Research on Cooperative Water Pollution Governance Based on Tripartite Evolutionary Game in China’s Yangtze River Basin

Abstract

Cooperative governance of water pollution is an effective initiative to implement the strategy for the protection of the Yangtze River Basin. Based on the stakeholder theory, this paper constructs a tripartite evolutionary game model of water pollution in the Yangtze River Basin from the perspective of “cost–benefit”. This paper analyzes the stability of possible equilibrium points of the evolutionary game system by scenarios and further explores the influence of key factors on the evolution of the cooperative governance system of water pollution in the Yangtze River Basin using numerical simulation. According to the findings, (1) the watershed system comprises three key stakeholders: local governments, enterprises, and the public. Each stakeholder’s behavioral strategy choice is influenced by its unique factors and the behavioral strategy choices of the other two stakeholders. (2) Equilibrium points represent the potential strategic equilibrium presented by each stakeholder. When the net income of a particular behavioral strategy within the set exceeds zero, stakeholders will be more inclined to choose that behavioral strategy. (3) The key influencing factors in the evolutionary game are regulatory costs, reputation loss, material rewards, and violation fines. Therefore, this paper proposes to construct a cooperative governance mechanism for water pollution in the Yangtze River Basin from three aspects: an efficient regulatory mechanism, a dynamic reward and punishment mechanism, and a multi-faceted incentive mechanism, with a view to promoting a higher-quality development of the ecological environment in the Yangtze River Basin.

1. Introduction

The Yangtze River is regarded as the “mother river” and “life river” of the Chinese nation, playing a major role in Chinese modernization, as well as its ecological protection. In recent years, the Chinese government has accorded considerable importance to the ecological protection of the Yangtze River Basin. Moreover, comprehensive measures have been implemented to manage the ecological environment of the riverine areas. Such measures have notably enhanced the water ecological environment of the basin. Nevertheless, with the extensive implementation of the development strategy of the Yangtze River Economic Belt, water environment problems, characterized by a transboundary nature and negative externalities, have occurred frequently in the basin. The water ecological environmental protection in the basin remains critical. Accordingly, during the fourteenth five-year plan period, the ecological environment and other relevant departments collaborated to develop the “Key Basin Water Ecological Environment Protection Plan” (henceforth referred to as the “Plan”). This initiative underscores continued synergistic promotion of water ecological environment protection to strengthen the systematic and holistic nature of environmental governance. However, the watershed water environment requires diverse stakeholders, including governments, enterprises, and other relevant parties. It is crucial to clarify the diverse interests and strategic relationships among the multiple parties. This entails coordinating the strategic decisions and managing behavioral conflicts among the stakeholders, as well as addressing challenges associated with the collective action in governing water pollution within the basin. The objective is to establish a system of coordinated governance of river basin water pollution aligned with the stakeholders’ interests, which is crucial to achieve sustainable development in the basin.

2. Literature Review

2.1. Study on Synergistic Ecological Governance in Watersheds

As the birthplace of collaborative governance theory, western scholars have been researching watershed ecological and environmental governance for nearly a half a century.

Regarding the main body of watershed ecological and environmental governance, Williams reported that the integrated roles of government and market should be played simultaneously [1]. Meanwhile, Goss and Rother considered that the integrated watershed governance structure is crucial, emphasizing the establishment of a multi-interest coordination organization and promoting cooperative governance among government departments [2,3]. Moreover, Lockwood suggests that collaborative ecological and environmental governance requires the inclusion of as many subjects as possible, including the government, market, and society [4]. Of these, public participation is a critical factor influencing the collaborative governance of watershed ecosystems. Meanwhile, strategies for watershed ecosystem governance have been proposed by Ostrom, who summarized eight principles of public resource system design [5], and others, who have put forward a collaborative governance model, representing a revelation of collaborative governance of watersheds [6,7]. However, others have focused on dissecting and promoting eco-collaborative governance cases, along with the distinctions and objectives of such governance [8,9]. Collectively, these studies have provided a rich source of ideas for the development of watershed ecological and environmental collaborative governance strategies and practice models.

Recently, collaborative watershed ecological governance has also become a research hotspot in China. Currently, watershed ecological governance focuses on watershed ecological pollution having “mobility” and “intersectionality”, with regions in the Yangtze River subjected to different ecological pressures. The variability in the degree of economic development and environmental resources in the watershed has further triggered water ecological governance conflict among local governments [10]. Traditional watershed ecological and environmental governance is dominated by the government, raising concerns over a single governance subject [11]. Although the main body of watershed governance is gradually diversified, there are certain challenges associated with government, market, social, and multiple-subject synergy [11]. In addition, the differences in interests lead to behavioral dissonance and choice dissonance among the subjects involved. How best to resolve the interests and conflicts among the subjects is the crucial point of multiple governance [11]. Based on the realistic needs of watershed development, the construction of an ecological compensation mechanism has been explored at the macro level between the upstream and downstream local governments [12]. Moreover, the mechanisms associated with performance accountability, information sharing, scientific rewards and punishments, and feedback response for watershed ecological and environmental governance have been explored from the micro level of government, market, and society [13]. From the perspective of basin holism, local law enforcement collaboration on the basin is facing challenges, including ill-defined responsibilities for law enforcement collaboration and insufficient supervision and constraints. It is, therefore, necessary to construct a joint law enforcement mechanism with multiple synergies in the basin to break down barriers of territorialized management [14].

2.2. Study on Ecological Governance and Evolutionary Game in Watersheds

Ecological environment governance involves a game of interests and strategic choices among government, enterprise, the public, and other parties [15]. Due to differences in resources, economy, politics, and other aspects, each subject prefers different behavioral strategies in the governance process [16]. The strategy choices of the finite rationality co-management subjects are not only affected by each other’s strategies but can cause dynamic changes in the strategies of others until a stable state is ultimately reached [17]. Game theory is the study of the theory and method of participants competing with each other, which constitutes an important branch of economic theory [18] and provides a solution for solving the strategic choices of multiple subjects. In order to obtain a stable game strategy solution, John Nash proposed the concept of “Nash equilibrium” in 1950, suggesting that in multi-party interactions, individual rational choices can form an equilibrium state, but this equilibrium state is not necessarily the optimal state, which further expands the application of game theory [19]. Since then, Simon and other scholars have supplemented and expanded the Nash equilibrium theory, applying it to human behavior, organizational decision making, and other fields of research, providing a new way of thinking for solving the problem of how the strategy combinations of each participant can reach a stable state [20]. Therefore, this type of interactive game characteristic between multiple individuals makes the watershed environment governance issue applicable to the dynamic evolutionary game method of research [21].

Firstly, the two-party subject game focuses on the environmental governance of the government under the decentralization perspective [22]. An evolutionary game model between the central government and local governments revealed that inter-governmental ecological governance of watersheds is superior to territorial governance [23]. Meanwhile, the strategic interaction between governments and firms has revealed that government environmental regulation is significantly associated with firm innovation [24,25]. However, some scholars have focused on the ecological governance practices in watersheds. Foreign scholars have analyzed the environmental crises and good governance effects of the Tennessee, Rhone, Rhine, and other watersheds and summarized the centrally led and locally led watershed governance mechanisms [26,27,28,29]. Domestic scholars have paid attention to the ecological and environmental governance practices of urban agglomerations, analyzed the strategic interaction effects among multiple subjects, and explored the effects of coordinated ecological and environmental governance in the Yangtze River Delta, Beijing–Tianjin–Hebei, and other regions, as well as their influencing factors [30,31,32], but not much research has been carried out in terms of the multi-party evolutionary games of coordinated ecological governance of watersheds and governance mechanism research has not been carried out more.

Secondly, the three-party subject game has been applied in studies by incorporating the government, enterprises, public, and other multiple subjects of the game evolution, analyzing the strategy selection process of the tripartite subjects [33,34,35,36,37]. Some have focused on the collaborative governance of environmental pollution in the Yellow River Basin and explored the important factors affecting the stability of the basin’s ecological and environmental gaming system. Among them, Li et al. constructed a tripartite subjective evolutionary game between the central government, local governments, and enterprises, revealing that government fines and subsidies affect corporate strategies [32]. Meanwhile, some found that the intensity of local government supervision has a key role in watershed ecological governance by constructing a tripartite evolutionary game model [38].

The ecological governance of the Yangtze River Basin involves multiple players such as the government and enterprises, which is in line with the application conditions of Nash equilibrium theory. On the basis of existing literature research, this paper proposes to apply the evolutionary game to the study of ecological governance of the Yangtze River basin, with a view to providing a new perspective for the collaborative ecological governance of the Yangtze River basin.

2.3. Study on Ecological Governance and Sustainable Development of Watersheds

The purpose of ecological environment governance is to provide sustainable resources for economic and social development, while the process of economic and social development should also focus on ecological environment governance. There is a complex coupling relationship between the two, which determines that synergistic development should be maintained between watershed ecological environment and sustainable development [39].

In recent years, academics have explored how to realize the synergistic development of ecological governance and sustainable goals in different socio-economic contexts. In Europe and the United States, the sustainable development of watersheds mainly consists of three ecological governance mechanisms. The first is the central government ad hoc agency-led governance mechanism. The US government made the decision to centralize and integrate the integrated development and management of the Tennessee Basin in 1933 and established the Tennessee Basin Authority [26]. France has developed a unique basin-wide management system for the governance of the Rhone River, which is based on different basins for the unified management of the rivers in the regions within the whole country, and has established a special basin committee and a basin finance bureau [27]. The second is the local joint organization-led governance mechanism. In the 1950s, Germany, France, the Netherlands and other countries jointly set up the International Commission for the Protection of the Rhine against Pollution (ICPR) [28], which cooperated in ecological compensation and collaborative governance of water resources, among other things. The third is a joint governance mechanism with civil organizations as the main focus and the government as a supplement. The Mississippi River Basin and Ohio River Basin in the United States have established basin councils in accordance with federal or state laws, and the basin councils have comprehensive management of water resources, and the voting rights of each state are equal, so that the governments and people of each state can cooperate with each other and develop their economies in a coordinated manner [29].

In China, sustainable watershed development consists of two main ecological governance mechanisms. The first is a vertical governance mechanism. The central leadership group has set up special central governance groups in accordance with ecological elements, forming a temporary organization that is synergistic between sectors. As an important part of the Yangtze River Basin, the Taihu Lake Basin was established as a management bureau, with the main responsibilities of developing, utilizing, supervising, monitoring, and guiding the protection of the water resources in the Taihu Lake Basin, as well as comprehensively managing the water environment in the Taihu Lake area [40,41]. The second is a horizontal governance mechanism. In order to solve the water quality problems faced by the Taihu Lake region for a long time, China has taken the Development and Reform Commission as the lead, and has joined 11 departments, including Jiangsu, Zhejiang, and Shanghai, to convene a provincial-level inter-departmental joint meeting on the comprehensive management of the water environment in the Taihu Lake region and to set up a collaborative organization for the work of the comprehensive improvement of the water environment in the region among the three provinces of Suzhou, Zhejiang, and Shanghai [40,41].

It can be found that both domestic and foreign governmental agencies do not rely on a single subject to solve the problems between watershed ecological environment and sustainable development but need to collaborate with multiple subjects to realize the synergistic development of the watershed ecological environment and sustainable development.

In summary, existing studies have certain deficiencies. In terms of research perspectives, many scholars have explored watershed governance using the Yellow River Basin as an example. In contrast, they have not yet defined the relevant subjects of water pollution in the Yangtze River Basin from a stakeholder perspective, which needs to be explored. In terms of research methodology, most of the domestic and foreign studies are limited to the multi-party game analysis among central government, local government, and enterprise. Even when some of them involve the public, only a few scholars put the public, enterprise, and local governments in the Yangtze River Basin water pollution control game analysis framework, failing to analyze the interactive mechanisms and influencing factors of the choice of behavioral strategies of the basin stakeholders in depth.

In light of the aforementioned considerations, this study takes a stakeholder perspective by integrating local governments, enterprises, and the public into a comprehensive analytical framework in the Yangtze River Basin. It develops a dynamic evolutionary game model involving the parties and analyzes their behavioral strategies. On this basis, the research uses numerical simulations to pinpoint the key factors influencing watershed pollution governance by the stakeholders. Finally, the study gives some policy recommendations for a synergistic watershed governance mechanism with a view to promoting sustainable watershed development. The research framework is shown below. See Figure 1.

3. Material and Methods

3.1. Study Area

The Yangtze River Basin is the largest river in China and the third largest in the world. As the mother river of the Chinese nation, the basin is rich in natural resources and is a major ecological barrier for China. Meanwhile, the basin is also an essential support for the national strategy of integrated development of the Yangtze River Delta region. However, the basin has recently faced unprecedented ecological and environmental crises due to both its high-quality development and increase in irrational human activities. As an important part of the Yangtze River Basin, with the rapid development of the local economy and society, the eutrophication of the Taihu Lake water body makes the drinking water of the residents in the basin and the survival of aquatic organisms increasingly subject to serious threats [38]. In 2007, the outbreak of cyanobacteria in the Taihu Lake Basin seriously affected the normal life of citizens and caused a large negative impact on the local economic and social development [41]. The cyanobacteria incident is a concentrated manifestation of the ecological crisis of Lake Taihu, which also prompted the government to start the comprehensive remediation of the Lake Tai basin. At the same time, the Yangtze River Basin is under great pressure to control pollution, and local water environment problems are prominent, including the destruction of basin habitats, damage to ecosystems, and the high incidence of water environment risks. In such a context, in November 2018, China’s central government explicitly advocated for the exploration of synergistic efforts to promote the sustainable improvement of the basin with the goal of “grasping great protection and not engaging in large-scale development”, with the leadership of “ecological priority and green development”.

3.2. Stakeholder Definition

The ecological environment governance of the Yangtze River Basin is a complex systematic project that involves the interests and synergy of multiple subjects [41]. Based on Freeman’s stakeholder theory [42], the present study defines the stakeholders of synergistic ecological governance in the basin as the local government, enterprise, and the public. It further analyzes the roles and interests of the different subjects to construct a logical relationship among the stakeholders of pollution governance.

The government is the core actor and the first responsible body in ecological environment governance [43], with a leading role in watershed governance. Local governments are the centralized representatives of all public interests in the basin, focusing on the synergistic development of economy and ecology [41]. Since the inception and implementation of the Yangtze River Protection Plan in 2018, the region along the river has organized a range of dedicated actions focusing on resolving outstanding ecological issues. Local governments have reinforced sewage discharge regulations in industrial parks and promoted the active transformation of highly polluting enterprises. In addition, local governments promote rural sewage and garbage treatment, provide the public with reliable water resources, guide the public in the basin to actively participate in water pollution control, and ensure the sustainable development of water resources. These tasks involve several governmental functional organizations, such as ecological and environmental departments, water conservancy departments, administrative law enforcement departments, administrative and legislative departments, and relevant responsible departments, which need to collaborate and cooperate with these governmental departments to solve the water ecological and environmental problems in the Yangtze River Basin.

Enterprises are the executors of ecological governance, and they represent one of the indispensable subjects in the coordinated governance of water pollution in the watershed; their environmental responsibility is also a public interest [44]. In practice, relevant enterprises must assume social responsibility while pursuing benefits [41]. Firstly, enterprises should actively improve their production behavior and reduce pollution emissions according to the government’s comprehensive water environment governance requirements and national industrial development policies. For enterprises that are unable to achieve this, the government is legally permitted to shut them down. Secondly, enterprises should actively promote green production through technological innovation. Thirdly, enterprises, mainly wastewater treatment operators, are actively involved in water treatment and restoration, providing wastewater treatment equipment and services to water-using enterprises, upgrading the technical level of the wastewater treatment industry, and providing specialized solutions for water pollution control.

The public represents a key subject in ecological environment governance [44,45]. The two primary means by which the public can participate in collaborative governance are (1) taking the initiative to participate in ecological governance by improving their own lifestyles and reflecting pollution problems through letters and visits, the media, and other means; (2) assisting the government and enterprises in environmental governance by joining green organizations. Concurrently, the government provides the public with information on ecological and environmental governance through open websites.

Therefore, the three main stakeholders in the Yangtze River Basin influence and constrain each other. These stakeholders adopt behavioral strategies driven by their respective interests, thus further affecting the ecological balance of the basin.

3.3. Model Assumptions

Drawing on existing studies [32,45,46,47,48], this study puts forward the following basic assumptions. These were formulated by considering all factors affecting strategy selection in the participating subjects combined with the actual pollution governance in the basin.

Assumption 1.

The three stakeholders (i.e., local government, enterprises, and the public) constitute a complete game system. No consideration is made of other subjects that influence the game system in the basin.

Assumption 2.

Considering that the three stakeholders are limited rational subjects, there are two strategy choices for all subjects in the game system. The strategy space of local government is {strict regulation; loose regulation}; the strategy space of enterprises is {green production; illegal production}; and the behavioral strategy set of the public is {active participation, negative participation}.

Assumption 3.

Considering the possibility of mixed strategies, the probability that the local government chooses strict regulation is x, and loose regulation is 1 − x; the probability that the enterprise chooses green production is y, and illegal production is 1 − y; and the probability that the public chooses active participation is z, and negative participation is 1 − z.

Assumption 4.

When the local government chooses the strict regulation strategy, it must invest considerable human, material, and financial resources; the current cost of expenditure is C₁, the local government can obtain additional benefits S_1, such as increased investment in the project and increased credibility; enterprises will obtain subsidies B from the local government department if they produce in a green way, whereas if they produce in a non-compliant way, they will be fined by the local government department F; and if the public actively participates in the governance, they will receive incentives J. If the local government adopts a lenient regulatory approach, the increase in water pollution in the watershed causes losses to the local government, such as reduced project investment and decreased credibility N₁.

Assumption 5.

When an enterprise chooses green production, it must increase investment in technology and R&D, and the cost of expenditure is C₂; accordingly, the enterprise can obtain additional benefits, such as deepening cooperation and image enhancement, etc., S₂. However, when an enterprise chooses non-compliance with the law, although it can briefly save the cost of production, with the deterioration of the public environment in human habitats, it will be required to spend the cost of public relations, compensation, etc., C₃. This behavior can also cause L to the company, such as decreased sales and cooperation.

Assumption 6.

When the public actively participates in the governance, it must invest costs C₄ for monitoring and reporting the illegal production behavior of enterprises, at which time the public can obtain certain additional benefits S₃, such as higher environmental quality and compliance of enterprises. On the contrary, when the public negatively participates in the governance, the traditional production mode of enterprises will lead to environmental pollution and cause physical and mental health loss N₂ to the public. The specific parameter settings are presented in 

Table 1. Parameter settings.

Category	Parameter	Meaning
Local Government Parameters	C1	Costs of human and material resources expended in the case of strict regulation
	S1	Additional benefits such as increased investment in projects and credibility in case of strict regulation
	N1	Losses caused by reduced investment in projects and decreased credibility in the case of loose regulation
	B	Subsidies for green production enterprises in the case of strict regulation
	F	Fines imposed on non-compliant companies in the case of strict regulation
	J	Rewards for active participation by the public in case of strict regulation
Enterprise Parameters	C2	Costs of technology, R&D, etc., incurred in the case of green production
	S2	Additional benefits including increased cooperation and image enhancement in the case of green production
	C3	Costs of public relations and compensation in the case of illegal production
	L	Losses such as decreased sales and cooperation caused by illegal production
Public Parameters	C4	Costs of monitoring, reporting, etc., in the case of active participation
	S3	Additional benefits such as higher environmental quality and corporate compliance in the case of active participation
	N2	Physical and psychological losses due to environmental pollution in the case of negative participation

.

3.4. Model Construction

According to the model assumptions and parameter settings, the tripartite evolutionary game payoff matrix for the basin was constructed (

Table 2. Evolutionary game payoff matrix.

Gaming Party				Public
				Active Participation (z)	Negative Participation (1 − z)
Local government	Strict regulation (x)	Enterprise	Green production (y)	S1 − C1 − B − J	S1 − C1 − B
				S2 − C2 + B	S2 − C2 + B
				S3 − C4 + J	0
			Illegal production (1 − y)	S1 − C1 + F	S1 − C1 + F
				−C3 − L − F	− C3 − L − F
				S3 − C4 + J	−N2
Local government	Loose regulation (1 − x)	Enterprise	Green production (y)	0	0
				S2 − C2	S2 − C2
				S3 − C4	0
			Illegal production(1 − y)	−N1	−N1
				−C3 − L	−C3 − L
				S3 − C4	−N2

).

4. Results

4.1. Analysis of the Evolutionary Game Model

4.1.1. Replication of Dynamic Equations

According to the previous analysis of the game relationship between the participating subjects, combined with the research results of Neuman, Nash, Pan et al. [15,18,19,20], the dynamic equation of replication between the government, enterprises, and the public in the context of ecological governance of the Yangtze River Basin was constructed.

Let the expected returns of local governments choosing the strict regulation strategy be V₁₁, the expected returns of local governments choosing the loose regulation strategy be V₁₂, and the average return be V₁:

V₁₁ = y × z × (−C₁ + S1 − B − J) + (1 − y) × z × (−C₁ + S₁ + F) + y × (1 − z) × (−C₁ + S₁ − B) + (1 − y) × (1 − z) × (−C₁ + S₁ + F)

(1)

V₁₂ = y × z × (0) + (1 − y) × z × (−N₁) + y × (1 − z) × (0) + (1 − y) × (1 − z) × (−N₁)

(2)

V₁ = xV₁₁ + (1 − x)V₁₂

(3)

= F × x − C₁ × x − N₁ + N₁ × x + N₁ × y + S₁ × x − B × x × y − F × x × y − N₁ × x × y − J × x × y × z

(4)

The replicated dynamic equation for constructing local government behavioral strategies is given by:

F(x) = dx/dt = x (V₁₁ − V₁)

(5)

= x × (x − 1) × (C₁ − F − N₁ − S₁ + B × y + F × y + N₁ × y + J × y × z)

(6)

Similarly, the enterprise’s expected return for choosing green production is V₂₁, the expected return for choosing illegal production is V₂₂, and the average return is V₂:

V₂₁ = x × z × (−C₂ + S₂ + B) + (1 − x) × z × (−C₂ + S₂) + x × (1 − z) × (−C₂ + S₂ + B) + (1 − x) × (1 − z) × (−C₂ + S₂)

(7)

V₂₂ = x × z × (−C₃ − L − F) + (1 − x) × z × (−C₃ − L) + x × (1 − z) × (−C₃ − L − F) + (1 − x) × (1 − z) × (−C₃ − L)

(8)

V₂ = yV₂₁ + (1 − y)V₂₂

(9)

= C₃ × y − L − C₂ × y − C₃ − F × x + L × y + S₂ × y + B × x × y + F × x × y

(10)

The replication dynamic equation for constructing enterprise behavioral strategies is:

F(y) = dy/dt = y (V₂₁ − V₂)

(11)

= −y × (y − 1) × (C₃ − C₂ + L + S₂ + B × x + F × x)

(12)

Similarly, the public has an expected return of V₃₁ for choosing active participation, V₃₂ for choosing passive participation, and an average return of V₃:

V₃₁ = x × y × (−C₄ + S₃ + J) + x × (1 − y) × (−C₄ + S₃ + J) + (1 − x) × y × (−C₄ + S₃) + (1 − x) × (1 − y) × (−C₄ + S₃)

(13)

V₃₂ = x × y × (0) + x × (1 − y) × (−N₂) + (1 − x) × y × (0) + (1 − x) × (1 − y) × (−N₂)

(14)

V₃ = zV₃₁ + (1 − z)V₃₂

(15)

= N₂ × y − C₄ × z − N₂ + N₂ × z + S₃ × z + J × x × z − N₂ × y × z

(16)

The replication dynamic equation for constructing public behavioral strategies is:

F(z) = dz/dt = z (V₃₁ − V₃)

(17)

= −z × (z − 1) × (N₂ − C₄ + S₃ + J × x − N₂ × y)

(18)

In summary, this paper constructs the following table (

Table 3. Replication of dynamic equations.

Gaming Party	Replication of Dynamic Equations
Local government	F(x) = dx/dt = x × (x − 1) × (C1 − F − N1 − S1 + B × y + F × y + N1 × y + J × y × z)
Enterprise	F(y) = dy/dt = − y × (y − 1) × (C3 − C2 + L + S2 + B × x + F × x)
Public	F(z) = dz/dt = − z × (z − 1) × (N2 − C4 + S3 + J × x − N2 × y)

) of replication dynamic equations for local government, enterprises, and the public.

4.1.2. Equilibrium Stability Analysis

Based on the replicated dynamic equations of the three stakeholders and by analyzing the local stability of the Jacobi matrix, the evolutionary stabilization strategy under the joint action of the stakeholders could be further discussed. Accordingly, the replication dynamic equations were combined to construct the Jacobi matrix of the evolutionary system:

$$J=\left[\begin{array}{ccc}{J}_1& J_2& J_3\\ J_4& J_5& J_6\\ J_7& J_8& J_9\end{array}\right]=\left[\begin{array}{ccc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}\end{array}\right]$$

(19)

$$=\left[\begin{array}{ccc}\begin{array}{l}(2\times \mathrm{x} - 1)\times (\mathrm{C}1 - \mathrm{F} - \mathrm{N}1 - \mathrm{S}1+\\ \mathrm{B}\times \mathrm{y}+\mathrm{F}\times \mathrm{y}+\mathrm{N}1\times \mathrm{y}+\mathrm{J}\times \mathrm{y}\times \mathrm{z})\end{array}& \mathrm{x}\times (\mathrm{x} - 1)\times (\mathrm{B}+\mathrm{F}+\mathrm{N}1+\mathrm{J}\times \mathrm{z})& \mathrm{J}\times \mathrm{x}\times \mathrm{y}\times (\mathrm{x} - 1)\\ -\mathrm{y}\times (\mathrm{y} - 1)\times (\mathrm{B}+\mathrm{F})& -(2\times \mathrm{y} - 1)\times (\mathrm{C}3 - \mathrm{C}2+\mathrm{L}+\mathrm{S}2+\mathrm{B}\times \mathrm{x}+\mathrm{F}\times \mathrm{x})& 0\\ -\mathrm{J}\times \mathrm{z}\times (\mathrm{z} - 1)& \mathrm{N}2\times \mathrm{z}\times (\mathrm{z} - 1)& -(2\times \mathrm{z} - 1)\times (\mathrm{N}2 - \mathrm{C}4+\mathrm{S}3+\mathrm{J}\times \mathrm{x} - \mathrm{N}2\times \mathrm{y})\end{array}\right]$$

(20)

According to Ritzberger and Weibull [49], in the multi-group evolutionary game, the evolutionary stabilization strategy is a pure strategy Nash equilibrium; thus, only eight pure strategy equilibrium points are required when F(x) = 0, F(y) = 0, F(z) = 0. The eight equilibrium points were substituted into the Jacobi matrix; the corresponding matrix values were obtained (

Table 4. Evolutionary game equilibrium points and characteristic values.

Equilibrium Point	Characteristic Value λ1	Characteristic Value λ2	Characteristic Value λ3
E1 (0,0,0)	F − C1 + N1 + S1	C3 − C2 + L + S2	N2 − C4 + S3
E2 (1,0,0)	C1 − F − N1 − S1	B − C2 + C3 + F + L + S2	J − C4 + N2 + S3
E3 (0,1,0)	S1 − C1 − B	C2 − C3 − L − S2	S3 − C4
E4 (0,0,1)	F − C1 + N1 + S1	C3 − C2 + L + S2	C4 − N2 − S3
E5 (1,1,0)	B + C1 − S1	C2 − B − C3 − F − L − S2	J − C4 + S3
E6 (1,0,1)	C1–F − N1 − S1	B − C2 + C3 + F + L + S2	C4 − J − N2 − S3
E7 (0,1,1)	S1 − C1 − J − B	C2 − C3 − L − S2	C4 − S3
E8 (1,1,1)	B + C1 + J − S1	C2 − B − C3 − F − L − S2	C4 − J − S3

).

Furthermore, according to the Friedman Jacobi matrix analysis and Lyapunov discriminant methods, when all characteristic values are non-positive, the equilibrium point corresponds to the evolutionary stability point (ESS) of the system [17,37,50]. Therefore, five stabilization points were obtained from the eight equilibrium points. The stability of the equilibrium point is discussed in the following scenarios.

Scenario 1: Initial stage

Stability point (0,0,0) denotes {loose regulation by local government, illegal production by enterprises, negative participation by the public}, the stability condition is {F − C₁ + N₁ + S₁ < 0, C₃ − C₂ + L + S₂ < 0, N₂ − C₄ + S₃ < 0}. In this scenario, the local government and the market are in a dysfunctional state. The expense incurred from loose regulation by the local government outweighs the fines collected from enterprises. Due to loose regulation, the probability of illegal production behavior by an enterprise being detected would be reduced, and to obtain higher operating profits, illegal production would be the optimal choice for the enterprise. The cost of active public participation exceeds the benefit of active participation, i.e., the relative net benefit of active participation is < 0, and the public’s willingness to participate decreases.

Scenario 2: Local government shifts to strict regulation stage

Stability point (1,0,0) denotes {strict regulation by local government, illegal production by enterprises, negative participation by the public}, the stability condition is {C₁ − F − N₁ − S₁ < 0, B − C₂ + C₃ + F + L + S₂ < 0, J − C₄ + N₂ + S₃ < 0}. In this case, the relative net benefit of strict regulation is > 0, and the choice is to increase the regulation. Due to the strict regulation, the fines for illegal production by enterprises also increase, but to maximize the cost savings, enterprises would still choose production of illegal sewage discharge. The benefit of active public participation increases, but the relative net benefit is <0. The public chooses the negative participation strategy.

Scenario 3: Enterprises shift to green production strategy under strict local government regulation

Stability point (1,1,0) denotes {strict regulation by local government, green production by enterprises, and negative participation by the public} and the stability condition is {B + C₁ − S₁ < 0, C₂ − B − C₃ − F − L − S₂ < 0, J − C₄ + S₃ < 0}. In this scenario, the relative net benefit of strict regulation is >0. The local government, considering the behavioral strategy of enterprises, increases the subsidy for enterprises’ green production. Enterprises may initially choose to violate the production regulations, but with increased local government supervision, enterprises will pay more fines if they continue to violate the production regulations. Given that green production can be subsidized, enterprises will gradually choose green production in later stages. Considering the strategic choices of enterprises, the public will not gain benefits even if they actively participate and choose to participate negatively.

Scenario 4: Public shift to active participation strategy under strict local government regulation

Stability point (1,0,1) denotes {strict regulation by local government, illegal production by enterprises, active participation by the public}, and the stability condition is {C₁ − F − N₁ − S₁ < 0, B − C₂ + C₃ + F + L + S₂ < 0, C₄ − J − N₂ − S₃ < 0}. In this scenario, the public chooses to actively participate as the relative net benefit of active participation is >0. The local government will consider the reward for the public and the fine for violating enterprises and will choose the active participation strategy if the loss caused by the lax regulation is large. Due to the active participation of the public, the local government chooses strict regulation if the loss from lax regulation is large, considering the rewards to the public and the fines to the non-compliant enterprises. Considering the image damage caused by public participation and the public relations compensation, if the relative net benefit of violating production regulations is still > 0 after deducting the fines and the losses, the enterprises will choose the strategy of violating production regulations.

Scenario 5: Ideal state

Stability point (1,1,1) denotes {strict regulation by local government, green production by enterprises, and active participation by the public}, and the stability condition is {B + C1 + J − S₁ < 0, C₂ − B − C₃ − F − L − S₂ < 0, C₄ − J − S₃ < 0}. In this scenario, the cost of strict regulation is reduced gradually with the improvement of the regulatory system and the upgrading of the regulatory technology. Under the driving force of strict regulation, the cost and loss of non-compliance for the enterprise are increased significantly, and the enterprise chooses green production. The net benefit of public participation is >0. Consequently, the three stakeholders in the synergistic environmental governance in the watershed achieve a positive interaction situation.

4.2. Evolutionary Game Simulation Analysis

In the process of coordinated water pollution governance in the Yangtze River Basin, the behavioral strategies of local governments, enterprises, and the public are closely related. To further explore the evolutionary stabilization strategies, MATLAB R2023a software was used to simulate the game model.

4.2.1. Initial Setup of System Simulation

It is assumed that the probabilities of local governments, enterprises, and the public choosing strict regulation, green production, and active participation, respectively, are [0.5, 0.5., 0.5]. The vertical axis represents the probability that local government x, enterprise y, and the public z choose their respective strategies. The horizontal axis represents time t. Referring to related studies combined with the reality of the basin [15,45,51], the variables are assigned initial values: C₁ = 2, S₁ = 8, N₁ = 4, B = 2, F = 1, J = 3, C₂ = 5, S₂ = 2, C₃ = 1, L = 1, C₄ = 6, N₂ = 2, and S₃ = 4. Based on the numerical simulation, when B + C₁ + J − S₁ < 0, C₂ − B − C₃ − F − L − S₂ < 0, and C₄ − J − S₃ < 0, the watershed system of the three stakeholders will evolve to the desired steady state of x = 1, y = 1, z = 1, i.e., the asymptotic stability point (1,1,1). Initial simulations verified Assumptions 1, 2, and 3. In this case, the local government, enterprises, and the public choose strict regulation, green production, and active participation behavior strategies, respectively. The simulation of the initial state system evolution game is shown in Figure 2.

4.2.2. Effects of Changing C₁ and N₁ on the Evolving System

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The cost of strict regulation is increased while other parameters remain constant, i.e., from C₁ = 2 to C₁ = 6. The simulation results are shown in Figure 3. The cost of strict regulation by local government affects strategy choice and significantly impacts the stability of the evolving system. Simulation of the cost parameters of strict regulation by local governments verifies Assumption 4. When the cost of regulation is relatively low (C₁ = 2), at the same node, the probability of choosing strict regulation is higher than when the cost of regulation is relatively high (C₁ = 6), and the evolutionary system reaches a stable state relatively quickly compared with the benchmark figure. When the cost of strict regulation is higher (C₁ = 6), the local government, considering the relative net benefit and the green production behavior of the enterprises, may gradually reduce the regulation, while the enterprises, realizing this, will gradually shift to the illegal production behavior, aggravating the water pollution in the basin. Considering social responsibility and people’s well-being, local governments must increase regulatory effort. As a result, local governments have opted for strict regulatory behavior conducive to collaborative governance. In addition, when the cost of strict regulation is controlled within a reasonable range, local governments are inclined to opt for strict regulation.

(2)

The loss of local government lax regulation is increased while other parameters remain constant, i.e., from N₁ = 4 to N₁ = 8. The simulation results are shown in Figure 4. Simulation of the loss parameter of local government lax regulation simulation similarly validates Assumption 4. If the loss of loose regulation is relatively high (N₁ = 8), then the probability that the local government chooses to regulate strictly at the same node increases, and the time for the evolved system to reach a stable state is shortened greatly compared with the baseline graph. If the local government’s loose regulation loss is relatively low (N₁ = 4), the evolutionary system will slowly reach a steady state. Considering that enterprises and the public choose green production and active participation strategies, respectively, the local government may lower regulation. However, in the long-term evolutionary process, enterprises and the public might begin to shift to illegal production and negative participation behavior, and as credibility decreases and project investment decreases, local governments will be required to shift to a strict regulatory strategy. Therefore, to minimize losses, local governments must establish a good regulatory image and take multiple initiatives to synchronize governance, promoting cooperative governance among enterprises and the public and improving the reputation evaluation of local governments.

4.2.3. Effects of Changing B and F on the Evolving System

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The subsidy provided by the local government to the enterprise for green production is increased while other parameters remain constant, i.e., from B = 2 to B = 6. The simulation results are shown in Figure 5. Simulation of enterprise green subsidy parameters validates Assumption 5. When the subsidy is relatively low (B = 2), the cost of strict regulation is reduced, and the rate of increase in the probability of the evolutionary system converging to a stable state increases compared with the baseline figure. However, due to the lower subsidies given by the local government, considering the costs and benefits, the probability of enterprises choosing green production will gradually decrease, and the system may evolve into an ineffective state of strict regulation, illegal production, and active participation. When the enterprise green production subsidy is relatively high (B = 6), the local government must pay higher regulatory costs, and green production is the best behavioral strategy for enterprises in the short term. However, when the local government determines that the enterprise’s green production has been effective and has gained sufficient benefits, it may reduce the regulatory efforts and subsidies. Consequently, the lax local government regulation may prompt the enterprise to violate the production rules, which will be actively reported by the public, forcing the local government to once again increase regulation. This cycle repeats, and the evolutionary system struggles to reach a stable state. Therefore, local governments must establish a dynamic subsidy mechanism under strict regulation, with neither too low nor too high as a long-term synergistic governance model.

(2)

The fine imposed by the local government on enterprises is increased while other parameters remain constant, i.e., from F = 1 to F = 9. The simulation results are shown in Figure 6. Under this scenario, the fine for illegal production by enterprises not only affects the enterprise’s own strategy choice but also impacts the stability of the evolving system. Simulation of corporate violation fine parameters similarly validates Assumption 5. Before t = 0.4, the probability of green production by enterprises increases with increased enterprise fines, indicating that a high fine by the local government places more direct pressure on the enterprises to encourage faster production transformation. After t = 0.4, the green production by the enterprise probability increases with decreasing enterprise fines, suggesting that local governments may reduce the fines for non-compliant production enterprises considering the increase in additional benefits from strict regulation. Additionally, due to the active participation of the public, the probability of the enterprise’s illegal production being reported increases significantly. After weighing the benefits of green production and the costs of illegal production, enterprises choose green production strategies, and the evolutionary system achieves a stable state gradually. As a result, local governments must establish a dynamic penalization mechanism along with strict regulation in order to improve the effectiveness of environmental governance in the watershed.

4.2.4. Effect of Changing J on the Evolutionary System

The simulation results of increasing the local government’s reward for active public participation, i.e., from J = 3 to J = 7, are shown in Figure 7. Under the scenario, the reward for active public participation affects the steady state of the evolutionary system. Simulation of the public reward parameters validates Assumption 6. Compared with the baseline figure, increasing the reward for active public participation can shorten the time for the system evolution to reach a stable state, indicating that material rewards can greatly increase public participation. When the reward is relatively high (J = 7), the evolution of the probability of public active participation behavior slows, indicating that, considering the green production behavior of enterprises and the beautiful habitat of the watershed, the public will not incur any loss even if their willingness to participate decreases, and relying on the rewards of local governments for active public participation alone can no longer play a maximum role. Therefore, local governments must establish multiple incentives to improve the public’s comprehensive literacy, which can save regulatory costs and enable the public to have a sense of gain and achievement.

5. Discussion

5.1. Research Findings

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Stakeholders in the coordinated governance of water pollution in the Yangtze River Basin

Due to the public nature and complexity of water environment issues, watershed governance requires mutual cooperation among multiple stakeholders. According to the stakeholder theory [42] and drawing on studies related to watershed governance [52,53], this study defines three main stakeholders (local governments, enterprises, and the public) in the collaborative governance of water pollution in the Yangtze River Basin, in which local governments play a leading role. Some studies have also pointed out that the central government is a key player in the process of ecological governance, formulating a series of policies that require local governments to implement and improve environmental conditions [44,54]. However, in the actual governance process, the central government and local governments assume different positions. Local governments are guarantors of economic development and implementers of water pollution governance, with diversified strategic choices. Therefore, this study focuses on integrating the central government’s behavioral strategies of watershed water pollution governance into the policy context and explores the behavioral strategies of the three main stakeholders.

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Evolutionary game for coordinated governance of water pollution in the Yangtze River Basin

Given that three stakeholders are limited rational subjects in the process of coordinated governance in the basin, constantly working to achieve equilibrium, the choice of evolutionary game theory in the analysis of the behavioral strategies of the stakeholders has stronger interpretability. As existing applications of the tripartite evolutionary game model in environmental governance are mainly concentrated in the Yellow River Basin and the Beijing–Tianjin–Hebei regional air pollution [16,32], relatively limited research is available on the evolutionary game of water pollution in the Yangtze River Basin. Consequently, the present study develops a tripartite evolutionary game model of local governments, enterprises, and the public. In addition, comparison with the evolutionary game model for governments and enterprises in existing studies reveals that synergistic governance of environmental pollution cannot be effectively achieved by relying on strict government regulation and green production of enterprises. Rather, it requires active participation of the public in the form of supervision and reporting to improve the efficiency of regulation by local governments and production compliance by enterprises [17,34,55], which are consistent with the conclusions reached in the present study. Differing from previous studies, by analyzing the stability of the equilibrium point under different scenarios, in addition to strict regulation, the active participation of the public can also accelerate enterprise transformation to green production in the case of loose regulation. Therefore, regardless of whether or not the local government drops its regulatory efforts, as long as the watershed has a sound market mechanism and supervision mechanism, enterprises can be encouraged to choose green production strategies.

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Key influencing factors of cooperative water pollution governance in the Yangtze River Basin

From the perspective of costs and benefits of relevant stakeholders and according to simulation results, the present study determined the key influencing factors as regulatory costs (costs of human, material, and financial resources spent by the local government on strict regulation), reputational losses (losses of reduced investment in the project and credibility brought about by the local government’s lax regulation), green subsidies (provided to enterprises for green production under strict local government regulation), material rewards (provided to the public for active participation under strict government regulation), and fines for non-compliance (fines imposed on non-compliant production enterprises when local governments strictly regulate). Comparison with existing studies reveals that most used the qualitative research method of case study to analyze the multiple subjects and influencing factors. Additionally, their influencing factors were selected primarily based on the objectives of the governance subjects, the structure, the operation, and other factors [38,41,44]. The present study focused on factors such as costs and benefits, which further enriches current studies that quantitatively analyze the stakeholders in watershed water governance.

5.2. Limitations and Future Research

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The present study explored the incentives and disincentives of strict local government regulatory strategies for enterprises and the public simply from a cost–benefit perspective. However, local government choice of behavioral strategies for water pollution governance in the watershed is based on considerations that extend beyond simply costs and benefits. Factors such as industrial development status and external environmental policies influence aspects of water pollution governance in the watershed, and their degree of influence must be considered further. Therefore, on the basis of the synergistic governance relationship among local governments, enterprises, and the public, future research must introduce other representative local government parameters to make the study of watershed water pollution governance more convincing.

(2)

The simulation results based on the proposed parameters in this study are a generalization of the actual situation and may not comprehensively reflect the objective situation. Future research should select specific cases in the Yangtze River Basin to obtain actual data to carry out more accurate research, such as the Taihu Lake Basin.

(3)

This paper analyzes the strategy selection among the subjects of collaborative water pollution governance in the Yangtze River Basin based on the evolutionary game model. However, it is found in the study that when the strategy of one of the subjects changes, it will have an impact on the behavioral strategy of the subjects in the subsequent links. Subsequently, the subgame perfect Nash equilibrium is applied to this aspect of the study, trying to obtain the optimal strategy adopted by each participating subject at each point in time and realizing the dynamic, time-sequential, and coherent strategy analysis.

5.3. Policy Recommendations

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Formulating an efficient regulatory mechanism: The cost of local government regulation and reputation loss have important impacts on coordinated governance in the basin. Efficient regulation of local governments can use artificial intelligence and big data technology to build a digital platform for water pollution governance, saving regulatory costs and improving regulatory efficiency. In addition, efficient local government regulation can incorporate a reputation mechanism of public participation, adjusting the regulatory strategy of enterprises based on the public’s evaluation of the enterprises, i.e., increasing the regulatory efforts for enterprises with poor reputations and relaxing the regulatory efforts for those with good reputations.

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Formulating a dynamic reward and punishment mechanism: The simulation results demonstrate that green subsidies and fines imposed by the local government on enterprises for non-compliance can encourage enterprises to choose green production strategies. Given the existence of an effective threshold for the range of rewards and punishments, local governments need to adopt a dynamic reward and punishment mechanism. For example, in the early stage of regulation, local governments can choose a mechanism based on fines to quickly solve the problem of non-compliant production by enterprises. When enterprises tend to green production, local governments can choose a subsidy-based mechanism to guide enterprises to govern water pollution in the watershed.

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Formulating multiple incentive mechanisms: The evolution of public behavioral strategies is affected by the available incentives. Firstly, local governments need to systematically refine the subject, mode, and scope of public participation and introduce diversified forms of public participation in major decision making and ecological compensation for water ecological environment governance in the basin so as to achieve openness and transparency. Secondly, in addition to directly giving a certain amount of material rewards, the local government can also create a good atmosphere for public participation in watershed governance through news media publicity, the selection of advanced people, green civilization honors, and other ways to actively participate in the public to give spiritual rewards.

6. Conclusions

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Local governments, enterprises, and the public are the three main stakeholders in the Yangtze River Basin. Each stakeholder’s behavioral strategy choice is not only related to its own influencing factors but also those of the other two stakeholders. According to the numerical simulation analysis, increasing the cost of strict regulation and increasing the fines for illegal production by the enterprises will impact the behavioral strategy choices of the three main stakeholders. Among them, enterprises will choose green production, and the public will choose active participation more rapidly so that the game system will converge to an ideal state. Local governments increase the green production subsidies, and in the short term, the probability of enterprises choosing green production increases. However, over time, extremely high green subsidies are not conducive for the stability of the evolutionary game system. Furthermore, increasing the public’s active participation reward can accelerate the speed of enterprises choosing the green production behavior strategy, which is conducive for the public obtaining a higher-quality ecological environment.

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There are five equilibrium stability points in the evolutionary game system, which represent the possible strategic equilibrium presented by each stakeholder. By analyzing the stability of equilibrium points under different scenarios, this study found that when the relative net benefit is greater than zero, stakeholders will be more inclined to choose that behavioral strategy. Scenarios 3 and 5 are the two ideal situations in the coordinated governance. In Scenario 3, under the strict regulation by the local government, enterprises shift to green production, reflecting the positive role of the local government’s environmental regulation. In Scenario 5, strict regulation by the local government, green production by enterprises, and active participation by the public indicate that with the normalization of local government regulation and improved market and supervision mechanisms, enterprises focus on social responsibility, and public awareness of environmental protection is enhanced, which is a desirable situation for collaborative governance by the three stakeholders.

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Regulatory costs (human, material, and financial costs incurred by the local government in strict regulation), reputation loss (loss of project investment and credibility due to loose regulation by the local government), green subsidies (subsidies given to enterprises for green production), material incentives (incentives given to the public for active participation), and fines for non-compliance (fines imposed on non-compliant production enterprises) are the key factors influencing the evolutionary game of the three stakeholders. Therefore, the present study proposes formulating a watershed synergy mechanism from three aspects: an efficient regulatory mechanism, a dynamic reward and punishment mechanism, and a multi-faceted incentive mechanism. Among them, the efficient regulatory mechanism targets the regulatory cost and reputation losses of local governments, the dynamic reward and punishment mechanism targets the green subsidies and violation fines of enterprises, and the multiple incentives mechanism targets the material rewards of the public.