R]\left(1-2y\right)& (A+B)y(1-y)\\ -(A+B)z(1-z)& -(A+B)z(1-z)& [S-G+2B-T-\left(A+B\right)\left(x+y\right)](1-2z)\end{array}\right]$$

3.4. Stability Analysis of Equilibrium Points in Evolutionary Game Systems

The eigenvalues of the Jacobian matrix associated with the aforementioned equilibrium points are presented in

Table 3. Local stability analysis of equilibrium points.

Equilibrium Point	Eigenvalue	Symbol	Stability
$E_1\left(\mathrm{0,0},0\right)$	$-W$	$-$	saddle point
	$-R$	$-$
	$S-G+2B-T$	$+$
$E_2\left(1,\mathrm{0,0}\right)$	$W$	$+$	unstable point
	$N(1-F)-R$	$+$
	$S-G+B-A-T$	$+$
$E_3\left(0,1,0\right)$	$NF-W$	$+$	unstable point
	$R$	$+$
	$S-G+B-A-T$	$+$
$E_4\left(0,0,1\right)$	$A+B-W$	$+$	saddle point
	$A+B-R$	$+$
	$-S+G-2B+T$	$-$
$E_5\left(1,1,0\right)$	$W-NF$	$-$	when $S>G+T+2A$, the eigenvalue $>0$, and the point is a saddle point
	$R-N(1-F)$	$-$	when $S<G+T+2A,$ the eigenvalue is $<0$, and the point is a stable point
	$S-G-T-2A$	$+,-$
$E_6\left(\mathrm{0,1},1\right)$	$A+B+NF-W$	$+$	saddle point
	$R-(A+B)$	$-$
	$-S+G-B+T+A$	$-$
$E_7\left(1,0,1\right)$	$W-A-B$	$-$	saddle point
	$A+B+N(1-F)-R$	$+$
	$-S+G-B+T+A$	$-$
$E_8\left(1,1,1\right)$	$W-A-B-NF$	$-$	when $S>G+T+2A$, the eigenvalue is $<0$, and the point is stable point
	$R-A-B-N(1-F)$	$-$	when $S<G+T+2A,$ the eigenvalue is $>0$, and the point is a saddle point
	$-S+G+T+2A$	$+,-$

.

Based on Lyapunov theory, the stability of equilibrium points is assessed by examining the signs of the eigenvalues of the Jacobian matrix constructed from the eight identified equilibrium points. Specifically, if all eigenvalues of the Jacobian matrix at a particular equilibrium point are positive, the point is deemed unstable; if there are both positive and negative eigenvalues, the point is indicated as a saddle point; and if all eigenvalues are negative, the point is considered an evolutionarily stable point. According to the results presented in Table 3, equilibrium points $E_1(\mathrm{0,0},0),E_2(\mathrm{1,0},0),E_3(\mathrm{0,1},0),E_4(\mathrm{0,0},1),E_6(\mathrm{0,1},1)$, and $E_7(\mathrm{1,0},1)$ can be excluded from further analysis, narrowing our focus to the remaining two equilibrium points: $E_5(\mathrm{1,1},0)$ and $E_8(\mathrm{1,1},1)$.

Scenario 1: When the benefit the government receives from supporting is lower than the sum of the benefit from not supporting, the cost of supporting, and the total incentives given to research institutions and traditional automotive enterprises (i.e., $S<G+T+2A$), $E_5(\mathrm{1,1},0)$ becomes the evolutionarily stable point. This implies that the optimal evolutionary strategy for the system is a collaboration between research institutions and traditional automotive enterprises, with the government not providing support (collaborate, collaborate, not support).

Scenario 2: Conversely, when the benefit the government receives from supporting exceeds the sum of the benefit from not supporting, the cost of supporting, and the total incentives given to research institutions and traditional automotive enterprises (i.e., $S>G+T+2A$), $E_8(\mathrm{1,1},1)$ becomes the evolutionary equilibrium point. In this scenario, both research institutions and traditional automotive enterprises choose to collaborate, while the government chooses to support (collaborate, collaborate, support), forming the evolutionarily stable strategy combination for the system.

4. Numerical Simulation

In the process of the new energy transition, the collaboration among research institutions, traditional automotive enterprises, and the government primarily focuses on strategic choices. This joint effort aims to vigorously promote the rapid development of the new energy technology industry, accelerate industrial upgrading, and ultimately enhance the country’s scientific and technological strength. During this process, the strategic choices of these three parties are deeply influenced by numerous complex factors, and even small changes in variables may alter the evolutionary trajectory of the system, leading to different stable strategic configurations.

As a core participant in the new energy transition, the government plays a crucial role. By continuously optimizing the institutional environment that supports the new energy transition, the government lays a solid foundation for the emergence of new energy transition achievements. Therefore, government support policies are crucial for the new energy transition.

Based on the established evolutionary game model, this study further employs simulation methods to delve into the evolutionary game paths among research institutions, traditional automotive enterprises, and the government in complex dynamic environments. During the simulation process, parameter settings closely align with the dynamic fluctuations of various factors in the model and their high sensitivity to the system’s stable strategies. We systematically adjusted core parameters including costs, rewards, penalties, and benefits, and carefully analyzed how these factors influence each participant’s strategic choices.

It should be clarified that the parameter values set in this paper are solely for theoretical analysis and do not directly correspond to specific values in real economic and social environments. By drawing lessons from Nie Q et al. [43], Li J et al. [45], and other methods for setting relevant parameters, the parameters are set as follows: $A=1.8,B=3,N=4.6,F=0.6,$ $T=2.4,R=4.5,W=6,S=12,G=3.6.$ This setup allows the research to be focused on the potential mechanisms and dynamic changes in collaboration strategies during the new energy transition, providing theoretical support and scientific guidance for policymakers.

4.1. Sensitivity Analysis of Evolutionarily Stable Strategies for Governments, Traditional Automotive Enterprises, and Scientific Research Institutions

Based on the simulated parameter configurations, we can clearly observe the strategic evolution trajectories of governments, traditional automotive enterprises, and scientific research institutions under specific conditions, as shown in Figure 1. Under the premise of satisfying all assumed conditions, we initiated the game with x, y, and z set to 0.2, 0.5, and 0.8, respectively, while keeping other parameters constant, resulting in Figure 1.

As shown in Figure 1, as the probability of research institutes choosing to collaborate with traditional automobile enterprises (x) and the probability of traditional automobile enterprises choosing to collaborate with scientific research institutions (y) increase, both research institutes and traditional automobile enterprises exhibit a trend of accelerating convergence towards collaboration, with the evolutionary timeframe shortened. For governments, as x and y rise, their action rates decline. This is because both parties are actively evolving towards collaboration, resulting in a gradual weakening of the government’s role and a corresponding reduction in support to conserve fiscal expenditures. Additionally, the figure also reveals that as z increases, the willingness to collaborate between research institutes and traditional automobile enterprises intensifies, and the government’s support also increases correspondingly with a heightened willingness to support.

Furthermore, it is noteworthy that even starting from such a low initial point, the system will self-adjust and continuously evolve, ultimately converging to a stable point $(\mathrm{1,1},1)$ when key factors (such as benefits, profit distribution ratios, and costs) remain within an appropriate range. This indicates that as time progresses and strategic collaboration deepens, research institutes, traditional automobile enterprises, and governments will continuously adjust their strategies, ultimately forming a stable and efficient “collaborate-collaborate-support” model. This finding not only validates the rationality and effectiveness of the theoretical model but also provides a solid theoretical foundation for practical decision-making, highlighting the feasibility of guiding and promoting long-term stable collaboration among all parties in the process of new energy transformation through scientific regulation of relevant factors.

4.2. Sensitivity Analysis of Tripartite Evolutionarily Stability in the Process of New Energy Transformation

Under the conditions of $W-A-B-NF<0,R-A-B-N(1-F)<0$, and $-S+G+T+2A<0,$ the initial parameters were set to $A=1.8,B=3,N=4.6,F=0.6,T=2.4,R=4.5,$ $W=6,S=12,\mathrm{and}G=3.6,$ and $(0.5,0.5,0.5)$ was used as the initial strategic combination, representing the initial willingness to collaborate with research institutes, traditional automobile enterprises, and governments, respectively. Fifty simulations were conducted for the tripartite evolution in the process of new energy transformation, resulting in that shown in Figure 2. As can be seen from Figure 2, the tripartite evolutionary equilibrium point in the process of new energy transformation is $E_8(1,1,1)$ (i.e., the research institute collaborates, the traditional automobile enterprise collaborates, and the government supports). This result holds significant scientific importance as it demonstrates that, under reasonable initial conditions and parameter settings, tripartite cooperation in the process of new energy transformation is achievable and stable. This provides crucial theoretical support for our understanding of the cooperation mechanisms involved in new energy transformation and offers guidance for formulating relevant policies.

Under the conditions of $W-NF<0,R-N(1-F)<0,$ and $S-G-T-2A<0,$ the initial parameters were set to $A=1.8,B=3,N=10,F=0.6,T=2.4,R=2.5,W=6,S=9,\mathrm{a}\mathrm{n}\mathrm{d}G=3.6.$ With $(0.5,0.5,0.5)$ serving as the initial strategic combination representing the willingness to collaborate among the three parties, 50 simulations were conducted for the tripartite evolution in the process of new energy transformation, resulting in Figure 3. As shown in Figure 3, the tripartite equilibrium point in the process of new energy transformation is $E_5\left(1,1,0\right),$ which indicates that the research institute collaborates, the traditional automobile enterprise collaborates, and the government does not support. This result also carries significant scientific importance. It indicates that, under different initial conditions and parameter settings, the state of tripartite cooperation in the process of new energy transformation may vary. In particular, changes in the government’s benefits or costs can influence its willingness to cooperate. This discovery offers an important perspective for understanding the government’s role and decision-making in the process of new energy transformation and provides guidance on the factors that need to be considered when formulating relevant policies. Additionally, it serves as a reminder that, in promoting the transition to new energy, it is essential to fully consider the interest relationships and cooperation willingness of all parties to achieve more stable and sustainable development.

4.3. Sensitivity Analysis of Research and Development Costs (W) of Research Institutes on Their Strategic Choices in the Process of New Energy Transformation

In this study, five simulation runs were conducted by adjusting different values of the research and development costs $(W=2,4,6,8,10)$ of research institutes while keeping other parameters constant. The results are shown in Figure 4. The analysis reveals that when W exceeds 6, the tripartite evolutionary strategy of the system changes.

Analysis of the five simulation results revealed a significant impact of the W value on the convergence speed of research institutes’ strategic choices. Specifically, as W decreases, the convergence rate towards 1 (representing a high level of collaboration) significantly accelerates, with the shortest time required. This indicates that when research and development costs are lower, research institutes are more inclined to collaborate with traditional automobile enterprises, as the expected benefits obtained from such collaboration may exceed the costs required for independent research. Conversely, as W increases, the convergence speed towards 1 gradually decreases, and when exceeding a threshold of 6.8, the system shifts towards convergence at 0, implying an increased likelihood of research institutes choosing a non-collaborative strategy.

4.4. Sensitivity Analysis of the Impact of Rewards (A) and Penalties (B) on the Strategic Choices of Traditional Automobile Enterprises

While keeping other parameter values constant, this study conducted simulation analyses by setting multiple gradient levels for rewards (A) provided to traditional automobile enterprises that choose to collaboratively participate in the new energy transformation and penalties (B) imposed on those that choose not to collaborate. Specifically, the rewards (A) were varied at levels of 0.4, 0.8, 1.2, 1.6, and 2.0, while the penalties (B) were adjusted to 1, 2, 3, 4, and 5. Through five iterative simulations, we delved into the dynamic changes in traditional automobile enterprises’ strategic choices as A and B vary, with the results presented in Figure 5 and Figure 6.

Figure 5 visually demonstrates the impact of government-provided rewards (A) on the strategic choices of traditional automobile enterprises. When the rewards (A) offered by the government are low (e.g., $A=0.4$), the probability of traditional automobile enterprises choosing to collaborate with research institutes significantly decreases, tending towards non-collaboration, reflecting inadequate government incentives to stimulate the willingness of traditional automobile enterprises to collaborate. As the value of A gradually increases, so does the probability of traditional automobile enterprises choosing collaboration. Once A exceeds 1.2, the trend leans towards full collaboration (i.e., a probability of 1), and the higher the value of A, the faster the convergence speed. This robustly validates the effectiveness of government incentives in promoting collaboration between traditional automobile enterprises and research institutes for new energy transformation.

On the other hand, Figure 6 reveals the significant impact of penalties (B) on the behavioral choices of traditional automobile enterprises. When penalties (B) are low (e.g., $B=1$), the cost of default for traditional automobile enterprises is correspondingly low, leading to a decreased probability of collaboration and a tendency towards non-collaboration. However, as the value of B increases, especially reaching higher levels (e.g., $B=3$), the probability of collaboration among traditional automobile enterprises rapidly rises, tending towards higher levels of collaboration (when considering potential normalization or proportional representation in the model, this is a probability of 1). This indicates that implementing severe penalties for non-compliant traditional automobile enterprises can effectively constrain their behavior and, driven by the pursuit of profit maximization, prompt them to fulfill collaboration agreements and actively collaborate with research institutes for new energy transformation.

Further comparison of the simulation results for rewards (A) and penalties (B) reveals that increasing A to 1.6 is sufficient to guide collaboration between research institutes and traditional automobile enterprises, while B needs to be increased to 3 to promote such collaboration. This finding illustrates the effectiveness of government incentives in stimulating the willingness of traditional automobile enterprises to collaborate and in facilitating collaboration between research institutes and traditional automobile enterprises. Additionally, it suggests that relatively smaller changes in rewards (A) compared to penalties (B) result in collaboration between research institutes and traditional automobile enterprises, indicating that A is more incentivizing than B. Therefore, when formulating relevant policies, the government should weigh the synergistic effects of rewards and penalties, prioritizing incentive measures while supplementing them with penalty measures to establish a more effective incentive mechanism.

4.5. Sensitivity Analysis of Changes in Government Support Costs on Government Strategic Choices in the Process of New Energy Transformation

Based on the aforementioned Figure 7, as government support costs (G) continue to rise, the speed of the government adopting supportive strategies gradually slows down with increasing support costs, and the evolutionary cycle slightly extends, as shown by the green line in the figure. This is attributed to the increase in government support costs leading to a corresponding increase in fiscal expenditure, thereby exacerbating the government’s financial pressure. Therefore, the speed of adopting supportive strategies decreases. For research institutes and traditional automobile enterprises, their choices of collaboration are also affected by changes in government support costs. As shown by the red and blue lines in the figure, when the government reduces the support rate due to rising costs, the collaboration rate between research institutes and traditional automobile enterprises is similarly affected, showing varying degrees of decline.

5. Discussion

5.1. Multidimensional Considerations of Government Roles

In analyzing the synergistic transformation towards renewable energy among governments, traditional automotive enterprises, and scientific research institutions under the “dual carbon” targets, the significance of government roles is self-evident. Governments act not only as policymakers and executors but also as constructors of market incentive and restraint mechanisms. Their behavioral choices directly influence the efficiency and effectiveness of the renewable energy transition. This study finds that governments’ support strategies (to support or not to support) hinge on whether the net benefits derived from support exceed those without support. This conclusion underscores the need for governments to comprehensively consider economic, social, and environmental benefits when formulating renewable energy policies, ensuring that policies are both attractive and sustainable.

Furthermore, the impact of governments’ support costs (G) on their strategic choices merits in-depth discussion. As support costs rise, governments’ enthusiasm for adopting supportive strategies decreases, reflecting the practical constraints of fiscal pressure on policy formulation and implementation. Consequently, achieving maximized policy effects with limited fiscal resources has become a challenge that governments must confront. Future research could further explore how governments can reduce support costs and enhance policy implementation efficiency by innovating financing models and introducing social capital.

5.2. Synergistic Mechanism Between Scientific Research Institutions and Traditional Automotive Enterprises

The synergy between scientific research institutions and traditional automotive enterprises is crucial for the success of the renewable energy transition. This study reveals the synergistic pathways of both under different conditions by constructing an evolutionary game model. Especially when government support is insufficient $(S<G+T+2A)$, even without direct government support, scientific research institutions and traditional automotive enterprises may spontaneously form a synergistic relationship $\left(E_5\right(\mathrm{1,1},0\left)\right)$ for the maximization of their own interests. This indicates that the guidance of market mechanisms and the incentive role of interest-driven factors cannot be ignored.

However, the synergistic process also faces multiple influencing factors such as research and development costs (W), rewards (A), and penalties (B). When research and development costs are excessively high, the willingness of scientific research institutions to collaborate decreases. Conversely, well-designed reward or penalty mechanisms can effectively stimulate the synergistic motivation of traditional automotive enterprises. This suggests that building an effective synergistic mechanism requires comprehensive consideration of cost sharing, benefit sharing, risk sharing, and other factors to form reasonable incentive and restraint mechanisms, thereby promoting long-term and stable cooperation among all parties.

5.3. Strategic Adjustments in Complex Dynamic Environments

The transition to renewable energy is a complex and lengthy process involving interactions across technology, economy, policy, society, and other dimensions. This study demonstrates the evolutionary pathways of strategic choices by scientific research institutions, traditional automotive enterprises, and governments in complex dynamic environments through numerical simulations. The results show that even with different initial conditions, the system will gradually converge to a stable state through self-adjustment. This finding emphasizes the importance of system dynamics and self-organization and suggests that when formulating policies, attention should be paid to policy flexibility and adaptability to adjust strategies promptly in response to environmental changes.

Simultaneously, sensitivity analysis reveals the impact of changes in key parameters on system stability. For instance, variations in research and development costs, rewards, and penalties significantly affect the convergence speed and direction of strategic choices among all parties. This requires policymakers to not only focus on the direct effects of policy objectives but also assess their potential chain reactions and long-term impacts when designing policies, ensuring policy scientificity and rationality.

6. Conclusions, Suggestions, Limitations, and Future Research Directions

6.1. Conclusions

This study, grounded in Lyapunov theory, constructs an evolutionary game model for the new energy transition among governments, traditional automotive enterprises, and scientific research institutions under the “dual carbon” goals. It analyzes the game processes and evolutionarily stable strategies in the new energy transition. The research findings are as follows:

(1)

When S > G + T + 2A, i.e., when the government’s support benefits exceed the sum of support costs, non-support benefits, and rewards to other entities, the government tends to provide support. The system evolves and adjusts, ultimately leading to an ideal state of government support with collaboration between traditional automotive enterprises and scientific research institutions.

(2)

The cooperation between scientific research institutions and traditional automotive enterprises is primarily influenced by research and development (R&D) costs and reward and punishment mechanisms. Reducing R&D costs, increasing reward incentives, or implementing stricter punishment measures can facilitate collaboration between the two parties. Furthermore, under the same intensity, rewards have a more pronounced incentive effect on traditional automotive enterprises choosing cooperation strategies compared to the constraining effect of punishments.

(3)

Appropriate government support costs are a crucial factor in shaping the government’s support strategy. The system demonstrates self-adjustment and continuous evolution characteristics in a complex dynamic environment, ultimately converging to a stable state.

6.2. Suggestions

Based on the above conclusions, the following policy suggestions are proposed:

(1)

Optimize government support mechanisms: Governments should comprehensively consider economic, social, and environmental benefits to formulate scientific and reasonable support policies. Meanwhile, they should explore diversified financing channels to reduce support costs and improve policy implementation efficiency.

(2)

Build an effective synergistic mechanism: Governments should establish reasonable mechanisms for cost sharing, benefit sharing, and risk sharing to form stable cooperative relationships. They should promote in-depth synergy between scientific research institutions and traditional automotive enterprises by signing long-term cooperation agreements and establishing joint research and development funds.

(3)

Improve incentive and restraint mechanisms: Governments should design reasonable reward and penalty mechanisms to incentivize scientific research institutions and traditional automotive enterprises to actively participate in the renewable energy transition while effectively constraining default behaviors. Additionally, they should strengthen policy promotion and guidance to enhance awareness and enthusiasm for the renewable energy transition among all parties.

(4)

Enhance system adaptability: When formulating policies, attention should be paid to policy flexibility and adaptability to adjust strategies promptly in response to environmental changes. Meanwhile, governments should strengthen policy evaluation and feedback mechanisms to promptly identify and address issues.

6.3. Limitations

Although this study has achieved certain results, it still has some limitations:

(1)

Parameter settings: The parameter values in this study are only used for theoretical analysis and do not directly correspond to specific values in the real economic and social environment. Therefore, in practical applications, parameters need to be appropriately adjusted according to specific circumstances.

(2)

Model simplification: To simplify analysis, this study abstracts and generalizes real-world situations to a certain extent. For example, external factors such as technological progress and changes in market demand are not considered in the model. This may result in a certain deviation between model results and actual situations.

(3)

Data acquisition: As the transition to renewable energy is an emerging field, relevant data are relatively scarce. This study uses hypothetical parameter values in numerical simulations, which limits the accuracy and reliability of the research results to some extent.

6.4. Future Research Directions

Addressing the above limitations, future research can be expanded in the following directions:

(1)

Parameter optimization and validation: Future research can collect more actual data to estimate and validate the parameters in the model more accurately. Meanwhile, researchers can consider incorporating external factors such as technological progress and changes in market demand into the model to improve its accuracy and practicality.

(2)

Multi-agent interaction research: Beyond governments, scientific research institutions, and traditional automotive enterprises, the transition to renewable energy also involves consumers, financial institutions, environmental protection organizations, and other agents. Future research can further explore the interaction relationships among these agents and their impact on the renewable energy transition.

(3)

Policy effect evaluation: Future research can adopt a combination of quantitative and qualitative analysis methods to comprehensively evaluate policy effects. Researchers can assess the driving role of policies in the renewable energy transition and their economic, social, and environmental benefits by constructing indicator systems, collecting data, and establishing models.

(4)

Interdisciplinary research: The transition to renewable energy is a complex issue involving multiple disciplines. Future research can integrate knowledge and methods from economics, management, environmental science, engineering technology, and other disciplines to conduct interdisciplinary research, providing more comprehensive and in-depth theoretical support and practical guidance for the renewable energy transition.