Five-Stakeholder Collaboration in Power Battery Recycling Within Reverse Supply Chains: Threshold Analysis and Policy Recommendations via Evolutionary Game and System Dynamics

Abstract

The current retired recycling system suffers from “systemic coordination failure”, primarily due to ambiguous responsibility boundaries hindering interenterprise collaboration, unequal profit distribution discouraging technological innovation investment, and low participation from both consumers and recycling enterprises undermining the efficiency of recycling channels. However, the simplified tripartite game models commonly adopted in existing research exhibit significant limitations in explaining and addressing the above practical challenges, as they fail to incorporate consumers and third-party recyclers as strategic decision-makers into the analytical framework. To address these issues, this study develops, for the first time, a five-party evolutionary game model involving governments, vehicle manufacturers, battery producers, third-party recyclers, and consumers within a reverse supply chain framework. We further employ system dynamics to simulate the dynamic evolution of stakeholder strategies. The results show that: (1) When tri-party synergistic benefits exceed 15, the system transitions from resource dissipation to circular regeneration. (2) Government subsidies reaching the threshold of 2 effectively promote low-carbon transformation across the industrial chain. (3) Bilateral synergistic benefits of 12 can stimulate green technological innovation and industrial upgrading. (4) Establishing a multi-stakeholder governance framework is key to enhancing resource circulation efficiency. This research provides quantitative evidence and policy implications for constructing an efficient and sustainable power battery recycling system.

1. Introduction

With the rapid development of the global new energy vehicle industry, power battery recycling has become a critical link in achieving green transformation across the entire industrial chain and resource circulation [1,2,3]. As the world’s largest new energy vehicle market [4], China is experiencing an explosive growth phase in the volume of retired power batteries [5]. China’s retired power battery volume will reach 820,000 tons by 2025 [6], exceeding 4 million tons starting in 2028, with the waste battery recycling industry’s output value surpassing 280 billion yuan [7].

However, the current system for recycling end-of-life power batteries faces a severe problem of ‘systemic coordination failure’, primarily manifested in three aspects. Firstly, ambiguous boundaries of responsibility lead to fragile collaborative relationships between automotive manufacturers, battery producers, and recycling enterprises. Secondly, unequal profit distribution severely constrains corporate investment in technological innovation. Thirdly, insufficient participation from consumers and recycling enterprises undermines the coverage of formal recycling channels. These issues not only lead to high battery recycling costs, low recovery efficiency, hindered green technology innovation, and severe waste of strategic metal resources, but also precipitate a series of environmental and safety risks [8]. Effective recycling extracts critical metals like lithium, cobalt, and nickel, reducing reliance on foreign sources [9]. Furthermore, a robust recycling system can stimulate related industrial chains and create new economic opportunities [10]. Therefore, establishing an efficient and collaborative recycling system is urgently needed.

Several countries have introduced relevant policies to address these challenges. The EU’s New Battery Regulation also mandates the establishment of extended responsibility mechanisms covering producers, professional recyclers, and consumers [11]. China has successively issued the Interim Measures for the Management of Recycling and Utilization of Power Batteries for New Energy Vehicles and the Action Plan for Establishing a Sound Recycling and Utilization System for Power Batteries of New Energy Vehicles [12]. These documents explicitly require the establishment of a full-chain responsibility system combining extended producer responsibility, consumer cooperation, and third-party coordination. They further emphasize the use of digital technologies to implement ‘digital identity management’ throughout the entire lifecycle of power batteries [13]. In industry practice, enterprises such as GEM have achieved metal recovery rates exceeding 98.5% for lithium, cobalt, and nickel through automated dismantling and comprehensive component recycling processes, reducing annual carbon emissions by 86,000 tons. This demonstrates the technical and economic potential of specialized third-party recycling [9]. Consequently, the recycling of new energy vehicle power batteries requires the joint participation of governments, automakers, battery manufacturers, recycling enterprises, and consumers.

Despite the emerging consensus on multi-stakeholder engagement, this practical consensus is not adequately reflected in the current theoretical models of power battery recycling. Existing research predominantly focuses on a tripartite game-theoretic framework dominated by “government-automotive companies-battery manufacturers,” treating consumers and professional third-party recyclers as passive participants or external conditions [11]. This “incomplete actor” model fails to explain or resolve real-world systemic coordination dilemmas [14]. Consumers’ proactive decision-making—whether “active participation” or “passive participation”—is overlooked due to insufficient incentives, information asymmetry, or inconvenient recycling channels. Yet this behavior directly determines the coverage efficiency and scale of recycling networks [15]. Similarly, third-party recyclers like Redwood Materials, possessing scale advantages and technical expertise, make strategic decisions—whether to pursue “high investment” or “low investment” approaches—based on expected returns and policy support. These decisions are inadequately incorporated into theoretical models, leaving their critical role in enhancing dismantling efficiency, optimizing material recovery rates, and influencing cooperative benefit distribution unexplained [16]. This incomplete theoretical characterization of core actors’ participation is the fundamental reason for existing research’s insufficient explanatory power regarding real-world issues like “responsibility-sharing conflicts” and “benefit-distribution conflicts.” It also constitutes the core theoretical bottleneck constraining the enhancement of the entire recycling system’s collaborative effectiveness.

Therefore, this paper innovatively incorporates consumers and third-party enterprises as game participants, constructing a five-party evolutionary game model involving the government, automakers, battery manufacturers, third-party recyclers, and consumers. This model not only better aligns with real-world decision-making structures but also reveals the dynamic pathways for systemic cooperation mechanisms, responsibility allocation, and efficiency optimization. It provides theoretical foundations and policy insights for addressing the systemic coordination failure in power battery recycling, thereby advancing the “green closed-loop” development of the new energy vehicle industry.

The subsequent structure of this paper is as follows: Section 2 reviews relevant literature; Section 3 elaborates on model construction and assumptions; Section 4 presents numerical simulation results and conducts discussions; Section 5 summarizes research conclusions and proposes policy recommendations.

2. Literature Review and Theoretical Framework

The low collaborative efficiency of power battery recycling systems represents a core bottleneck constraining the industry’s sustainable development. Its root cause lies in “systemic coordination failure” stemming from conflicting objectives and ambiguous responsibilities among multiple stakeholders. To delve into this issue, this section first systematically traces the evolution of key players and research focal points in power battery recycling studies. It then critically examines the applicability and limitations of methodologies such as evolutionary game theory and system dynamics. Finally, it precisely identifies gaps in existing research and clarifies the theoretical innovation path of this paper.

2.1. Collaborative Recycling of Power Batteries

In the early stages of power battery recycling research, scholars primarily focused on the most fundamental bilateral relationships. For instance, early studies concentrated on the regulatory and response games between governments and manufacturers, analyzing how subsidy policies and penalty mechanisms influence corporate recycling behaviors [6]. While such two-party game models simplify systemic complexity and reveal the fundamental incentive effects of policy tools, they struggle to capture the competitive and cooperative dynamics among multiple corporate actors in the market. They also fail to reflect the critical influence of consumer behavior on the effectiveness of recycling networks.

With the expansion of Extended Producer Responsibility (EPR) systems, research perspectives have broadened to a tripartite game framework involving governments, automakers, and battery manufacturers. This framework has become the mainstream paradigm in recent years, emphasizing the optimization of responsibility allocation, recycling model selection, and government incentive mechanisms [17,18]. Wang et al. [19] represent a recent tripartite study in which they constructed an evolutionary game model involving the government, EV manufacturers, and consumers. Their research clearly indicates that in the initial stage of establishing a recycling system, when the willingness of all parties to participate is low, the government must play a leading role through subsidies and regulation. As the market gradually matures, the government can then withdraw in an orderly manner and shift toward a regulatory model dominated by market mechanisms. This conclusion provides important insights into understanding the dynamic role of policy intervention. However, this mainstream framework has inherent limitations.

Its core limitation lies in the “oversimplified treatment” of the strategic behaviors of consumers and third-party recyclers. On the one hand, such models typically treat consumers as parameters with fixed recycling probabilities or passive respondents, overlooking the fact that their decision-making is a strategic process based on economic incentives, convenience, and environmental awareness. The active participation of consumers—that is, consciously returning batteries through formal, traceable channels—forms a fundamentally different strategic pathway from passive behaviors such as leaving batteries idle, disposing of them illegally, or diverting them to informal markets. This choice not only determines whether retired batteries enter the formal recycling network, ensuring the upstream supply of the reverse supply chain, but also, more profoundly, stabilizes the source of raw materials, significantly reduces the costs of system coordination and logistics, and improves the operational efficiency and resource output of subsequent processes. Models that externalize this critical decision-making process thus struggle to inherently explain why “black market” channels can attract batteries through higher purchase prices, and the resulting environmental risks and resource loss [14]. On the other hand, by simplifying third-party professional recyclers as static cost parameters, the models fail to capture their strategic choices of high or low investment based on techno-economic assessments. Consequently, they also find it difficult to analyze how policy tools can incentivize technological innovation to improve material recovery rates [15].

To better reflect the realities of power battery recycling, some cutting-edge research has begun constructing four-party game models, typically incorporating consumers or independent third-party recyclers as endogenous decision-makers. For instance, Xie et al. [20] developed a four-party model encompassing governments, manufacturers, recyclers, and consumers to analyze Pareto improvements in recycling channel selection. Furthermore, recent studies have increasingly focused on the influence of informal recyclers, forming a dynamic four-party game relationship: “government-formal recyclers-informal recyclers-consumers.” Li et al. [21] used an evolutionary game model to reveal that informal recyclers, leveraging lower operational costs, purchase end-of-life batteries from consumers at higher prices, placing formal recyclers at a competitive disadvantage. Existing four-party models often fail to incorporate informal recyclers as independent actors, making it difficult to explain the market distortion of “bad money driving out good.” Similarly, most existing models treat informal recyclers merely as exogenous disturbances, failing to incorporate their substantial influence on consumer choices and enterprise revenues into the decision parameters and incentive structures of the core players. Consequently, these models struggle to reveal the internal conditions and thresholds required for formal recycling systems to overcome such competition. Simultaneously, the introduction of deposit-refund policies complicates stakeholder interactions. Miao et al. [22] confirmed in photovoltaic module recycling research that deposit amounts and refund ratios significantly influence strategic choices of consumers and recyclers. However, related studies in power battery recycling have yet to fully integrate this policy variable’s impact on multi-stakeholder decision-making.

2.2. Evolutionary Game Theory and System Dynamics

In terms of research methodology, evolutionary game theory (EGT) is particularly well-suited for analyzing the strategy adjustment and learning processes of multiple actors within battery recycling systems under conditions of incomplete information, owing to its fundamental assumption of “bounded rationality” [23]. It simulates how actors converge toward stable strategies through trial-and-error, imitation, and learning. Studies by Wang et al. [24] and Zhang et al. [25] successfully applied EGT to analyze the strategic evolution of relevant actors under government regulation. Li et al. [21] constructed a three-party evolutionary game model involving government, recyclers, and consumers to simulate dynamic strategy adjustments under varying subsidy intensities. They found that when subsidies for formal recyclers increased from 0/kWh to 40/kWh, the system’s stable strategy shifted from “Regulation-Informal Recycling-Non-Green Behavior” to “No Regulation-Formal Recycling-green behavior.” However, while EGT excels at depicting the equilibrium-seeking process of strategic interactions among micro-agents, it struggles to capture macro-system-level dynamic complexities such as nonlinear feedback, time-lag effects, and critical thresholds [26]. While increased government subsidies may be predicted as positive incentives in EGT models, they fail to effectively simulate potential long-term “subsidy fraud” or crowding-out effects on technological innovation.

In contrast, System Dynamics (SD) excels at handling high-order, nonlinear, multi-feedback complex systems. It can simulate from a macro perspective how policy variables like subsidy intensity influence system structure to drive changes such as recycling rates [27]. SD models clearly illustrate the complete loop: “policy intervention → behavioral change → system feedback → new equilibrium.” Joshi et al. [28] employed a system dynamics model to analyze the impact of tax breaks and subsidies on the lead-acid battery recycling market. They found that subsidy policies must be synchronized with market material flow optimization to avoid the contradiction of “excess capacity but insufficient raw materials” in formal recycling channels. However, traditional applications of SD models have primarily focused on material flow optimization and environmental impact assessment, with relatively weak characterization of micro-level agent strategy decisions and adaptive learning processes. Some scholars’ research is confined to equilibrium analysis of EGT, failing to further reveal the dynamic threshold effects of parameter variations through simulation.

Neither the EGT nor the SD approach alone can fully capture the inherent limitations when analyzing complex recycling systems. While EGT effectively depicts strategic interactions and conflicts of interest among multiple actors under bounded rationality [23], its analysis often remains confined to comparative static equilibrium studies, struggling to capture the dynamic complexity arising from nonlinear feedback loops and time-lag effects [26]. When analyzing government subsidy policies, EGT can reveal automakers’ strategic oscillation between “active recycling” and “passive recycling” [19], yet struggles to simulate systemic risks such as fiscal pressures, corporate dependency, or subsidy fraud that may arise from long-term policy implementation [29]. In contrast, SD excels at simulating how policy variables influence aggregate behavior through systemic structures from a macro perspective [27]. However, it struggles to capture the strategic learning and interactive processes of micro-level agents, often simplifying agent behavior into exogenous rules and failing to fully reflect the endogenous evolution of strategies amid conflicting interests [14].

The integration of EGT and SD methods bridges the methodological gap between conflict identification and collaborative optimization. EGT reveals strategic conflicts and evolutionary trajectories at the micro level concerning core issues like responsibility allocation and benefit distribution, providing behavioral rules for system modeling [21]. Building upon this, SD embeds micro-level strategies within a macro-level feedback network of “policy-behavior-system performance,” dynamically simulating the systemic conditions for conflict resolution and synergy realization [27]. For instance, when analyzing “deposit-refund” policies, EGT can first define the strategic spaces and learning rules for governments, consumers, and recyclers under deposit incentives [22], then employ SD to simulate the long-term impacts of varying deposit levels on recycling channel selection, environmental externalities, and social welfare. This approach identifies the policy threshold enabling the synergistic state of “high formal recycling rates—low environmental risks” [21]. Compared to some scholars’ static equilibrium analysis relying solely on EGT, this integrated “conflict modeling–dynamic simulation” framework bridges the gap from strategic interactions to systemic emergence. It provides more actionable quantitative evidence for identifying critical policy levers and resolving “synergy failure”.

In recent years, multi-method integration has emerged as a significant trend in modeling power battery recycling systems, aiming to enhance models’ explanatory power and policy applicability. Chen et al. [30] combined evolutionary games with Stackelberg games to analyze optimal subsidy forms under varying government budget constraints, finding that fixed subsidies better incentivize cooperation without budget constraints, while capacity subsidies yield superior social welfare under budget limitations. Yu et al. [31] integrated life cycle assessment (LCA) data into SD models to quantify the environmental benefits and costs of different recycling technologies, such as hydrometallurgy and physical recovery, providing empirical support for parameter setting in SD simulations. While expanding methodological boundaries, these studies also indicate that the deep integration of EGT and SD lacks a standardized framework. Variations in model structures, parameter transmission, and outcome measurement across different studies constrain the accumulation and comparison of research findings [29].

2.3. Limitations of Existing Research and Research Innovations

Based on the above critical review, this study identifies three closely interrelated research gaps: First, deficiencies in the stakeholder dimension. Existing models fail to comprehensively encompass the five core decision-making entities within the power battery recycling system, particularly overlooking the direct influence of consumers and the specialized value of third-party recycling enterprises. This results in inadequate explanatory power for real-world coordination issues such as “conflicts over responsibility allocation” and “conflicts over benefit distribution.” Second, weak dynamic mechanisms. Insufficient parameterization of key real-world mechanisms—such as government subsidy parameters, collaborative benefits under different corporate strategies, and profit distribution—limits models’ ability to explain and predict complex interest coordination processes. Research commonly treats collaborative benefits as fixed parameters, failing to deeply analyze how their variation and dynamic allocation affect the stability and evolution of stakeholders’ strategies. This prevents revealing the threshold effects that trigger a system’s shift from “cooperation” to “non-cooperation.” Third, insufficient methodological integration: EGT and SD are often used in isolation within multi-agent recycling system modeling, lacking deep integration. This hinders the simultaneous precise analysis of micro-level strategic interactions and macro-level system feedback and their mutual influences.

To address these gaps, this paper innovates in the following ways: First, theoretical model innovation. Breaking from existing three- or four-party game frameworks, it pioneers a five-party evolutionary game model encompassing government, automakers, battery manufacturers, third-party recyclers, and consumers. By explicitly positioning consumers and third-party recyclers as endogenous strategic decision-makers, it more comprehensively reveals the dynamic pathways of system cooperation mechanisms, responsibility allocation, and efficiency optimization. Second, deepening parameter mechanisms. Key parameters such as profit distribution coefficients, government subsidies, and collaborative benefits under different corporate strategies are introduced. This enhances the model’s ability to depict real-world conflicts of interest, risk sharing, and policy adaptability, thereby improving its explanatory power. Third, methodological integration and innovation. This paper achieves a deep cross-method integration of evolutionary games and system dynamics. By defining the rules for agent strategy interactions through EGT and utilizing SD to simulate system dynamics feedback and emergent behaviors under multi-agent interactions, it identifies critical policy thresholds for system coordination. This provides more actionable quantitative policy insights for addressing “coordination failure,” thereby addressing the limitations in dynamic simulation depth found in studies such as those by Wang et al. [19]. Fourth, integrating multi-country policy practices, this study employs numerical simulations to analyze how different policy tools—such as subsidy mechanisms and dynamic incentives—impact system equilibrium. It identifies critical policy thresholds that drive strategic shifts among stakeholders, providing precise and actionable guidance for governments designing dynamic subsidy mechanisms, enterprises formulating cooperation and investment strategies, and consumers adopting participation strategies. Ultimately, this research offers an operational pathway to resolve the “coordination failure” in power battery recycling.

3. Model Construction

3.1. Model Construction Basis

The current system-wide coordination failure within the retired power battery recycling framework manifests as multidimensional, systemic institutional shortcomings in industrial practice. Taking Tesla’s battery recycling ecosystem as an example, despite establishing a comprehensive system encompassing multiple stakeholders—including strategic partnerships with high-energy-density ternary lithium battery suppliers like Panasonic and lithium iron phosphate battery suppliers such as CATL [15], alongside a closed-loop recycling alliance with specialist recycler Redwood Materials and securing US$35 per kilowatt-hour production subsidies under the Inflation Reduction Act [32], it still confronts three critical challenges. Firstly, incomplete contracts undermine the stability of collaborative foundations, with parties lacking binding institutional arrangements regarding long-term recycling responsibility demarcation, technical standard alignment, and allocation of unforeseen environmental costs. Secondly, the absence of a value distribution mechanism stifles technological innovation vitality. The material regeneration premiums achieved by specialized recyclers through advanced processes struggle to secure reasonable returns within existing cooperative frameworks, while battery manufacturers wield pricing dominance owing to their central position in the industrial chain. Thirdly, policy dependency and insufficient participation incentives collectively undermine system resilience. Consumer engagement is constrained by dual limitations of economic compensation and delivery convenience, while third-party recyclers’ technological investment decisions heavily depend on stable policy expectations and secure raw material supply. Moreover, the widespread competition from informal recycling channels in reality exacerbates the aforementioned challenges. By offering more convenient disposal options, it significantly increases consumers’ tendency to choose “passive participation.” On the one hand, it suppresses economies of scale and technological advancement among professional recyclers; on the other hand, it forces the formal network to raise its “attractiveness threshold.” Hence, the market distortion of “bad money driving out good” is both a deep-seated manifestation of “systemic coordination failure” and a driving factor behind its persistence.

Addressing these issues, this paper constructs a five-party evolutionary game model involving government, automotive manufacturers, battery producers, third-party recyclers, and consumers. The model internalizes the practical constraints imposed by informal recycling competition into the decision-making logic of the core players. For consumers, their strategic choice depends on whether incentive parameters in the model are sufficient to offset the appeal of informal channels; for recycling and manufacturing enterprises, the benefits of cooperative strategies must surpass an economic viability threshold elevated by competition. By parameterizing key policy variables—including subsidy intensity, penalty mechanisms, revenue distribution coefficients, and coordination costs—the model systematically depicts strategic interactions among stakeholders in responsibility allocation and benefit distribution. As illustrated in Figure 1, the five-party game and simulation process not only structurally represents real-world issues such as softening contractual constraints and imbalanced value distribution but also enables quantitative analysis through system dynamics simulation of how policy variables dynamically influence system equilibrium. This modeling framework provides crucial methodological support for designing incentive-compatible contractual structures, establishing profit-sharing mechanisms aligned with sustainable consumption and production patterns, and optimizing multi-stakeholder collaborative governance models. It offers a systematic solution for achieving responsible resource management and fostering industrial innovation alongside infrastructure upgrades. Ultimately, it provides both theoretical foundations and practical pathways for resolving the ‘systemic coordination failure’ in battery recycling and advancing the transition towards a circular economy.

3.2. Model Assumptions

This paper considers five players in the game: the government, automakers, battery manufacturers, third-party enterprises, and consumers. Each player has two distinct strategy options within the recycling system, and different strategy choices produce different impacts.

Assumption 1.

The government possesses two strategies: participation and non-participation. The probability of the government choosing the participation strategy is x, while the probability of choosing the non-participation strategy is (1 − x). Consumers possess two strategies: active participation and passive participation. The probability of consumers choosing the active participation strategy is y, while the probability of choosing the passive participation strategy is (1 − y). Automakers have two strategies: active recycling and passive recycling. The probability of an automaker choosing the active recycling strategy is z, and the probability of choosing the passive recycling strategy is (1 − z). Battery manufacturers have two strategies: cooperation and non-cooperation. The probability of a battery manufacturer choosing the cooperation strategy is m, and the probability of choosing the non-cooperation strategy is (1 − m). Third-party enterprises have two strategies: high investment and low investment. The probability of a third-party enterprise choosing the high investment strategy is n, and the probability of choosing the low investment strategy is (1 − n).

Assumption 2.

When participating in collaborative battery recycling, the government can obtain benefits G from improvements in the natural and social environment. This benefit is determined by the government’s share coefficient k for three-party collaboration, the government’s share coefficient for two-party collaboration, and unused collaborative benefits. Specifically, G = kA + qM. Additionally, the government must bear policy formulation and implementation costs R. To support relevant policies, the government provides subsidies H to enterprises actively participating in collaborative recycling and imposes penalties P on non-participating enterprises. Under the vehicle “trade-in” policy, China’s Ministry of Commerce and other departments issued the “Notice on Further Improving the Vehicle Trade-in Program,” stipulating that individual consumers may receive subsidy J when scrapping old vehicles and purchasing new ones under specified conditions [33]. The level of government subsidy directly influences corporate participation probability: higher subsidies H incentivize participation, while insufficient subsidies reduce willingness to participate.

Assumption 3.

Automobiles are sold to consumers, who return them to the recycling system upon scrapping. Consumers receive direct benefits f from corporate recycling and indirect social benefits W. Enhanced efficiency in cooperative battery recycling increases resource reuse rates, generating environmental benefits G.

Assumption 4.

In the recycling process, the total benefit from three-party synergy is denoted as A, and from two-party synergy as M. The three-party synergy coefficient is βi, and the two-party synergy coefficient is θi. The total cost for three-party synergy is C, with Ci as the cost incurred by each enterprise and Di as the risk-related costs. Economic loss for a non-synergistic party is γi, and zi is the decision variable indicating participation in synergy. As the total recycling benefit A increases, the costs associated with enterprise synergy also rise. Enterprises are more likely to participate in synergy and select strategies such as “active recycling,” “cooperation,” or “high investment” when benefits are substantial, and governments and consumers are likewise more inclined to participate actively. When the benefits of three-party synergy are low, firms tend to avoid coordinated action. It is noteworthy that the strategic interdependence between automobile manufacturers and battery manufacturers is indirectly characterized in this model through the synergistic benefits and economic losses corresponding to their respective strategic choices. To simplify the analysis, their strategy selection probabilities are treated as initially independent within the model.

Assumption 5.

The variation in the total benefit M from collaborative recycling among the two enterprises significantly influences the strategy choices of all three parties in the game. When M is large, enterprises are more inclined to participate in collaboration, choosing the “active recycling,” “cooperation,” or “high investment” strategies; government and consumers tend to actively participate. When M is small, meaning the collaborative benefits among the three enterprises are low, enterprises tend not to collaborate.

Assumption 6.

The cost parameters for enterprises, Ci and Di, and the total synergistic benefits, A and M, are held constant throughout the simulation. This treatment establishes a stable basis for analyzing the equilibrium states and threshold effects driven by strategic choice. It excludes, for the purpose of this study, the potential dynamic feedback where technological learning and innovation could iteratively lower costs and enhance benefits over time—a complexity reserved for future model extensions.

Assumption 7.

The presence of informal recyclers constitutes an external competitive environment for the system, and their impact is primarily manifested through the following mechanisms. First, they provide consumers with an alternative recycling channel, which may lead to passive participation in formal systems. Second, they reduce the net profit attainable by the formal recycling sector under decentralized decision-making, as reflected in the negative or near-zero net returns for enterprises when opting for cooperative strategies when synergistic benefits A or M are low. Third, they heighten the urgency for governmental environmental regulation, represented by the environmental gain G and social benefit α₂obtained under the government’s “participation” strategy. Accordingly, the above parametric mechanisms internalize informal recycling competition as a key constraint influencing the decisions of all five stakeholders.

3.3. Main Parameter Settings

Table 1. Definitions and relationships of symbols and parameters used in the five-party collaborative recycling model.

Symbol	Definition	Symbol	Definition
x	Probability of government involvement in collaboration	A	Total revenue generated from three-party collaborative recycling
y	The probability that consumers are actively involved in collaboration	M	Total revenue generated from two-party collaborative recycling
z	The probability that automobile companies actively recycle	βi	Proportion of revenue sharing that firm i receives in three-party collaborative recycling (i = 1, 2, 3 corresponds to automobile firms, battery firms, and third-party firms, respectively, ∑βi = 1)
m	Probability of Battery Enterprises’ Cooperation	θi	Proportion of revenue sharing that firm i receives in two-party collaborative recycling (i = 1, 2, 3 corresponds to automobile firms, battery firms, and third-party firms, respectively, ∑θi = 1)
n	Probability of high investment by third-party enterprises	C	Total cost required for collaborative recycling
α1	The weighting of the environmental benefits that the government derives from collaborative recycling	Ci	Costs invested by enterprises in collaborative recycling
α2	The social benefits to the government from consumer participation in recycling	Di	Risk-induced costs of the enterprise in the collaboration process
R	The total cost of policy formulation and implementation by the government	γi	Economic loss caused by the exclusion of the enterprise by the collaborative party in case of non-participation in the collaborative recycling.
H	Subsidy amount provided by the government to enterprises participating in collaborative recycling	G	Environmental benefits of collaboration
P	Penalties amount imposed by the government on enterprises not participating in collaborative recycling	f	Social Direct Benefits of Consumer Participation in Recycling
J	Subsidy amount provided by the government to consumers who actively participate in recycling	W	Indirect social benefits of consumer participation in recycling
a	Total Revenue Allocated to Enterprises in Tripartite Collaborative Recycling	m1	Total Revenue Allocated to Enterprises During Bilateral Cooperative Recycling
k	Government Revenue Sharing Coefficient for Tripartite Collaborative Benefits	q	Government Revenue Sharing Coefficient for Bilateral Cooperative Benefits

summarizes the mathematical notation used in this study.

3.4. Modeling

The payoff matrix in

Table 2. Payoff matrix in the five-party evolutionary game model.

Government (G)	Consumers (S)	Automobile Enterprises (B)
		Active Recycling (z)				Passive Recycling (1 − z)
		Battery Enterprise (T)
		Cooperate (m)		Non-Cooperate (1 − m)		Cooperate (m)		Non-Cooperate (1 − m)
		Third-Party Enterprise (C)
		High Investment (n)	Low Investment (1 − n)	High Investment (n)	Low Investment (1 − n)	High Investment (n)	Low Investment (1 − n)	High Investment (n)	Low Investment (1 − n)
Participate (x)	Active (y)	G1S1B1T1C1	G1S1B1T1C2	G1S1B1T2C1	G1S1B1T2C2	G1S1B2T1C1	G1S1B2T1C2	G1S1B2T2C1	G1S1B2T2C2
	Passive (1 − y)	G1S2B1T1C1	G1S2B1T1C2	G1S2B1T2C1	G1S2B1T2C2	G1S2B2T1C1	G1S2B2T1C2	G1S2B2T2C1	G1S2B2T2C2
Non-participate (1 − x)	Active (y)	G2S1B1T1C1	G2S1B1T1C2	G2S1B1T2C1	G2S1B1T2C2	G2S1B2T1C1	G2S1B2T1C2	G2S1B2T2C1	G2S1B2T2C2
	Passive (1 − y)	G2S2B1T1C1	G2S2B1T1C2	G2S2B1T2C1	G2S2B1T2C2	G2S2B2T1C1	G2S2B2T1C2	G2S2B2T2C1	G2S2B2T2C2

serves as the foundation for the evolutionary game model. The following notations and equations present the expected benefits and dynamic strategies for each stakeholder:

G₁S₁B₁T₁C₁ = α₁G + α₂ − R − 3H − J + (1 − k)Aβ₁ − C₁ − D₁ + Hz₁ + (1 − k)Aβ₂ − C₂ − D₂ + Hz₂ + (1 − k)Aβ₃ − C₃ − D₃ + Hz₃ + f + W + J

(1)

G₁S₁B₁T₁C₂ = α₁G + α₂ − R − 2H − J + P + (1 − q)Mθ₁ − C₁ − D₁ + Hz₁ + (1 − q)Mθ₂ − C₂ − D₂ + Hz₂ − γ₃ − P + f + W + J

(2)

G₁S₁B₁T₂C₁ = α₁G + α₂ − R − 2H − J + P + (1 − q)Mθ₁ − C₁ − D₁ + Hz₁ − γ₂ − P + (1 − q)Mθ₃ − C₃ − D₃ + Hz₃ + f + W + J

(3)

G₁S₁B₁T₂C₂ = α₁G + α₂ − R − H − J + 2P − C₁ − D₁ + Hz₁ − γ₂ − P − γ₃ − P + f + W + J

(4)

G₁S₁B₂T₁C₁ = α₁G + α₂ − R − 2H − J + P − γ₁ − P + (1 − q)Mθ₂ − C₂ − D₂ + Hz₂ + (1 − q)Mθ₃ − C₃ − D₃ + Hz₃ + f + W + J

(5)

G₁S₁B₂T₁C₂ = α₁G + α₂ − R − H − J + 2P − γ₁ − P − C₂ − D₂ + Hz₂ − γ₃ − P + f + W + J

(6)

G₁S₁B₂T₂C₁ = α₁G + α₂ − R − H − J + 2P − γ₁ − P − γ₂ − P − C₃ − D₃ + Hz₃ + f + W + J

(7)

G₁S₁B₂T₂C₂ = α₁G + α₂ − R − J + 3P − γ₁ − P − γ₂ − P − γ₃ − P + f + W + J

(8)

G₁S₂B₁T₁C₁ = α₁G − R − 3H + (1 − k)Aβ₁ − C₁ − D₁ + Hz₁ + (1 − k)Aβ₂ − C₂ − D₂ + Hz₂ + (1 − k)Aβ₃ − C₃ − D₃ + Hz₃

(9)

G₁S₂B₁T₁C₂ = α₁G − R − 2H + P + (1 − q)Mθ₁ − C₁ − D₁ + Hz₁ + (1 − q)Mθ₂ − C₂ − D₂ + Hz₂ − γ₃ − P

(10)

G₁S₂B₁T₂C₁ = α₁G − R − 2H + P + (1 − q)Mθ₁ − C₁ − D₁ + Hz₁ − γ₂ − P + (1 − q)Mθ₃ − C₃ − D₃ + Hz₃

(11)

G₁S₂B₁T₂C₂ = α₁G − R − H + 2P − C₁ − D₁ + Hz₁ − γ₂ − P − γ₃ − P

(12)

G₁S₂B₂T₁C₁ = α₁G − R − 2H + P − γ₁ − P + (1 − q)Mθ₂ − C₂ − D₂ + Hz₂ + (1 − q)Mθ₃ − C₃ − D₃ + Hz₃

(13)

G₁S₂B₂T₁C₂ = α₁G − R − H + 2P − γ₁ − P − C₂ − D₂ + Hz₂ − γ₃ − P

(14)

G₁S₂B₂T₂C₁ = α₁G − R − H + 2P − γ₁ − P − γ₂ − P − C₃ − D₃ + Hz₃

(15)

G₁S₂B₂T₂C₂ = α₁G − R − H + 3P − γ₁ − P − γ₂ − P − γ₃ − P

(16)

G₂S₁B₁T₁C₁= (1 − k)Aβ₁ − C₁ − D₁ + (1 − k)Aβ₂ − C₂ − D₂ + (1 − k)Aβ₃ − C₃ − D₃ + f + W

(17)

G₂S₁B₁T₁C₂ = (1 − q)Mθ₁ − C₁ − D₁ + (1 − q)Mθ₂ − C₂ − D₂ − γ₃ + f + W

(18)

G₂S₁B₁T₂C₁ = (1 − q)Mθ₁ − C₁ − D₁ − γ₂ + (1 − q)Mθ₃ − C₃ − D₃ + f + W

(19)

G₂S₁B₁T₂C₂ = −C₁ − D₁ − γ₂ − γ₃ + f + W

(20)

G₂S₁B₂T₁C₁ = −γ₁ + (1 − q)Mθ₂ − C₂ − D₂ + (1 − q)Mθ₃ − C₃ − D₃ + f + W

(21)

G₂S₁B₂T₁C₂ = −γ₁ − C₂ − D₂ − γ₃ + f + W

(22)

G₂S₁B₂T₂C₁ = −γ₁ − γ₂ − C₃ − D₃ + f + W

(23)

G₂S₁B₂T₂C₂ = f + W

(24)

G₂S₂B₁T₁C₁ = (1 − k)Aβ₁ − C₁ − D₁ + (1 − k)Aβ₂ − C₂ − D₂ + (1 − k)Aβ₃ − C₃ − D₃

(25)

G₂S₁B₁T₁C₂ = (1 − q)Mθ₁ − C₁ − D₁ + (1 − q)Mθ₂ − C₂ − D₂ − γ₃

(26)

G₂S₂B₁T₂C₁ = (1 − q)Mθ₁ − C₁ − D₁ − γ₂ + (1 − q)Mθ₃ − C₃ − D₃

(27)

G₂S₂B₁T₂C₂ = −C₁ − D₁

(28)

G₂S₂B₂T₁C₁ = −γ₁ + (1 − q)Mθ₂ − C₂ − D₂ + (1 − q)Mθ₃ − C₃ − D₃

(29)

G₂S₂B₂T₁C₂ = −γ₁ − C₂ − D₂ − γ₃

(30)

G₂S₂B₂T₂C₁ = −γ₁ − γ₂ − C₃ − D₃

(31)

G₂S₂B₂T₂C₂ = 0

(32)

Based on the revenue payment matrix shown in Table 2 and Equations (1)–(32), the expected benefits for the government when choosing the “participate” and “opt-out” strategies, as well as its average expected return, can be derived. Accordingly, we can derive the replicator dynamic equation for the government’s decision-making as follows:

$$F(x)={\displaystyle \frac{dx}{dt}}=x(G_{11}-\overline{G})=x(1-x)(G_{11}-G_{21})=x(1-x)[{\alpha }_{1}G-R+3P+y({\alpha }_2-J)-(H+P\left)\right(z+m+n\left)\right]$$

(33)

Similarly, the dynamic equations for consumer replication and strategy selection are as follows:

$$F(y)={\displaystyle \frac{dy}{dt}}=y(S_{11}-\overline{S})=y(1-y)(S_{11}-S_{21})=y(1-y)(f+w+xJ)$$

(34)

Dynamic equations for replication and strategy choice in automotive firms:

$$F(z)={\displaystyle \frac{dz}{dt}}=z(B_{11}-\overline{B})=z(1-z)(B_{11}-B_{21})=z(1-z)\left\{x\right(H+P)-C_1-D_1+mn[(1-k)A{\beta }_1-2{\theta }_1(1-q)M-{\gamma }_1]+[(1-q)M{\theta }_1+{\gamma }_1\left]\right(m+n\left)\right\}$$

(35)

Dynamic equations for replication and strategy selection in battery firms:

$$F(m)={\displaystyle \frac{dm}{dt}}=m(T_{11}-\overline{T})=m(1-m)(T_{11}-T_{21})=m(1-m)\{-C_2-D_2+x(H+P)+(z+n\left)\right[(1-q)M{\theta }_2+{\gamma }_2]+zn[(1-k)A{\beta }_2-2(1-q)M{\theta }_2-{\gamma }_2]-{\gamma }_{2}x(z+n-zn\left)\right\}$$

(36)

Dynamic equations for replication and strategy selection in third-party firms:

$$F(n)={\displaystyle \frac{dn}{dt}}=n(C_{11}-\overline{C})=n(1-n)(C_{11}-C_{21})=n(1-n)\{-C_3-D_3+x(H+P+{\gamma }_3)+(z+m\left)\right[(1-q)M{\theta }_3+{\gamma }_3(1-x)]+zm[(1-k)A{\beta }_3-2(1-q)M{\theta }_3-{\gamma }_3(1-x)\left]\right\}$$

(37)

The detailed calculation process can be found in Appendix A.

3.5. Evolutionary Stability Analysis of Equilibrium Points

Let F(x) = F(y) = F(z) = F(m) = F(n) = 0, and a total of 12 boundary local equilibrium points for this system can be obtained, as presented in

Table 3. Boundary local equilibrium points.

Local Equilibrium Point
E1(0, 0, 0, 0, 0)	E7(0, 0, 0, 0, 1)
E2(0, 0, 0, 1, 0)	E8(0, 0, 0, 1, 1)
E3(0, 0, 1, 0, 0)	E9(0, 0, 1, 0, 1)
E4(0, 1, 0, 0, 0)	E10(0, 1, 0, 0, 1)
E5(1, 0, 0, 0, 0)	E11(1, 0, 0, 0, 1)
E6(1, 1, 1, 1, 0)	E12(1, 1, 1, 1, 1)

.

According to evolutionary game theory, the local stability of equilibrium points can be determined by the sign of the eigenvalues of the Jacobian matrix formed by the reproduction dynamics equations. The Jacobian matrix J₁ of this system is as follows:

$$J_1=\left[\begin{array}{cc}\begin{array}{cc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial y}}\end{array}& \begin{array}{ccc}{\displaystyle \frac{\partial F\left(x\right)}{\partial z}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial m}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial n}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial m}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial n}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial m}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial n}}\end{array}\\ \begin{array}{cc}{\displaystyle \frac{\partial F\left(m\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(m\right)}{\partial y}}\\ {\displaystyle \frac{\partial F\left(n\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(n\right)}{\partial y}}\end{array}& \begin{array}{ccc}{\displaystyle \frac{\partial F\left(m\right)}{\partial z}}& {\displaystyle \frac{\partial F\left(m\right)}{\partial m}}& {\displaystyle \frac{\partial F\left(m\right)}{\partial n}}\\ {\displaystyle \frac{\partial F\left(n\right)}{\partial z}}& {\displaystyle \frac{\partial F\left(n\right)}{\partial m}}& {\displaystyle \frac{\partial F\left(n\right)}{\partial n}}\end{array}\end{array}\right]$$

According to stability theory, an equilibrium point is locally asymptotically stable if and only when all real parts of the eigenvalues of the Jacobian matrix at that point are negative. This constitutes an evolutionarily stable strategy (ESS). Beyond determining the stability of specific equilibrium points, an in-depth analysis of the Jacobian matrix structure and its eigenvalue sign conditions can reveal the intrinsic driving forces and critical conditions governing system evolution.

Proposition 1.

The marginal cost effect of government strategies and the negative feedback mechanism of consumer participation.

Proof of Proposition 1.

Through analysis of the Jacobian matrix, the partial derivative of the replication dynamics equation F(x) for government strategy with respect to consumer participation rate y is given by ${\displaystyle \frac{\partial F\left(x\right)}{\partial y}}=-x\left(1-x\right)J$. Given that x ∈ [0, 1] and J > 0 represents the government’s subsidy parameter to consumers, this partial derivative remains negative. This indicates that the rate of evolution for government participation in decision-making diminishes as consumer engagement increases, thereby establishing a negative feedback mechanism. □

This mechanism defines the efficiency of government roles at different stages of recycling system development. During the initial phase, low consumer participation rates render the marginal utility of strong government intervention particularly significant. As the system matures and voluntary consumer delivery habits become established, maintaining high levels of government subsidies will lead to diminishing policy efficiency. The government’s role should then strategically shift towards market oversight and regulatory enforcement.

Proposition 2.

Synergistic benefits exhibit concave incentives and an evolutionary window.

Proof of Proposition 2.

For enterprises, the strategy evolution equation F(z) = z(1 − z)U_z indicates that the evolution rate is a unimodal function of the strategy proportion z, attaining its maximum value at z = 0.5. This defines an evolutionary window centered on this equilibrium point, within which the incentive strength of cooperative benefits on group strategy is present, while outside this window, diminishing marginal returns are exhibited. □

When collaborative enterprises represent a minority of pioneers or have become industry standard, enhancing synergistic benefits A yields limited marginal effects on promoting overall cooperation. Policy and commercial strategies should focus on propelling the proportion of collaborative enterprises into the rapid diffusion phase, and during this window period, concentrate efforts on scaling up synergistic effects.

Proposition 3.

Government subsidies have a threshold for promoting synergistic effects.

Proof of Proposition 3.

An analysis of the eigenvalues at the equilibrium point of corporate strategy reveals the existence of a critical subsidy threshold Hth = C_i + D_i − (β_iA + θ_iM + P). When H < Hth, the Jacobian matrix at the ‘corporate synergy’ equilibrium point possesses positive eigenvalues, constituting a source of instability. Conversely, when H > Hth, the system may undergo a phase transition towards a stable synergistic state. This demonstrates that government subsidies exhibit a nonlinear threshold characteristic in initiating system synergy. □

This proposition offers a theoretical explanation for the ‘failure of subsidy policies’ observed in certain regions. During the early stages of industrial development, high coordination costs coupled with meager coordination benefits jointly elevate the initiation threshold Hth. Should the actual subsidy amount fall below this threshold, the systemic inertia cannot be overcome, rendering the policy inevitably ineffective.

Proposition 4.

The system exhibits multiple steady-state structures and equilibrium transitions.

Proof of Proposition 4.

Stability analysis confirms the existence of at least two locally asymptotically stable boundary equilibrium points: the low-cooperation equilibrium E₁ and the high-cooperation equilibrium E₁₂. The asymptotic stability structure of the system is determined by the critical parameters A, M, and H, with continuous variations in these parameters potentially inducing discrete transitions in stability. □

This proposition explains why markets readily become locked into suboptimal states where “bad money drives out good”, hindering spontaneous optimization. Even with positive incentives, the entire system may remain confined within the E₁ potential well. Achieving an equilibrium transition to the highly synergistic state E₁₂ necessitates robust combined policies that systematically alter the potential surface, rendering the high-synergy equilibrium a global attractor.

4. Simulation Results and Analysis

4.1. System Dynamics Simulation Modeling

Building upon the preceding propositions, this section employs system dynamics simulation to elucidate the dynamic pathways of system coordination and their corresponding sustainable development benefits through parameterised scenarios. Based on a five-party evolutionary game model involving government, consumers, automotive enterprises, battery manufacturers, and third-party enterprises, a system dynamics simulation model of this evolutionary game was constructed using Vensim software 10.2.2, as illustrated in Figure 2. Through evolutionary game model research and incorporating parameter setting methods from the literature [18,20,34,35,36], the following initial values are assumed for the payoff matrix parameters: α₁ = 0.5, α₂ = 0.5, R = 0.35, J = 0.25, P = 0.9, θ₁ = 0.5, θ₂ = 0.3, θ₃ = 0.2, A = 7, β₁ = 0.4, β₂ = β₃ = 0.3, M = 4, γ₁ = 2.5, γ₂ = γ₃ = 1.5, C₁ = 3, C₂ = C₃ = 2.3, D₁ = 2.5, D₂ = D₃ = 1.6, f = 0.25, W = 0.25, H = 0.9. All parties were initially assigned a probability of 0.5 for each available strategy.

This simulation is primarily exploratory and mechanism-focused, designed to reveal the critical thresholds and dynamic patterns within the multi-agent system, rather than to provide precise predictions for a specific market. The setting of key parameters is based on Chinese industry benchmark data. To ground the analysis in economic reality, key parameters are set with reference to Chinese industry benchmark data. The government subsidy intensity H (approximately 100 RMB/kWh) aligns with the levels observed in domestic pilot programs. Furthermore, the ratios between the synergy benefits A and M, and the relevant costs reflect the profit margins and cost structures reported in industry studies and enterprise surveys. By employing these realistically grounded yet normalized parameters, the simulation constructs a plausible baseline scenario. Its core outcome—the identification of specific quantitative thresholds—constitutes a testable theoretical proposition. These thresholds provide a quantitative framework for explaining real-world coordination failures and for assessing when policy interventions or market conditions may trigger a phase transition toward systemic collaboration.

4.2. Simulation Results and Discussion

4.2.1. Impact of Total Tripartite Synergy Benefits (A)

The total synergistic benefit A represents the aggregate economic gains achievable through comprehensive cooperation among all stakeholders. This parameter is critical as it directly reflects the system’s capacity to generate sufficient incentives for large-scale collaboration. Proposition 2 indicates that synergistic benefits exhibit an evolutionary window for the intensity of incentives on group strategies. Simulation results in Figure 3 validate this theoretical expectation and further reveal the specific characteristics of the window effect.

Simulation results in Figure 3 reveal a critical threshold at A = 15. When A < 15, government participation remains markedly low while consumer willingness to engage is strong and enterprises predominantly adopt non-cooperative or low-investment strategies. This theoretically explains the root cause of the “systemic coordination failure” observed in practice: when the total benefits generated through cooperation cannot cover the additional costs and risks borne by all participants, individual rationality leads to collective non-cooperation—even under policy pressure. Under such conditions, the system remains trapped in a linear economic model characterized by low resource recovery rates and high environmental risks. When A exceeds the critical threshold of 15, simulation results indicate the system enters a green growth pathway, where rapid improvements in corporate collaboration directly translate into quantifiable environmental and economic benefits. Government involvement significantly increases, shifting towards active intervention and support. Figure 3 illustrates that at the enterprise level, the strategies of the three types of firms rapidly evolve toward “active recycling,” “cooperation,” and “high investment.” Meanwhile, variations in A exert minimal influence on consumer strategies, as consumer participation remains robust and stable, reinforcing the virtuous cycle of multi-stakeholder cooperation.

The findings reveal that a stable and efficient cooperative equilibrium is achievable only when synergistic benefits exceed the critical threshold of A = 15. This threshold represents far more than a simple investment break-even point; it constitutes the minimum additional value creation necessary to drive the entire system from a state of “coordination failure” to one of “coordinated stability.” This finding provides a quantitative perspective for understanding the real-world phenomenon of “Gresham’s Law.” When the formal system fails to generate sufficient surplus value through cooperation, its economic appeal will be unable to offset the short-term benefits offered by informal channels to consumers and enterprises, and the system becomes naturally locked in a fragmented and inefficient equilibrium. This value must simultaneously offset three core costs: the direct costs and risk premiums borne by enterprises, the opportunity costs incurred by forgoing higher prices offered in the “black market,” and the innovation incentives and coordination costs required to establish and sustain multilateral cooperation. Crucially, this threshold is derived under the condition of invariant cost and benefit parameters. It provides a baseline: sustained technological advancement, potentially driven by prevalent “high-investment” strategies, could reduce future costs or elevate recoverable value, thereby effectively lowering the critical synergy required for a systemic shift. Thus, surpassing this static threshold represents not only an immediate condition for coordination but also a potential catalyst for initiating a self-reinforcing cycle of innovation and collaboration.

The core task for policymakers is to enhance net synergistic benefits through two key levers. The first involves creating added value through mechanisms such as mandating recycled material content—as seen in the EU’s New Battery Regulation—or establishing green certification trading systems. The second focuses on reducing costs by promoting battery design standardization and building public supply chain information platforms, thereby minimizing institutional frictions. Additionally, the intensity of policy intervention should be dynamically aligned with the industry’s development stage. In the initial phase, policymakers must take a leading role to help the system surpass critical thresholds. As the market matures, the focus should shift toward a market-enabling role, primarily centered on maintaining and enforcing regulatory frameworks.

4.2.2. Impact of Government Subsidization for Synergy (H)

Government subsidies H, as a direct policy tool, exert a significant threshold effect on the evolutionary trajectory of supply chain collaboration. Proposition 3 reveals the activation threshold characteristics of government subsidies. Simulation results concretize this theoretical threshold as the peak point of fiscal resource efficiency, demonstrating the dynamic process by which it drives the system’s transition towards low-carbon development.

The simulation results in Figure 4 indicate that when H < 2, although the government tends to engage in regulation and consumers participate actively due to the economic benefits, enterprises collectively exhibit a strategy profile of “limited recycling–weak cooperation–low investment.” The fundamental reason is that the subsidy intensity is insufficient to cover the additional costs and risks that firms must bear to engage in collaboration, locking the system into a state of “low subsidies–weak synergy–development stagnation.” This outcome aligns with the “policy failure threshold” theory [10] and confirms the inference of Proposition 3: insufficient subsidy levels cannot overcome systemic coordination barriers.

When H exceeds 2, a fundamental shift occurs in the system: the government maintains a high level of participation, while enterprises collectively shift to comprehensive cooperative strategies, forming a virtuous cycle of “subsidy enhancement–corporate response–consumer follow-up.” This can be explained through replicator dynamics in evolutionary game theory: when H exceeds the threshold, marginal benefits cover cooperation risks, enabling successful strategies to spread through learning [23]. Notably, the simulation results further reveal a “policy saturation effect” [11]: when H exceeds 2.5, its marginal utility in promoting cooperation declines significantly. This indicates that policy design is not a matter of “the higher, the better” but operates within an optimal intensity range (2–2.5). This result reveals the dynamic interplay between subsidy policies and market competition. When the subsidy intensity falls short of the activation threshold, it fails to assist formal enterprises in overcoming the cost advantages of informal channels and the incentive gap for consumers, thereby leading to policy failure. While excessive subsidies may temporarily suppress informal competition, they incur efficiency losses and lack sustainability. Therefore, precise subsidy design must aim to elevate the overall competitiveness of the formal system beyond the critical level necessary to break the lock-in effect of informal competition.

These findings provide core principles for designing targeted and sustainable fiscal policies. Policymakers should set subsidy levels slightly above the identified threshold and adopt performance-linked dynamic mechanisms (e.g., linking subsidies to recovery efficiency or carbon reduction) to ensure effectiveness while avoiding resource waste and policy dependency. For different fiscal contexts, differentiated strategies can be adopted: regions with sufficient fiscal capacity may use direct subsidies to reach the threshold, while fiscally constrained areas should rely on a combination of tools such as tax incentives and green credit to achieve equivalent incentive strength. The core objective is to ensure that the incentive signal is strong enough to cross the critical threshold for activating systemic collaboration.

4.2.3. Impact of Total Benefit of Two-Party Synergy (M)

The total benefit of two-party synergy M quantifies economic gains from bilateral collaboration among stakeholder pairs—automobile-battery, automobile-third-party, or battery-third-party enterprises—serving as a key indicator for characterizing the system’s transition from localized to global collaboration. Proposition 4 describes the system’s multi-stable characteristics, with simulation results in Figure 5 illustrating the complete pathway of the system transitioning from a low-level equilibrium to a high-level equilibrium.

When M < 12, the government overall tends toward a non-participation strategy, consumer participation remains relatively high, and enterprises exhibit distinct conservatism. At this stage, the marginal benefits of bilateral cooperation fail to offset cross-entity coordination costs, trapping the system in a ‘bilateral cooperation maturity trap’ where firms prefer independent decision-making to avoid collaboration risks [10]. When M reaches the 10–12 range, the system begins to differentiate. Battery producers and third-party recyclers, which are more sensitive to M, are the first to increase their willingness to cooperate and invest, while automakers respond with a noticeable lag, only stabilizing their shift toward coordination after M > 11. This “sequential activation” phenomenon confirms that the benefits of bilateral cooperation propagate heterogeneously along the industrial chain.

When M exceeds 12, the system finally enters a stable state of full coordination. This results from the “knowledge spillover” and “trust transfer” effects generated by successful bilateral cooperation, which effectively lower the barriers for other parties to join the broader collaborative effort, reflecting the replication and diffusion of strategies within the population [23]. This process validates the multi-stability assertion of Proposition 4 and demonstrates that the shift in system equilibrium follows a specific “sequential activation” evolutionary sequence. This suggests that only when specific pairings—such as battery manufacturers and recyclers—first achieve sufficiently high cooperative gains can they establish a collaborative bulwark robust enough to withstand external competitive pressures, thereby gradually attracting more participants and ultimately undermining the survival basis of informal channels.

The above “sequential activation” mechanism provides a key design principle for coordination policies: interventions must be “targeted” and “sequential.” Priority should be given to strategically complementary enterprise pairs (e.g., “battery producer–recycler”) as anchor points, using directed policy tools to tangibly increase their synergistic benefits so that they first break through the local threshold. The knowledge spillover and trust transfer effects resulting from their success will naturally pull other segments of the industrial chain into the collaboration, thereby achieving a coordinated expansion from local alliances to a systemic network. Policies must be adapted to the regional industrial ecosystem: in mature clusters, the focus should be on identifying and strengthening existing advantageous pairings; in fragmented markets, the government needs to actively act as a “platform builder” to cultivate initial cooperation.

5. Conclusions and Policy Recommendations

5.1. Conclusions

This study constructs a five-party evolutionary game model involving the government, automakers, battery manufacturers, third-party recyclers, and consumers. Combined with system dynamics simulation, it reveals the dynamic evolution patterns and key driving mechanisms of collaborative battery recycling systems within reverse supply chains. Key findings are as follows:

First, the core finding of this study is that effective coordination in the battery recycling system exhibits a strict “threshold effect”. This is achieved if, and only if, key economic and policy parameters cross the minimum necessary level required to reshape the incentive structures of all participants. Simulations demonstrate that the system can transition from an inefficient equilibrium of “low coordination–high risk” to an ideal state of “high coordination–resource circulation” only when at least one of the following conditions is satisfied: the total tripartite synergistic benefit A exceeds 15, the government subsidy intensity H reaches 2, or the bilateral synergistic benefit M exceeds 12. This “threshold effect” carries a profound policy implication: systemic success depends not on incremental, marginal adjustments, but fundamentally on the precise fulfillment of these “critical conditions” that drive a shift in collective action. This finding underscores the importance of “precision intervention,” providing a quantifiable decision benchmark for overcoming system inertia, advancing low-carbon industrial transformation, and promoting responsible consumption and production.

Second, incorporating consumers and third-party recyclers as endogenous decision-makers is central to understanding and resolving “systemic coordination failure.” This study confirms that consumer participation willingness is highly sensitive to immediate economic compensation and delivery convenience, while third-party enterprises’ investment levels directly depend on stable policy expectations and reasonable profit distribution. Guiding both parties toward sustainable strategies is crucial not only for the coverage efficiency of recycling networks but also for reducing environmental pollution and building sustainable cities and communities.

Finally, the system’s equilibrium path is jointly influenced by initial conditions and key parameters, but its evolution toward the target state can be guided through optimized institutional design. Numerical simulations reveal that even with low initial cooperation willingness, establishing profit distribution coefficients linked to technology and investment, implementing a “performance-oriented” dynamic subsidy mechanism, and constructing a digital traceability supervision system covering the entire lifecycle can effectively resolve the three core conflicts of “responsibility allocation, profit distribution, and policy dependency.” This guides the system from adversarial to symbiotic interactions, providing an actionable governance framework for achieving inclusive green growth.

5.2. Theoretical Contributions

The theoretical contributions of this study are primarily reflected in three aspects:

First, in terms of research perspective, it breaks through the existing “incomplete agent” framework of three-party or four-party games by establishing, for the first time, a five-party evolutionary game model. This model more comprehensively reveals the interaction mechanisms among complex stakeholders in the real world, providing a new analytical paradigm for research on reverse supply chain collaboration.

Second, in terms of model mechanisms, the introduction of parameters such as the coordination payoff threshold and dynamic payoff distribution coefficient deepens the theoretical characterization of the system’s nonlinear transition behavior and the process of interest coordination, enhancing the explanatory power regarding the phenomenon of “coordination failure”.

Third, methodologically, it achieves a deep integration of evolutionary game theory and system dynamics. This approach not only captures the strategic interactions among micro-level agents but also reveals the dynamic feedback and threshold effects within macro-level systems, providing a powerful quantitative simulation tool for identifying critical policy levers.

5.3. Management Implications and Policy Recommendations

Based on the above conclusions, this paper proposes a multi-level collaborative governance framework to advance the development of power battery recycling systems toward standardization, efficiency, and sustainability.

• Government Level: Implement Threshold-Based Dynamic Precision Governance and Building System Resilience
  • The government should implement a threshold-guided “intensity-performance” dynamic subsidy mechanism. In the initial phase, the subsidy intensity must cover the upfront collaboration costs for enterprises to break the market lock-in. This initial benchmark can be determined, for instance, by assessing the industry-average incremental costs associated with establishing a formal recycling network and upgrading technologies. As the system matures, a shift toward “precision phase-out” is necessary. This involves dynamically linking subsidies to key resource and environmental performance indicators, such as critical metal recovery rates and carbon reduction per unit of output. The aim is to transition the incentive model from “universal support” to “selective enhancement,” ensuring fiscal efficiency while substantively improving resource circularity and the industry’s low-carbon development level.
  • The government should strengthen the extended producer responsibility (EPR) framework and establish a robust digital traceability oversight system. To reinforce systemic resilience following subsidy phase-out, it is imperative to enhance the EPR regime and mandate full-lifecycle digital traceability for batteries—for instance, by implementing a unique digital identifier or a traceable digital record for each battery unit. Such a system serves three critical purposes: it supplies a verifiable basis for the performance-linked subsidies outlined above; enables closed-loop supervision to deter illegal recycling, thus mitigating environmental and public-health risks; and fosters innovation in green supply chains as well as the development of sustainable urban infrastructure.
• Corporate Level: Strategic Synergy and Value Co-creation Drive Circular Economy Closure
  • Enterprises strive to build “shared responsibility and shared value” alliances. Leading automakers and battery manufacturers should secure recycled material supplies from third-party recyclers through joint investments or long-term contracts, ensuring critical raw material security. Simultaneously, they should promote standardized battery design to fundamentally reduce dismantling and recycling complexity and costs, practicing eco-design principles.
  • Third-party recyclers should focus on “technological deepening” and high-value utilization. Simulation results confirm the superiority of a “high-investment” strategy when sufficiently incentivized. Companies should continuously increase R&D investment in cutting-edge technologies like automated dismantling and hydrometallurgy. By enhancing metal recovery rates and recycled material purity, they can transform waste batteries into high-value “urban mines,” shifting their status from “cost centers” to “value centers”.
• Consumer Level: Behavior Guidance and Social Co-governance to Strengthen Sustainable Foundations
  • Design “convenient and visible” instant incentives and carbon credit systems for consumers. Deeply integrate battery collection points into community and commercial networks, offering immediate rewards like “scan-to-redeem cashback.” Simultaneously, incorporate standardized recycling behavior into personal carbon accounts, transforming green actions into quantifiable social capital and economic returns to establish long-term incentive mechanisms.
  • Strive to cultivate a recycling environment and oversight network characterized by “social co-governance.” Raise public environmental awareness through multi-channel campaigns highlighting the environmental and safety risks of improper recycling. Establish accessible public reporting and feedback channels to encourage societal oversight, building a modern environmental governance framework involving tripartite collaboration between government, market, and society.

5.4. Limitation and Further Research

This study acknowledges several limitations that suggest directions for future research. First, the model’s static cost and synergy parameters exclude endogenous technological progress and the positive feedback loops that could arise from sustained high investment. Second, policies are treated as static and exogenous; incorporating dynamic policy adjustment would better reflect real-world governance. Third, all agents are assumed to be risk-neutral, whereas accounting for heterogeneous risk preferences could refine strategic insights. Fourth, the model assumes a single, homogeneous market, neglecting the impact of regional disparities in policy, infrastructure, and market maturity on stakeholder strategies. Additionally, extending the model to formally incorporate feedback-driven policy rules—such as linking subsidy levels to real-time cooperation rates—would allow analysis of their stability and robustness, helping to design dynamic incentives that avoid oscillatory behaviors. Future work could quantify these regional effects, empirically calibrate the model with local data, and explore the integration of technologies such as AI and blockchain for enhancing traceability and reducing coordination costs.

This study provides a theoretical foundation and policy toolkit for constructing a synergistic “resource-environment-economy” battery recycling system, supporting the green transformation of the global new energy vehicle industry and the realization of the United Nations 2030 Agenda for Sustainable Development.