Research on New Energy Vehicle Power Battery Recycling Deposit System Based on Evolutionary Game Perspective

Abstract

With the booming development of the new energy vehicle (NEV) industry, the issue of power battery recycling has increasingly attracted attention. Standardized recycling of power batteries can reduce environmental pollution and promote sustainable resource utilization. This paper employs evolutionary game theory to construct two models of deposit systems for the recycling of new energy vehicle power batteries: one under market mechanisms and the other with government participation. The evolutionary stable strategies among vehicle manufacturers, consumers, and the government are examined, and the stable equilibrium points of the models are analyzed. Finally, Matlab is used to conduct a simulation analysis of the deposit system with government participation. The results indicate that the deposit system under market mechanisms is difficult to constrain consumer behavior, while the deposit system with government participation is conducive to promoting the achievement of long-term environmental protection goals. These findings provide valuable insights for policymakers in designing deposit–refund systems and contribute to advancing the sustainable development of the NEV industry.

1. Introduction

Since the economic globalization, in the face of increasingly serious resource shortages and environmental pollution, new energy vehicles (NEVs) seem to have become the best choice to replace traditional fuel vehicles due to their energy-saving and emission-reducing characteristics. China’s new energy vehicle industry is currently experiencing rapid growth. According to data from the China Association of Automobile Manufacturers (CAAM), in 2024 alone, NEV production hit 12.888 million units, marking a 34.4% year-on-year increase, while sales reached 12.866 million units, up 35.5% from the previous year [1]. As the core component of new energy vehicles, power batteries can enable sustainable utilization of their metal resources when proper recycling processes and procedures are implemented [2]. At the end of their service life, power batteries will face the issue of retirement and disposal. It is estimated that by 2025, the sales of new energy vehicles in China will reach 5 million units, accounting for 44% of the global new energy vehicle market capacity, while the scale of the power battery recycling market will reach CNY 20.371 billion [3]. Faced with such a large-scale high-value waste battery recycling market, random disposal or failure to carry out proper disassembly will not only waste resources but also cause serious pollution to the environment.

According to the “Research Report by the Development Research Center of the State Council” in 2023, the standardized recycling rate of new energy vehicle power batteries in China is less than 25%, and there are issues such as unclear closed-loop supply chain recycling chains, generally low recycling technology, and an imperfect policy system, which seriously affect the green development of the new energy vehicle industry chain. Currently, the recycling channels for waste power batteries include formal and informal channels [4]. Formal channels refer to enterprises that have equipment and technology in line with relevant regulations and can safely and efficiently recycle and process waste power batteries to produce new power batteries; however, due to the imperfect regulatory and management systems of the government, a large number of informal recyclers have emerged in the field of waste power battery recycling. In the field of waste power battery recycling, informal recyclers usually refer to individuals or enterprises that have not obtained the corresponding government or industry certification and do not comply with relevant laws and regulations during the recycling process. There are about 64,000 waste power battery recyclers in China, but only about 5% of the recyclers are authorized by the government, leading to nearly 80% of waste power batteries ultimately flowing into informal recycling channels [5]. The market recycling volume of power batteries is also far below expectations, with a market recycling volume of 5472 tons in 2018, accounting for only 7.4% of the total amount of scrapped power batteries [6].

The standardized recycling of power batteries is the foundation for achieving the graded utilization of batteries and the sustainable regeneration of materials, a process that is inseparable from policy guidance and regulation. Developed countries have taken the lead in the field of power battery recycling. The United States has established a deposit system through the Battery Association to encourage consumers to actively surrender used battery products [7]. Germany requires manufacturers to register with the government, and consumers must pay a deposit when purchasing power batteries and are obliged to transfer retired batteries in a standardized manner [8,9]. The Chinese government has also taken a series of measures, attempting a deposit system for power battery recycling within urban areas. In Shenzhen, the “Shenzhen City National New Energy Vehicle Power Battery Supervision, Recycling, and Utilization System Construction Pilot Work Plan (2018–2020)” was carried out, requiring enterprises to allocate a certain amount of funds for the recycling and treatment of power batteries per kilowatt-hour. After the enterprises recover the batteries, this portion of the funds is returned in the form of subsidies [10].

Although the Chinese government has begun to pilot a deposit system for the recycling of new energy vehicle power batteries, this special deposit system for waste power batteries from new energy vehicles is not aimed at consumers but at new energy vehicle retailers. It is still unclear whether it is conducive to the recycling of waste power batteries and what impact the implementation of the deposit system has on the recycling entities. Therefore, this paper focuses on consumer behavior, exploring the deposit system under market mechanisms and government regulation, and how the implementation of the deposit system will affect consumer behavior and the recycling of power batteries. Specifically, this paper addresses the following issues:

(1) In the power battery recycling supply chain involving automobile manufacturers and consumers, what impact will the deposit system have on the strategies and profits of all parties involved?

(2) Can government participation in the regulation and implementation of the deposit system enhance battery recycling efficiency compared to enterprise implementation of the deposit system?

(3) What factors influence whether consumers participate in formal recycling behavior?

2. Literature Review

The literature review related to this study mainly focuses on three aspects: research on power battery recycling, the application of deposit systems in the field of battery recycling, and evolutionary game theory.

2.1. Research on Power Battery Recycling

The recycling industry chain for used power batteries in new energy vehicles faces issues such as unclear definitions of recycling responsibilities, low enthusiasm from enterprises for recycling, and high recycling costs [11]. Existing research mainly discusses the current recycling situation, the recycling strategy choices of participating entities, economic and environmental impacts, and regulatory strategies. Zeng et al. [12] believe that the current recycling of used power batteries lacks effective regulation, collection systems, and recycling technologies; Lu et al. [13] analyze the pricing strategy for battery recycling considering the dual risks of demand and quality; Xie et al. [14] conduct contract coordination under a closed-loop supply chain led by battery production enterprises. However, the supply chain system is quite complex, involving manufacturers, vehicle manufacturers, dealers, and consumers. In 2018, the state issued the “Interim Regulations on the Traceability Management of Recycling and Utilization of Power Storage Batteries for New Energy Vehicles”, which clearly stipulates that vehicle companies must assume the main recycling responsibility [15]. Based on this, Wei and Wang [16] explored the battery recycling market with the participation of vehicle enterprises under government regulation. Zhang Chuan [17] studied the optimal strategy problem in the closed-loop supply chain of power batteries considering government subsidies and scale effects, reflecting the consumer market through the recycling rate. However, in practice, consumers often face high battery replacement prices, a lack of subsidies and support, and compared to the “white list” enterprises that meet the “Comprehensive Utilization Industry Norm Conditions for Used Power Batteries for New Energy Vehicles” issued by the Ministry of Industry and Information Technology, consumers are more willing to choose informal recycling workshops that offer higher recycling prices. These informal recycling enterprises have low recycling technology and serious pollution emissions, yet they occupy a large part of the used power battery market due to price advantages, leading to most used power batteries flowing into informal recycling channels; thus, the recycling rate of power batteries is far from reaching expectations [18]. Gao and Li [19] discussed recycling models involving informal organizations, pointing out that the government and responsible enterprises should intervene and regulate the behavior of privately dismantling and reselling batteries [20]. With government regulation and enterprise participation, consumers’ recycling tendencies will significantly change. Wang et al. [21] explored the impact of subsidies on the recycling volume, recycling prices, and profits of both formal and informal recycling channels by establishing a channel competition model. This study explores the existence of both formal and informal recycling channels in the recycling industry chain and how consumer behavior will affect the power battery recycling market.

In the field of recycling mode selection, numerous scholars have employed decision-making models to analyze optimal recycling strategies. Hu et al. [22] examined a dual-channel recycling model involving battery manufacturers and third-party recyclers, investigating the impact of government subsidies on supply chain preferences and recycling incentives. Zhou et al. [23] introduced blockchain technology to evaluate four distinct recycling supply chain models: Battery Manufacturer-Led (BML), Vehicle Manufacturer-Led (VML), Manufacturer Alliance-Led (MAL), and Third-Party-Led (TPL), with recycling efficiency quantified using a DEA model. Hao et al. [24] conducted a cost–benefit analysis of these four models, assessing eight key cost factors to determine recycling expenses and profitability. These scholars collectively established an analytical framework for power battery recycling decision-making that integrates “policy incentives—stakeholder—mode selection—benefit evaluation” [25,26,27]. While this framework innovatively incorporates environmental constraints and policy variables into closed-loop supply chain analysis, most studies rely on qualitative decision models with limited empirical case validation.

Dong and Tang [28,29] examined Beijing’s battery recycling practices, revealing that automaker-led recycling remains dominant in the short term. Wang et al. [30] analyzed China’s EV battery recycling policies through a multi-party cooperative game model, highlighting automakers as key players. Given their access to battery lifecycle data and stable supply channels, vehicle manufacturers hold structural advantages in recycling operations [31,32]. Accordingly, this study adopts an NEV manufacturer-led recycling framework.

2.2. Research on the Application of the Deposit System in the Field of Battery Recycling

Numerous studies have confirmed that the deposit system plays a significant positive role in promoting the recycling of waste products. Kulshreshtha and Sarangi [33] have analyzed the operational mechanism of the deposit system, highlighting its policy advantages in pollution prevention and resource recycling, and categorizing the deposit system into those established by enterprises and those established by governments. Similarly, Huang et al. [34] believe that the deposit system is divided into market-driven and government-driven types. The former is spontaneously generated by manufacturers for individual economic goals, while the latter is generated by governments for societal environmental objectives. The deposit system encourages consumers to proactively hand over batteries through formal channels when they are replaced or scrapped [35], thereby recovering part of the additional costs paid when purchasing power batteries or new energy vehicles; at the same time, the deposit refund system also ensures that manufacturers take on recycling responsibilities proactively, actively participate in collection and dismantling work, and thus improve the recycling rate of waste products [36]. Linderhof et al. [37] documented 4–15.7 percentage point increases in recycling rates for small electronics (60.7%→64.7–76.4%) and batteries (86.9%→87.2–89.2%) in the Netherlands with EUR 5–15 deposits. Georgakellos et al. [38] reported automotive sector recycling rates of 80–90% under DRS regimes across multiple countries.

The system’s core strength lies in its dual economic mechanism—combining financial constraints with positive incentives to align stakeholder behaviors with circular economy objectives. Recent scholarly attention has extended this proven approach to power battery recycling [39]. Li and Wu et al. [6,40] specifically validated DRS’s potential to significantly improve EV battery recovery rates, with Li examining its application across four recycling models and Wu comparing its effectiveness against subsidies and environmental taxes. However, their research also revealed a critical calibration challenge—deposit amounts must be carefully balanced to avoid either manufacturer resistance (from excessive deposits impacting sales) or insufficient incentivization (from inadequate deposit levels). This underscores the need for rigorous economic analysis to determine optimal deposit pricing strategies.

2.3. Research on Evolutionary Game Theory

Evolutionary game theory (EGT) originates from the mathematical modeling of competitive and cooperative behaviors in the process of biological evolution [41]. It is a theory that integrates game-theoretic analysis with dynamic evolutionary processes. According to EGT, individual decision-making is achieved through a dynamic process of imitation, learning, and mutation among individuals. When a particular strategy exhibits a fitness superior to the average level of the population, this strategy will diffuse within the population through mechanisms of imitation and learning and will eventually be widely adopted [41]. EGT focuses on participants with bounded rationality and attempts to explain and predict the evolutionary trends of group behavior decisions [42]. In recent years, many scholars have applied it to the field of power battery recycling. In the area of enterprise cooperation research, Xu et al. [43] analyzed the cooperative business model selection strategies for cascade utilization under market mechanisms and policy impacts based on EGT and conducted stability analysis and numerical simulations. In terms of policy incentives, Li Yan and Zhang [44] constructed a tripartite game model for low-carbon innovation in power battery recycling, pointing out that government incentive measures play a key role in motivating manufacturers and recyclers to achieve low-carbon innovation. Li Gang et al. [45] discussed a tripartite evolutionary game model among vehicle manufacturers, power battery manufacturers, and power battery recyclers, simulating the dynamic evolution process of each player’s strategy. Cao et al. analyzed the development of the new energy vehicle industry under government regulation using EGT [46]. In terms of information sharing, Gao et al. [47] simulated the impact of the willingness and information barriers of participants in the power battery recycling supply chain on the strategy choices of all parties based on EGT.

In the power battery recycling supply chain, all participants are boundedly rational agents. The decision-making among consumer groups, vehicle enterprises, and the government that implements the system is a long-term interactive process. EGT can effectively analyze the interactive relationships among these agents, help the government formulate more effective regulatory strategies, analyze the influencing factors of consumer behavior, and provide theoretical support for enterprises to choose the optimal recycling strategies. Therefore, this paper considers applying EGT to the research on power battery recycling decision-making problems.

Table 1. Relevant literature summary.

Author(s)	Recycling Mode	Power Battery Recycling	Government Participation	Informal Recycling	Deposit System	Consumer Behavior
Li X. et al. (2022) [6]	VM, BM, TP	√	√		√
Wei et al. (2023) [16]	VM	√	√	√		√
Zhang et al. (2021) [17]	VM, BM, TP	√	√
Dong et al. (2022) [18]	---	√				√
Gao et al. (2024) [19]	VM, BM		√	√
Jiao et al. (2024) [25]	VM, BM, TP	√	√
Huang et al. (2024) [34]	VM, BM, TP		√		√
Wang et al. (2021) [36]	VM, BM		√		√	√
Linderhof et al. (2019) [37]	BM				√	√
Cao et al. (2018) [46]	---		√			√
This paper	VM	√	√	√	√	√

Note: VM: Vehicle manufacturer, BM: Battery manufacturer, TP: Third-party recycler.

is provided to further distinguish the current and the most relevant work from previous studies. Through comparative analysis of research themes in the relevant literature, existing scholarship has predominantly focused on battery recycling model selection and the impact of government intervention while largely overlooking the potential of deposit systems in restricting informal recycling channels and guiding consumer recycling behavior. In summary, based on the research in the existing literature, the main contributions of this paper are as follows: (1) from the perspectives of market mechanisms and government participation, discussing the role of the deposit system in regulating the power battery recycling market, with consumers and vehicle manufacturers as the deposit payers; (2) exploring the strategic choices of consumers when facing formal and informal power battery recycling channels, revealing the motivations behind changes in consumer behavior and validating the conclusions through simulation analysis; and (3) discussing system stability strategies under different scenarios, analyzing the specific impacts of deposit amounts, subsidy levels, and consumers’ environmental awareness on system evolution strategies, providing a theoretical basis and practical guidance for the formulation and optimization of power battery recycling policies.

3. Deposit System Under Market Mechanisms

Used power batteries are regarded as valuable commodities in China. They can be reused or recycled based on their capacity, similar to the deposit system for other discarded electronic products, and economic incentive mechanisms can be used to promote the recycling of power batteries [48]. The deposit system model proposed in this section is based on market mechanisms, simulating the economic behavior between vehicle manufacturers and consumers. This is a mechanism that spontaneously forms in the market, where vehicle manufacturers reach an agreement with consumers to improve battery recycling rates: consumers pay a deposit to the vehicle manufacturer when purchasing a car, and this deposit is managed by the vehicle manufacturer. When the battery is scrapped, if consumers hand over the used power battery to the vehicle manufacturer through formal channels, the manufacturer will return the corresponding deposit.

3.1. Parameter Setting and Payment Matrix

In order to construct the game model and analyze the stability of the two-party game and its equilibrium point, the following assumptions are made:

Assumption 1.

According to the Management Measures for Comprehensive Utilization of Power Battery in New Energy Vehicles issued by the Ministry of Industry and Information Technology of the State in 2023, automobile manufacturers should assume the main responsibility for power battery recycling of installed power batteries, according to which this paper positions the vehicle enterprises as the responsible main body for power battery recycling. The strategy set of the car enterprise is (implementation, no implementation), the probability of implementing the deposit system is $x$, and the probability of not implementing the deposit system is $1-x$. The implementation of a deposit system by vehicle manufacturers incurs certain operating costs of $C_1$. Prepresents the revenue of the vehicle enterprise when consumers choose formal recycling. When the deposit system is implemented, when a consumer purchases a new energy vehicle, the purchase cost already includes a deposit of $d$ per kWh, which is returned when the consumer recycles the power battery through formal channels. Vehicle manufacturers will receive higher recognition and potential benefits such as brand awareness $P_b$ due to the implementation of the deposit return system and fulfillment of its social responsibility, and $C_1>P_b$.

Assumption 2.

The strategy set of consumers is (formal recycling, informal recycling), the probability of choosing formal recycling channels is $y$ and the probability of choosing informal recycling channels is $1-y$. Consumers will gain $R_1$ by recycling used power batteries through the formal channels, and if used power batteries are handed over to informal recycling channels for recycling, due to the fact that the small workshops and non-standardized enterprises have almost no environmental protection and safety in the recycling and treatment of power batteries, and thus can acquire retired power batteries from consumers at a higher price, the consumers gain $R_2$, and $R_2>R_1$.

Assumption 3.

If the vehicle enterprise does not implement the deposit system, and if consumers pay for the battery through informal recycling channels, the vehicle enterprise will be responsible for dealing with the cost of pollution brought by non-standardized enterprise battery recycling to the environment $C_2$; if the vehicle enterprise implements the deposit system, and consumers use formal recycling channels for battery recycling to avoid environmental pollution, then the consumer will get the environmental preference benefit $\mu C_2$. $\mu$ indicates the degree of consumer perception of the benefit, reflecting the consumer’s own environmental awareness, $\mu \in \left(0,1\right)$, where the larger the value of $\mu$, the stronger is the consumer’s environmental awareness, and $R_2>\mu C_2$.

The payment matrix of complete vehicle enterprises and consumers under the market mechanism is listed in

Table 2. Payment matrix for a deposit system under the market mechanism.

		Consumers
		$\mathrm{Formal} \mathrm{recycling} \left(y\right)$	$\mathrm{Informal} \mathrm{recycling} \left(1-y\right)$
Vehicle manufacturer	Implementation $\left(x\right)$	$P-C_1+P_b$ $R_1+\mu C_2$	$-C_1+d+P_b$ $R_2-d$
	Non-implementation $(1-x)$	$P$ $R_1$	$-C_2$ $R_2$

.

3.2. Two-Party Game Model and Solution

In evolutionary game theory, the replicator dynamics equation, as a mathematical model, can describe the rate of change of the proportion of strategy $x_i$ in a population over time $t$. This equation was proposed by Taylor and Jonker in 1978 [49]. Its basic form is as follows:

$$f(x)={\displaystyle \frac{d{x}_i}{dt}}=x_i\left(E(x_i)-\overline{E}\right)$$

where $f(x)$ represents the rate of change of the proportion of the i-th strategy, which is the replicator dynamics equation; $E(x_i)$ denotes the payoff of individuals adopting the i-th strategy, $\overline{E}$ represents the average payoff of the population, and it satisfies $\overline{E}={\displaystyle \sum _{i=1}^n{x}_{i}E(x_i)}$, where n represents the number of different strategies that individuals in the population can adopt.

Based on the payment matrix in Table 2, the expected return and average return of the vehicle enterprises in the two strategies of “implementing deposit system” and “not implementing deposit system” are, respectively, the following:

Expected benefits of implementing a deposit system:

$$e_{m1}=y\left(P-C_1+P_b\right)+\left(1-y\right)\left(-C_1+d+P_b\right)$$

Expected benefits of not implementing a deposit system:

$$e_{m2}=yP+\left(1-y\right)(-C_2)$$

Average earnings of vehicle manufacturer:

$$e_m=x{e}_{m1}+\left(1-x\right)e_{m2}$$

The replication dynamic equation for the whole-vehicle firms choosing to implement a deposit system is the following:

$$f_m\left(x\right)={\displaystyle \frac{dx}{dt}}=x(e_{m1}-e_m)=x\left(1-x\right)\left(e_{m1}-e_{m2}\right)=x\left(x-1\right)\left(C_1-d-P_b+dy+C_2\left(1-y\right)\right)$$

Similarly, using $e_{c1}$ and $e_{c2}$ to denote the expected returns to consumers for participating in formal recycling versus not participating in formal recycling, the equation for the replication dynamics of consumers choosing to recycle through formal channels is as follows:

$$f_c\left(y\right)={\displaystyle \frac{dy}{dt}}=y(e_{c1}-e_c)=y\left(1-y\right)\left(e_{c1}-e_{c2}\right)=\left(1-y\right)y\left(R_1-R_2+x\left(d+\mu C_2\right)\right)$$

The system of joint equations $\left\{\begin{array}{c}{f}_m\left(x\right)=0\\ f_c\left(y\right)=0\end{array}\right.$ can be obtained with five equilibrium points: $\left\{x\to 0,y\to 0\right\}$, $\left\{x\to 1,y\to 0\right\}$, $\left\{x\to 0,y\to 1\right\}$, $\left\{x\to 1,y\to 1\right\}$, and $\left\{x^{*}\to {\displaystyle \frac{-R_1+R_2}{d+\mu C_2}},y^{*}\to {\displaystyle \frac{-C_1+C_2+d+P_b}{d+C_2}}\right\}$, which are denoted as $e_0$, $e_1$, $e_2$, $e_3$, and $e_{*}$, respectively.

The local stability of the evolutionary system can be obtained by analyzing the Jacobi matrix of the system. The Jacobi matrix under this two-party game system is as follows:

$${\mathit{J}}_1=\left[\begin{array}{cc}{\displaystyle \frac{\partial f_m\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial f_m\left(x\right)}{\partial y}}\\ {\displaystyle \frac{\partial f_c\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial f_c\left(y\right)}{\partial y}}\end{array}\right]=\left[\begin{array}{cc}\left(-1+2x\right)\left(C_1-P_b-d+C_2\left(y-1\right)+\mathrm{d}y\right)& \left(d+C_2\right)\left(-1+x\right)x\\ \left(d+\mu C_2\right)\left(1-y\right)y& \left(1-2y\right)\left(R_1-{\mathrm{R}}_2+x\left(d+\mu C_2\right)\right)\end{array}\right]$$

$Det\left(J_1\right)$ and $Tr\left(J_1\right)$ are the determinant and trace of the matrix $J_1$, respectively.

According to the Friedman criterion [50], the local stability of the Jacobian matrix $J_1$ is determined as follows: when $Det\left(J_1\right)>0$ and $Tr\left(J_1\right)<0$ at the equilibrium solution, the equilibrium solution is a stable strategy (ESS); when $Det\left(J_1\right)>0$ and $Tr\left(J_1\right)>0$, the equilibrium solution is an unstable point; when $Det\left(J_1\right)<0$, the equilibrium solution is a saddle point.

Substituting the five equilibrium points, the determinant and trace of the corresponding equilibrium solution are calculated, as shown in

Table 3. Determinants and traces of equilibrium points of the two-party game.

Equilibrium Point	$\mathit{D}\mathit{e}\mathit{t}\left({\mathit{J}}_1\right)$	$\mathit{T}\mathit{r}\left({\mathit{J}}_1\right)$
$e_0\left(0,0\right)$	$-\left(C_1-C_2-d-P_b\right)\left(R_1-R_2\right)$	$-C_1+C_2+d+P_b+R_1-R_2$
$e_1\left(1,0\right)$	$\left(C_1-C_2-d-P_b\right)\left(d+R_1-R_2+\mu C_2\right)$	$C_1-P_b+R_1-R_2+C_2\left(-1+\mu \right)$
$e_2\left(0,1\right)$	$\left(C_1-P_b\right)\left(R_1-R_2\right)$	$-C_1+P_b-R_1+R_2$
$e_3\left(1,1\right)$	$-\left(C_1-P_b\right)\left(d+R_1-R_2+\mu C_2\right)$	$C_1-d-P_b-R_1+R_2-\mu C_2$
$e_{*}\left(x^{*},y^{*}\right)$	$\left(C_1-P_b\right)\left(d+R_1-R_2+\mu C_2\right)x^{*}{y}^{*}$	0

:

The next step is to analyze the evolutionary stabilization strategy of the deposit system under the market mechanism, to explore the changes in the behaviors of vehicle manufacturers and consumers in the game by changing the size of the unit deposit in the two-party game, and to draw the corresponding dynamic evolutionary phase diagrams.

Proposition 1.

In the early stages of the evolution of the deposit system under the market mechanism, when the deposit amount is too small, there is a stable point $\left(0,0\right)$: vehicle manufacturers tend to avoid implementing the deposit system, while consumers tend to participate in informal recycling.

Proof. 

According to Table 2, when $d<min\left\{C_1-P_b-C_2,R_2-R_1-\mu C_2\right\}$, at this time $Det>0$ and $Tr<0$; then, {The vehicle manufacturers do not implement the deposit system, Consumers participate in informal recycling} for the evolutionary equilibrium strategy (ESS). Similarly, $e_1$ and $e_2$ are the saddle points, $e_3$ is the unstable point, and the corresponding dynamic evolution phase diagram is shown in Figure 1a. □

Proposition 2.

When the deposit increases to a certain value, the vehicle manufacturers will choose whether to implement the deposit system based on the operating costs of the deposit system, potential benefits, and the amount of pollution costs paid. However, consumers will always adopt informal recycling strategies, at which point there are two evolutionarily stable points $\left(1,0\right)$ or $\left(0,0\right)$.

Proof. 

When $C_1-P_b-C_2<d<{\mathrm{R}}_2-R_1-\mu C_2$, at this point $Det>0$ and $Tr<0$; then, {The vehicle manufacturers implement the deposit system, Consumers participate in informal recycling} is an evolutionary equilibrium strategy (ESS), with $e_0$ and $e_2$ as saddle points and $e_3$ as an unstable point; when ${\mathrm{R}}_2-R_1-\mu C_2<d<C_1-P_b-C_2$, at this point $Det>0$ and $Tr<0$; then, {The vehicle manufacturers do not implement the deposit system, Consumers participate in informal recycling} is an evolutionary equilibrium strategy (ESS), with $e_2$ and $e_3$ as saddle points and $e_1$ as an unstable point. The corresponding dynamic evolution phase diagrams are shown in Figure 1b,c. □

Proposition 3.

When $d>max\left\{C_1-P_b-C_2,R_2-R_1-\mu C_2\right\}$, the system does not have an evolutionary stability point and the strategies of the vehicle firms and consumers show cyclical changes.

Proof. 

According to Table 2, there exists a mixed strategy $e_{*}$ at time $d>\max \left\{C_1-P_b-C_2,{\mathrm{R}}_2-R_1-\mu C_2\right\}$ and $Det<0$ for points $e_0$, $e_1$, $e_2$, and $e_3$, so there is no stabilizing strategy in the system at this point. The corresponding phase diagram changes are shown in Figure 1d. At this point, the strategy $\left(x,y\right)$ trajectories of the two parties are closed-loop curves, and the system oscillates on the curve around the point $e_{*}$. At this point, the function of the strategies of the two parties with respect to time is a periodic function. □

Conclusion 1: As a matter of fact, under the deposit system formed by the market mechanism, the main participants of power battery recycling are vehicle manufacturers and consumers, and as the dominant player, vehicle manufacturers hold the decision of whether to introduce the deposit system and its specific amount. Regardless of the strategy adopted by manufacturers, consumers’ behavioral choices in this game seem to be inclined to maximize their personal interests. They tend not to choose formal recycling because such a decision is not based on the long-term perspective of regulating the market and promoting battery laddering or dismantling and utilization in their consideration but is purely based on their own gain; when consumers recycle new energy vehicles, regardless of whether they have previously paid a deposit to the enterprise or not, the consumers will inevitably choose to participate in informal recycling for their personal interests. This phenomenon reveals the limitations of the market mechanism in promoting the standardization of power battery recycling. Therefore, in order to standardize the recycling market, reduce pollution emissions, and promote resource recycling, government involvement becomes crucial. The government needs to actively intervene in the system and play a strong supervisory and regulatory role to ensure the standardization and sustainability of the power battery recycling process.

4. Deposit System with Government Participation

Through the analysis in the previous section, it can be known that the implementation of the deposit system by enterprises has relative limitations, and the deposit system formed under the market mechanism does not regulate the behavior of consumers well, so this section considers the deposit system model with government participation, where the government, as a decision-making body, decides whether or not to implement the deposit system by comprehensively considering the social and environmental benefits and the cost of regulation. This deposit system requires vehicle manufacturers to pay a deposit to the government based on the capacity of the power battery per kilowatt-hour when selling new energy vehicles and to take responsibility for battery recycling [10]. After the vehicle manufacturers recycle the power batteries, the government will refund the corresponding deposit; otherwise, the deposit will be deducted by the government.

4.1. Description of Symbols and Payment Matrices

At this time, the government participates in the game model, and the government’s strategy set is (Regulate, Do not regulate). The probability of the government choosing to regulate is $z$, and the probability of not regulating is $1-z$. If the government participates in regulation, it will implement a deposit system and standardize consumer behavior. At this point, the entity implementing and operating the deposit system changes from the vehicle manufacturers to the government, and the entity paying the deposit changes from consumers to vehicle manufacturers. The strategy set for vehicle manufacturers changes to (Actively participate in recycling, Negatively participate in recycling), while the strategy set for consumers remains unchanged, still being (Formal recycling, Informal recycling). The following assumptions are made, and the relevant symbols are shown in

Table 4. Description of symbols and their meanings.

Strategist	Symbol	Meaning
Vehicle manufacturer	$P$	Benefits to businesses when consumers participate in formal recycling
	$P_b$	Potential benefits to the enterprise
	$s$	Subsidies given by companies to consumers
Consumer	$R_1$	Battery gains from formal consumer recycling
	$R_2$	Battery gains from informal consumer recycling
	$\mu$	Consumer’s environmental awareness
Government	$R_g$	Benefits of the government achieving carbon reduction targets
	$d$	Deposit
	$\alpha$	Penalties for informal recycling enterprises
	$C_1$	Supervision costs, operating costs of the deposit system
	$C_2$	Environmental treatment costs

:

Assumption 4.

When the government adopts a regulatory strategy, (i) the government collects deposits from vehi-cle manufacturers, and if vehicle manufacturers actively participate in recycling and consumers re-turn batteries through formal recycling channels, then the government returns the deposits to the enterprises, and conversely, the government deducts the deposits from vehicle manufacturers; (ii) the government increases the penalties on informal recycling enterprises, and collects fines from in-formal recycling enterprises αR₂, with α denoting the government’s punitive strength; (iii) When consumers return the batteries through formal recycling channels, the government gains credibility-enhancing benefits due to the fulfill-ment of its commitment to reduce emissions and pollution R_g. When the government adopts a strategy of not regulating, the government will no longer pay for the operating costs of the deposit system C₁. In addition when there are batteries on the market that flow into informal recycling channels, the government will need to pay for the environmental treatment costs of this portion of the batteries C₂.

Assumption 5.

Vehicle enterprises are no longer responsible for the operating costs of the deposit system, have become the subject of deposit payment, and have lost the means to bind consumers downwards. The Interim Measures for the Administration of Power Battery Recycling for New Energy Vehicles encourages automobile manufacturers to improve the enthusiasm of new energy vehicle owners to hand over used power batteries through measures such as repurchase, trade-in, and granting subsidies, at which time enterprises stimulate consumers to participate in formal recycling by means of subsidies. If the enterprise actively participates in recycling, it will give subsidies to consumers who participate in formal recycling channels according to the capacity of recycled batteries per kWh to compensate for the time, energy, and other costs paid by consumers; at the same time, active participation in recycling will also improve the enterprise’s reputation and allow them to obtain potential benefits $P_b$. Other benefits are the same as the two sides of the game.

Assumption 6.

When the government strengthens regulatory efforts, informal recycling enterprises will face a risk cost. To alleviate this burden, these enterprises will attempt to transfer costs by lowering recycling prices [16]; at this time, the recycling price for consumers through informal channels is $(1-\alpha )R_2$.

The payment matrix of the three-party game at this point is shown in

Table 5. Payment matrix for a deposit system with government participation.

		Government
		Regulate $\left(\mathit{z}\right)$		Do Not Regulate $\left(1-\mathit{z}\right)$
		$\mathbf{Formal} \mathbf{Recycling} \left(\mathit{y}\right)$	$\mathbf{Informal} \mathbf{Recycling} \left(1-\mathit{y}\right)$	$\mathbf{Formal} \mathbf{Recycling} \left(\mathit{y}\right)$	$\mathbf{Informal} \mathbf{Recycling} \left(1-\mathit{y}\right)$
Vehicle manufacturer	$\mathrm{Positive} \left(x\right)$	$P+P_b-s$	$P_b-d$	$P+P_b-s$	$P_b$
		$R_1+\mu C_2+s$	$(1-\alpha )R_2$	$R_1+\mu C_2+s$	$R_2$
		$R_g-C_1$	$-C_1-C_2+\alpha R_2+d$	$0$	$-C_2$
	$\mathrm{Negative} \left(1-x\right)$	$P-d$	$-d$	$P$	$0$
		$R_1$	$(1-\alpha )R_2$	$R_1$	$R_2$
		$R_g-C_1+d$	$-C_1-C_2+\alpha R_2+d$	$0$	$-C_2$

.

4.2. Solution and Stability Analysis of the Three-Party Game Model

4.2.1. Analysis of Evolutionarily Stable Strategies of Each Party in a Three-Party Game

According to Table 5 of the payment matrix, the expected returns and average returns for the government under the two strategies of “Regulate” and “Do not regulate” are as follows:

Expected benefits of implementing regulatory strategies:

$$\begin{array}{ll}\hfill E_{g1}& =xy\left(R_g-C_1\right)+x\left(1-y\right)\left(-C_1-C_2+\alpha R_2+d\right)+y\left(1-x\right)\left(R_g-C_1+d\right)\\ & +\left(1-x\right)\left(1-y\right)\left(-C_1-C_2+\alpha R_2+d\right)\end{array}$$

Expected returns without implementing regulatory strategies:

$$E_{g2}=x\left(1-y\right)\left(-C_2\right)+\left(1-x\right)\left(1-y\right)\left(-C_2\right)$$

Average government revenue:

$$E_g=z{E}_{g1}+\left(1-z\right)E_{g2}$$

The dynamic equation for the replication strategy of government supervision is as follows:

$$\begin{array}{ll}{F}_g\left(z\right)& ={\displaystyle \frac{dz}{dt}}=z\left(E_{g1}-E_g\right)=z\left(1-z\right)\left(E_{g1}-E_{g2}\right)\\ & =\left(C_1-\alpha R_2+\alpha R_{2}y-R_{g}y+d\left(-1+xy\right)\right)\left(-1+z\right)z\end{array}$$

Similarly, let $E_{m1}$ and $E_{m2}$ represent the benefits of vehicle manufacturers choosing to actively participate in recycling and passively participate in recycling, respectively, and let $F_m\left(x\right)$ represent the dynamic equation for the replication of the active participation strategy in recycling by vehicle manufacturers. Then, the following are given:

$$E_{m1}=yz\left(P+P_b-s\right)+z\left(1-y\right)\left(P_b-d\right)+y\left(1-z\right)\left(P+P_b-s\right)+\left(1-y\right)\left(1-z\right)\left(P_b\right)$$

$$E_{m2}=yz\left(P-d\right)+z\left(1-y\right)\left(-d\right)+y\left(1-z\right)P$$

$$F_m\left(x\right)={\displaystyle \frac{dx}{dt}}=x\left(1-x\right)\left(E_{m1}-E_{m2}\right)=\left(1-x\right)x\left(P_b-\mathrm{s}y+dyz\right)$$

Let $E_{c1}$ and $E_{c2}$ represent the benefits of consumers choosing to participate in formal recycling channels and informal recycling channels, respectively, and let $F_c\left(y\right)$ be the replicative dynamic equation for consumers choosing formal recycling strategies. Then, the following are given:

$$E_{c1}=xz\left(R_1+\mu C_2+s\right)+x\left(1-z\right)\left(R_1+\mu C_2+s\right)+z\left(1-x\right)R_1+\left(1-x\right)\left(1-z\right)R_1$$

$$E_{c2}=xz(1-\alpha )R_2+x\left(1-z\right)R_2+z\left(1-x\right)(1-\alpha )R_2+\left(1-x\right)\left(1-z\right)R_2$$

$$F_c\left(y\right)={\displaystyle \frac{dy}{dt}}=y\left(1-y\right)\left(E_{c1}-E_{c2}\right)=\left(1-y\right)y\left(R_1-R_2+sx+\alpha R_{2}z+\mu C_{2}x\right)$$

According to the stability theorem of differential equations, when $F_m\left(x\right)=0$ and ${\displaystyle \frac{\partial F_m\left(x\right)}{\partial x}}<0$, the strategy $x$ of the vehicle manufacturers is a stable strategy. Let ${\displaystyle \frac{\partial F_m\left(x\right)}{\partial x}}<0$; solving gives that when $P_b-\mathrm{s}y+dyz>0$, $x=1$ is a stable strategy for the whole-vehicle enterprise. When $P_b>\mathrm{s}$, under this condition, the vehicle manufacturers will always choose to actively participate in recycling; when $P_b<\mathrm{s}$, the probability distribution of vehicle manufacturers choosing to actively participate is shown in Figure 2.

Proposition 4.

When the potential benefits of active participation in recycling are greater than the subsidies given to consumers, the firms will choose to actively participate in recycling; when the potential benefits are less than the subsidies given to consumers, the probability of the firms choosing to participate in formal recycling is positively correlated with the deposit and negatively correlated with the subsidies given to consumers.

Proof. 

Integrate $p_m$, when $P_b>\mathrm{s}$, $p_m=1$; when $P_b<\mathrm{s}$, there is $p_m={\displaystyle \frac{\left(1-{\displaystyle \int \left(\frac{s}{d}-\frac{P_b}{dy}\right)}dy\right)\times 1}{1\times 1\times 1}}=1+{\displaystyle \frac{P_b-s}{d}}-{\displaystyle \frac{P_b}{d}}\ln {\displaystyle \frac{P_b}{s}}$. Since ${\displaystyle \frac{\partial p_m}{\partial d}}>0$ and ${\displaystyle \frac{\partial p_m}{\partial s}}<0$, $p_m$ increases as $d$ increases and decreases as $s$ increases. □

Similarly, let ${\displaystyle \frac{\partial F_c\left(y\right)}{\partial y}}<0$, and when solving for $R_1-R_2+sx+\alpha R_{2}z+\mu C_{2}x>0$, $y=1$ is a stable strategy for the consumer. For the simplicity of calculation, define $R_2-R_1$ as the opportunity cost $\Delta R$ to the consumer when faced with two recycling channels and $\mu C_2$ as the consumer’s environmental awareness.

Proposition 5.

The probability of consumers choosing formal recycling increases with the level of subsidy by enterprises or the penalty by the government, and the higher the consumers’ own environmental awareness is, the more consumers tend toward formal recycling, and the higher the opportunity cost of participating in informal recycling channels is, the higher the probability of consumers participating in informal recycling.

Proof. 

Since $R_1-R_2+sx+\alpha R_{2}z+\mu C_{2}x=0$ is a straight line, there are five cases for the intersection points between the line and the coordinate axes. When $\Delta R>s+\mu C_2+\alpha R_2$, the probability of consumers participating in formal recycling is 0, and at this time, $y=0$ is a stability strategy; the probability that a consumer chooses to participate in formal recycling in the other cases is affected by $\alpha$, $s$, $\Delta R$, and $\mu C_2$. Here, we will only prove the case of $\alpha R_2<\Delta R<s+\mu C_2$, and the proof for the other cases is similar. The probability $p_c=1-{\displaystyle \frac{R_2-R_1-\frac{1}{2}\alpha R_2}{s+\mu C_2}}$ that a consumer chooses to participate in formal recycling at this time is shown in Figure 3. Since there are ${\displaystyle \frac{\partial p_c}{\partial \alpha }}>0$, ${\displaystyle \frac{\partial p_c}{\partial s}}>0$, ${\displaystyle \frac{\partial p_c}{\partial \left(\mu C_2\right)}}>0$, and ${\displaystyle \frac{\partial p_c}{\partial \left(\Delta R\right)}}<0$, $p_c$ increases as $\alpha$, $s$, or $\mu C_2$ increases and decreases as $\Delta R$ increases. □

The government’s stabilization strategy is analyzed next, specifically when $F_g\left(z\right)=0$ and ${\displaystyle \frac{\partial F_g\left(z\right)}{\partial z}}<0$ and when the government’s strategy $z$ is a stabilization strategy. Let ${\displaystyle \frac{\partial F_g\left(z\right)}{\partial z}}<0$; by solving when $C_1-\alpha R_2+\alpha R_{2}y-R_{g}y+d\left(-1+xy\right)<0$, $z=1$ is a stabilizing strategy for the government, and at this time, the probability that the government chooses the regulatory strategy is shown in Figure 4.

Proposition 6.

The probability that the government chooses to impose regulation is positively related to the government’s credibility gains, the amount of deposits, and the level of penalties imposed on informal recycling channels and negatively related to the operating costs of the deposit system.

Proof. 

When $C_1-\alpha R_2+\alpha R_{2}y-R_{g}y+d\left(-1+xy\right)<0$, based on the value ranges of $C_1$, $\alpha$, $d$, and $R_g$, multiple probability $p_g$ values regarding government regulation implementation can be obtained. Here, we discuss when $d+\alpha R_2>C_1$ and $R_g>\alpha R_2$; at this time, the following holds:

$$p_g={\displaystyle \iint C_1-\alpha R_2+\alpha R_{2}y-R_{g}y+d\left(-1+xy\right)}=1+{\displaystyle \frac{R_g-C_1}{d}}+\left(1+{\displaystyle \frac{\alpha R_2-C_1}{d}}\right)\ln {\displaystyle \frac{\alpha R_2-R_g}{d+\alpha R_2-C_1}}$$

Since there are ${\displaystyle \frac{\partial p_g}{\partial d}}>0$, ${\displaystyle \frac{\partial p_g}{\partial \alpha }}>0$, ${\displaystyle \frac{\partial p_g}{\partial R_g}}>0$, and ${\displaystyle \frac{\partial p_g}{\partial C_1}}<0$, $p_g$ increases as $\alpha$, $d$, and $R_g$ increase and decreases as $C_1$ increases. □

4.2.2. Stability Analysis of Equilibrium Points of Tripartite Evolutionary Game Systems

The system of simultaneous equations $F_g\left(z\right)=0,F_m\left(x\right)=0,F_c\left(y\right)=0$ yields a total of 14 solutions for $\left(x,y,z\right)$, among which there are six mixed strategies. In an asymmetric game, if the evolutionary game equilibrium e is an evolutionary stable equilibrium, then e must be a strict Nash equilibrium, which in turn is a pure strategy equilibrium, i.e., a mixed strategy equilibrium must not be an evolutionary stable equilibrium in an asymmetric game. Therefore, this article only explores the evolutionary stability of pure strategy equilibrium points, namely, $\left\{x\to 0,y\to 0,z\to 0\right\}$, $\left\{x\to 1,y\to 0,z\to 0\right\}$, $\left\{x\to 0,y\to 1,z\to 0\right\}$, $\left\{x\to 0,y\to 0,z\to 1\right\}$, $\left\{x\to 1,y\to 0,z\to 1\right\}$, $\left\{x\to 1,y\to 1,z\to 0\right\}$, $\left\{x\to 0,y\to 1,z\to 1\right\}$, and $\left\{x\to 1,y\to 1,z\to 1\right\}$, a total of eight equilibrium solutions, denoted as $e_5$, $e_6$, $e_7$, $e_8$, $e_9$, $e_{10}$, $e_{11}$, and $e_{12}$.

The Jacobian matrix under this three-party game system is as follows:

$$\begin{array}{cc}{J}_2& =\left[\begin{array}{lll}{\displaystyle \frac{\partial F_m(x)}{\partial x}}& {\displaystyle \frac{\partial F_m(x)}{\partial y}}& {\displaystyle \frac{\partial F_m(x)}{\partial z}}\\ {\displaystyle \frac{\partial F_c(y)}{\partial x}}& {\displaystyle \frac{\partial F_c(y)}{\partial y}}& {\displaystyle \frac{\partial F_c(y)}{\partial z}}\\ {\displaystyle \frac{\partial F_g(z)}{\partial x}}& {\displaystyle \frac{\partial F_g(z)}{\partial y}}& {\displaystyle \frac{\partial F_g(z)}{\partial z}}\end{array}\right]\\ & =\left[\begin{array}{ccc}(1-2x)(P_b-sy+dyz)& (1-x)x(-s+dz)& d(1-x)xy\\ (1-y)y(s+\mu C_2)& (1-2y)(R_1-R_2+sx+\alpha R_{2}z+\mu C_{2}x)& \alpha R_2(1-y)y\\ dy(-1+z)z& (\alpha R_2-R_g+dx)(-1+z)z& (C_1-\alpha R_2+\alpha R_{2}y-R_{g}y+d(-1+xy))(-1+2z)\end{array}\right]\end{array}$$

According to Lyapunov’s first discriminant method [51], the stability of the replicator dynamics system at an equilibrium point can be determined by the eigenvalues $\lambda$ of the Jacobian matrix under the game system. When all eigenvalues $\lambda$ of the Jacobian matrix have negative real parts, i.e., $\lambda <0$, the point is asymptotically stable. If there exists at least one eigenvalue with a positive real part, i.e., $\lambda >0$, the equilibrium point is unstable. When the eigenvalues $\lambda$ of the Jacobian matrix have zero real parts and no positive real parts, the stability of the equilibrium point cannot be determined. The following calculates the eigenvalues of the Jacobian matrix for the three-party game at the eight equilibrium points and determines their signs, as shown in

Table 6. Stability analysis of the equilibrium point of the three-party game.

	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$	Positive or Negative	Result
$e_5\left(0,0,0\right)$	$P_b$	$-C_1+d+\alpha R_2$	$R_1-R_2$	$\left(+,\ast ,-\right)$	Unstable
$e_6\left(1,0,0\right)$	$-P_b$	$-C_1+d+\alpha R_2$	$R_1-R_2+s+\mu C_2$	$\left(-,\ast ,\ast \right)$	ESS of Condition 1
$e_7\left(0,1,0\right)$	$-R_1+R_2$	$-C_1+d+R_g$	$P_b-s$	$\left(+,\ast ,+\right)$	Unstable
$e_8\left(0,0,1\right)$	$P_b$	$C_1-d-\alpha R_2$	$R_1+\alpha R_2-R_2$	$\left(+,\ast ,\ast \right)$	Unstable
$e_9\left(1,0,1\right)$	$-P_b$	$C_1-d-\alpha R_2$	$R_1-R_2+s+\mu C_2+\alpha R_2$	$\left(-,\ast ,\ast \right)$	ESS of Condition 2
$e_{10}\left(1,1,0\right)$	$-C_1+R_g$	$-P_b+s$	$-R_1+R_2-s-\mu C_2$	$\left(\ast ,-,\ast \right)$	ESS of Condition 3
$e_{11}\left(0,1,1\right)$	$-R_1+R_2-\alpha R_2$	$C_1-d-R_g$	$P_b-s+d$	$\left(\ast ,\ast ,+\right)$	Unstable
$e_{12}\left(1,1,1\right)$	$C_1-R_g$	$-P_b+s-d$	$-R_1+R_2-s-\mu C_2-\alpha R_2$	$\left(\ast ,-,\ast \right)$	ESS of Condition 4

Note: ∗ indicates that the positivity or negativity is uncertain. Condition 1: $C_1>d+\alpha R_2$ and $R_2-R_1>s+\mu C_2$. Condition 2: $C_1<d+\alpha R_2$ and $R_2-R_1>s+\mu C_2+\alpha R_2$. Condition 3: $C_1>R_g$ and $R_2-R_1<s+\mu C_2$. Condition 4: $C_1<R_g$ and $R_2-R_1<s+\mu C_2+\alpha R_2$.

.

Conclusion 2: In a deposit system implemented and supervised by the government, the active participation of the government plays a key role in standardizing the battery recycling market. (I) In the early stages of evolution, the system has a stable strategy of $e_6\left(1,0,0\right)$, where the recycling subsidies provided by enterprises and the low environmental awareness of consumers lead to high opportunity costs for consumers. The government’s implementation of deposit amounts and penalty costs is less than the cost of managing the deposit system. Consumers choose not to participate in formal recycling, and the government chooses not to implement supervision. In the battery recycling market, although vehicle manufacturers actively assume the extended producer responsibility system, the recycling efficiency is not high due to the lack of active participation and effective supervision from consumers and the government. (II) When the government gradually increases the amount of deposit and the cost of punishment so that $C_1<d+r$, from Proposition 6, the government chooses to enter the market to implement regulatory strategies to regulate the order of the recycling market, but due to the lack of practical experience, the deposit system fails to fully demonstrate its expected effect in the initial stage. At this stage of the evolutionary system’s development, consumers show hesitation and reluctance to participate in formal recycling channels despite government action, at which point the system reaches a stabilization point in $e_9\left(1,0,1\right)$. (III) After studying consumer recycling behavior, it can be inferred from Proposition 5 that vehicle manufacturers increase recycling subsidies, the government intensifies penalties for informal recycling activities, and simultaneously, it enhances consumer environmental awareness education. At this point, the system is in state $e_{12}\left(1,1,1\right)$, and the evolutionary system reaches a mature stage. In this stage, consumers are driven by both personal intrinsic factors and external benefits, tending to actively participate in formal recycling processes. With the cooperation of all parties, waste power batteries are utilized reasonably and efficiently, the government successfully achieves its pollution reduction and carbon reduction goals, and companies improve their recycling rates due to broader consumer participation in formal recycling, thereby increasing the material reuse rate, resulting in an ideal state for the recycling market. (IV) Along with the improvement in the deposit system and the standardized development of the recycling market, the government reduces the deposit amount and adopts the strategy of loose regulation. According to Proposition 6, the probability that the government implements supervision decreases, and the evolutionary system is in the stabilization stage, at which time the combination of evolutionary stabilization strategies is $e_{10}\left(1,1,0\right)$, and the government realizes that too much intervention may increase the financial burden and therefore gradually shifts to the strategy of not implementing supervision. This signifies that the battery recycling market has entered a regulated track and is operating in an orderly and efficient manner.

5. Game Model Simulation Discussion

From Conclusion 1, it can be seen that the deposit system formed under the market mechanism has limitations, and the “agreement-type” deposit system between vehicle enterprises and consumers cannot regulate the battery recycling market well, so this section only simulates and analyzes the three-party game model with government participation. Combining the “China New Energy Vehicle Industry Development Report (2023)” published by the China Automotive Technology Research Center and relevant references, we assign values to the parameters, as shown in

Table 7. Matlab simulation data values.

Symbol	Value	Symbol	Value Range
$C_1$	3	$\mu$	[0, 1]
$C_2$	1	$\alpha$	[0, 1]
$R_1$	3	$d$	[0, 3]
$R_2$	5	$s$	[0.2, 1.2]
$P_b$	1	$R_g$	[2, 4]

, and use Matlab R2019a software to simulate the evolution system; at the same time, we explore the key parameters $d$, $\alpha$, and $\mu$ and analyze their impact on the evolution process and results.

5.1. Stable Equilibrium Point Simulation

Set the combination of vehicle enterprises, consumers, and the government’s market entry strategy $\left(x,y,z\right)$ as a random distribution, and the participating subjects evolve under different conditions to eventually form a stable strategy. Assigning the values $d=0$, $\mu =0.2$, $\alpha =0$, $s=0.5$, and $R_g=3$ and conducting multiple simulations to obtain the results of Figure 5a, the evolutionary trajectory is stable at (1,0,0), and at this time, the evolutionary system is in the initial stage. At this time, the government did not implement regulation, consumers have little awareness of environmental protection, and consumers in the battery recycling market tend to give batteries to informal recycling enterprises to maximize their own revenue.

Assigning $d=3$, $\mu =0.2$, $\alpha =0.2$, $s=0.7$, and $R_g=3$, at this time to meet Condition 2, after simulation to obtain the results of Figure 5b, the evolutionary trajectory is stabilized at (1,0,1), and at this time, the evolutionary system is in the developmental stage. The government gradually recognizes the key role it plays in regulating the recycling market. In an effort to guide consumer behavior, the government raised the deposit amount and increased the cost of non-compliance. At the same time, automakers responded by creating recycling subsidies to incentivize consumers to participate in the formal recycling process. Nonetheless, consumers still prefer informal recycling channels because they are more profitable. Consumers’ low environmental awareness also influences their recycling behavior choices to a certain extent.

Assigning the values $d=3$, $\mu =0.9$, $\alpha =0.4$, $s=1.2$, and $R_g=4$ and conducting multiple simulations to obtain the results in Figure 5c, the evolutionary trajectory is stable at (1,1,1), at which time the evolutionary system is in the mature stage. After the government implemented the deposit system and increased the punishment, the battery recycling market gradually moved towards standardization. Consumers began to actively participate in the formal recycling process, and the awareness of recycling used batteries has been significantly improved. This series of government policies has won wide recognition in the community and effectively enhanced its credibility. In the process of implementing the deposit system, the government has continuously adjusted and optimized its management strategy based on market feedback, effectively reducing operating costs and demonstrating the government’s flexibility and efficiency in market regulation.

Assigning the values $d=3$, $\mu =0.9$, $\alpha =0.2$, $s=1.2$, and $R_g=2$ and conducting several simulations to obtain the results in Figure 5d, the evolutionary trajectory is stabilized at (1,1,0), at which time the evolutionary system is in a stable stage. The government decides to reduce regulations and interventions to save public expenditure, and at this time, the government no longer adopts the regulatory strategy. Consumer behavior has been standardized, environmental awareness has been raised, and vehicle companies have shown a positive attitude toward participation, taking the initiative to engage in the recycling of used batteries. Thanks to these initiatives, the recycling rate and the reuse rate of waste materials have achieved a significant increase, demonstrating the positive results of market self-regulation and corporate social responsibility.

5.2. Sensitivity Analysis

5.2.1. The Impact of Subsidies for Complete Vehicle Enterprises on System Evolution

When the vehicle manufacturers increase the recycling subsidies for consumers to improve the battery recycling rate, and when the deposit system is not implemented ($d=0$), the consumers’ environmental awareness $\mu$ is set at 0.5, the government’s regulatory intensity $\alpha$ is set at 0.2, and the subsidies from the vehicle manufacturers $s$ are set at three stages: low, medium, and high, with values of 0.2, 0.8, and 1.2, respectively. The initial evolution probabilities are (0.5, 0.5, 0.5), and the evolution trajectories of each entity are shown in the Figure 6. At this point, the system presents a stable strategy (Active participation by enterprises, Informal recycling by consumers, No regulation by the government), and with the increase in enterprise subsidies, the speed of convergence of the whole-vehicle enterprises slows down; for consumers, there is no constraint of the deposit system, and the increase in subsidies by enterprises can only slow down the speed of the consumers who choose to participate in the informal recycling strategy. As the subsidy from enterprises is provided by the whole-vehicle companies to consumers, it has little impact on the government’s decision. It is clear that without a deposit system, increased subsidies from vehicle manufacturers alone cannot achieve the goal of regulating the market.

5.2.2. The Impact of Consumer Environmental Awareness on System Evolution

When waste power batteries are disposed of without formal dismantling, flow through the dismantling technology is low, and the low investment in pollution control after the small workshop will increase carbon emissions and exacerbate environmental pollution. The consumer’s environmental awareness is reflected in the perception of the cost of pollution $\mu$, where the consumer’s environmental awareness is divided into low, medium, and high degrees; these three degrees take the value of 0.1, 0.5, and 0.9, respectively, and the initial evolution probability is (0.5,0.5,0.5). As can be seen from Figure 7, when consumers’ environmental awareness is low, consumers will not participate in formal recycling, and when $\mu$ gradually increases, consumers’ behavioral strategies change. This verifies the correctness of Proposition 5, that is, the improvement in consumers’ own environmental awareness is more likely to make consumers realize the necessity of returning batteries to formal treatment enterprises, but consumers’ choice to participate in formal recycling is also affected by other factors, and only the enhancement of consumers’ awareness of environmental protection does not completely change their strategies; under government regulation, with the improvement in consumers’ awareness of environmental protection, consumers realize the necessity of returning batteries to formal treatment enterprises and are less likely to choose informal recycling channels, causing the government to gradually reduce the regulation of informal recycling enterprises.

5.2.3. The Impact of Deposit Amount on System Evolution

Previous analyses have established that both increasing the subsidy of vehicle manufacturers and enhancing consumers’ environmental awareness can effectively increase the probability of consumers choosing formal recycling channels, but these measures are not sufficient to bring consumers’ behavioral strategies to a steady state. This section analyzes the initial implementation stage and the subsequent development stage of the deposit system and explores the impact of different deposit amounts on the evolutionary process of the system.

At the initial stage of the deposit system implementation, when consumers’ environmental awareness is low ($\mu =0.2$), the government’s punishment is not strong ($\alpha =0.1$), and the whole-vehicle enterprise as a recycler adopts a low recycling subsidy strategy for consumers ($s=0.2$). The deposit amount is taken to be the values of 0, 1.5, and 3, respectively, which represents that the government gradually increases the deposit amount, and the initial evolution probability is (0.5,0.5,0.5). From Figure 8, it can be seen that as the deposit amount increases, the government tends to choose to implement supervision, which verifies the correctness of Proposition 6; consumers tend to participate in informal recycling under low environmental awareness and low recycling subsidies; and OEMs will actively participate in the recycling of used batteries under the condition of supervision.

With the introduction and implementation of relevant policies, consumers’ environmental awareness is raised to a certain degree ($\mu =0.6$), the government strengthens the punishment of informal recycling enterprises ($\alpha =0.3$), and the whole-vehicle enterprises increase the recycling subsidy ($s=0.8$) such that the initial evolution probability is (0.5,0.5,0.5). The evolution results are shown in Figure 9, which reveals that when the government strengthens the punishment of the informal recycling industry and consumers have high environmental awareness, the choice of strategy of consumers will be to tend to choose to participate in formal recycling as the deposit amount increases; OEMs tend to see that consumers are all recycling batteries through formal channels, so that they can not only return their deposits but also make profits through laddering and dismantling, so they always choose to actively participate in recycling. The probability of the government’s choice to regulate is gradually converging to $z=1$, but it is affected by the operating costs and credibility gains, etc., and its strategy has convergence stability but does not satisfy the condition of ESS.

6. Conclusions

This article constructs two deposit systems for the recycling of power batteries for new energy vehicles based on evolutionary game theory. One is a deposit system formed under market mechanisms involving participation from enterprises and consumers, while the other is a deposit system implemented and supervised by the government. The stable equilibrium points of the two-party game model and the three-party game model are analyzed. Propositions 1–3 analyze the evolutionary stable strategies of vehicle manufacturers and consumers under the two-party game, while Propositions 4–6 analyze the stable strategies of each participant under the three-party game. Conclusions 1 and 2 analyze the evolutionary processes of the two deposit systems, and then numerical simulation analysis of the deposit system implemented and supervised by the government is conducted using Matlab software. This research shows the following:

(1) The deposit system formed by the market mechanism cannot achieve the stable strategy of (1,1), and the deposit is too large, which will cause the strategies of vehicle enterprises and consumers to show cyclical changes; the deposit system formed by the market mechanism is more flexible, which can respond to the market changes quickly, but the strategy of the consumers cannot be stabilized to the point that they “participate in the formal recycling”; furthermore, the deposit system under government regulation is more stable, which can help to achieve the long-term environmental goals and public interests. The government-regulated deposit system is more stable and helps to realize long-term environmental protection goals and social public interests.

(2) For the deposit system formed under the market mechanism, the strategy of vehicle manufacturers in choosing whether to implement the deposit system is related to the operating costs, potential revenue, and pollution control costs; in the case of the deposit system regulated by the government, vehicle manufacturers will always tend to actively participate in the recycling when the potential revenue they obtain is greater than the level of subsidy given to consumers.

(3) Enhancing consumers’ environmental awareness can help strengthen their understanding of the necessity of proper battery recycling. However, environmental awareness alone is not sufficient to fully drive the shift in recycling behavior. Even if consumers have a high level of environmental awareness, the price difference between formal and informal recycling channels may still be a key barrier. In a deposit system regulated by the government, consumer behavior is also related to the subsidy levels of enterprises and the amount of the deposit. Increasing the deposit amount and raising the subsidy levels of enterprises can both encourage consumers to participate in formal recycling.

Based on the above findings, this paper makes the following recommendations:

(1) The construction of a new energy vehicle power battery traceability system should be strengthened to monitor the entire life cycle of the battery, which can guarantee the effective management of every aspect of the battery from production, to use, to recycling; ensure the flow of deposit refunds; ensure the safety and environmental protection of the battery; and promote the effective utilization of resources and the sustainable development of the environment.

(2) The government should play a leading role in the supervision of the recycling market, improve regulatory systems, and restrict the entry of recycling enterprises with low recycling technology and high pollution emissions. At the same time, the government should also focus on the integration of informal recycling enterprises, promote their transformation and upgrading, and encourage them to undertake standardized renovations through policy guidance and financial support, thereby improving their recycling technology and management levels.

(3) The government needs to set deposit amounts reasonably in accordance with the current level of economic development and social structure and to ensure that the collection and refund processes of deposits are fair and transparent. Since the implementation of the deposit system involves the reallocation of economic responsibilities among stakeholders related to product production, consumption, and disposal, it is recommended that during the design and implementation stages of the deposit system, all relevant stakeholders be organized for full consultation and discussion to ensure their acceptance of the system.

(4) Through extensive publicity and educational activities, such as advertising investment, media promotion, and school education through multiple channels, consumers’ awareness of the importance of recycling new energy vehicle power batteries should be enhanced. Recycling entities are encouraged to add more recycling sites and provide convenient recycling services, such as quick registration, online appointment, and door-to-door recycling, to reduce the barriers and costs for consumers to recycle batteries.