Research on watershed water ecological management and compensation based on evolutionary game

The ecology of the river basin is an important part of the ecological environment (Zhou et al. 2018). The Huaihe River Basin is one of the important water transportation hubs and food bases in China. However, with the economic development, the degree of water resources development and utilization in some areas exceeds the water environment carrying capacity, which has brought about water ecological environment problems, exacerbated ecological problems such as water shortage, groundwater overexploitation, and serious water environment pollution in the Huaihe River Basin. The contradiction of ecological environment management in the basin is widespread. It is necessary to establish and improve the ecological compensation mechanism of the basin, fundamentally adjust the relationship between relevant stakeholders, and reverse the trend of water ecological destruction, promoting sustainable development of watershed environment and economy (Chen et al. 2021a).

Ecological compensation first refers to the payment of ecosystem services (PES). Domestic and foreign scholars mainly study ecological compensation from the aspects of ecological compensation definition (Engel et al. 2008; Li et al. 2022a; Zhan & Yang 2022), ecological compensation standard, ecological compensation method, and ecological compensation area. From the perspective of the definition of ecological compensation, Shen & Xie (2022) pointed out that the main body of river basin ecological compensation is the undertaker of ecological compensation responsibility, and the compensation object refers to the protector of the ecological environment and the victim of interests.

The research on ecological compensation standards mainly includes ecological footprint model (Chen et al. 2021b; Yang et al. 2022), ecosystem services value method (Costanza et al. 1998; Xie et al. 2015), willingness survey method (Aguilar et al. 2018; Liu et al. 2022a), opportunity cost method, etc. (Scheufele et al. 2018; Yang et al. 2018; Zhang et al. 2019). The compensation methods mainly include government-led (Xu & Han 2019; Wang & Zhang 2022) and marketization (Chen 2018; Liu et al. 2022c). The research field of ecological compensation mainly includes wetlands (Hu & Zhang 2022; Pang et al. 2022; Xie et al. 2022), cultivated land (Bai et al. 2021; Liu & Hu 2021), grassland (Hou et al. 2021; Zhao et al. 2021; Wei et al. 2022), watershed (Yang & Shi 2019; Liu & Wu 2020; Sheng & Han 2021; Wang et al. 2021a) among others.

Since the 1990s, the focus of game theory has shifted to evolutionary game theory based on bounded rationality (Zheng 2017). Evolutionary game theory was first proposed by Smith and Price in the study of symmetric population games, and proposed evolutionary stable strategy (ESS), but only limited to static game (Smith 1974). Friedman first applied evolutionary game theory to the economic field (Friedman & Fung 1996). Yang applies game theory to solving environmental decision problems (Yang et al. 2013). Bier et al. verified that the stable structure of the evolutionary game can have a positive impact on policy, which can improve the ecological environment of the basin (Bier & Lin 2013). Wang et al. (2021b) and others (Zheng et al. 2021) introduced incentive and restraint mechanisms to examine the interests of upstream and downstream governments in the basin. The evolutionary game model shows that a long-term mechanism for inter-provincial river basin ecological compensation can be established. Ren et al. (2020) examined the game characteristics and game mechanism of the central government, provincial governments, and municipal governments, and showed that the moderate intervention of the central government is the key to carrying out inter-provincial river basin ecological compensation. Wang & Peng (2019) analyzed the evolutionary game strategy of government-enterprise-resident; ALNabhani et al. (2016) and Ren (2022) respectively emphasize the importance of public participation in the development of environmental regulatory legislation and the promotion of corporate pollution control.

In summary, the current research on ecological compensation in river basins is mostly an intergovernmental game. It is not common to establish a three-party dynamic game model considering the public and enterprises, and the Huaihe River Basin is less studied. Based on the ecological compensation mechanism and evolutionary game model, this paper introduces public participation in the game mechanism to clarify the division of pollution responsibility, innovatively establishes a third-party intervention system, sorts out the interest demands of ecological compensation-related parties in the Huaihe River Basin, constructs a public-enterprise-local government tripartite evolutionary game model, analyzes the game results, and further simulates and analyzes, in order to promote the sustainable development of the Huaihe River Basin and provide reference for the governance compensation of the Huaihe River Basin.

The simulation analysis of this paper is based on the relevant data on the economic development status of the four provinces in the Huaihe River Basin from 2017 to 2021. The data mainly comes from the statistical yearbook of four provinces, and some information is sorted out according to the public information such as the official website of the provincial government. MATLAB R2018b and Arc Map 10.8 were used for drawing.

Starting from reality, the game model is constructed to analyze the stability of the strategies and equilibrium points of all parties and the influence relationship of each factor. The problems that may be encountered in the actual governance of the Huaihe River Basin and the solutions are discussed (Table 1).

Hypothesis 1: the public is participant 1, the polluting enterprise is participant 2, and the local government is participant 3. The three parties are participants of bounded rationality, and the strategy choice gradually evolves to the optimal strategy over time.

Hypothesis 2: Local governments consider environmental benefits and regulatory costs. The strategy set is {strict supervision, loose supervision}, and the probabilities are x, 1 − x, x ∈ [0,1]. Enterprises consider environmental benefits and governance costs, the strategy set is {positive governance, negative governance}, the probability is y, 1 − y, y ∈ [0,1]; people consider their own health loss and economic compensation, and their strategy set is {participation, silence}, and the probabilities are z, 1 − z, z ∈ [0,1].

Hypothesis 3: For the public, the cost of participation is C₁, and the reward given by the government to the participant is Q₂ (incentive mechanism). At the same time, when enterprises choose negative governance, due to environmental degradation, air, water, and other pollution, the health loss caused to the public is V. According to the principle of ‘polluter pays’, the implementation of compensation mechanism, negative governance enterprises due to excessive emissions need to compensate the public, pay ecological compensation E (compensation mechanism), if the enterprise actively governs, the public gains environmental improvement income M₁.

Hypothesis 4: For enterprises, when they choose the positive governance strategy, they need to invest a certain cost C₂, the government gives the positive governance of polluting enterprises reward Q₁ (reward mechanism), for negative governance requires a fine F (punishment mechanism). Public participation in corporate active governance brings reputation gains R₁, corporate negative governance was found reputation loss L₁.

Hypothesis 5: The government needs to invest in governance funds I, and the potential environmental governance improvement income brought by the active pollution control of enterprises is M₂, which is enjoyed by the government. Public participation in corporate governance active governance raises public praise for the current government segment, gains R₂, and conversely, reputation losses L₂. When the government chooses loose regulation, it will no longer subsidize active polluters and participants, and because of lax regulation, it will no longer fine enterprises that do not strictly pollute, setting the cost of strict government regulation as C.

According to the above assumptions, the mixed strategy game matrix of the public, enterprises, and local governments is shown in Table 2.

Table 2

Mixed strategy game matrix of public, enterprise, and government

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It can be seen that public participation depends on the decision-making probability of the enterprise and the government, the compensation, cost and reward of choosing different strategies in A place. The probability of the public choosing to participate is stable and must meet F(x) = 0 and F′(x) < 0.

Proposition 1: When y < y₁, z > z₁, the public stability strategy is whistling; when y > y₁, z < z₁, the public stability strategy is silence; when y = y₁, z = z₁, the stable strategy cannot be determined. Where the threshold y₁ = (zQ₂ − C₁ + E)/E,z₁ = (yE + C₁ − E)/Q₂.

Proof: Since ⁠, A(y,z) is a decreasing function with respect to y, when y < (zQ₂ − C₁ + E)/E = y₁, A(y,z) > 0, F(x)|_x=1 = 0 and F′(x)|_x=1 < 0, then x = 1 is ESS; when y > y₁, A(y,z) < 0, F(x)|_x=0 = 0 and F′(x)|_x=0 < 0, then x = 0 is ESS; when y = y₁, F(x) = 0 and F′(x) = 0, the stable strategy cannot be determined. From ⁠, the influence of the critical value z₁ on the stability of the strategy can be proved.

Proposition 1 shows that in the multi-subject co-governance of the current ecological environment when the enterprise is passively governed and the government is strictly supervised, the active participation of the public can be compensated to compensate for the health loss caused by environmental pollution. At the same time, there will be a reward from the government, and the public will change from silence to participation in rights protection. When enterprises are actively governed and the government is relaxed in supervision, the probability of government incentive mechanism is reduced, and the willingness of the public to participate is reduced, and eventually, the public will change from participation to silence.

Corollary 1: When the cost of participation increases, the government awards participants and the ecological compensation paid by enterprises to the people due to negative pollution control decreases, the people tend to choose the silence strategy; however, with the increasing emphasis on river basin environmental governance, the government's incentives are gradually increasing, and the amount of ecological compensation is gradually increasing, or when the participation cost is reduced, the people will choose the participation strategy.

Proof: According to the expression of enterprise participation probability V_x0, the first-order partial derivatives of C₁, E, Q₂, and other factors are obtained: ⁠.

According to the stability theorem of differential equation, the probability that an enterprise chooses active governance is stable must satisfy F(y) = 0 and F′(y) = 0.

Proposition 2: When x < x₂, z < z₂, the stability strategy of the enterprise is negative governance; when x > x₂, z > z₂, the public's stability strategy is active governance; when x = x₂, z = z₂, the stable strategy cannot be determined. Where the threshold x₂ = [C₂ + Sz(Q₁ + F)]/(R₁ + Q₁ + L₁), z₂ = [C₂ + S − x(R₁ + Q₁ + L₁)]/(Q₁ + F).

Proof: ⁠, so B(x,z) is an increasing function with respect to x, when x < x₂, B(x,z) < 0, F(y)|_y=0 = 0 and F′(y)|_y=0 < 0, then y = 0 is stable; when x > x₂, B(x,z) > 0, F(y)|_y=1 = 0 and F′(y)|_y=1 < 0, then y = 1 is stable; when x = x₂, F(y) = 0 and F′(y) = 0, stability strategy cannot be determined. ⁠, the influence of the critical value z₂ on the stability of the strategy can be proved.

Proposition 2 shows that when the public's tolerance for pollution behavior increases, the willingness to participate in rights decreases, and the government relaxes supervision, corporate decision-making will change from active governance to negative governance, and a compensation mechanism will be implemented. When the public's participation in watershed pollution control increases and the government strictly supervises, the cost of governance decreases and short-term additional benefits are obtained. However, the probability of government penalties and payment of ecological compensation will increase, so corporate decision-making will shift from passive to active governance.

Corollary 2: When corporate governance costs and negative governance gain additional economic benefits, the enterprise chooses the negative governance strategy; when the enterprise's positive governance obtains reputation gains, the enterprise's negative governance obtains reputation losses, the local government gives subsidies to the positive pollution control enterprises, and the enterprise's negative pollution control is fined, the enterprise chooses positive governance.

According to the stability theorem of differential equations, the probability that local governments choose strict supervision to be in a stable state must satisfy F(z) = 0 and F′(z) < 0.

Proposition 3: when x < x₃, y < y₃, the stability strategy of local governments is strict supervision; when x > x₃, y > y₃, the stability strategy of local government is loose governance; when x = x₃, y = y₃, the stable strategy cannot be determined. Here, the threshold x₃ = [−y(Q₁ + F) − C₃ + F]/Q₂, y₃ = (−xQ₂ − C₃ + F)/(Q₁ + F).

Proof: ⁠, so C(x,y) is a decreasing function of x, when x < x₃, C(x,y) > 0, F(z)|_z=1 = 0 and F′(z)|_z=1 < 0, then z = 1 is stable; then x > x₃, C(x,y) < 0, F(z)|_z=0 = 0 and F′(z)|_z=0 < 0, then z = 0 is stable; when x = x₃, F(z) = 0 and F′(z) = 0, the stable strategy cannot be determined. From the influence of critical value y₃ on strategy, stability can be proved.

Proposition 3 shows that if the probability of public participation and corporate active governance is reduced, local governments will change from a loose supervision strategy to a strict supervision strategy, and the reward and punishment mechanism and compensation mechanism between multiple governance subjects are the main mechanisms; when the probability of public participation and corporate active governance increases, local governments will change from strict supervision strategy to loose supervision strategy, and reward and punishment mechanism and compensation mechanism will be weakened.

Corollary 3: If the government strictly regulates costs, the government rewards participants and subsidies for active pollution control enterprises, and local governments choose to loosen supervision. When the fines imposed on enterprises for passive pollution control increased, local governments chose to strictly supervise.

Proof: According to the expression of the probability V_z0 of strict supervision by the local government, the first-order partial derivatives of C₃, Q₂, Q₁, F, and other elements are obtained: ⁠.

According to the first Lyapunov method, the stability of each equilibrium point is analyzed. Among the eight groups of equilibrium points, there are four groups of unstable points and four groups of stable points, as shown in Table 3.

Corollary 4: When −C₁ + E < 0, −C₃ + F < 0, the replication dynamic system has and only has a stable point E₁ (0,0,0).

Proof: According to Table 3, condition 1 is satisfied, so E₁ (0,0,0) is the asymptotically stable point of the system. If the other three conditions are not satisfied, the equilibrium points E₂ (1,0,0), E₄ (0,0,1), and E₆ (1,0,1) are meaningless.

Corollary 4 shows that when the ecological compensation paid by the enterprise due to environmental pollution is too low, the government's punishment for enterprises with negative governance is small, and the public participation cost and the government's strict supervision cost are very high, according to the different initial points of the three-party strategy selection, the evolution of the strategy portfolio is stable at public silence, enterprise negative governance, and government loose supervision. It can be seen that the rising cost of participation and the low ecological compensation reduce the probability of public participation. At the same time, government supervision lacks effectiveness and cannot effectively restrain corporate behavior resulting in passive governance of enterprises, increasing the probability of environmental pollution and posing a threat to public health. In order to avoid the emergence of a combination of stabilization strategies (public silence, passive corporate governance, and government laxity), regulators must set sufficiently large fines, and increase the implementation of compensation mechanisms to increase public participation.

Corollary 5: when C₁ − E < 0, R₁ + Q₁ + L₁ − C₂ − S < 0, −Q₂ − C₃ + F < 0, the replication dynamics system has and only has a stable point E₂ (1,0,0).

Proof: According to Table 3, at this time, condition 2 is satisfied, so E₂ (1,0,0) is the asymptotic stability point of the system. If the other three conditions are not satisfied, the equilibrium points E₁ (0,0,0), E₄ (0,0,1), and E₆ (1,0,1) are meaningless.

Corollary 5 shows that the sum of the reputation gains and losses obtained by active pollution control enterprises due to public participation and the government's reward for enterprises should be at least higher than the sum of the cost of corporate governance and the additional benefits obtained by negative corporate governance. At the same time, the government's fine for negative governance enterprises should be greater than the sum of the cost of government supervision and the government's reward for participation, so as to effectively prevent the stable strategy combination of the three-party game system (public participation, negative corporate governance, and loose government supervision). It can be seen that the reputation gains and losses brought by public participation to enterprises and the reasonable reward and punishment mechanism designed by the government can reduce watershed pollution and ensure the sustainable development of the ecological environment.

Corollary 6: when Q₂ − C₁ + E < 0, Q₁ + F − C₂ − S < 0, C₃ − F < 0, the replication dynamics system has and only has a stable point E₄ (0,0,1).

Proof: According to Table 3, condition 3 is satisfied, so E₄ (0,0,1) is the asymptotically stable point of the system. If the other three conditions are not satisfied, the equilibrium points E₂ (1,0,0), E₁ (0,0,0), and E₆ (1,0,1) are meaningless.

Corollary 6 shows that the public's reward for participation plus ecological compensation is greater than the cost of public participation, and the government's reward and punishment for enterprises is greater, so as to avoid the emergence of (public silence, negative corporate governance, and strict government supervision) balanced stability strategy. It can be seen that the public chooses to participate depending on whether the cost of the public's choice of participation strategy can be reimbursed. Local governments should increase the incentive for public participation, while enterprises internalize the pollution externalities by paying ecological compensation, which will increase the probability of public participation.

Corollary 7: when −Q₂ + C₁ − E < 0, R₁ + 2Q₁ + L₁ + F − C₂ − S < 0, Q₂ + C₃ − F < 0, the replication dynamics system has and only has a stable point E₆ (1,0,1).

Proof: According to Table 3, condition 4 is satisfied, so E₆ (1,0,1) is the asymptotically stable point of the system. If the other three conditions are not satisfied, the equilibrium points E₂ (1,0,0), E₁ (0,0,0), and E₄ (0,0,1) are meaningless.

Corollary 7 shows that when the sum of reputation gains, reputation losses, rewards and punishments given by the government is greater than the difference between the cost of the enterprise and the additional benefits of negative governance, the stable strategy combination of the three-party game system (public participation, corporate negative governance, and strict government supervision) can be effectively prevented. Moreover, the changes in the reputation gains and losses of the government's environmental improvement due to the active governance of enterprises do not change the evolutionary stability results. Visible, promoting enterprise active governance needs to focus on considering the following points: first, the government increase rewards and punishments. Secondly, reduce the cost of enterprise pollution control. Finally, reducing the production of high-pollution and high-energy products by enterprises will inhibit short-term economic growth, but it will bring long-term social welfare.

In order to verify the validity of the evolutionary stability analysis, the model is assigned a value according to the actual situation, and the numerical simulation is carried out by Matlab R2018b. Array 1: C₁ = 20, Q₂ = 10, V = 30, M₁ = 10, C₂ = 125, Q₁ = 30, S = 60, F = 50, E = 50, R₁ = 35, L₁ = 25, I = 100, M₂ = 20, R₂ = 80, L₂ = 60, C₃ = 30, meet the conditions in Corollary 10. On the basis of array 1, the influence of C₁, Q₂, F, E on the process and result of the evolutionary game is analyzed.

Figure 6 shows that during the evolution process, as C₁ increases, the probability of public participation decreases, and the probability of strict supervision by local governments increases. Therefore, while government regulation encourages the public to participate, it can be appropriately relaxed to ensure that the participation cost is reduced and the economic burden of the participation-public is reduced.

Figure 7 shows that in the process of system evolution to a stable point, with the increase of Q₂, the probability of public participation increases and the probability of strict government supervision decreases. Figure 8 shows that the increase of F will increase the probability of strict government supervision. It can be seen that although the government's incentive mechanism for public participation can promote its enthusiasm for participating in environmental governance, it is not conducive to the performance of local governments themselves. Therefore, the government should formulate a reasonable reward and punishment mechanism to replace the fixed payment to the public in the form of bonuses, so that the public and enterprises can share the responsibility of maintaining the sustainable development of the ecological environment with the government. Moreover, the implementation of severe administrative penalties by local governments can maintain a high rate of strict supervision and further increase the robustness of enterprises to actively control pollution.

Figure 9 shows that as E increases, the probability of public participation increases, and the probability of strict government supervision decreases.

According to Figure 10, the simulation results show that the equilibrium point of E₆ (1,0,1) condition 4 is established, and there is only one evolutionary strategy combination (public participation, negative corporate governance, and strict government supervision) in the system, which is consistent with the conclusion of Corollary 10. Figure 11 shows that there is only one evolutionarily stable point (0,0,0) when condition 1 is satisfied, namely (public silence, negative corporate governance, and loose government regulation), which is consistent with Corollary 7. Figure 12 shows that there is a unique evolutionary stable point (1,0,0) when condition 2 is satisfied (public participation, negative corporate governance, and loose government supervision), which is consistent with inference 8. Figure 13 shows that there is a unique evolutionary stable point (0,0,1) when condition 1 is satisfied (public silence, negative corporate governance, and strict government supervision), which is consistent with inference 9. It can be seen that the simulation analysis is consistent with the conclusion of the three-party strategy stability analysis and is effective, which has practical guiding significance for watershed management compensation.

To take the road of ecological priority and green development, the Huaihe River Basin needs to establish an ecological compensation mechanism. Considering the possible participation behavior of the public, this paper constructs a three-party evolutionary game model of the government, enterprises, and the public, analyzes the stability of the three-party combination strategy and the influence relationship of each factor, verifies the validity of the analysis conclusion through simulation analysis, and explores the compensation mechanism of the river basin, and draws the following conclusions: (1) The government's increase in rewards and punishments has significantly promoted the public to participation and enterprises to actively control pollution, but the increase in rewards and punishments will not be conducive to the local government's own performance of regulatory responsibilities. (2) Increasing the amount of compensation and participation incentives is an effective way to promote public participation. (3) Reputation mechanism and reward-penalty mechanism need to meet the condition that the sum of reputation gains, reputation losses and reward-penalty is greater than the difference between corporate governance costs and the additional benefits of negative governance, in order to ensure that the evolutionary enterprises actively control pollution.

In view of this, this paper attempts to explore the compensation path of watershed management in line with regional characteristics and scientific systems, in order to achieve a virtuous cycle of the Huaihe River Basin ecosystem and promote the improvement of the ecological compensation mechanism in the Huaihe River Basin. The specific recommendations are as follows: (1) The government should establish and improve the information sharing platform for stakeholders so that one party can understand the relevant demands of other parties in a timely, accurate and comprehensive manner, and avoid weakening the effectiveness of the ecological compensation mechanism due to information asymmetry. (2) Scientifically formulating reward and punishment mechanisms and ecological compensation mechanisms can not only make up for the cost of government supervision, but also bring certain economic pressure to negative governance enterprises, and promote local governments, enterprises and the public to actively participate in river basin governance. At the same time to explore a variety of rewards and punishments and forms of compensation, talent technology and advanced industrial advantages, improve the technical level of sewage enterprises, promote industrial restructuring, to protect the Huaihe River water quality continued to improve. (3) To establish and improve the ecological compensation laws and regulations, to regulate the cooperation agreement of stakeholders, to solve the contradiction between departments and regions, to coordinate the pace and measures of pollution control of relevant departments, to improve the reasonable water rights, water prices, and water market mechanism in the basin, and to ensure the effective implementation of basin management and compensation mechanism. (4) Watershed ecological management should start from the source. Industrial wastewater is still an important source of pollution in the Huaihe River Basin. We should develop a circular economy, improve the reuse rate of wastewater, introduce advanced technology, improve the efficiency of wastewater treatment, and reduce the cost of treatment.

This work was funded by the National Natural Science Foundation of China ‘Study on Spatial and Temporal Evolution, Early Warning and Dynamic Response Mechanism of Water Ecological Risk in Huaihe River Basin (72271005)’; Humanities and Social Sciences Planning Fund of the Education Ministry ‘Research on the priority assessment, amount measurement and cross-regional realization mechanism of ecological compensation in the Huaihe River Basin’ (22YJAZH025); Postgraduate Innovation Fund of Anhui University of Science and Technology ‘Multidimensional measurement and prediction of water resources carrying capacity of mining cities’ (2021CX1013).

Y.F. and G.H. conceptualized the study, designed the methodology, and interpreted the results. S.Z. acquired and processed the data and drafted the manuscript. H.J. assisted in data processing.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.