
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12320-1
10.1016/j.heliyon.2024.e36289
e36289
Research Article
Evolutionary game analysis and efficiency test of water pollution control driven by emission trading: Evidence from Zhejiang Province, China
Yang Xia xyang8731959@163.com
ab⁎1
He Gang a1
Zhu Zhihe c1
Zhao Shuhang a
Zhang Shiyu a
a School of Economics and Management, Anhui University of Science & Technology, Huainan, 232001, China
b School of Economics and Management, Huainan Normal University, Huainan, 232038, China
c School of Economics and Management, Anhui Agricultural University, Hefei, 230036, China
⁎ Corresponding author. School of Economics and Management, Anhui University of Science & Technology, Huainan, 232001, China. xyang8731959@163.com
1 Xia Yang, Gang He and Zhihe Zhu contributed equally to this work.

14 8 2024
30 8 2024
14 8 2024
10 16 e362899 5 2024
13 8 2024
13 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Presently, China is actively endorsing the pilot initiative for the remunerative use and trading of emission. By examining the operation and efficacy of emission trading in the context of water pollution control, one can contribute to the advancement and refinement of this system, thereby facilitating the attainment of regional pollution reduction, carbon reduction, and high-quality development objectives. In pursuit of this objective, we develop a theoretical framework for the local government and sewage enterprises evolutionary game of water pollution control, which includes two scenarios without considering and considering emission trading for studying the influencing factors and evolution trajectory of the game subject's. Through the stability analysis, the game interactive mechanism, the difference in evolutionary trajectory, and the response logic of the decision-making body in different situations become clearly visible. Further, the system sensitivity factors are analyzed by solving the partial derivation of the area formula of the phase diagram. And the efficacy of the sewage trading system in water pollution control in Zhejiang Province is empirically examined at the micro level by adopting the trading data of the first pilot area of sewage trading in the country and the case of pollution control in Jinhua City. The research reveals the following conclusions: Under specific circumstances, emission trading can incentivize businesses and even industries to enhance pollution control measures as a whole. The performance and degree of sensitivity factors vary across gaming systems, with public reputation evaluation and central government inspection serving as positive constraints. The initial cost of paid use of emission permits, as a fixed cost component for firms to address pollution, has no effect on the enterprises' behavioral actions to satisfy emission regulations. The findings can furnish local governments with a theoretical foundation and decision support in order to optimize regulatory strategies and enhance pollution control policies.

Keywords

Water pollution control
Emission trading
Evolutionary game
Efficiency test
Initial emission permits
==== Body
pmc1 Introduction

An article published in Nature in 2023 made a dire prediction that by the conclusion of this century, as many as 5.5 billion individuals may be exposed to contaminated water. The author compared the water contamination crisis to a “time bomb” that poses a significant risk to the health of the entire planet [1]. Today, with rapid economic development, the human living environment is getting worse and worse, and many diseases such as atrial fibrillation are induced by water pollution and air pollution [2]. Water pollution control has consistently been a top priority for China. In 2022, the 20th Party Congress issued a significant directive to “integrate the management of water resources, water environment, and water ecology, while promoting the ecological protection and management of significant rivers, lakes, and reservoirs.” Following the publication of the “Guiding Opinions on Further Promoting the Pilot Work of Paid Use and Trading of emission permits” in 2017, several pilot provinces, including Zhejiang, Hunan, Shaanxi, and others, have begun investigating the paid use of initial emission permits as an important economic policy for environmental governance. The most significant policy in water pollution management, “promote the industrialization of water pollution,” was proposed in the “Fourteenth Five-Year Plan for the Development of the National Economy and Society of the People's Republic of China and the Visionary Objectives of 2035″ in 2021. The Outline of the Fourteenth Five-Year Plan and Visionary Goals for 2035 for National Economic and Social Development of the People's Republic of China put forth the following proposal in 2021: “Facilitate, within a specified timeframe, the implementation of measures that mandate industrial pollution sources to adhere to emission standards; encourage the market-based exchange of rights to discharge, use energy, water, and carbon.” Nonetheless, water pollution is a matter of public concern and transcends national boundaries.

Consequently, governing bodies face challenges including power imbalances, conflicts of interest, and power dispersion. Notably, the ineffectiveness of water pollution governance has been significantly impacted by the dispersed layout of polluting enterprises along watersheds, the exorbitant expenses associated with equipment required to comply with discharge standards, and the inadequate internal motivation of these enterprises. Currently, the pilot phase of China's emission trading system is nearing completion. It is critical to examine the influence of this mechanism on the decision-making processes of polluting enterprises and the government regarding the control of water pollution. By doing so, suitable regulatory instruments can be selected to bolster the governing bodies' internal and external motivation. Such motivation will play a pivotal role in advancing regional pollution reduction, carbon mitigation, and high-quality development.

2 Literature review

The US National Environmental Protection Agency (EPA) first employed the principle of emission trading in 1968 to control the sources of air and river pollution. American economist Dales originally put up this idea. This was followed at the international level by the introduction of Emission Trading Schemes (ETS) that limit the number and price of emission units based on a market perspective [3]. In 1988, China initiated its investigation into the emission trading system. Chen Lei spearheaded the design of the policy's initial allocation system in 2005 [4]. Eleven provinces, namely Jiangsu, Tianjin, Zhejiang, and Hebei, initiated the SO2 emission trading program in 2007 [5]. Following this, some academics have moved the application of emission trading to the management of water resources and the prevention of water pollution. For example, H. Xu et al. introduced emission trading into the multi-agent collaborative management of coastal land source pollution and identified its influencing factors [6]. In the US state of Ohio, Woodward R. T. examined a water quality trading program [7]. Sewage trading is one of the key instruments for managing and controlling water pollution. Although different researchers have used different approaches to test the mechanism's ability to reduce pollution, they have produced varying conclusions in their recent studies. Some scholars have demonstrated that the European Union Emission Trading System (EUETS) has a significant dampening effect on carbon emission and leads to an increase in the economic performance of regulated firms [8].

Certain academics argue that we need to take into account the environmental quality improvement goals and the level of enterprise emission performance, in order to improve the initial sewage right quota approval and allocation [9]. First of all, we also need to adopt a scientific method to determine the initial allocation of sewage rights of enterprises, and at the same time, take into account the comprehensive consideration of the emission of pollutants, the right to sewage and the initial sewage rights of the market price and the marginal return [10]. The purpose of doing so is to explore and promote the allocation of paid use The purpose of this is to explore and promote the allocation of paid use, to prevent the occurrence of enterprise “rent-seeking” behavior [11]. In addition, it is also necessary to analyze the choice of interaction strategies among wastewater enterprises, the government and the public [12], whoes aim to pay attention to the additional impact of the level of consumer awareness on the emission reduction efforts of enterprises [13], and to enhance the consistency of the dynamics between the enterprises' pollution control inputs and the emission trading policy [14].

Given the imperfect management of wastewater discharge permits, Yuan et al. used a multi-objective optimization model to explore the coordinated allocation of water resources and wastewater discharge permits [15]. While water pollution control encompasses numerous facets, the governance functions performed by polluting enterprises and local governments are indispensable. As an analytical method for examining the evolutionary trend of group behavior from a systemic perspective, the evolutionary game theory founded on finite rationality and group decision-making, which has been widely applied in the field of environmental governance, where it has clarified the research ideas necessary for the government to implement the water pollution control strategy and improve the efficacy of governance. A four-party evolutionary game model involving the central government, local governments, polluting firms and the public is constructed to analyze the development and implementation of air pollution control policies in China [16], which provides a useful reference for the analysis of the evolutionary game of water pollution control. In order to examine the impact of various expenditure preferences of local governments on the production behavior of industrial polluters, Fan et al. developed an evolutionary game model [17]. The game behavior and equilibrium between pollutants and regulatory authorities were analyzed by Wang et al. [18].

Based on the evolutionary game theory, the integration of emission trading into water pollution control practice has become an important research tool. In the context of monitoring mechanism for exceeding emission standards, Zhang et al. [19] investigated the evolutionary process, influencing factors, and regulatory strategies between the government and businesses in the context of emission trading using evolutionary game theory. By constructing a spatially synergistic evolutionary game model of social governance for river basin water pollution, Bai et al. [20] were able to resolve the dilemma. Li established a regional cooperation profit system and implemented the trading of emission permits for the purpose of controlling industrial pollution across international borders. Li implements emission permit trading as a means of regulating transboundary industrial pollution and devises a profit distribution mechanism for regional cooperation [21]. A differential game model was developed by Lu et al. to analyze transboundary pollution within a multiregional alliance. The authors conclude that pollution control is more effectively managed through cooperation among three regions [22]. In their study, Wang et al. [23] examine the impact of foresight on the optimal emission level and optimal abatement in the transboundary industrial pollution game by incorporating emission permit trading and abatement policies.

In recent years, theoretical and applied research on water pollution control has proliferated, indicating a trend toward multi-method research. Despite the attainment of higher-quality outcomes, the subsequent areas for improvement continue to persist: At first, there was a lack of comprehensive research on the integration of emission trading and water pollution control. More scholars agree with and pay attention to the application of emission trading mechanisms to promote the control of pollutants during the practice of pollution control. However, the majority of their research focuses on the effect testing, system design, and decision-making impact of pollution control subjects, with less attention paid to the integration of emission trading and water pollution management. Furthermore, the precise implementation of effluent trading as a means to optimize water pollution management strategies remains ambiguous. Water pollution emission comprise an assortment of pollutants that impact the water environment. However, certain scholars have limited their focus to a single pollutant, such as nitrogen or phosphorus, and have not conducted a comprehensive analysis of the emission trading system's effectiveness in managing a wide range of pollutants in the water environment. Simultaneously, certain pilot municipalities are examining the implementation of initial emission permits accompanied by compensation. However, scholarly investigations into the theoretical aspects pertaining to behavioral decision-making in the context of pollution control by the government and businesses, including evolutionary mechanisms and influencing factors, remain insufficient. Thirdly, there is insufficiency in the empirical analysis of emission trading and the evolutionary game. The current body of research on the integration of evolutionary games and water pollution emission trading is limited, with the majority of studies focusing on theoretical analysis rather than conducting practical efficacy tests. Moreover, the evolutionary game simulation component lacks a micro-case empirical evaluation and relies primarily on parameter simulation assignment.

The purpose of this paper is to analyze the evolution trajectory and influencing factors of the behavioral strategies of the two game subjects, local government and sewage enterprises, and to reveal their interaction and mechanisms by comparing and analyzing the two scenarios without considering sewage trading. A simulation analysis is conducted to assess the operation case of the initial emission permits center in Zhejiang Province and the other in which emission trading is considered. The simulation analysis is predicated on the operational case of the inaugural National Emission Trading Center in Zhejiang Province and the case of enterprise water pollution control in Jinhua City. Its purpose is to assess the efficacy of emission trading in Zhejiang Province's water pollution control and to propose a management strategy that combines emission trading, public participation, central government oversight, and local government incentives and penalties in order to maximize manpower.

The marginal contributions of this paper are mainly manifested in the following aspects: First, it adopts the evolutionary game theory method, integrates the policy tools of control, market, and voluntary, analyzes the equilibrium mechanism of each subject of interest, and explores the differences in the evolutionary trajectory and the logic of the subject's decision-making response under different mechanisms. It then proposes a governance strategy using a combination of emission trading, public participation, and government rewards and penalties to reduce the free-riding behavior of local governments and improve the effectiveness of coordinated management of water pollution in the river basin. The second is to compare and analyze the influencing factors and mechanisms of the strategy behavior of the two game subjects, local government and enterprise, under the two circumstances of not considering sewage trading and considering sewage trading, and to simulate and analyze the operation case of the first national sewage trading center in Zhejiang Province and the actual enterprise sewage management case in Jinhua City to empirically test the efficacy of the sewage trading mechanism in the territorial governance of Zhejiang Province, which is of strong practical reality and practical value.

3 Materials and methods

3.1 Study design

The government actively regulates the stage of short-term efforts to encourage polluting enterprises to meet sewage standards, but the long-term will progressively devolve into a “cat-and-mouse” race cycle; therefore, it is prudent to give careful consideration to how to strengthen the internal motivation of the enterprise, given the dispersed layout and high cost of discharge equipment. Wang Jinnan and other scholars hold the view that emission trading facilitates industrial restructuring, transformation, and upgrading. To achieve this, the local government can establish control standards for total water pollutant emission, which would establish the initial emission permits of the aquatic environment in the region. Polluting enterprises could trade their emission rights for compensation or without charge [24]. Moreover, scholars such as Yuan have proposed strengthening the penalties of “polluter pays” programs, abandoning segmented watershed management, and building basin-wide water management systems [25].

In accordance with national or locally stipulated pollutant discharge standards, as well as requirements for the control of the total amount of pollutant discharged. The Management Measures for Compensated Use and Trading of Water Discharge Rights in the Xin'an River Basin (Pilot) of September 2020 states that discharge rights, which refer to the types and quantities of pollutants that a discharging unit is authorized to allow it to discharge within a certain period of time. As shown in Fig. 1, the two sides of the game are the local government and the sewage enterprises with limited rationality, which form a territorial governance structure, and the strategies of both sides tend to stabilize with the evolution of time. The local government's strategy set consists of two components: positive regulation and negative regulation. Polluting enterprises adopt the following strategy sets: standard discharge and exceeding the standard discharge. The probabilities associated with positive regulation and standard discharge are denoted as x and y, respectively. The probabilities of negative regulation and exceeding the standard discharge are 1-x and 1-y, with 0≤x, y ≤ 1. The discharge of water pollutants by a discharging enterprise is considered to be in compliance with the standards if it does not exceed the authorized allocation of the initial emission permits as stipulated by the state and local regulations. Conversely, if they surpass the standard discharge, they are considered to be exceeding the standard. The local government grants sewage licenses to polluting enterprises via the emission trading market; polluting enterprises may purchase or sell the right to discharge in real time, with the cost of compliance with the discharge fluctuating in accordance with the actual quantity of polluting enterprises involved. The administration and construction of the emission trading market fall under the purview of the local government. To encourage public participation in pollution monitoring and to oversee the water pollution discharge practices of polluting enterprises, the government implements a system of rewards and punishments. Concurrently, both municipal administrations and sewage companies are obligated to adhere to public reputation assessments.Fig. 1 Evolutionary game analysis framework for water pollution control evolution driven by emission trading.

Fig. 1

3.2 An evolutionary game model without considering emission trading scenarios

When the government actively regulates, it generates funds for prevention and control of water pollution control and regulation, establishes incentives for public participation in sewage regulation, and also gives subsidies and rewards to enterprises for meeting discharge standards (including rewards for the completion of water environment quality objectives and subsidies for equipment for enterprises to build new pollution control-related projects). Through sampling and monitoring of wastewater discharge outfalls, enterprises will be penalized if they are found to have exceeded discharge standards, misrepresented the amount of pollution discharged, or falsified data. On the contrary, when the government negatively regulates, it does not incur water pollution prevention and control costs, sewage subsidies, incentives for rewarding and punishing revenues, or obtain short-term gains.

The local government obtains long-term and short-term benefits when the sewage enterprise meets and exceeds the emission standards, respectively. Sewage enterprises meet the emission standards to obtain long-term gains, resulting in technological innovation, the introduction of pollution equipment, and other pollution control costs; exceeding the emission standards to obtain short-term gains does not produce enterprise pollution control costs, resulting in local government environmental degradation losses, and the central government inspectors give the local government negative regulatory penalties and environmental rectification costs (referred to as the cost of rectification of the local government). Rissman et al. believe that the public's support of environmental policy is an important foundation for democratic governance. Support is an important basis for democratic governance and can help improve nonpoint source pollution [26]. Drawing on this study, when local governments negatively regulate, the public suffers reputational damage to the government, and excessive emissions by polluting enterprises result in a loss of public image and reputation towards the company. Model parameters and descriptions are defined as shown in Table 1.Table 1 Model parameters and descriptions.

Table 1Parameter	Description	Notes	
C1	The government actively regulates the investment of funds paid for water pollution prevention and control	0 < C1 < C2	
R	The government actively regulates to give the public a reward for reporting incentives	0 < R	
S	The government actively regulates and gives subsidies and incentives to sewage enterprises to meet the emission standards	0 < S	
F	Penalties for over-emission, misreporting of pollutant emission and falsification of data by sewage enterprises in the context of active government regulation	0 < F	
S1	Long-term benefits to the Government when the discharging enterprise meets the emission standards	0 < S1	
S2	Short-term gains to the government when a discharging enterprise exceeds its emission standards	0 < S2 < S1	
U1	Long-term gains for polluters in meeting emission standards	0 < U1	
U2	Sewerage firms reap short-term gains by exceeding emission standards	0 < U2 < U1	
C2	Pollution control costs such as technological innovation and introduction of polluting equipment incurred by sewage enterprises to meet emission standards	0 < C2	
V	Losses from environmental degradation of local governments due to excessive emission by polluting enterprises	0 < V	
D1	Punishments and environmental remediation costs for negative regulation by local governments	0 < D1	
D2	When local governments negatively regulate, the public suffers reputational damage to the government	0 < D2 < D3 < D1	
D3	Excessive emission by polluting enterprises result in a loss of public image and reputation towards the company	0 < D3	

According to the above assumptions and parameter settings, the payment matrix of the water pollution control game without considering emission trading is formed, as shown in Table 2.Table 2 Payment matrix of water pollution control game without considering emission trading.

Table 2Gaming party	Polluting enterprises	
Compliance discharge (y)	Excessive discharge (1-y)	
Local government	Active regulation (x)	S1–C1-R-S,U1–C2+S	S2–C1-R + F–V,U2–F-D3	
Negative regulation (1-x)	S1-D1,U1–C2	S2-D1- D2-V,U2-D3	

In order to construct dynamic equations for the replication of the two scenarios, consider the following: Suppose the average expected return is and the expected returns for local governments implementing “active regulation” and “passive regulation” strategies are denoted by Ea1 and Ea2, as defined in equation (1).(1) {Ea1=y(S1−C1−R−S)+(1−y)(S2−C1−R+F−V)Ea2=y(S1−D1)+(1−y)(S2−D1−D2−V)Ea‾=xEa1+(1−x)Ea2

The replication-dynamic equation as shown in (2) for local government strategy choice is:(2) F(x)=dx/dt=x(Ea1−Ea‾)=x(1−x)(F−C1−R+D1+D2−D2y−Fy−Sy)

Assuming that the discharging firms' “meet emission standards” and “exceed emission standards” strategies have expected returns of Eb1 and Eb2, respectively, as shown in equation (3). And that the average expected return is:(3) {Eb1=x(U1−C2+S)+(1−x)(U1−C2)Eb2=x(U2−F−D3)+(1−x)(U2−D3)Eb‾=yEb1+(1−y)Eb2

The following equation (4) is the reproduced dynamic equation for the discharging firm's chosen strategy:(4) F(y)=dy/dt=y(Eb1−Eb‾)=y(1−y)(D3−C2+U1−U2+Fx+Sx)

A two-dimensional dynamical system is formed between the local government and the drainage enterprises; when the expectations of the two entities' distinct strategies are equivalent, the system maintains a stable state and an equilibrium point is reached. Given F(x) = dx/dt = 0 and F(y) = dy/dt = 0, the system's equilibrium points are as follows: (0,0), (0,1), (1,0), (1,1), and (x*,y*), where x*=C2−D3−U1+U2F+Sx*=C2−D3−U1+U2F+S , y*=−C1+D1+D2+F−RD2+F+S. Construct the Jacobi matrix J by taking the partial derivatives of F(x) and F(y), See equations (5), (6), (7) for details.(5) J=[∂F(x)∂x∂F(x)∂y∂F(y)∂x∂F(y)∂y]=[(1−2x)(D1−C1+D2+F−R−D2y−Fy−Sy)x(1−x)(−D2−F−S)y(1−y)(F+S)(1−2y)(D3−C2+U1−U2+Fx+Sx)]

(6) detJ=[c11c12c21c22]=c11c22−c12c21

(7) trJ=c11+c22

It is necessary to assess the stability of the system's evolutionary strategy (ESS), as the system equilibrium point does not invariably represent its ESS. A change in the (x*,y*) point causes an equivalent shift in the stable point of the evolutionary system. As per the determination of Ljaplov's First Law [27], the equilibrium point is ESS if all eigenvalues of the Jacobi matrix are less than zero. The point is unstable if any eigenvalues are greater than zero; and the mixed strategy point consists of combinations of zeroes and negatives. The values of the local equilibrium points at c11, c12, c21, and c22 are acquired through the solution of the Jacobi matrix (See Table 3 for details).Table 3 Stability judgment of local equilibrium points.

Table 3Balance point	c11	c12	c21	c22	
O (0,0)	-C1+D1+D2+F–R	0	0	-C2+D3+U1–U2	
A (0,1)	-C1+D1-R-S	0	0	C2-D3-U1 + U2	
B (1,0)	C1-D1-D2-F + R	0	0	-C2+D3+U1–U2+F + S	
C (1,1)	C1-D1+R + S	0	0	C2-D3-U1 + U2–F–S	
D (x*,y*)	0	M	N	0	
Note：M = (D2+F+S)(C2−D3−U1+U2−F−S)(C2−D3−U1+U2)(F+S)2, N = (−C1+D1+D2+F−R)(F+S)(C1−D1+R+S)(D2+F+S)2.

The system can be stabilized through four distinct strategies in the absence of emission trading. Consider point C (1,1) as an illustration: in this case, point (1,1) represents the equilibrium point of the ESS when C1-D1+R + S < 0 and C2-D3-U1 + U2–F–S < 0. At this point, the system executes the evolutionary gaming strategy of active regulation and emission compliance. U2–F-D3 < U1–C2 + S, the short-term benefit of enterprise over-standard emission is less than the long-term benefit of standard emission, and C1+R + S < D1, the sum of local government's positive regulation pollution control cost, public reward for reporting. Meanwhile enterprise subsidy for meeting the standard emission is less than the penalty and environmental rectification cost of the central government's inspection of local government's negative regulation. Subsequently, it can be deduced that the thresholds for regulating the penalties F and C2-D3-U1 + U2–S < F, respectively, should be set at C2-D3-U1 + U2–S and C2-D3-U1 + U2–S < R, to ensure that firms meet the standard emission requirements and exceed whichever they do so. Additional stabilization scenarios are not expounded upon.

3.3 An evolutionary game model considering emission trading scenarios

The three primary allocation modalities for initial emission permits are uncompensated, compensated, and mixed. Presently, China is endeavoring to enforce the compensated utilization of initial emission permits. To encourage emission-related businesses to comply with emission standards, an evolutionary game model is developed in this context that compensates for the initial emission permits in order to account for the trading situation of the emission right.

In order to obtain the local government's initial emission permits allocation T, enterprises that acquire emission permits pay the transaction cost C3 for the paid use of initial emission permits. If the actual emission volume falls below the initial emission level, the enterprise is considered to be in compliance with the standard. Furthermore, if the excess emission volume is sold for economic returns, the enterprise is exempt from the standard I. Conversely, enterprises that exceed the standard may purchase or lease the emission rights of other businesses in order to bring their own emission practices into compliance with the standard. This would exempt them from both the public and regulatory penalties associated with exceeding the standard. In contrast, enterprises that exceed the emission standards bring their own emission behavior into compliance with the standards by purchasing or leasing emission rights from other enterprises. In this way, they are exempted from local government penalties for exceeding the emission standards and from the image damage caused by the public against them. The amount in excess of the rated portion is responsible for covering the purchase cost W. On the emission market, the mean transaction price per tonne of emission right is P < W, D3 < W.

As shown in Table 4, The dynamic equation of replication between local governments and businesses is altered after taking emission trading into account. The revised equation (8) is as follows:(8) {F(x)=dx/dt=x(1−x)(D1+D2−C1−R+V−D2y−Sy−Vy)F(y)=dy/dt=y(1−y)(I+U1−U2−C2+D3−D3x+Sx+Wx)

Table 4 Payment matrix of local water pollution control game considering emission trading.

Table 4Gaming party	Polluting enterprises	
Compliance discharge (y)	Excessive discharge (1-y)	
Local government	Active regulation (x)	S1–C1-R-S + C3,U1–C2–C3+S + I	S2–C1-R + C3,U2–C3–W	
Negative regulation (1-x)	S1-D1 + C3,U1–C2– C3 + I	S2- D1-D2-V + C3,U2–C3- D3	

The equilibrium points of system O (0,0), A (0,1), B (1,0), C (1,1), and D (x*, y*) are obtained when F(x) = dx/dt = 0 and F(y) = dy/dt = 0. The solution of the Jacobi matrix J produces Table 5.where x*=−C2+D3+I+U1−U2D3−S−W , y*=−C1+D+1D2−R+VD2+S+V.Table 5 Stability judgment of local equilibrium points.

Table 5Equilibrium point	c11	c12	c21	c22	
O (0,0)	-C1+D1+D2-R + V	0	0	-C2+D3+I + U1–U2	
A (0,1)	-C1+D1-R-S	0	0	C2-D3-I-U1+U2	
B (1,0)	C1-D1-D2+R–V	0	0	-C2+I + S + U1–U2+W	
C (1,1)	C1-D1+R + S	0	0	C2–I–S–U1+U2–W	
D (x*,y*)	0	M1	N1	0	
Note：M1 = (C2−D3−I−U1+U2)(D2+S+V)(C2−I−S−U1+U2−w)(−D3+S+W)2，N1 = (C1−D1+R+S)(C1−D1−D2+R−V)(D3−S−W)(D2+S+V)2.

Table 5 illustrates the four possible scenarios where emission trading can intervene and bring the system to a steady state. Just the system's stability criteria at the (1,1) equilibrium point are covered in order to conserve space. The system has to do with putting together (active regulation, emission compliance) evolutionary stabilization methods with C1-D1+R + S < 0且C2-I-S-U1+U2–W < 0. The total cost of the public's reward for reporting pollution, the cost of local governments' active regulation of pollution control (C1+R + S < D1), and the subsidy for businesses meeting the standard is less than the cost of the central government's inspection of the fine and environmental rectification of local governments' negative regulation, and local governments adopt positive regulation. U2–W < U1–C2+S + I, which is derived from U2–C3–W < U1–C2–C3+S + I, shows that following the emission trading mechanism's intervention, the businesses generate surplus emission trading revenues; their benefits from adhering to the standard outweigh their benefits from going above and beyond the standard; and they opt to follow the standard emission strategy. Currently, the corporate emission trading buy cost W requires C2–I–S–U1+U2 < W, and the government meets the standard emission subsidy S threshold, which should be managed in C2–I –U1+U2–W < S < D1-C1-R.

4 Results

4.1 Case simulation analysis-case introduction and parameter assignment

The first emission trading center in China opened for business in Jiaxing, Zhejiang Province, on November 10, 2007. Jiaxing is the most active region in the nation when it comes to emission trading, and is currently actively pursuing the model of paid use of initial emission permits. Founded in 1966, Zhejiang Huachuan Industrial Group Co., Ltd (Huachuan Industrial for short), as a national high-tech enterprise in Yiwu City, Jinhua City, Zhejiang Province, its main business involves papermaking, waste incineration power generation, sludge treatment, printing and dyeing and other fields. In 2021, the enterprise declared the sewage biogas and urban sludge resource utilization and thermoelectricity cooling and gas cogeneration project, with a total project investment of 311.63 Million RMB. The funds are used for the introduction and installation of six drying production lines, circulating fluidized bed boilers, centrifugal air compressors, drying equipment, lithium bromide refrigeration units, and other pollution treatment equipment purchases, with a service life of the equipment of 30 years, in order to effectively control the discharge of the water environment pollutants generated by the enterprise. From a micro point of view, it has certain practical value to test the effectiveness of the role of emission trading in water pollution control in Zhejiang Province through case simulation.

The simulation data sources in this section are mainly the Zhejiang Province Emission Trading Network (http://60.191.19.180/cms/), the Zhejiang Province Statistical Yearbook (http://tjj.zj.gov.cn/col/col1525563/index.html), the Jinhua Municipal Finance ureau (http://czj.jinhua.gov.cn/art/2022/4/27/art_1229436291_3970813.html), and the official website of Huachuan Industrial Enterprises (http://www.huachuangroup.net/index.html?t=zh-cn). The data sources of some indicators are measured with reference to the relevant scholars' practices.

The specific process is as follows: According to the 2021 financial budget implementation of Jinhua City Finance Bureau, in 2021, the city government actively regulates the cost of C1 = 125.95 Million RMB, and the central government inspector's environmental rectification cost of D1 (mainly used for pollution prevention and control) = 32.07 Million RMB. Depreciated according to the straight-line method of depreciation of equipment investment, the cost of corporate pollution control in 2021 is rounded up to C2 = 103.87 Million RMB.

According to the Notice on the Issuance of Funding Subsidy Measures for Pollution Control Projects in Hangzhou, the enterprise meets the standard emission government subsidy S = 3 Million RMB. Referring to Fang's paper [28], U1 = 2C2 = 207.74 Million RMB, U2=U1/1.2 = 173.11 Million RMB, D2 = 10%U2 = 17.31 Million RMB and D3 = 20 % U2 = 34.62 Million RMB. Referring to the paper of Liu and other scholars [29], the loss of exceeding the standard emission is measured by 2 % of the GDP of Jinhua City in 2021, and V = 1.07 Million RMB. In 2021, the Jinhua City Bureau of Ecology and Environment will hand-arrange for the city's 17 enterprises in the water environment an over-discharge discharge fine of 3.37 Million RMB, an average of 1,983,000 RMB per enterprise fine, according to which the enterprise over-discharge fine F = 0.2 Million RMB is set. In addition, according to the Phoenix website, Jinhua City 2021 January to April public reward for reporting reward 0.5 Million RMB, set the annual reward R = 0.015 Million RMB.

Table 6 presents the average yearly trade prices for Zhejiang Province's four main pollutants in 2021: chemical oxygen demand, ammonia nitrogen, sulfur dioxide, and nitrogen oxides. The data was gathered from the Zhejiang Province emission trading network. The company's initial emission permits verification quantities for 2021 during the same period are as follows: 450.46 tonnes/year, 24.66 tonnes/year, 174.06 tonnes/year, and 214.842 tonnes/year for chemical oxygen demand, ammonia nitrogen, sulfur dioxide, and nitrogen oxides (data source: Jinhua Eco-Environmental Bureau). Since the firm's real over-discharge data is currently unavailable, it is suggested that in 2021 the enterprise will over-discharge at a rate of 10 % for each pollutant. This will result in a cost of 1.13 Million RMB for acquiring other enterprises' discharge volumes. The sewage enterprise is abbreviated as E in the simulation diagram, and the local government is denoted as G. The aforementioned data serves as the simulation benchmark data.Table 6 Annual average trading prices of emission rights in Zhejiang Province in 2021. Unit: RMB/ton · year.

Table 6Days of one's life	Chemical oxygen demand
(an environmental indicator)	Ammonia	Sulfur dioxide SO2	Nitrogen oxide	
January 2021	16660.43	26416.29	8522.69	6579.36	
February 2021	15492.07	23417.51	5864.28	3735.96	
March 2021	13484.50	23980.12	6552.77	5322.65	
April 2021	26912.29	25316.22	4282.16	3781.07	
May 2021	33354.14	25855.36	3755.83	3044.61	
June 2021	13725.96	15842.32	5303.96	6110.83	
July 2021	33354.14	30175.12	4838.15	4777.84	
August 2021	31469.13	46078.61	4417.02	3449.22	
September 2021	27915.06	22300.18	4836.45	2932.40	
October 2021	14338.29	11447.77	4001.01	2562.64	
November 2021	26063.53	33620.73	2133.84	2917.91	
December 2021	14068.84	67241.46	1623.66	2510.05	
Average annual transaction prices for each pollutant	20064.57	26505.91	4499.83	3977.05	
Source: Zhejiang Province Emission Trading Network.

4.2 Impact of emission trading on the system

To examine the impact of emission trading on the evolution strategy and decision-making behavior of the two primary players, the benchmark data for the case is initially inputted into the simulation without taking into account the emission trading scenario. In addition, we change the parameter values and put them into the replicated dynamic equation system along with the stability conditions shown in Table 2 for the (1,1) stable equilibrium point. We leave out the emission trading case at first and then account for it. Three scenarios were developed: emission uninvolved-baseline data（EN-BD）, emission uninvolved-adjusted data（EN-AD）, and emission-involved-adjusted data（EI-AD）. Based on the data presented in Fig. 2(a), it is evident that the evolutionary trajectories of both parties in the emission rights uninvolved-baseline scenario converge over time to a negative state of zero. Ultimately, the dynamic evolution of the evolutionary game between the enterprise and the local government will be stable at a value of zero, which signifies that the environmental regulation implemented by the local government is ineffective. Additionally, Fig. 2(a) shows that the long-term region supports this conclusion. Conversely, the optimal stable state of (1,1) is attained by both emission-right uninvolved-adjusted data and emission-right involved-adjusted data scenarios. With the emission trading mechanism in place, companies that discharge can switch to the strategic behavior of 1-attainment discharge more quickly, using the same adjustment data.Fig. 2 The impact of emission trading on the system.

Fig. 2

The case firm's new pollution control project in FY2021 is costly, and it may not be able to afford to spend such a high pollution control cost in comparison with other firms in the industry. Therefore, it is necessary to further explore how the firm's decision of whether to build a new pollution control project and introduce pollution control equipment affects the evolutionary behavior of both sides of the game. As illustrated in Fig. 2(b), the simulation is run based on the four possibilities of whether or not the firm develops a new pollution control project and whether or not the emission trading mechanism is included. The government's award for fulfilling the emission criteria will no longer be given to the firm in the event that it decides not to build a new project, and the other baseline statistics in the case stay the same. The evolution paths of the government and the business are (0,0), (0,1), (0,0), and (0,1) for the four scenarios of “Emission right not Involved-New Projects (ERN-NP), Emission right not Involved-No New Projects (ERN-NNP), Emission right involved-New projects (ER-NP) and Emission right involved - No new projects (ER-NNP)”.

According to the case-base data, the cost of new pollution control projects by enterprises is high, and the internal motivation of enterprises to meet emission standards gradually decreases as a result of the government's investment in pollution control, the cost of environmental rectification by central government inspectors, and the low subsidies for meeting emission standards. Whether or not emission trading is included, businesses will tend to avoid developing new projects due to behavioral judgments. It can be seen that the behavioral decision-making of enterprises to meet the emission standards is affected by their own pollution control costs and benefits of emission standards, and the local government must pay full attention to the cost input factors of enterprises when formulating the environmental regulation strategy. Otherwise, just relying on the implementation of the emission trading mechanism can't promote the two sides of the government-enterprise game to achieve the (1,1) ideal stable state.

4.3 Analysis of significant sensitivities

4.3.1 Change in S value

According to the Notice on the Issuance of Funding Subsidy Measures for Pollution Control Projects in Hangzhou, the subsidy standard for water pollution control projects of enterprises in the territory is 30 % of the actual total investment in the project (limited to pollution control facilities), and the maximum amount of subsidy for each enterprise is up to 3 Million RMB. In the case baseline data environment and the case adjustment data environment, respectively, the standard discharge subsidy is set to 3 Million RMB and the enterprise is required to meet the standard discharge pollution control cost C2 of 10 % of the two options simulation. As shown in Fig. 3(a) and (b), firstly, the higher the value of S, the faster the enterprise evolves to the behavioral strategy of complying with the standard emission, the longer the time to support the enterprise to comply with the standard emission. The slower the time to recede to the negative emission. Secondly, for the same amount of subsidy for complying with the standard emission, the difference in the influence role of the government is not obvious between the intervention of the emission trading mechanism and the non-involvement of the emission trading. For the enterprises, the former can be quicker to the former can be a faster way for enterprises to meet emission standards.Fig. 3 The impact of S value changes on the system.

Fig. 3

4.3.2 Change in F value

The “Law of the People's Republic of China on Prevention and Control of Water Pollution” states that if an enterprise is found to have exceeded the standard discharge, the people's government's competent department of environmental protection at or above the county level will order it to make corrections, order production to be restricted or suspended. A further fine of not less than 0.1 Million RMB and not more than 1 Million RMB will be imposed. If the circumstances are serious, it will be reported to the people's government with approval authority for approval and be ordered to suspend business or close down. As a result, three modeling alternatives for enterprise over-emission fines were set: 0.2 Million RMB, 0.6 Million RMB, and 1 Million RMB. As illustrated in Fig. 4, the quicker an enterprise reaches the point of fulfilling emission regulations, the higher the penalty for exceeding emission. To fully consider the cost-benefit of the enterprise and the local government, as well as to arrange a reasonable amount of subsidies and penalties, it is important to keep in mind that there are thresholds for both subsidies and penalties for over-emission. These thresholds must be combined with the conditions of the steady point (1, 1) in Table 5.Fig. 4 The impact of F value changes on the system.

Fig. 4

4.3.3 Change in the value of W

The important factors in the emission trading mechanism are the cost of purchasing other enterprises' emission rights W and the income from the sale of its own surplus emission rights I. The case enterprise is in over-emission at this stage, and there is a demand for purchasing emission rights. As shown in Fig. 5, as the value of W rises and breaks through the threshold limit of C2–I–S–U1+U2 < W, the gradual increase of W from the initial 1.13 Million RMB to 67.8 Million RMB will promote the evolution of the system from (1,0) to (1,1) stable state. Usually the cost factor will be considered a negative factor for enterprises, the reason for not decreasing but increasing may be due to the intervention of the sewage right trading mechanism. In this mechanism, it is no longer an individual enterprise's behavior to meet the emission standards to control water pollution. W and I, as variables with intermediary transmission effect, if the cost of the enterprise's emission right purchase is too low, it means that the trading income of the enterprises in the industry's emission right surplus is not enough to mobilize the enterprise's motivation to reduce emissions and sell. Therefore, the value of W can only be raised to a level acceptable to other enterprises in the industry in order to reach emissions trading. In turn, this will promote the benign and sustainable interactive development of the emissions trading market and promote the overall pollution control level of enterprises and even the whole industry.Fig. 5 The impact of W value changes on the system.

Fig. 5

5 Discussion

In order to gain a deeper understanding of the differences that occur in the simulations described above, it is necessary to perform a sensitivity analysis of the many influencing factors in the models. We determine the monotonicity of the function by solving the partial derivatives of each parameter in the area formula of the phase diagram of the gaming system, in accordance with the techniques put forth by academics like Wang Jiang [30]. This allows us to understand how each parameter's change in sensitivity affects the stability of the system.(9) SABCD=1−(x*+y*)/2

The variables x* and y* in equation (9) represent the equilibrium points (x*,y*) in the case where emission trading is not accounted for and when emission trading is considered, respectively. The calculations determine the phase area changes caused by variations in each parameter listed in Table 6 and the system stabilization strategy.

Table 7 demonstrates:(1) Irrespective of the involvement of emission rights, the system progressively approaches a stable state of (active regulation, emission compliance) as D2 and D3 values increase. This suggests that the evaluation of the public's reputation exerts a clear constraint on both the government and enterprises, thereby serving as a positive influence factor within the system.

(2) In the case of emission trading, which disregards the public's reward for reporting R and the cost of environmental protection regulation of the local government C1, the cost of pollution control C and the cost of rectification of local government D increase as enterprises gradually adopt the strategy of active regulation and emission compliance. As the expenses associated with pollution control (C2) and local government rectification (D1) escalate, there is a growing trend among local governments and businesses to implement the active supervision and emission compliance strategy. In light of the emission trading scenario, the aforementioned four parameters exhibit inverse sensitivity changes. Specifically, the local government and businesses are strongly encouraged to implement proactive strategies aimed at promoting water pollution control and ecological restoration as the value of environmental degradation loss V escalates.

(3) As crucial parameters of change, the penalty for exceeding the standard F, the subsidy for adhering to the standard S, and the purchasing cost for emission trading W can only be realized within the range of the stability analysis's threshold change in the two distinct scenarios. As critical parameters, we cannot definitively determine the positivity or negativity of the results following bias derivation until they fall within the range of threshold change in the stability analysis; thus, their sensitivity is variable.

Table 7 Sensitivity analysis of model parameters.

Table 7Game scenario	Function monotonicity	Parameter variation	Phase area change and evolution stability strategy	Game scenario	Function monotonicity	Parameter variation	Phase area change and evolution stability strategy	
No consideration of emission trading	∂SABCD/∂C1<0∂SABCD/∂C2>0	C1↓
C2↑	SABCD↑,（Active regulation，Compliance discharge）	Considera-tion of emission trading	∂SABCD/∂C1>0∂SABCD/∂C2<0	C1↑
C2↓	SABCD↑,（Active regulation，Compliance discharge）	
∂SABCD/∂D1>0∂SABCD/∂D2>0∂SABCD/∂D3>0	D1↑
D2↑
D3↑	SABCD↑,（Active regulation，Compliance discharge）	∂SABCD/∂D1<0
∂SABCD/∂D2>0∂SABCD/∂D3>0	D1↓
D2↑
D3↑	SABCD↑,（Active regulation，Compliance discharge）	
∂SABCD/∂R>0	R↓	SABCD↑,（Active regulation，Compliance discharge）	∂SABCD/∂R>0	R↑	SABCD↑,（Active regulation，Compliance discharge）	
∂SABCD/∂F？	F？	SABCD？, Strategic uncertainty	∂SABCD/∂I>0	I↑	SABCD↑,（Active regulation，Compliance discharge）	
∂SABCD/∂S？	S？	SABCD？, Strategic uncertainty	∂SABCD/∂V>0	V↑	SABCD↑,（Active regulation，Compliance discharge）	
Remarks: ? Indicates that the positivity or negativity cannot be determined	∂SABCD/∂W？	W？	SABCD？, Strategic uncertainty	
∂SABCD/∂S？	S？	SABCD？, Strategic uncertainty	

In various circumstances, local government and enterprise pollution control expenses, local government rectification costs, and local government rewards for reporting incentive spending. Sensitivity to the opposing change could be because of not implementing emission trading pilot areas; in China's ecological and environmental governance policy, there is a high-pressure situation; the current stage of the local government is still the main body of watershed water pollution control; the cost of pollution control is high; and enterprise pollution management. With lower passion and investment in governance, central government inspectors discovered that local government negative regulation is frequently lax in the application of administrative fines and less involved in the economic level of environmental governance and rectification. Meanwhile, in recent years, local governments have begun to focus on mobilizing the public to participate in environmental monitoring, with some regions implementing rules that provide significant benefits for reporting. According to the Ministry of Ecology and Environment, 30 provincial, 313 prefectural, and municipal ecological and environmental departments have developed and implemented regulations on reporting incentives. In 2020, a total of 13,870 reward cases were implemented countrywide, totaling 7.19 Million RMB. From the geographical distribution of cases, Henan, Anhui, Sichuan, Shandong, and Guangdong top; from the total amount of awards, Guangdong, Hebei, Henan, Anhui, and Jiangsu top; emission rights are not pilot trading provinces, accounting for the majority.

Conversely, the Chinese emission trading market is still in its early stages of research and development, with little firm engagement, low trading volume, inactive primary and secondary markets, and other problems. Local governments have implemented a number of policies to encourage enterprises to take the lead in water pollution control in order to promote emission trading mechanisms that quickly contribute to the reduction of water pollution. These policies include the establishment of initial emission permits, reimbursable use of the payment method, enterprise emission rewards, penalties for exceeding the standard discharge, and other measures. However, when it comes to the enterprise emission standards for new projects and equipment investment amounts, the government incentive compared to the amount of the gap is very small. In addition, since local governments see businesses as the primary source of pollution management, pollution control investments are comparatively less expensive.

Therefore, in order to achieve the ideal steady state of the government and enterprises (active supervision, discharge standards) of water pollution management, the pilot areas in the introduction of emission trading mechanism should be coordinated use of control-based, market-based, and voluntary policy tools. Specific strategies are as follows: first, improve the local government pollution control cost input C1. Second multi-measures to mobilize enterprise pollution control enthusiasm at the same time, reduce the burden of unnecessary costs of enterprises to reduce the C2. Third, the central government moderate give way to reduce the cost of rectification of the central inspectorate D1, so that the local government has more room to incentivize enterprises to meet the standard emission. Fourth, focus on the role of public supervision, improve the public reward for reporting incentives R.

Through sensitivity analysis and case simulation analysis in the previous text, if local governments want to improve the efficiency of water pollution control, they can improve their work in the following aspects.(1) Dynamically adapting the government's pollution control input structure. In the event of an emission trading intervention, the local government should dynamically adjust the input structure of pollution control costs, environmental rectification costs, subsidies for enterprises meeting emission standards, and incentives for public participation in monitoring, taking into account the high and low costs of pollution control for polluting enterprises, as well as the fluctuating price of emission trading.

(2) Create and implement more targeted incentives and punishments for businesses to reduce pollution. Based on the thresholds for incentives and subsidies in the stability conditions (active supervision, compliance with emission standards), and taking into account whether or not the polluting enterprises are building new high-value pollution control projects, more targeted incentives and penalties should be designed for each situation so that enterprises can actively innovate in technology and improve their capacity and willingness to control contamination, as well as the cost of violating laws for the polluting enterprises.

(3) Increasing the development of a secondary market for emission trading. At the moment, the development of emission trading in many locations is still in the primary market stage, and the average trading price of enterprises' emission rights is generally low, so enterprise excitement for emission trading is low. Local governments should appropriately “decentralize” and expand the secondary market, promote inter-regional trading of emission rights, raise the trading price of emission rights, increase enterprise motivation to sell their emission rights, and lower the industry's marginal cost of sewage treatment.

(4) The combined application of multidimensional environmental regulatory policy mechanisms. When emission trading is introduced in pilot areas, control, market, and voluntary policy tools should be used together to create a situation where the central government oversees the environment, local governments regulate the market for emission, and the public is involved in overseeing the market. This will make water pollution control more effective and reach the ideal homeostatic state of active government regulation.

The shortcomings of the article are that it does not consider the heterogeneity of enterprises, and the sample size of enterprise cases needs to be enriched urgently, which will be the focus of our future work and research direction.

6 Conclusion

(1) Emission trading, under certain conditions, can reduce the cost of enterprise pollution control while also improving the enterprise and industry's overall level of pollution control. Because of the role of emission surplus trading revenue and buy cost components, emission trading markets can be linked to other enterprises to reduce emission, but the role of emission trading mechanisms must take into account the role of the local government and the firm, both costs and advantages. The current high cost of pollution control for case enterprises, the low input of local government pollution control, subsidy incentives, and public participation incentives, as well as the low trading price and inactivity in the emission rights market, all have an impact on case governments' and enterprises' pollution control objectives.

(2) The game system's sensitivity parameters have varying degrees of influence and sensitivity, resulting in diverse effects on the evolution of the game subjects' behavioral trajectory. Whether or not carbon trading is included, the public's perception of a positive impact factor has a clear binding effect on both government enterprises. The four types of parts in the two evolutionary game theory models have different patterns. These are the local government environmental protection supervision cost, the local government rectification cost, the public reward reporting expenditure, and the enterprise compliance emission treatment cost. The enterprise exceeds the standard emission penalty, meets the standard emission subsidy, emission surplus trading income, and purchase cost as the important sensitive factors of the system; the penalty and subsidy factors can only affect the enterprise's own emission reduction behaviors and decision-making; the trading income and purchase cost can affect the emission reduction behaviors of other enterprises, but they need to clarify the threshold value in order to play.

(3) Following the implementation of emission trading, the cost of paid usage of the initial emission permits has no bearing on whether the firm decides to fulfill the emission standards. By analyzing and considering the dynamic equation of the game system replication between the government and enterprises in the case of emission trading, it is found that when the local government adopts the way of paid use of the initial emission permits and issues the sewage discharge permit to the polluting enterprises as a rigid necessity, the enterprises have no other choice but to obtain the initial emission permits, regardless of whether they reduce emission or not. As a result, meeting emission requirements is not a critical issue in company decision-making.

Data availability statement

Data included in article/supp. material/referenced in article.

CRediT authorship contribution statement

Xia Yang: Writing – review & editing, Writing – original draft, Supervision, Project administration, Conceptualization. Gang He: Conceptualization. Zhihe Zhu: Writing – review & editing. Shuhang Zhao: Supervision, Resources. Shiyu Zhang: Writing – review & editing.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:Gang He reports financial support was provided by 10.13039/100018977 Anhui Philosophy and Social Sciences Planning Project . If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This article is funded by Anhui Philosophy and Social Sciences Planning Project (AHSKY2022D124 ).
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