Sustainable Development Pathways for China’s Copper Industry: A Three-Way Evolutionary Game Approach

Abstract

Sustainable development is a tripartite game among the central (CG) and local governments (LGs) and enterprises, with economic factors as key drivers. China consumed about 16.2 million metric tons during this period, accounting for approximately 61% of global consumption, thereby reinforcing its position as the world’s leading copper consumer. Seeking a balance of acceptable interests among the three parties may be a feasible method to explore the sustainable development of China’s copper enterprises (CEs). Therefore, based on evolutionary game theory, we construct a three-party evolutionary game model. Using the financial data of Chinese CEs and actual survey data on the CG and LGs, we identified 31 environmental impact parameters from the CG, LGs, and CEs. Then, we used MATLAB R2023b to simulate an evolution model and determined the influence of various factors on the evolutionary stable state. The results show that LGs, as local managers, have implemented more direct and expedited regulations than the CG. Enterprises with less brand impact frequently face difficulties in complying with governmental regulatory demands. When interests are balanced, 30% of enterprises cannot meet standards within 40 months, which may cause 500 small and medium-sized enterprises to stop production, thus resulting in high unemployment costs for LGs. A scenario analysis evaluates the economic benefits of environmental measures based on evolutionary game results. The results show that the introduction of advanced hydrometallurgy technology has the highest economic benefits; after 5 years, the economic benefits of China’s entire copper industry will reach CNY 147.2 billion.

1. Introduction

Copper (Cu), recognized as the first metallic element discovered and utilized by ancient civilizations, has played a pivotal role in human technological development since the dawn of metallurgy. Its exceptional electrical conductivity, malleability, and corrosion resistance has enabled widespread applications across industrial production and daily applications. In the Chinese economic framework, the copper industry has consistently served as a crucial pillar industry since the mid-20th century, significantly contributing to national economic development through its extensive upstream–downstream industrial chain integration [1]. In the global copper industry landscape, China plays a dual, prominent role. According to data from the International Copper Study Group (ICSG), in 2023, global refined copper production increased by 4.9%, totaling approximately 26.5 million metric tons. China consumed about 16.2 million metric tons during this period, accounting for approximately 61% of global consumption, thereby reinforcing its position as the world’s leading copper consumer.

According to China’s 14th Five-Year Plan, China’s copper consumption was projected to grow at an average annual rate of 4% [2]. This growth has also driven the increase in refined copper production. From 2011 to 2020, the average annual growth rate of refined copper production was around 11.7% (11.9% from 2011 to 2015 and 11.5% from 2016 to 2020), while that of apparent consumption was 6.1% (8.9% from 2011 to 2015 and 3.3% from 2016 to 2020), indicating a dynamic and growing copper market in China [3,4,5,6]. The variation in China’s copper production is shown in Figure 1, based on data from the China Nonferrous Metals Fabrication Industry Association.

Although China is the world’s largest copper consumer, its copper reserves only account for 5.5% of the global total, most of which is dependent on imports. Official data show that China’s copper concentrate imports will reach 21.78 million tons in 2020 and that China’s foreign dependence on copper raw materials will reach 73% [7]. According to new research commissioned by the International Copper Association (ICA), the demand for electric vehicles is expected to see major growth over the next ten years. This increase will cause a greater demand for copper, and the copper industry will maintain a sustainable development trend [8]. The main raw material of copper pyrometallurgy is usually a copper sulfide concentrate enriched via beneficiation [9]. At the same time, China is the world’s largest producer of electrolytic copper [10]. In 2020, the global output of electrolytic copper was 23.9 million tons, of which China’s output was 10.02 million tons, accounting for about 42% of the world’s total output.

China’s copper mines are mainly small and medium-sized deposits, and the proportion of small mines with reserves less than 100,000 tons exceeds 85%; at the same time, their ore grade is relatively low. These factors have led to Chinese copper mining enterprises being small in scale and difficult to mine [11]. The problem of the concentrated development of copper resources has also led to a series of problems, such as an uneven distribution of production capacity in China’s copper smelting industry. In addition, some small and medium-sized enterprises still face a series of problems such as backward technology, high pollution, and high energy consumption. Moreover, the waste gas, wastewater, polluted acid, and solid waste produced during copper smelting cause serious pollution to the surrounding environment [12]. At present, most of China’s copper enterprises (CEs) still use traditional methods to treat wastewater, waste gas, and waste residue, which lead to a series of problems, such as large investments, high operating costs, and substandard treatments, making the survival and development of such CEs under the new environmental standards difficult [13]. As the Chinese government’s environmental protection policies become more and more demanding, the copper industry’s development path needs to change to promote progression. After China implemented an access and announcement system for the copper industry, which has raised the industry’s entry threshold, prompted the gradual withdrawal of small and polluting enterprises, and reorganized the Chinese copper industry, large-scale smelting enterprises have dominated the industry [14,15].

China’s 14th Five-Year Plan for the Development of the Raw Materials Industry put forward new requirements for the sustainable development of the copper industry [16], i.e., newly promulgated ultra-low emission standards for pollutants, breaking the original balance of interests among the three parties [17]. As the policy issuer and regulator, the central government (CG) not only requires the copper industry to reduce pollutant emissions and meet higher environmental protection requirements but also requires the copper industry to transform and make upgrades, increase its comprehensive strength, and obtain better financial returns [18]. Local governments (LGs), as policy executors, are required to meet the central government’s environmental protection requirements and emission standards and require CEs to save energy, reduce emissions, and implement environmental protection measures. At the same time, they also require the copper industry to continue to develop and provide both more taxes and more jobs [19]. CEs make up the foundation of sustainable development in the copper industry: on the one hand, investments into environmental protection facilities and the cost of operating environmental protection equipment will erode corporate profits; on the other hand, eliminating enterprises that do not meet the environmental protection standards will open up more market space for raw materials and products, and the transformation of enterprises will also bring about higher economic benefits.

In this tripartite sustainable development relationship, economic interests play the most critical role in balancing leverage. The CG ensures the implementation of sustainable development by formulating incentive policies and fines and enforcing environmental protection measures in key industry-intensive areas; LGs promote sustainable development through fines for companies that violate regulations and local incentive policies; and CEs invest in upgrades and transformations to optimize their industrial structure so as to achieve the sustainable development of their enterprise. However, previous national policies, local standards, and corporate environmental protection measures have not met the sustainable development of the copper industry under the new plan. In order to speed up structural adjustments in the copper industry, the three parties need to adopt new cleaner production measures, the whole-process management model, etc. The key to the sustainable development of the copper industry is finding a new balance of the best interests acceptable to the three parties.

By identifying the optimal equilibrium points for stakeholders, this research provides valuable insights into policy formulation and industry regulation. The key contributions of this study offer a novel framework for analyzing the dynamic interactions among the CG, LGs, and CEs in sustainable development, integrating economic, environmental, and policy-driven factors to demonstrate how policy mechanisms shape corporate behavior. It highlights local governments’ role in decentralized environmental governance. From a practical perspective, the findings contribute to policy design, emphasizing well-calibrated fines and subsidies as mechanisms to drive cleaner production while minimizing economic burdens. The study also underscores brand image benefits as key incentives for sustainable business practices. Additionally, it highlights how enterprises can enhance efficiency and profitability by adopting hydrometallurgical processes, which reduce emissions, optimize resource utilization, lower energy consumption, and improve environmental compliance. Such technological advancements not only align with sustainability goals but also offer long-term economic advantages, reinforcing the feasibility of green industry transitions.

The remaining sections of this paper are organized as follows: Section 2 provides an analysis of China’s copper industry via evolutionary game theory, focusing on the roles of the central government, local governments, and copper enterprises. Section 3 outlines the used methods, including the construction of the evolutionary game model. Section 4 presents the results and discusses the impacts of fines, subsidies, and brand image benefits on the three parties. Section 5 concludes this study by summarizing the findings and offering policy recommendations.

2. Literature Review

Although CEs that maintain traditional copper smelting technologies can achieve considerable profits, the cost of the environmental pressure brought about by copper smelting is enormous. It will affect not only the image and authority of the government but also the economic growth and social development of the country. In China, CEs try to meet the requirements of political centralization and economic decentralization policies, while the LGs try to enforce these policies while still taking the interests of these CEs into account [20,21] by comparing the interests of multiple enterprises before they act. Recent studies on green closed-loop supply chains highlight the dynamic interactions between governmental regulations, environmental incentives, and corporate decision-making, demonstrating how economic and environmental factors influence strategic choices [22]. Specifically, in the field of environmental governance, China’s current environmental governance system is a hierarchical territorial management system. On the one hand, the high efficiency and benefits of high-pollution enterprises can bring tax revenues to LGs and improve their performance; on the other hand, LGs struggle to maintain the balance between socio-economic development and environmental protection. Some LGs’ anti-pollution actions result in negative effects and even work in collaboration with polluting enterprises [23,24]. Studies on environmental policy and industrial governance show that government-led incentives and public perception significantly influence corporate compliance with sustainability regulations [25]. From the one-task dimension of “competition for growth” to the multi-task dimension of “competition for high-quality development”, Song (2020) established a theoretical model under a consistent logical framework to explore the effectiveness and mechanism of local government competition [26]. Therefore, LGs, CG, and CEs participate in a complex, dynamic, and repeated evolutionary game. Friedman was the first to suggest that limited rational participants can be balanced through continuous strategic interaction [27]. Since then, evolutionary game theory has been widely used in the field of environmental policy research.

In this study, the three parties in the game model are the CG, LGs, and CEs. In this tripartite sustainable development relationship, economic interests play the most critical role in balancing leverage [28]. The CG formulates and promulgates environmental protection policies; constrains the environmental protection status of LGs and CEs; and, at the same time, requires central taxation and the development of the copper industry, which often creates opposing goals. The CG also supervises LGs and CEs. Once LGs are found to be ineffective at supervising CEs, the CG will take corresponding punitive measures against the LGs and CEs. However, due to information asymmetry in reality and the wide distribution of CEs, the CG often struggles to notice issues such as weak supervision [28]. In this game, LGs also have antagonistic goals of both implementing the central government’s environmental protection policies and pursuing local economic development. Fully implementing these environmental protection policies may lead to lower local taxes and fiscal deficits while condoning enterprise development may lead to environmental degradation and a loss of government credibility. Additionally, even if the LG adopts a regulatory strategy, rule violations by CEs may not be discovered [29,30]. The economic activities of CEs are bound by reason, and enterprises pay more attention to whether environmental protection can bring higher economic benefits: if the economic return from not implementing environmental protection strategies is higher than that when implementing environmental protection strategies or if CEs can still make a profit after paying fines from violating such policies, CEs will choose not to implement environmental protection strategies [30]. Despite the CG and LGs punishing CEs if they do not implement environmental protection strategies, if the punishment is not strict, the fines paid by the CEs will not affect their business activities, and thus, CEs will continue their activities as is and refuse to implement environmental protection strategies [31].

In order to solve the contradictions and problems among these three parties, a method is needed to reveal the evolutionary trend for a balanced relationship among these three parties. Therefore, this study constructs an evolutionary game model, analyzes the relevant influencing factors, and conducts a scenario analysis of the economic benefits of a series of environmental protection measures to propose solutions for the sustainable development of China’s copper industry.

3. Methods

Due to historical and practical reasons, CEs frequently cause pollution and occasionally engage in illegal production, which are not conducive to the sustainable development of the copper industry. In order to effectively solve this problem, this study introduces three parties—CG, LGs, and CEs—into an evolutionary game model of China’s copper industry and analyzes the game evolution process and the factors that affect the stable evolution of the game system. This approach allows us to simulate the decision-making process over time and to understand the stability of various equilibrium points under changing policies and economic conditions. The model’s applicability lies in its ability to capture the complex, adaptive nature of real-world interactions in the context of environmental policy implementation and economic constraints in order to promote the sustainable development of CEs, enhance the ability of LGs to perform their duties, and provide insights to the CG regarding issuing policies and putting forward effective regulatory strategies.

3.1. Problem Description and Basic Assumptions

Assumption 1. 

In this game model, the CG implements two strategies: strict supervision of the LGs, recorded as x (0 < x < 1), or loose supervision of the LGs, recorded as 1 − x. The CEs also implement two strategies: implementing environmental protection measures, recorded as y (0 < y < 1), or not, recorded as 1 − y. Similarly, the LGs implement two strategies: monitoring enterprises’ behavior, recorded as z (0 < z < 1), or not, recorded as 1 − z. As seen from the nature of evolutionary games, during a game, each player will choose a strategy that suits them the best according to the game situation. Therefore, during each game cycle, x, y, and z change continuously due to various factors.

Assumption 2. 

Assuming that the annual economic benefits of copper companies due to mining, sales, and other work are Se0, the annual labor, chemical material, mechanical equipment maintenance, depreciation, and other costs are Ce0. When CEs choose to implement environmental protection measures, the annual treatment fee for tail water and tailings, and the cost of introducing new construction technology and management experience due to scrap copper recycling are recorded as Ce1. The potential benefit of newly introduced technical experience is Ce2; however, the introduction of new technologies and experience also has certain risks. The coefficient for the application of the CG’s current development plan is σ. The income obtained from the implementation of environmental protection measures, resulting in a good enterprise image being established among the residents of the surrounding industrial zone, is recorded as Se1. On the contrary, when CEs do not implement environmental protection measures, they do not pay the above-mentioned costs but they also do not obtain the above-mentioned additional benefits. Instead, hidden losses, such as image damage and reputation loss, will be recorded as Ke2 due to their disregard of the ecological environment. CEs can also expand the production scale of enterprises in exchange for higher economic benefits at the expense of the environment, which is recorded as Se3.

Assumption 3. 

The annual tax paid by an enterprise is recorded as Tg0; the cost of repairing the damaged environment is recorded as Cg1; and the compensation for the residents of the surrounding community is recorded as Cg2. The social welfare cost of LGs, paid to unemployed residents, is recorded as Cg3. In order to accurately monitor the surrounding environment of the industrial zone, enterprises will accrue costs from purchasing relevant testing equipment and hiring professionals, which is recorded as Cg0. The LGs will give administrative subsidies to CEs that actively implement environmental protection strategies, which are recorded as Fe1. Fines for CEs that choose not to implement environmental protection strategies are recorded as Ke1, and the annual corporate tax revenue collected by the LGs in accordance with its relevant proportions are recorded as Sg0. Even if the LGs implement strict regulatory policies, they may not be able to completely detect speculative behavior by CEs, and so the parameter θ (0 < θ < 1) is introduced to represent the probability that LGs catch CEs not implementing environmental protection measures in accordance with the regulatory policy.

Assumption 4. 

The loss of CEs caught by the CG for performing illegal acts is Ce3. For LGs with outstanding performance in environmental restoration work, the CG will arrange for personnel to inspect their work, and this inspection cost is Cz3. At the same time, the income of the LGs from performance appraisals for the current year is Fe0. The tax preference for CEs is recorded as Fe2. If the LGs choose not to monitor enterprises, the penalty imposed by the CG on the LGs is recorded as Kz1. The social benefits obtained by the CG due to the timely control of local environmental pollution are recorded as Kz2, and the appropriate economic compensation given by the CG to the residents of the industrial zone is recorded as Cz1. When the CG chooses not to regulate CEs and LGs, the public will doubt the ability of government departments to handle affairs, thus causing invisible losses, which are recorded as Cz2. The annual corporate tax revenue collected by the CG in accordance with its relevant proportions is recorded as Sz0, and the cost of supervision by the CG is recorded as Cz2. During actual supervision by the CG, the probability of a successful inspection is μ (0 < μ < 1).

Based on the financial data of Chinese CEs and actual documented data of the CG and LGs, this study determines 31 environmental impact parameters that have significant effects on the sustainable development of the industry and normalizes them to obtain estimated values. The author collected relevant data on the resource integration and overall environmental restoration work carried out by a copper industry company in Jiangxi, China, since May 2016. The relevant actual operation data were taken in October 2021. The company’s main business covers the mining, smelting, and processing of copper; the extraction and processing of scattered metals; and other fields. Therefore, it is an important copper production base in China.

The correlation coefficient was assigned based on the Notice of the State Council on Comprehensively Rectifying and Regulating the Order of Mineral Resources’ Development, Access Conditions for Copper Smelting Industry, Cleaner Production Standards for the Copper Smelting Industry, Guidelines for Feasible Technology in the Prevention and Control of Copper Smelting Pollution, Jiangxi Province’s the 14th Five-Year Natural Resource Protection and Utilization Plan, and other relevant documents. At the same time, actual data from the environmental impact report of the company over the years were also used. The relevant information is shown in

Table 1. Definition of parameters.

Parameters	Descriptions	Assignment
Ce0	Costs of human resources, equipment, and raw chemical materials	CNY 560 million
Ce1	Costs of tail water and tailing treatments, and scrap copper recovery	CNY 450 million
Ce2	Future benefits from technology upgrades	CNY 110–310 million
Ce3	Fines imposed by the CG on CEs	CNY 100–300 million
Se0	Annual sales revenue of CEs	CNY 120 million
Se1	Brand image benefits	CNY 60–180 million
Se2	Benefits when CEs destroy the environment to promote development	CNY 370 million
Ke1	Fines imposed by LGs on CEs	CNY 30–110 million
Ke2	Public relation expenses for CEs	CNY 90 million
Tg0	Resource tax rate for CEs	27%
Cg0	Labor and equipment costs for LGs	CNY 60 million
Cg1	Cost of LGs’ management of the damaged ecological environment	CNY 630 million
Cg2	Compensation paid by LGs to residents	CNY 50 million
Cg3	Cost of the social benefit for unemployment	CNY 100 million
Sg0	LGs’ tax revenues	CNY 150 million
Kz1	Fines imposed by the CG on LGs	CNY 750 million
Kz2	Social benefits of the CG’s protection of the environment	CNY 150 million
Cz0	The CG’s supervision costs	CNY 80 million
Cz1	Special compensation from the CG for the residents of industrial zones	CNY 70 million
Cz2	Public happiness index benefits under the supervision of the CG	CNY 120 million
Cz3	Cost of the CG organizing people to learn from local work experience	CNY 50 million
Fe0	LGs’ benefits from environmental protection	CNY 170 million
Fe1	Subsidies given by LGs to CEs	CNY 20–100 million
Fe2	Subsidies given by the CG to CEs	CNY 60–100 million
Sz0	CG tax revenues	CNY 250 million
μ	Probability of a successful CG inspection	90%
θ	Probability of LGs catching CEs performing illegal acts	80%
σ	Technical applicability coefficient	70%
x	Initial probability of the CG’s behaviorial strategy	50%
y	Initial probability of CEs’ behavioral strategy	50%
z	Initial probability of LGs’ behavioral strategy	50%

.

3.2. Payoff Matrices and Game Equilibrium Points

Based on the above data, the return matrix of the eight strategies among the three game subjects is established, as shown in

Table 2. Game strategy payoff matrix.

	LGs Monitor z		LGs Do Not Monitor 1 − z
	CEs Implement y	CEs Do Not Implement 1 − y	CEs Implement y	CEs Do Not Implement 1 − y
The CG supervises x	$\left({\prod }_{\mathrm{e}1},{\prod }_{\mathrm{g}1},{\prod }_{\mathrm{z}1}\right)$	$\left({\prod }_{\mathrm{e}3},{\prod }_{\mathrm{g}3},{\prod }_{\mathrm{z}3}\right)$	$\left({\prod }_{\mathrm{e}2},{\prod }_{\mathrm{g}2},{\prod }_{\mathrm{z}2}\right)$	$\left({\prod }_{\mathrm{e}4},{\prod }_{\mathrm{g}4},{\prod }_{\mathrm{z}4}\right)$
The CG does not supervise 1 − x	$\left({\prod }_{\mathrm{e}5},{\prod }_{\mathrm{g}5},{\prod }_{\mathrm{z}5}\right)$	$\left({\prod }_{\mathrm{e}7},{\prod }_{\mathrm{g}7},{\prod }_{\mathrm{z}7}\right)$	$\left({\prod }_{\mathrm{e}6},{\prod }_{\mathrm{g}6},{\prod }_{\mathrm{z}6}\right)$	$\left({\prod }_{\mathrm{e}8},{\prod }_{\mathrm{g}8},{\prod }_{\mathrm{z}8}\right)$

.

$$\begin{gathered} \left({\prod }_{\mathrm{e}1},{\prod }_{\mathrm{g}1},{\prod }_{\mathrm{z}1}\right)=S_{z0}-C_{z0}-C_{z3}+K_{z2}-F_{e2},S_{e0}-C_{e0}-C_{e1}+S_{e1}+{\sigma C}_{e2}+F_{e1}-T_{g0}+F_{e2},T_{g0}-F_{e1}-C_{g0}-C_{g3}+S_{g0}+F_{e0} \\ \left({\prod }_{\mathrm{e}2},{\prod }_{\mathrm{g}2},{\prod }_{\mathrm{z}2}\right)=-C_{z0}+\mu K_{z1}-F_{e2}+K_{z2}+S_{Z0},S_{e0}-C_{e0}-C_{e1}+S_{e1}+\sigma C_{e2}+F_{e1}-T_{g0}+F_{e2},-F_{e1}+T_{g0}+S_{g0}-\mu K_{z1}+F_{e0} \\ \left({\prod }_{\mathrm{e}3},{\prod }_{\mathrm{g}3},{\prod }_{\mathrm{z}3}\right)=-C_{z0}-C_{z1}+C_{e3}+S_{z0},S_{e0}-C_{e0}-{\theta K}_{e1}-K_{e2}+S_{e2}-T_{g0}-C_{e3},\theta K_{e1}+T_{g0}-C_{g1}-C_{g2}-C_{g0}+S_{g0} \\ \left({\prod }_{\mathrm{e}4},{\prod }_{\mathrm{g}4},{\prod }_{\mathrm{z}4}\right)=-C_{z0}-C_{Z1}+C_{e3}+S_{z0}+\mu K_{z1},S_{e0}-C_{e0}-C_{e3}-K_{e2}+S_{e2}-T_{g0},T_{g0}-C_{g1}-C_{g2}+S_{g0}-\mu K_{z1} \\ \left({\prod }_{\mathrm{e}5},{\prod }_{\mathrm{g}5},{\prod }_{\mathrm{z}5}\right)=S_{z0}-C_{z2},S_{e0}-C_{e0}-C_{e1}+S_{e1}+\sigma C_{e2}-T_{g0},T_{g0}-C_{g0}+S_{g0}-C_{g3}+F_{e0} \\ \left({\prod }_{\mathrm{e}6},{\prod }_{\mathrm{g}6},{\prod }_{\mathrm{z}6}\right)=S_{z0}-C_{z2},S_{e0}-C_{e0}-C_{e1}+S_{e1}+\sigma C_{e2}-T_{g0},T_{g0}+S_{g0}+F_{e0} \\ \left({\prod }_{\mathrm{e}7},{\prod }_{\mathrm{g}7},{\prod }_{\mathrm{z}7}\right)=-C_{z2}+S_{z0},S_{e0}-C_{e0}-\theta K_{e1}-K_{e2}+S_{e2}-T_{g0},T_{g0}+\theta K_{e1}+S_{g0}-C_{g1}-C_{g2}-C_{g0} \\ \left({\prod }_{\mathrm{e}8},{\prod }_{\mathrm{g}8},{\prod }_{\mathrm{z}8}\right)=-C_{z2}+S_{z0},S_{e0}-C_{e0}+S_{e2}-T_{g0}-K_{e2},T_{g0}-C_{g1}-C_{g2}+S_{g0} \end{gathered}$$

Additionally, according to the definition of the above symbols, we constructed a compositional replication dynamic system.

$$\left\{\begin{array}{c}{\displaystyle \frac{dx}{dt}}=F\left(x\right)=x\left(1-x\right)[-yz{C}_{z3}+y\left(C_{z1}-F_{e2}-K_{z2}-C_{e3}-C_{z2}\right)+K_{z2}-C_{z0}-C_{z1}+C_{z2}+C_{e3}]\\ {\displaystyle \frac{dy}{dt}}=F\left(y\right)=y\left(1-y\right)[-xz\left(F_{e1}+\theta K_{e1}+K_{e2}-C_{e3}\right)+x\left(F_{e1}+F_{e2}+K_{e2}\right)+z\left(F_{e1}+{\theta K}_{e1}-K_{e2}\right)+S_{e1}-S_{e2}+C_{e3}+{\sigma C}_{e2}-C_{e1}]\\ {\displaystyle \frac{dz}{dt}}=F\left(z\right)=z\left(1-z\right)[xy\left(-\theta K_{e1}-{\mu K}_{z1}\right)+x\left({2\mu K}_{z1}-K_{e1}+{\mu F}_{e0}\right)+y{\mu K}_{z1}-C_{g0}-{\mu K}_{z1}]\end{array}\right.$$

According to the replication dynamic system, the Jacobian J can be calculated as follows:

$$\mathrm{J}=\left[\begin{array}{ccc}{\displaystyle \frac{\partial F\left(X\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(X\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(X\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}\end{array}\right]$$

The determinant detJ and the trace trJ of the Jacobian matrix can be obtained via calculation, and nine equilibrium points—P1(0, 0, 0), P2(1, 0, 0), P3(0, 1, 0), P4(0, 0, 1), P5(1, 1, 0), P6(1, 0, 1), P7(0, 1, 1), P8(1, 1, 1), and P9(x*, y*, z*)—are substituted into the determinant and trace of the matrix and then the detJ and trJ values of each equilibrium point can be obtained, as shown in Table S1. Only when detJ > 0, can trJ < 0 be the point be used as a stable point in the evolutionary game.

Considering the above assumptions, the benefit matrices for the CG, LGs, and CEs under various strategic combinations were computed and are visually represented as a game tree in Figure 2.

4. Results and Discussion

For the evolutionary game analysis based on the evolutionary game simulation model and assignment data, Figure 3 can be obtained.

4.1. The Impacts of Fines on the Three Parties

In the copper industry, fines are a punitive measure imposed by the government on enterprises that violate environmental protection and other relevant regulations. Their significance lies in deterring enterprises’ behavior and prompting them to comply with regulations and actively adopt environmental protection measures. If the fine is high enough, enterprises will realize that non-compliance will result in substantial economic losses. This incentivizes enterprises to invest resources in environmentally friendly production to avoid fines. For example, high fines may prompt enterprises to abandon short-term, environmentally harmful production methods in favor of more sustainable and eco-friendly production models.

Figure 3 presents the changes in the CG, CEs, and LGs based on the fines imposed on CEs by the CG and LGs. As seen in Figure 3, the CG and the LGs are less sensitive to the fines, while CEs are more sensitive to the fines, and as fines increase incrementally, CEs will modify their operational strategies accordingly.

Figure 3a–c present the changes in the CG, CEs, and LGs, respectively, based on the fines imposed by the CG on CEs. With the increase in the benefits from technology upgrades, when the fines are set at CNY 200 million, CEs will be more inclined to implement environmental protection measures. Additionally, when CEs relax their environmental protection work, they are subjected to multiple levels of supervision and punishment, which reduce their economic benefits and encourage them to continue to undertake environmental protection responsibilities. This results in a curve for the changes in CEs due to fines. When the fines are set at CNY 300 million, CEs will thoroughly implement environmental protection measures and will not change their strategies over time. Additionally, after 40 months, the behavioral strategy probability of the three parties reaches one and then remains stable. As the fines continue to rise, due to less CG and LG supervision, the stable state is reached later, and the probability for the CG may even decrease, resulting in a breakdown of the tripartite balance. This shows that when the fines are set at CNY 300 million, the three parties can achieve the best balance among their interests after 40 months. The high fines imposed by the CG increase costs for CEs if they do not implement environmental protection measures, forcing enterprises to re-evaluate their strategic choices. In order to ensure their own economic benefits, they have to choose to implement environmental protection measures.

Figure 3d–f present the changes in the CG, CEs, and LGs, respectively, based on the fines imposed by the LGs on CEs. When the fines are set at CNY 110 million, after 26 months, the behavioral strategy probability of the three parties reaches one and then remains stable. As the fines continue to rise, the LGs’ stable state is reached later. This shows that when the fines are set at CNY 110 million, the three parties reach a balance of interests the quickest.

Comparing Figure 3b and e, the fines imposed by LGs on CEs and the time point at which balance in interests is achieved are less and shorter, respectively, than when the CG imposes fines on CEs, which shows that LGs, as local managers, are more familiar with the CEs within their territory and therefore implement the more direct and expedited regulation of CEs. The CG needs to consider the environmental conditions of the entire industry and even the whole country, and the cycle of formulation and issuance of punitive measures is relatively long. Therefore, LGs play an essential role in controlling the behavior of CEs in order to encourage enterprises to implement environmental protection measures in the short term and accelerate the green transformation of CEs.

4.2. The Impacts of Subsidies on the Three Parties

Subsidies are financial support provided by the government to encourage enterprises to implement environmental protection measures and invest in green technologies. For copper enterprises, research and development into and updates to environmental protection technologies often require substantial capital investment. Subsidies can, to some extent, alleviate the financial burden on enterprises and increase their enthusiasm for environmental protection transformation. Especially for small and medium-sized enterprises with relatively weak financial strength, subsidies may be a decisive factor in their ability to carry out environmental protection projects. At the macro level, subsidies contribute to shifting the entire copper industry onto a more environmentally friendly and sustainable development path.

Figure 3g–i present the changes in the CG, CEs, and LGs, respectively, based on the subsidies issued by the CG to CEs. As seen in a comparison of the three figures, CEs are more sensitive to the subsidies. When the subsidies are set at CNY 80 million, CEs begin to consider implementing environmental protection measures, but over time, their choices will fluctuate. Moreover, with further increases in subsidies, these fluctuations become more obvious, and the duration of stability during the first stage shortens from 10 months to 2–3 months, but CEs implement environmental protection measures for a longer period of time during the second stage. When subsidies are set at CNY 100 million, the behavioral strategy probability of the three parties reaches one after 36 months and then remains stable. As the subsidies continue to rise, due to less CG and LG supervision, the probability of CEs implementing environmental protection strategies will decrease to below one after a period of time. This shows that when the number of subsidies are set at CNY 100 million, the three parties can achieve the best balance in their interests after 36 months. The analysis shows that low subsidies are not enough to change the strategic choice of CEs, with the probability of CEs choosing to implement environmental protection measures being low, and, thus, the three parties will struggle to maintain a balance of interests.

Figure 3j–l present the changes in the CG, CEs, and LGs, respectively, based on the number of subsidies issued by the LGs to CEs. When the subsidies are set at CNY 20 million or less, CEs will prioritize implementing environmental protection measures when formulating their production plans. However, after short-term investigations and practices, CEs will immediately change their strategies to ensure the most economic benefits. When the subsidies are increased to CNY 40 million, CEs will choose to consciously implement environmental protection measures. The choice of strategy for the CG and LGs does not change. When the subsidies are set at CNY 100 million, after 14 months, the behavioral strategy probability of the three parties reaches one and remains stable. As the subsidies continue to rise, due to less supervision, the probability of CEs implementing environmental protection strategies will decrease to below one after a period of time. Therefore, only when the number of subsidies is CNY 100 million will the three parties maintain the best balance of interests after 14 months. A comprehensive analysis of the CG’s and LGs’ subsidies shows that the main reason for CEs not choosing to implement environmental protection measures is that enterprises alone bear the cost of implementing environmental protection measures, while environmental protection benefits are shared by society as a whole; at the same time, converting environmental benefits into economic benefits is difficult for enterprises within a short period of time, which increases the financial pressure on enterprises. The subsidies provided by the CG and LGs make up for these economic losses in time, and so profit-seeking enterprises will begin to implement environmental protection measures. This shows that LGs should reward CEs that choose environmental governance in a timely manner and form a scientific reward and punishment mechanism to promote progress in environmental protection work in an orderly manner.

These findings indicate that insufficient subsidies fail to provide enough financial incentive for enterprises to implement environmental measures and invest in necessary green technologies. On the other hand, while subsidies are essential to encourage enterprises to adopt environmentally friendly technologies, overly generous subsidies can result in unsustainable fiscal burdens on the government. Therefore, a critical balance must be struck, with subsidies aligning with the actual costs and benefits of environmental compliance, ensuring that they are economically viable and sufficient to motivate significant environmental improvements.

4.3. The Impacts of Brand Image Benefits on the Three Parties

Brand image benefits are crucial for the long-term development of enterprises. A good brand image can enhance an enterprise’s market competitiveness and industry status, giving it more advantages in the market. With the currently increasing environmental awareness, consumers and partners are paying more attention to enterprises’ environmental performance. Enterprises with a good environmental image are more likely to gain market recognition and thus obtain more brand image benefits. Furthermore, brand image benefits also affect enterprises’ decision-making. To maintain a good brand image, enterprises are more willing to take initiatives to adopt environmental protection measures.

Figure 3m–o present the changes in the CG, CEs, and LGs, respectively, based on the brand image benefits. As seen in a comparison of the three figures, as the brand image benefits of CEs increase, supervision by the CG and LGs will gradually become more lenient. Additionally, with the increase in brand image benefits, the choices of CEs fluctuate, with supervision by the CG and LGs further relaxed. When the brand image benefits are CNY 150 million, the strategic choices of CEs tend to become stable. During the 43rd month, the CG’s supervision of CEs is the most relaxed, which leads to a neglect in environmental protection work by CEs. Thus, the CG is prompted to strengthen their supervision of CEs’ environmental protection work again. Additionally, the changes in the strategic choices of LGs are relatively smooth. When the brand image benefits are CNY 180 million, the CEs will choose to consciously implement environmental protection measures. However, the strategic choices of the CG and LGs have huge changes during the 15th and 30th months, respectively. In particular, during the 55th month, the CG has the most relaxed supervision, but a decline in LGs’ enforcement of policies promotes the CG’s supervision of CEs’ environmental protection work.

This suggests that enterprises with less brand impact frequently face difficulties in complying with governmental regulatory demands. Furthermore, the less the brand benefits, the higher the probability that these enterprises will incur fines from the CG and LGs, a situation that is evidently unsustainable. It can be seen from the image that no matter how high the brand image benefits, the behavioral strategy probability of the three parties cannot be maintained at one for a long time, and the three parties cannot reach a stable state; this shows that the requirements for reaching a balance are too high. In addition, the sustainable development of the country is a process of industrial structural transformation. Therefore, outdated production capacities and some small enterprises that cannot meet environmental standards need to be eliminated. The probability of environmental protection policy implementation achieving a balance can be appropriately reduced to ensure that the three parties reach a stable state and the balance is reached during the policy implementation period. When the brand image benefits are CNY 150 million, after 10 months, the behavioral strategy probability of the three parties exceeds 0.7 and remains stable. Therefore, this time is set as the best balance of interests of the three parties. The analysis shows that for CEs, as profit-seeking economic entities, high brand image benefits can not only encourage enterprises to actively choose and implement environmental protection measures but also reduce government supervision of environmental protection at all levels. According to Figure 3, when the interests of the three parties reach a balance under these requirements, 30% of enterprises cannot meet the standard within 40 months, which may cause 500 small and medium-sized enterprises to close down or stop production, which will seriously affect local government tax revenue and employment.

Figure 4 is drawn based on the data from China’s seventh population census and the number of Chinese enterprises, which shows the change in unemployment in relation to the income generated by copper enterprises due to their brand image.

When the income generated due to a CE’s brand image reaches CNY 150 million, which is the point during the policy implementation period when the three parties reach a relative balance in their interests, about 100,000 to 120,000 copper industry employees will lose their jobs. At the same time, the taxes and finances of LGs will be affected, which is obviously unsustainable. Therefore, from the perspective of LGs, appropriately relaxing environmental protection policies and standards is conducive to ensuring the stability of local finances and employment and maintaining the sustainable development of the three parties.

4.4. Economic Benefits of Different Scenarios

In recent years, the Chinese government has formulated new environmental protection systems or revised existing regulations almost every year. The number of policies related to the copper smelting industry in China has steadily increased, with the frequency of policy issuance rising and the scope of covered content becoming progressively more comprehensive. At the same time, in order to cope with increasingly severe climate change, China officially announced their strategic goals for a carbon peak by 2030 and carbon neutrality by 2060. Carbon neutrality is the most important way to deal with climate change; specifically, cleaner production from the copper industry is an important method of achieving carbon neutrality and basically guarantees carbon sequestration. In order to speed up the structural adjustment of the copper industry, the three parties also need to cooperate in adopting new cleaner production measures, as well as adopting the whole-process management model to achieve a new optimal balance of interests acceptable to the three parties. Based on the above evolutionary game analysis, this study models a series of sub-scenarios. Starting from the normal production of the copper industry, eight sub-scenarios were formulated from three aspects: production, measures, and management measures. The scenarios are used to simulate future changes in China’s copper industry. In a separate sub-scenario, the economic benefits that can be achieved by implementing the measure are extrapolated, and the data are taken as industry averages. The results can provide a reference for the sustainable development of China’s copper industry.

The main purpose of the simulated scenarios is to show that many possible paths exist. In fact, the rollout of any number of key methods can have a significant impact on the industry, but determining the magnitude of the impacts of these methods on likely future developments is important, and quantification using economic benefits can help reveal their impacts, but may not provide the overall picture.

Figure 5 shows the economic benefits of the eight scenarios. In the envisaged scenario, the production, treatment, and management measures under the influence of various policies will improve the economic benefits of CEs, and the introduction of advanced hydrometallurgy technology has greater potential in improving economic benefits. Under the premise that the three parties implement this measure, the economic benefit after 5 years will reach CNY 147.2 billion, which is the highest value among the various scenarios. This is because hydrometallurgical copper smelting equipment is simple and easy to operate, without the need to use blasting and smelting equipment, and can be used at room temperature, which can save on fuel. The smelting cost of copper is thus greatly reduced, and so better economic benefits are achieved.

The use of oxygen-enriched smelting technology in production measures can also achieve good economic benefits, which can reach CNY 62.2 billion. This is because oxygen-enriched smelting not only improves the smelting effect and reduces the amount of flue gas but also increases the SO₂ concentration in the flue gas, which greatly improves the recovery rate of sulfur.

In the treatment measures, the change from a fabric filter to an electrostatic fabric filter has also achieved good economic benefits. The economic benefits after 5 years can reach CNY 74.8 billion. Due to the low operating resistance of an electrostatic fabric filter, the filter bag cleaning cycle time becomes long, leading to a series of advantages, such as an energy-saving effect and low operation and maintenance costs. The implementation of a clean production audit in the management measures can also transform the copper industry from the perspective of clean production, such as energy savings, consumption reductions, pollution reductions, and efficiency enhancements, thereby achieving good economic benefits. The economic benefits after 5 years can reach CNY 35 billion.

Although other scenarios have achieved certain economic benefits, they have less impacts on the development of the copper industry than the above-mentioned measures. Therefore, the CG should cooperate with LGs and CEs to use the above four measures to promote emission reductions, resource utilization, energy savings, and efficiency improvements in the copper industry; reduce environmental pollution caused by the copper industry; and increase the economic benefits of the copper industry.

5. Conclusions

This study underscores the complex dynamics of sustainable development within China’s copper industry through a tripartite evolutionary game model involving the central government (CG), local governments (LGs), and copper enterprises (CEs). The model quantifies influential factors and tracks the evolution of balance among these stakeholders, aiming for a sustainable equilibrium.

1. The regulatory impacts of increasing the fines for non-compliance have effectively incentivized CEs to adopt environmental measures. Local governments have been quicker and more direct in enforcing these regulations due to their proximity and familiarity with enterprises, contrasting with the slower, broader approach of the CG. Despite increased fines and subsidies enhancing compliance, insufficient subsidies have made sustaining this balance challenging. In conclusion, the sustainable development of the copper industry necessitates that both the central and local governments implement well-balanced fines and subsidies to encourage enterprises to engage in environmental conservation measures. LGs play an essential role in controlling the behavior of CEs in order to encourage enterprises to implement environmental protection measures in the short term and to accelerate the green transformation of CEs. The CG and LGs need to develop reasonable economic incentives and penalties for CEs to not only protect the environment but also foster the healthy development of the copper industry.

2. The benefits from image and technological upgrades brought about by the implementation of environmental protection policies to CEs will in turn increase the enthusiasm of enterprises to implement environmental protection measures. However, the time required for the behavioral strategy probability of the three parties to stabilize at one is too long, far exceeding the implementation period of relevant environmental protection policies, and such a probability cannot be maintained at one for a long time; so, maintaining this balance is also difficult. This suggests that enterprises with less brand impact frequently face difficulties in complying with governmental regulatory demands and bearing the financial burden of fines. Furthermore, the less brand benefits, the higher the probability that these enterprises will incur fines from the CG and LGs, which can lead to economic losses and the potential shutdown of up to 30% of small and medium-sized enterprises, affecting approximately 100,000 to 120,000 jobs. However, large investments will lead to losses of economic benefits, which are obviously unsustainable for CEs.

3. Under the premise that existing national policies, local standards, and corporate environmental measures fall short of achieving sustainable development in the copper industry under new plans, this research has conducted a scenario analysis based on evolutionary game theory to identify the most cost-effective clean production methods. The analysis reveals significant economic benefits associated with specific environmental measures. The introduction of advanced hydrometallurgy technology is projected to yield the highest economic returns, with an estimated benefit of CNY 147.2 billion over five years. Similarly, the adoption of oxygen-enriched smelting and the transition from fabric filters to electrostatic fabric filters is expected to generate CNY 62.2 billion and CNY 74.8 billion of economic benefits, respectively. Additionally, cleaner production audits could contribute CNY 35 billion in economic benefits. In light of these findings, the central government (CG), local governments (LGs), and copper enterprises (CEs) are recommended to prioritize these measures to enhance resource utilization, energy efficiency, and environmental protection in the copper industry. This approach not only addresses environmental challenges but also supports the industry’s economic development, providing a viable reference for the sustainable advancement of China’s copper industry.

Limitations

This study has several limitations. First, the evolutionary game model relies on certain assumptions that may not fully capture the complexities of real-world interactions. Second, data collection was capped at 2021 due to comprehensive and reliable financial and policy data being available only up to that point. While this cap in data collection may limit this study’s ability to reflect the very latest industry changes, the chosen timeframe provides a robust basis for analyzing long-term trends and the initial impacts of recent policy shifts. Future studies could extend this analysis with updated data to capture ongoing developments in the copper industry.