Main and branch water pollution treatment cost sharing method considering regional difference and medium

Abstract

The invention is suitable for the technical field of water pollution control, and provides a main and branch water pollution control cost sharing method considering regional difference and a medium, and the method comprises the following steps: analyzing pollution control cost difference influence factors between regions; constructing a pollution control cost difference coefficient based on the influence factors; the pollution control cost difference coefficient is incorporated into a differential game model, and a Nash non-cooperative mechanism and a cost sharing model among the main stream and the two branches are constructed; and solving the differential game model, and carrying out empirical analysis on an influence rule of each influence factor on game equilibrium. According to the method provided by the invention, a decision maker can be helped to expand to a main stream and a plurality of branches from the upstream and downstream view angles, and the difference between different regions can be considered more comprehensively, so that the accuracy and reliability of a decision result are improved, and the problem of incomprehensiveness caused by calculation depending on the upstream and downstream view angles of a drainage basin is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of water pollution control, and in particular relates to a method and medium for sharing the cost of water pollution control in main and tributary rivers taking into account regional differences. Background Art

[0002] The river basin is a complex system of mutual influence composed of the main stream and multiple, multi-level tributaries, and the river basin area is large and flows through many regions. As the water body flows, the pollution of the upstream and tributaries will directly affect the water quality of the downstream and the main stream. In order to continuously improve the quality of the water environment, it is necessary to adhere to source prevention and control, comprehensive measures, and strengthen the coordinated control of multiple pollutants and regional coordinated governance. The goal is to achieve an 8% decrease in the total amount of chemical oxygen demand and ammonia nitrogen emissions, and basically eliminate the goal of Class V national control sections. For this reason, the problem of transboundary water pollution in the river basin has become an important issue that needs to be solved in my country. At present, most of the research on the problem of transboundary water pollution in the river basin focuses on the upstream and downstream perspectives and less on the perspectives of the main and tributary streams. The research results based on the upstream and downstream perspectives can be extended and applied to the relationship between the main stream government and a tributary government. When it comes to the main stream and multiple tributaries, the tributary government determines the pollution control strategy based on its own situation. It not only needs to cooperate with the main stream government, but also needs to cooperate with other tributary governments. Therefore, based on the perspective of the main and tributary streams, studying the pollution control cooperation relationship between the main stream and multiple tributary governments has important theoretical and practical significance.

[0003] The Yellow River Basin is an important ecological barrier, food production area, and resource and energy area, which is vital to my country's ecological security and economic and social development. In September 2019, my country implemented the national strategy of ecological protection and high-quality development of the Yellow River Basin, focusing on controlling serious pollution in the middle reaches. However, the environmental pollution in the Yellow River Basin is serious, the water quality is generally worse than the national average, and the water quality of tributaries is worse than that of the main stream. Some fundamental problems affecting the water quality of rivers in some tributaries have not been solved for a long time. In order to solve the water pollution problem in the Yellow River Basin systematically and source-oriented, it is necessary to coordinate the governance of multiple regions of the main and tributary rivers in the basin. The Yellow River flows through a wide range and many provinces, and there are differences in the ecological environment and economic development conditions in various regions. Differentiated ecological environment and economic development conditions lead to different pollution control strategies in various regions. For this reason, the present invention proposes a cost-sharing method and medium for water pollution control of main and tributary rivers that takes into account regional differences, and conducts an empirical analysis using the Yellow River Basin as an example. Summary of the invention

[0004] The purpose of the present invention is to provide a method and medium for sharing the cost of pollution control of main and tributary rivers taking into account regional differences, aiming to solve the problems raised in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for sharing the cost of main and tributary water pollution control considering regional differences includes the following steps:

[0007] Step 1: Analyze the factors affecting the differences in pollution control costs among regions;

[0008] Step 2: Construct the pollution control cost difference coefficient based on the influencing factors;

[0009] Step 3: Incorporate the pollution control cost difference coefficient into the differential game model to construct the Nash non-cooperative mechanism and cost sharing model between the main stream and the two tributaries;

[0010] Step 4: Solve the differential game model and empirically analyze the influence of various influencing factors on the game equilibrium.

[0011] Furthermore, the specific process of step 1 is as follows:

[0012] Select indicators from two aspects: natural endowment and economic development for analysis;

[0013] In terms of natural endowment: the total water resources X1 indicator is selected to reflect the characteristics of the regional water resources environment;

[0014] Economic development: per capita gross domestic product (PGDP) X2, the proportion of urban population in the total population at the end of the year X3, the proportion of secondary industry added value in regional GDP X4, industrial water consumption X5, industrial wastewater discharge X6 and domestic patent application authorization X7 are selected to measure regional economic development;

[0015] The fixed effect model is selected for regression analysis, and the model form is as follows:

[0016] Formula 1: ln Y it =β0+β1ln X 1it +β2ln X 2it +β3X 3it +β4X 4it +β5ln X 5it +β6ln X 6it +β7ln X 7it +u i +v t +ε it ;

[0017] Where Y is the investment amount of the industrial wastewater pollution control project completed this year, β1~β7 represent the coefficients of the independent variables, u i represents the cross-sectional random error component, v t represents the temporal random error component, ε it Represents the random error component.

[0018] Furthermore, the specific process of step 2 is as follows:

[0019] Select the influencing factors that affect the investment in industrial water pollution control at the 10% significance level as the main influencing factors causing the differences in the costs of industrial water pollution control among regions; the differential expressions for positive and negative indicators are shown in Equations 2 and 3 respectively:

[0020] Equation 2:

[0021] Equation 3:

[0022] Then the coefficient of difference k in the costs of industrial water pollution control among regions is expressed as:

[0023] Equation 4:

[0024] Where X i1 is the indicator of Region 1, X i2 is the indicator of Region 2, T is the research period, T > 1, in the present invention, T takes 10, t is the year, X ij is the indicator of Region j, j = 1, 2, β i is the coefficient of the independent variable of the i-th indicator.

[0025] Furthermore, the specific process of Step 3 is as follows:

[0026] Conduct model assumptions and model construction:

[0027] Assumption 1: Assume that the pollution control efforts of the governments of Branch 1, Branch 2 and the main stream are A, B, and Z respectively; 0 < A < 1, 0 < B < 1, 0 < Z < 1, representing the policies, personnel and capital investments formulated by the two branch governments and the main stream government for water pollution control;

[0028] Assumption 2: The water pollution control of the two branches is a competitive relationship, and a competition coefficient α is set, 0 < α < 1, to measure the economic development pressure of the two branch governments;

[0029] Assumption 3: The reduction in pollutants in the basin is expressed as the following dynamic differential equation:

[0030] Equation 5:

[0031] Where q(t) represents the reduction in pollutants of the two branches at time t. Assume that the initial state of the system q(0) ≥ 0, ξ > 0, η > 0, q > 0, representing the pollution elimination amounts of the governments of Branch 1, Branch 2 and the main stream for each unit of pollution control effort respectively, and δ represents the reduction attenuation coefficient caused by the aging of sewage treatment equipment;

[0032] Hypothesis 4: Assume that the effort of the tributary 1 government is linearly related to the competition of the tributary 2 government and the supervision of the mainstream government, that is, A = A0-αB+d1Z; the effort of the tributary 2 government is B = B0-αA+d2Z, A0≥0, B0≥0, representing the initial pollution control efforts of the tributary 1 government and the tributary 2 government when weighing their own benefits and costs without considering the competition factors and the supervision of the mainstream, where d1 and d2 are the influence coefficients of the mainstream government on the effort of the tributary 1 government and the tributary 2 government respectively;

[0033] Hypothesis 5: The social welfare effect of water pollution control and pollutant emission reduction by the two tributary governments and the mainstream government is:

[0034] Formula 6: S(t)=S0+λq(t);

[0035] S0>0 represents the initial welfare status of the basin, and λ>0 represents the coefficient of the impact of basin emission reduction on the social welfare effect of the basin;

[0036] Assumption 6: The pollution control cost of tributary 1 government is a quadratic function The pollution control cost of the tributary 2 government is a quadratic function k represents the difference coefficient of pollution control costs between the two tributaries, and the effort cost of the mainstream government is c represents the mainstream government effort cost coefficient;

[0037] Hypothesis 7: The environmental benefits of eliminating unit pollutants for the two tributary governments are ξAr1 and ηBr2 respectively, and the environmental benefits of eliminating unit pollutants for the mainstream government are qZr3. r1, r2, and r3 represent the differences in environmental benefits of eliminating unit pollutants in tributary 1, tributary 2, and the mainstream, respectively, and are reflected by the ecological fragility of each region.

[0038] Assumption 8: The revenue coefficients of the governments of Tributary 1, Tributary 2 and Main Stream are π1, π2 and π3 respectively, π1>0, π2>0 and π3>0, and the governments of Tributary 1, Tributary 2 and Main Stream have the same discount rate ρ at any time, ρ>0.

[0039] Furthermore, in the step of solving the differential game model, the solution method includes solving the Nash non-cooperative game model and the Stackelberg master-slave game model;

[0040] The solution process of the Nash non-cooperative game model is as follows:

[0041] Based on the above assumptions, and considering that the governments of tributary 1, tributary 2, and the main stream are all limited rational entities, the benefit functions of the three governments are obtained;

[0042] The revenue function of the government in Tributary 1 is:

[0043] Formula 7:

[0044] Among them, q1-ξA is the total amount of pollutants discharged by tributary 1, h1 represents the benefits brought by relieving the pollution control pressure of tributary 1 due to the pollution control of tributary 2, ω is the environmental protection tax paid by the taxable water pollutants discharged by the two tributaries, and J1 is the benefits obtained by the government of tributary 1 from the pollution discharge;

[0045] The revenue function of the government in tributary 2 is:

[0046] Formula 8:

[0047] Among them, q2-ηB is the total amount of pollutants discharged by tributary 2, h2 represents the benefits brought by relieving the pollution control pressure of tributary 2 due to the treatment of tributary 1, and J2 is the benefits obtained by the government from the discharge of pollutants in tributary 2;

[0048] The revenue function of the mainstream government is:

[0049] Formula 9:

[0050] An assessment section is set at the main stream, q0 is the total amount of water pollutants that the three parties need to treat when the assessment section meets the standard; P is the ecological compensation received by the main stream government for each unit of pollutants that is better than the assessment section when the main stream assessment section meets the standard, or the ecological compensation paid by the main stream government for each unit of pollutants that is worse than the assessment section when the main stream assessment section exceeds the standard;

[0051] In order to make equation 7-9 have a continuous and unique solution q(t), it is necessary to construct a set of bounded, continuous, and differentiable value functions V1(q), V2(q), and V3(q), and construct the HJB equations of tributary 1 government, tributary 2 government, and main stream government respectively:

[0052] Formula 10:

[0053] Formula 11:

[0054] Formula 12:

[0055] Substitute the right side of equation 10-12 into the right side of the HJB equation to find the first-order maximization condition for A, B, and Z, and assume that the function V i The expression of (q) is in linear form, and the game equilibrium solution is obtained:

[0056] Formula 13:

[0057] Formula 14:

[0058] Formula 15:

[0059] The optimal benefits of the main and tributary governments under equilibrium conditions are:

[0060] Formula 16:

[0061] Formula 17:

[0062] Formula 18:

[0063] Among them, V1'(q), V2'(q), V3'(q) are the first-order derivatives of the value functions V1(q), V2(q), and V3(q), respectively. * ,B * ,Z * are the optimal equilibrium solutions of the government efforts of tributary 1, tributary 2, and main stream under the Nash non-cooperative game model, V1 * , , V3 * are the optimal equilibrium solutions of the government revenue of tributary 1, tributary 2 and main stream under the Nash non-cooperative game model, q * is the pollutant emission reduction of the two tributaries under the Nash non-cooperative game model;

[0064] The solution process of the Stackelberg master-slave game model is as follows:

[0065] First, the mainstream government determines the pollution control efforts and the cost sharing ratios m and n for the governments of tributaries 1 and 2. Then the two tributary governments determine their own optimal strategies. Using the reverse induction method, we first find the optimal decisions of the governments of tributaries 1 and 2. The objective function satisfies the HJB equation:

[0066] Formula 19:

[0067] Formula 20:

[0068] Solve the first-order conditions for maximizing A and B on the right side of Equation 19 and Equation 20, and substitute them into the HJB equation of the mainstream government to obtain:

[0069] Formula 21:

[0070] Assume that the function V i The expression of (q) is in linear form, and the Stackelberg equilibrium solution of the two tributaries and the main stream government under the cost sharing mechanism is:

[0071] Formula 22:

[0072] Formula 23:

[0073] Formula 24:

[0074] Formula 25:

[0075] Formula 26:

[0076] The optimal return for the three parties is:

[0077] Formula 27:

[0078] Formula 28: Formula 29:

[0079] Among them A ** ,B ** ,Z ** are the optimal equilibrium solutions for the efforts of the governments of tributary 1, tributary 2, and the main stream in the Stackelberg master-slave game model, V1 ** , , V3 ** are the optimal equilibrium solutions of the government revenues of tributary 1, tributary 2, and main stream in the Stackelberg master-slave game model, q ** It is the pollutant emission reduction of the two tributaries under the Stackelberg master-slave game model.

[0080] Furthermore, in step 4, an empirical analysis is performed on the influence of various influencing factors on the game equilibrium in the study area.

[0081] A storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for sharing the cost of main and tributary water pollution control taking into account regional differences.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] The cost-sharing method for water pollution control in main and tributary rivers that takes into account regional differences proposed in the present invention can help decision makers expand their perspectives from upstream and downstream to the main stream and multiple tributaries, and can more comprehensively consider the differences between different regions, thereby improving the accuracy and reliability of decision results and solving the problem of incompleteness caused by relying on calculations from the upstream and downstream perspectives of the basin. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 Schematic diagram of the method of the present invention.

[0085] Figure 2 It is a schematic diagram of the process of the present invention.

[0086] Figure 3 The Shanxi Province X in Example 1 of the present invention 31 Impact on the amount of pollutants removed.

[0087] Figure 4 X in Shaanxi Province in Example 1 of the present invention 32 Impact on the amount of pollutants removed.

[0088] Figure 5 The Shanxi Province X in Example 1 of the present invention 31 Impact on the three government revenues; (a) is the revenue of the Shanxi provincial government, (b) is the revenue of the Shaanxi provincial government, and (c) is the revenue of the Henan provincial government.

[0089] Figure 6 X in Shaanxi Province in Example 1 of the present invention 32 Impact on the three government revenues; (a) is the revenue of the Shanxi provincial government, (b) is the revenue of the Shaanxi provincial government, and (c) is the revenue of the Henan provincial government.

[0090] Figure 7 The Shanxi Province X in Example 1 of the present invention 41 Impact on the amount of pollutants removed.

[0091] Figure 8 X in Shaanxi Province in Example 1 of the present invention 42 Impact on pollutant removal

[0092] Fig. 9 The Shanxi Province X in Example 1 of the present invention 41 Impact on the three government revenues; (a) is the revenue of the Shanxi provincial government, (b) is the revenue of the Shaanxi provincial government, and (c) is the revenue of the Henan provincial government.

[0093] Fig.10 X in Shaanxi Province in Example 1 of the present invention 42 Impact on the three government revenues; (a) is the revenue of the Shanxi provincial government, (b) is the revenue of the Shaanxi provincial government, and (c) is the revenue of the Henan provincial government. DETAILED DESCRIPTION

[0094] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0095] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0096] like Figure 1 and Figure 2As shown, a method for sharing the cost of pollution control of main and tributary rivers considering regional differences is provided in one embodiment of the present invention, comprising the following steps:

[0097] Step 1: Analyze the factors affecting the differences in pollution control costs among regions;

[0098] Step 2: Construct the pollution control cost difference coefficient based on the influencing factors;

[0099] Step 3: Incorporate the pollution control cost difference coefficient into the differential game model to construct the Nash non-cooperative mechanism and cost-sharing model between the main stream and the two tributaries;

[0100] Step 4: Solve the differential game model and empirically analyze the influence of various influencing factors on the game equilibrium.

[0101] As a preferred embodiment of the present invention, the specific process of step 1 is:

[0102] Indicators are selected from the two aspects of natural endowment and economic development for analysis. In terms of natural endowment: the regional water environment affects the industrial structure and development of the region, and the total water resources indicator is selected to reflect the characteristics of the water resources environment in the region. In terms of economic development: the regional economic development is measured from four aspects: per capita gross regional product (PGDP), urbanization, industrialization, and technological development level. PGDP can be obtained from the statistical yearbooks of each region. Urbanization is represented by the indicator of urbanization rate, and is calculated by "the proportion of urban population in the total population at the end of the year". Industrialization is measured by three indicators: "the proportion of the added value of the secondary industry in the regional GDP", industrial water consumption, and industrial wastewater discharge. The technological development level is measured by "the number of domestic patent applications authorized (items)". In summary, the variables are described as shown in Table 1:

[0103] Table 1 Variable description and units

[0104]

[0105] The present invention takes the main stream of the Yellow River and its two tributaries, the Fen River and the Wei River, as examples. The Fen River is a first-level tributary of the Yellow River. It originates from Guancen Mountain. The main stream runs through the two major basins of Taiyuan and Linfen from north to south. It is the largest river in Shanxi Province. The Wei River is the largest tributary of the Yellow River. The Wei River basin in Shaanxi Province covers an area of ​​67,100 km 2 , which concentrates 63% of the province's population and more than 63% of its GDP, is the political, economic and cultural center of Shaanxi Province, with the Weihe River as its tributary and Shaanxi Province as its tributary government. The Fenhe River and the Weihe River flow into Henan Province after merging into the mainstream of the Yellow River, so Henan Province is the mainstream government.

[0106] Variable data were collected, and missing data were filled by interpolation and extrapolation. The descriptive statistical results of the basic characteristics of the original data are shown in Table 2:

[0107] Table 2 Descriptive statistics

[0108]

[0109]

[0110] From the descriptive statistics, we can see that the sample observation value is 135. The analysis of the standard deviation of the variables shows that the variables change both with individuals and over time. Comparing the size of the standard deviation within and between groups of each variable, the standard deviation within the group of GDP per capita and the proportion of urban population to the total population at the end of the year is greater than the standard deviation between groups, indicating that the GDP per capita and the proportion of urban population to the total population at the end of the year change greatly over time. The standard deviation between groups of other indicators is greater than the standard deviation within the group, indicating that these indicators change greatly with individuals. When performing regression analysis on panel data, in order to alleviate the biased estimation results caused by heteroscedasticity, autocorrelation, and cross-sectional correlation, the original data of the dependent variable Y and some independent variable data (X1:X2, X5:X7) are logarithmized. Since the value range after logarithm processing is (1,10), in order to make all values ​​in the same range, X3 and X4 are expanded by 10 times so that their values ​​fall within (1,10).

[0111] In order to avoid the result deviation caused by pseudo regression, it is necessary to perform unit root test on the data. The present invention uses LLC test method to perform unit root test on the data, and Table 3 is the unit root test result. The test result shows that the data is a stationary sequence and regression analysis can be performed.

[0112] Table 3 Unit root test results

[0113]

[0114]

[0115] In order to select a suitable regression model for regression analysis, the data needs to be tested for the model. The present invention uses the F test method to test the model. The F test results are shown in Table 4:

[0116] Table 4 Model verification

[0117]

[0118] As shown in Table 4, the results show that the mixed effect model is rejected and the fixed effect model should be selected. The model form is as follows:

[0119] Formula 1: ln Y it =β0+β1ln X 1it+β2ln X 2it +β3X 3it +β4X 4it +β5ln X 5it +β6ln X 6it +β7ln X 7it +u i +v t +ε it ;

[0120] Where Y is the investment amount of the industrial wastewater pollution control project completed this year, β1~β7 represent the coefficients of the independent variables, u i represents the cross-sectional random error component, v t represents the temporal random error component, ε it Represents the random error component. The fixed effect regression model was used to perform regression analysis on the data, and the regression results are shown in Table 5.

[0121] Table 5 Regression results

[0122]

[0123] Note: Standard error is in brackets, *p<0.1, **p<0.05, ***p<0.01

[0124] The regression results in Table 5 show that at the 10% significance level, the factors affecting the investment amount of industrial wastewater pollution control projects this year include industrial water consumption, the proportion of urban population in the total population at the end of the year, the added value of the secondary industry in the regional GDP, the amount of industrial wastewater discharged, and the number of domestic patent applications (items). At the 10% significance level, the per capita regional GDP and the total amount of water resources have no significant impact on the investment amount of industrial wastewater pollution control projects this year.

[0125] As a preferred embodiment of the present invention, the specific process of step 2 is:

[0126] The factors affecting the investment amount of industrial water pollution at the 10% significance level are selected as the main factors causing the difference in the cost of industrial water pollution control among regions; since each indicator has a positive and negative impact on the cost, the difference expressions of positive indicators and negative indicators are shown in Formula 2 and Formula 3 respectively:

[0127] Formula 2:

[0128] Formula 3:

[0129] The difference coefficient k of industrial water pollution control costs among regions is expressed as:

[0130] Formula 4:

[0131] where X i1 is an indicator for Region 1, and X i2 is an indicator for Region 2, T is the research period, T > 1, and in the present invention, T takes the value of 10, t is the year, and X ij is an indicator for Region j, j = 1, 2, and β i is the coefficient of the independent variable of the i-th indicator.

[0132] As a preferred embodiment of the present invention, the specific process of step 3 is as follows:

[0133] In order to eliminate basin pollutants and improve the basin water environment, water pollution control needs to be carried out simultaneously in the main stream and the tributaries. At the same time, in order to examine the pollution control effect of the main stream government, a assessment section is set at the main stream. If the water quality exceeds the standard, the main stream government needs to make ecological compensation; if the water quality meets the standard, the main stream government will receive ecological compensation. The water in the main stream is汇入 by two tributaries, and the water environment governance status of the tributaries will directly affect the water pollution control effect of the main stream. If the water environment of the tributaries deteriorates, it will directly affect the water pollution control of the main stream and cause the assessment section of the main stream to exceed the standard. Therefore, the main stream forms a pollution control supervision relationship between the two tributaries. In addition, the pollution control of the two tributaries will also bring environmental benefits to the main stream. At the same time, considering the pressure of economic development and the cost of pollution control, one tributary may invest more and have a good pollution control effect; the other tributary will invest less and have a poor pollution control effect for its own development, thus forming a pollution control competition relationship between the governments of the two tributaries. It is on this basis that the model assumptions and model construction are made.

[0134] Hypothesis 1: Assume that the pollution control efforts of the governments of Tributary 1, Tributary 2, and the main stream are A, B, and Z respectively; 0 < A < 1, 0 < B < 1, 0 < Z < 1, representing the policies, personnel, and capital investments made by the governments of the two tributaries and the main stream for water pollution control;

[0135] Hypothesis 2: Since both tributaries are reluctant to invest in policies and funds for pollution control for their own economic development, for the requirement of pollutant elimination targets, the water pollution control of the two tributaries is a competitive relationship. A competitive coefficient α, 0 < α < 1, is set to measure the economic development pressure of the governments of the two tributaries;

[0136] Hypothesis 3: The reduction of pollutants in the basin is the result of the pollution control of the governments of the main stream and the two tributaries, and it is a dynamic change process over time. Then the reduction of pollutants in the basin can be expressed as the following dynamic differential equation:

[0137] Equation 5:

[0138] Where q(t) represents the pollutant emission reduction of the two tributaries at time t. Assuming that the initial state of the system is q(0) ≥ 0, ξ>0, η>0, q>0, respectively represents the pollution elimination amount per unit pollution control effort made by the governments of tributary 1, tributary 2 and the mainstream, and δ represents the attenuation coefficient of emission reduction caused by the aging of sewage treatment equipment;

[0139] Hypothesis 4: The pollution control efforts of the tributary 1 government are not only affected by the competition coefficient α, but also by the supervision of the mainstream government. It is assumed that the efforts of the tributary 1 government are linearly related to the competition of the tributary 2 government and the supervision of the mainstream government, that is, A = A0-αB+d1Z; the efforts of the tributary 2 government are B = B0-αA+d2Z, A0≥0, B0≥0, representing the initial pollution control efforts of the tributary 1 government and the tributary 2 government when weighing their own benefits and costs without considering the competition factor and the supervision of the mainstream, where d1 and d2 are the influence coefficients of the mainstream government on the efforts of the tributary 1 government and the tributary 2 government respectively;

[0140] Hypothesis 5: The social welfare effect of water pollution control and pollutant emission reduction by the two tributary governments and the mainstream government is:

[0141] Formula 6: S(t)=S0+λq(t);

[0142] S0>0 represents the initial welfare status of the basin, and λ>0 represents the coefficient of the impact of basin emission reduction on the social welfare effect of the basin;

[0143] Assumption 6: The pollution control cost of tributary 1 government is a quadratic function The pollution control cost of the tributary 2 government is a quadratic function k represents the difference coefficient of pollution control costs between the two tributaries, and the effort cost of the mainstream government is c represents the mainstream government effort cost coefficient;

[0144] Hypothesis 7: Due to the different ecological fragility of each region, the environmental benefits brought by pollution control of the two tributaries and the main stream are also different. The environmental benefits brought by the elimination of unit pollutants by the governments of the two tributaries are ξAr1 and ηBr2 respectively, and the environmental benefits brought by the elimination of unit pollutants by the government of the main stream is qZr3. r1, r2, and r3 represent the differences in environmental benefits of unit pollutant control in tributary 1, tributary 2, and the main stream, respectively, which are reflected by the ecological fragility of each region.

[0145] Assumption 8: The revenue coefficients of the governments of Tributary 1, Tributary 2 and Main Stream are π1, π2 and π3 respectively, π1>0, π2>0 and π3>0, and the governments of Tributary 1, Tributary 2 and Main Stream have the same discount rate ρ at any time, ρ>0.

[0146] As a preferred embodiment of the present invention, in the step of solving the differential game model, the solution method includes solving the Nash non-cooperative game model and the Stackelberg master-slave game model;

[0147] The solution process of the Nash non-cooperative game model is as follows:

[0148] Based on the above assumptions, and considering that the governments of tributary 1, tributary 2, and the main stream are all limited rational entities, the benefit functions of the three governments are obtained;

[0149] The revenue function of the government in Tributary 1 is:

[0150] Formula 7:

[0151] Among them, q1-ξA is the total amount of pollutants discharged by tributary 1, h1 represents the benefits brought by relieving the pollution control pressure of tributary 1 due to the pollution control of tributary 2, ω is the environmental protection tax paid by the taxable water pollutants discharged by the two tributaries, and J1 is the benefits obtained by the government of tributary 1 from the pollution discharge;

[0152] The revenue function of the government in tributary 2 is:

[0153] Formula 8:

[0154] Among them, q2-ηB is the total amount of pollutants discharged by tributary 2, h2 represents the benefits brought by relieving the pollution control pressure of tributary 2 due to the treatment of tributary 1, and J2 is the benefits obtained by the government from the discharge of pollutants in tributary 2;

[0155] The revenue function of the mainstream government is:

[0156] Formula 9:

[0157] An assessment section is set at the main stream, q0 is the total amount of water pollutants that the three parties need to treat when the assessment section meets the standard; P is the ecological compensation received by the main stream government for each unit of pollutants that is better than the assessment section when the main stream assessment section meets the standard, or the ecological compensation paid by the main stream government for each unit of pollutants that is worse than the assessment section when the main stream assessment section exceeds the standard;

[0158] In order to make equation 7-9 have a continuous and unique solution q(t), it is necessary to construct a set of bounded, continuous, and differentiable value functions V1(q), V2(q), and V3(q). The Hamilton-Jacobi-Bellman-Fleming (HJB) equations for tributary 1 government, tributary 2 government, and main stream government are constructed as follows:

[0159] Formula 10:

[0160] Formula 11:

[0161] Formula 12:

[0162] Substitute the right side of equation 10-12 into the right side of the HJB equation to find the first-order maximization condition for A, B, and Z, and assume that the function V i The expression of (q) is in linear form, and the game equilibrium solution is obtained:

[0163] Formula 13:

[0164] Formula 14:

[0165] Formula 15:

[0166] The optimal benefits of the main and tributary governments under equilibrium conditions are:

[0167] Formula 16:

[0168] Formula 17:

[0169] Formula 18:

[0170] Among them, V1'(q), V2'(q), V3'(q) are the first-order derivatives of the value functions V1(q), V2(q), and V3(q), and A * , B * , Z * is the optimal equilibrium solution of the government efforts of tributary 1, tributary 2, and main stream under the Nash non-cooperative game model, V1 * for, for, is the optimal equilibrium solution of the government revenue of tributary 1, tributary 2 and main stream under the Nash non-cooperative game model, q * is the pollutant emission reduction of the two tributaries under the Nash non-cooperative game model;

[0171] The solution process of the Stackelberg master-slave game model is as follows:

[0172] Pollution control of the two tributaries will generate benefits for the mainstream, and the mainstream can obtain ecological compensation without paying a large pollution control cost. Therefore, the mainstream government shares a certain proportion of the pollution control costs with the two tributary governments. The decision-making order is that the mainstream government first determines the pollution control efforts and the cost sharing ratios m and n for the governments of tributaries 1 and 2, and then the two tributary governments determine their own optimal strategies; using the reverse induction method, first find the optimal decision of the governments of tributaries 1 and 2, and the objective function satisfies the HJB equation:

[0173] Formula 19:

[0174] Formula 20:

[0175] Solve the first-order conditions for maximizing A and B on the right side of Equation 19 and Equation 20, and substitute them into the HJB equation of the mainstream government to obtain:

[0176] Formula 21:

[0177] Also assume that the function V i The expression of (q) is in linear form, and the Stackelberg equilibrium solution of the two tributaries and the main stream government under the cost sharing mechanism is:

[0178] Formula 22:

[0179] Formula 23:

[0180] Formula 24:

[0181] Formula 25:

[0182] Formula 26:

[0183] The optimal return for the three parties is:

[0184] Formula 27:

[0185] Formula 28: Formula 29:

[0186] Among them A ** ,B ** ,Z ** are the optimal equilibrium solutions for the efforts of the governments of tributary 1, tributary 2, and the main stream in the Stackelberg master-slave game model, V1 ** , , V3 ** are the optimal equilibrium solutions for the government revenues of tributary 1, tributary 2, and main stream in the Stackelberg master-slave game model, q ** It is the pollutant emission reduction of the two tributaries under the Stackelberg master-slave game model.

[0187] As a preferred embodiment of the present invention, in step 4, the influence of various influencing factors on the game equilibrium is empirically analyzed in the study area.

[0188] A storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for sharing the cost of main and tributary water pollution control taking into account regional differences.

[0189] Example 1. This example is based on the 2020 "Shanxi Statistical Yearbook" and "Shaanxi Statistical Yearbook". Q1 and Q2 select the industrial wastewater discharge in 2019, which are 199.136 million and 239.3745 million tons, respectively. J1 and J2 select the industrial added value in 2019, which are 656.951 billion and 266.2311 billion yuan, respectively. Since the higher the industrial output value, the higher the benefits of alleviating the pressure of pollution control in the region, the higher the benefits brought by relieving the pressure of pollution control, according to the proportion of the industrial added value of Shanxi Province and Shaanxi Province in the sum of the industrial added value of the two provinces, the values ​​are assigned based on the difference in the output value of industrial enterprises in the two regions, h1=0.2, h2=0.8. The difference coefficient k of the pollution control cost between the two regions is calculated to be 5.08. According to the "Henan Statistical Yearbook", c2 takes the total investment of 308 million yuan in water pollution control of industrial enterprises in Henan Province. According to the "Environmental Protection Tax Law of the People's Republic of China", take ω=1.4 yuan / m 3 d1 and d2 are both 0.5. δ=0.2, r=0.2.

[0190] Due to the treatment of water pollution, the attractiveness of regional investment is improved, regional industrial development is brought about, and the social welfare of the basin is increased. S0 is the initial social welfare status of the basin. The sum of the GDP of the three provinces in 2019 is selected. According to the calculation, S0 = 9707907 billion yuan. The economic development status of the three provinces is different, and the development brought by water pollution control to each province is also different. π1, π2, and π3 are assigned according to the proportion of the GDP of Shanxi Province, Shaanxi Province, and Henan Province in the sum of the GDP of the three provinces, respectively, π1 = 0.17, π2 = 0.27, and π3 = 0.56. r1, r2, and r3 are the ecological fragility of Shanxi Province, Shaanxi Province, and Henan Province, respectively, 0.74, 0.23, and 0.62. According to the "Horizontal Ecological Protection Compensation Agreement of the Yellow River Basin (Henan-Shandong Section)", P = 0.6.

[0191] Based on the values ​​of the above parameters, numerical simulation is carried out to analyze the changes in the competition coefficient between the two tributaries' governments and the main factors affecting the differences in industrial water pollution control costs among regions, and their effects on the amount of pollutants eliminated, the degree of pollution control efforts and the benefits of the governments of the mainstream and the two tributaries.

[0192] Analyze the impact of urbanization rate on pollutant elimination and the benefits of the three governments:

[0193] 1) Impact on the amount of pollutants removed;

[0194] Take Shanxi Province urbanization rate X 31 =0.32,0.72,X 31The change in the amount of pollutants removed in the basin is as follows Figure 3-7 As shown. Figure 3 It can be seen that with the urbanization rate of Shanxi Province 31 The increase will further widen the cost difference between Shanxi Province and Shaanxi Province. The pollution control cost of the Shaanxi Provincial Government will be more significant than that of Shanxi Province. Therefore, the Shaanxi Provincial Government will reduce its pollution control efforts. Therefore, with the increase of the urbanization rate in Shanxi Province, the amount of pollutant elimination will decrease under both the Nash non-cooperative mechanism and the cost-sharing mechanism.

[0195] Take the urbanization rate of Shaanxi Province X 32 =0.38,0.78,X 32 The change in the amount of pollutants removed in the basin is as follows Figure 4 As the urbanization rate of Shaanxi Province 32 As the urbanization rate in Shaanxi Province increases, the pollution control costs of the Shaanxi Provincial Government will decrease, so the Shaanxi Provincial Government will increase its pollution control efforts to improve the environment. Therefore, with the increase of the urbanization rate in Shaanxi Province, the amount of pollutant elimination will increase under both the Nash non-cooperative mechanism and the cost-sharing mechanism.

[0196] 2) Impact on the three government revenues;

[0197] Take X respectively 31 =0.32, 0.72, the revenue of Shanxi, Shaanxi and Henan provincial governments changes over time as follows Figure 5 As shown in (a), (b), and (c). Figure 5 It can be seen that the impact of Shanxi Province's urbanization rate on the benefits of the three governments is consistent. With the increase of Shanxi Province's urbanization rate, the benefits of the three governments will decrease under both the Nash non-cooperative mechanism and the cost-sharing mechanism. This is because with the increase of Shanxi Province's urbanization rate, the cost difference between Shanxi Province and Shaanxi Province will be further expanded. Compared with the pollution control cost of Shanxi Province, the pollution control cost of the Shaanxi Provincial Government will be more significant. The Shaanxi Provincial Government will reduce its pollution control efforts, so the Shanxi Provincial Government needs to make more efforts to eliminate pollutants, so the benefits of Shanxi Province will decrease. Similarly, Shaanxi Province will discharge more wastewater to Henan Province, increasing the pollution control cost of Henan Province. At the same time, the amount of pollutant elimination will decrease, and the overall environmental and social welfare of the basin will also decrease, so the benefits of the three governments will decrease. And under the cost-sharing mechanism, the benefits of the three governments will decrease more. As the difference in pollution control costs between the two provinces widens, the impact on the benefits of the three parties under the cost-sharing mechanism is greater than that of the Nash non-cooperative mechanism.

[0198] Take X respectively 32 =0.38, 0.78, the revenue of Shanxi, Shaanxi and Henan provincial governments changes over time as follows Figure 6 As shown in (a), (b), and (c). Figure 6It can be seen that the impact of Shaanxi's urbanization rate on the three-party government revenue is consistent. With the increase of Shaanxi's urbanization rate, the revenue of the three-party government will increase under both the Nash non-cooperative mechanism and the cost-sharing mechanism. As the urbanization rate of the Shaanxi Provincial Government increases, the cost of pollution control will decrease, so the Shaanxi Provincial Government will increase its own pollution control efforts, eliminate the amount of pollutants, and bring about the improvement of the overall environmental and social welfare of the basin, so the revenue of the three-party government will be improved. For the Shanxi Provincial Government, the Shaanxi Provincial Government's pollution control efforts have increased, easing the pollution control pressure of the Shanxi Provincial Government. Therefore, the Shanxi Provincial Government can continue to maintain its own development, and the revenue of the Shanxi Provincial Government will further increase. For the Henan Provincial Government, the upstream Shaanxi Provincial Government's pollution control efforts have increased, which will also reduce the pollution control costs of the Henan Provincial Government, so the revenue of the Henan Provincial Government will also increase. Under the cost-sharing mechanism, with the increase of Shaanxi's urbanization rate, the added value of the three-party government revenue is greater than that under the Nash non-cooperative mechanism.

[0199] Analyze the impact of industrialization on pollutant elimination and the benefits of the three governments:

[0200] 1) Impact on the amount of pollutants removed;

[0201] Take Shanxi Province Industrialization 41 =0.33,0.73. Figure 7 It can be seen that with the industrialization of Shanxi Province 41 With the improvement of the cost-sharing mechanism, the amount of pollutants eliminated will increase under both the Nash non-cooperative mechanism and the cost-sharing mechanism. This is because with the improvement of Shanxi Province's industrialization, the pollution control costs of the Shanxi Provincial Government will increase, but the cost difference between the Shanxi Provincial Government and the Shaanxi Provincial Government will decrease. Compared with the pollution control costs of Shanxi Province, the pollution control costs of the Shaanxi Provincial Government are relatively small, so the Shaanxi Provincial Government will increase its pollution control efforts, and the amount of pollutants eliminated will increase under both mechanisms.

[0202] Take Shaanxi Province Industrialization 42 =0.29,0.69. Figure 8 It can be seen that the amount of pollutant elimination will decrease under both the Nash non-cooperative mechanism and the cost-sharing mechanism. This is because with the industrialization of Shaanxi Province, 42 With the increase of pollution control cost in Shaanxi Province, Shaanxi Province will increase, so Shaanxi Province is unwilling to make more efforts to control water pollution. The amount of pollutants eliminated will decrease under both mechanisms.

[0203] 2) Impact on the three government revenues;

[0204] Take Shanxi Province Industrialization 41 =0.33, 0.73, the revenue of Shanxi, Shaanxi and Henan provincial governments changes over time as follows Fig. 9 As shown in (a), (b), and (c). Fig. 9It can be seen that with the improvement of the industrialization level of Shanxi Province, the benefits of the three governments will increase under both the Nash non-cooperative mechanism and the cost-sharing mechanism, and the benefits of the three governments will increase more under the cost-sharing mechanism. Because with the improvement of Shanxi Province's industrialization, the pollution control costs of the Shanxi Provincial Government will increase, and the cost difference between the Shanxi Provincial Government and the Shaanxi Provincial Government will decrease. Compared with the pollution control costs of Shanxi Province, the pollution control costs of the Shaanxi Provincial Government are relatively small. The Shaanxi Provincial Government will increase its own pollution control efforts, which will bring about the improvement of the overall environmental and social welfare of the basin, so the benefits of the three governments will be improved. The Shaanxi Provincial Government's increased efforts in pollution control have eased the pollution control pressure of the Shanxi Provincial Government, so the Shanxi Provincial Government can continue to maintain its own development, and its benefits will increase further. The upstream Shaanxi Provincial Government's increased efforts in pollution control will also reduce the pollution control costs of the Henan Provincial Government, and its benefits will also increase further. Under the cost-sharing mechanism, since Shanxi Province and Shaanxi Province receive pollution control cost subsidies from Henan Province, the amount of pollutant control increases, bringing more overall welfare to the basin, and the benefits of the three provinces increase more than under the Nash non-cooperative mechanism.

[0205] Take Shaanxi Province Industrialization 42 =0.29, 0.69. The revenue of Shanxi, Shaanxi and Henan provincial governments changes over time as follows Fig.10 As shown in (a), (b), and (c). Fig.10 It can be seen that with the improvement of Shaanxi Province's industrialization, the benefits of the three governments will decrease under both the Nash non-cooperative mechanism and the cost-sharing mechanism. As Shaanxi Province's industrialization level increases and pollution control costs increase, the Shaanxi Provincial Government will reduce its own pollution control efforts and transfer the pressure of water pollution control to the Shanxi Provincial Government, so the benefits of the Shanxi Provincial Government under both mechanisms are reduced. However, under the cost-sharing mechanism, although the Shanxi Provincial Government is under great pressure to control pollution, it can obtain pollution control cost subsidies from the Henan Provincial Government, so the benefits of the Shanxi Provincial Government under the cost-sharing mechanism decrease slowly. For Henan Province, due to the increase in pollution control costs of the Shaanxi Provincial Government, the pollution control efforts have been reduced, the wastewater discharge has increased, and the pollution control costs of the Henan Provincial Government have increased, so the benefits of the Henan Provincial Government under both mechanisms have decreased.

[0206] To sum up, the cost-sharing method for water pollution control in main and tributary rivers that takes into account regional differences proposed in the present invention can help decision makers expand from the upstream and downstream perspectives to the main stream and multiple tributaries, and can more comprehensively consider the differences between different regions, thereby improving the accuracy and reliability of decision results and solving the incompleteness problem caused by relying on calculations from the upstream and downstream perspectives of the basin.

[0207] The above are only preferred embodiments of the present invention. It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention. These should also be regarded as the protection scope of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent.

Claims

1. A method for sharing the cost of main and tributary water pollution control considering regional differences, characterized in that: It includes the following steps: Step 1: Analyze the influencing factors of the difference in pollution control costs between regions; Step 2: Construct a pollution control cost difference coefficient based on the influencing factors; Step 3: Incorporate the pollution control cost difference coefficient into the differential game model, and construct a Nash non-cooperative mechanism and a cost sharing model among the main stream and the two tributaries; Step 4: Solve the differential game model and empirically analyze the influence law of each influencing factor on the game equilibrium.

2. The method for sharing the cost of main and tributary water pollution control considering regional differences according to claim 1 is characterized in that: The specific process of Step 1 is as follows: Select indicators from two aspects of natural endowment and economic development for analysis; In terms of natural endowment: Select the total water resources X1 indicator to reflect the regional water resources environment characteristics; In terms of economic development: Select the per capita GDP X2, the proportion of the urban population at the end of the year in the total population X3, the proportion of the added value of the secondary industry in the regional GDP X4, the industrial water consumption X5, the industrial wastewater discharge X6, and the number of domestic patent applications authorized X7 to measure the regional economic development situation; Select a fixed effect model for regression analysis, and the model form is as follows: Equation 1: ln Y it = β0 + β1ln X 1it + β2ln X 2it + β3X 3it + β4X 4it + β5ln X 5it + β6ln X 6it + β7ln X 7it + u i + v t + ε it ; Where Y is the investment amount of the industrial wastewater pollution control project completed this year, β1~β7 represent the coefficients of the independent variables, u i represents the cross-sectional random error component, v t represents the temporal random error component, ε it Represents the random error component.

3. The method for sharing the cost of main and tributary water pollution control considering regional differences according to claim 1 is characterized in that: The specific process of Step 2 is as follows: Select the influencing factors that affect the industrial water pollution investment amount at the 10% significance level as the main influencing factors causing the difference in industrial water pollution control costs between regions; the differential expression methods for positive indicators and negative indicators are shown in Equations 2 and 3 respectively: Formula 2: Formula 3: Then the industrial water pollution control cost difference coefficient k between regions is expressed as: Formula 4: Where X i1 is the index of region 1, X i2 is the indicator of region 2, T is the research period, T>1, T is 10, t is the year, X ij is the index of region j, j = 1, 2, β i is the coefficient of the independent variable of the ith indicator.

4. The method for sharing the cost of main and tributary water pollution control considering regional differences according to claim 1 is characterized in that: The specific process of Step 3 is as follows: Conduct model assumptions and model construction: Assumption 1: The pollution control efforts of the governments of Tributary 1, Tributary 2, and the main stream are A, B, and Z respectively; 0 < A < 1, 0 < B < 1, 0 < Z < 1, representing the policies, personnel, and capital investments formulated by the governments of the two tributaries and the main stream for water pollution control; Assumption 2: The water pollution control of the two tributaries is a competitive relationship, and a competition coefficient α is set, 0 < α < 1, to measure the economic development pressure of the governments of the two tributaries; Assumption 3: The pollutant reduction amount in the basin is expressed as the following dynamic differential equation: Formula 5: Where q(t) represents the pollutant reduction amount of the two tributaries at time t. Assume that the initial state of the system q(0) ≥ 0, ξ > 0, η > 0, q > 0, which represent the pollution elimination amounts of the governments of Tributary 1, Tributary 2, and the main stream for each unit of pollution control effort respectively, and δ represents the reduction coefficient of the reduction amount due to the aging of sewage treatment equipment; Assumption 4: Assume that the effort degree of the government of Tributary 1 has a linear function relationship with the competition of the government of Tributary 2 and the supervision of the main stream government, that is, A = A0 - αB + d1Z; the effort degree of the government of Tributary 2 is B = B0 - αA + d2Z, A0 ≥ 0, B0 ≥ 0, representing the initial pollution control efforts of the governments of Tributary 1 and Tributary 2 when weighing their own benefits and costs without considering the competition factor and the supervision role of the main stream. Among them, d1 and d2 are the influence coefficients of the main stream government on the effort degrees of the governments of Tributary 1 and Tributary 2 respectively; Assumption 5: The social welfare effects brought by the governments of the two tributaries and the main stream for water pollution control and reducing pollutant emissions are: Equation 6: S(t) = S0 + λq(t); S0 > 0 represents the initial welfare status of the basin, and λ > 0 represents the influence coefficient of the reduction amount of the basin on the social welfare effect of the basin; Assumption 6: The pollution control cost of tributary 1 government is a quadratic function The pollution control cost of the tributary 2 government is a quadratic function k represents the difference coefficient of pollution control costs between the two tributaries, and the effort cost of the mainstream government is c represents the mainstream government effort cost coefficient; Hypothesis 7: The environmental benefits of eliminating unit pollutants for the two tributary governments are ξAr1 and ηBr2 respectively, and the environmental benefits of eliminating unit pollutants for the mainstream government are qZr3. r1, r2, and r3 represent the differences in environmental benefits of eliminating unit pollutants in tributary 1, tributary 2, and the mainstream, respectively, and are reflected by the ecological fragility of each region. Assumption 8: The revenue coefficients of the governments of Tributary 1, Tributary 2 and Main Stream are π1, π2 and π3 respectively, π1>0, π2>0 and π3>0, and the governments of Tributary 1, Tributary 2 and Main Stream have the same discount rate ρ at any time, ρ>0.

5. The method for sharing the cost of main and tributary water pollution control considering regional differences according to claim 4 is characterized in that: In the step of solving the differential game model, the solution method includes solving the Nash non-cooperative game model and the Stackelberg master-slave game model; The solution process of the Nash non-cooperative game model is as follows: Based on the above assumptions, and considering that the governments of tributary 1, tributary 2, and the main stream are all limited rational entities, the benefit functions of the three governments are obtained; The revenue function of the government in Tributary 1 is: Formula 7: Among them, q1-ξA is the total amount of pollutants discharged by tributary 1, h1 represents the benefits brought by relieving the pollution control pressure of tributary 1 due to the pollution control of tributary 2, ω is the environmental protection tax paid by the taxable water pollutants discharged by the two tributaries, and J1 is the benefits obtained by the government of tributary 1 from the pollution discharge; The revenue function of the government in tributary 2 is: Formula 8: Among them, q2-ηB is the total amount of pollutants discharged by tributary 2, h2 represents the benefits brought by relieving the pollution control pressure of tributary 2 due to the treatment of tributary 1, and J2 is the benefits obtained by the government from the discharge of pollutants in tributary 2; The revenue function of the mainstream government is: Formula 9: Set up an assessment section at the main stream, q 0 The total amount of water pollutants that the three parties need to treat when the assessment section meets the standards; P is the ecological compensation received by the mainstream government for each unit of pollutant that is better than the assessment section when the mainstream assessment section meets the standard, or the ecological compensation paid by the mainstream government for each unit of pollutant that is worse than the assessment section when the mainstream assessment section exceeds the standard; In order to make equation 7-9 have a continuous and unique solution q(t), a set of bounded, continuous and differentiable value functions V1(q), V2(q), and V3(q) are constructed, and the HJB equations of tributary 1 government, tributary 2 government, and main stream government are constructed respectively: Formula 10: Formula 11: Formula 12: Substitute the right side of equation 10-12 into the right side of the HJB equation to find the first-order maximization condition for A, B, and Z, and assume that the function V i The expression of (q) is in linear form, and the game equilibrium solution is obtained: Formula 13: Formula 14: Formula 15: The optimal benefits of the main and tributary governments under equilibrium conditions are: Formula 16: Formula 17: Formula 18: Among them, V1'(q), V2'(q), V3'(q) are the first-order derivatives of the value functions V1(q), V2(q), and V3(q), respectively. * ,B * ,Z * are the optimal equilibrium solutions for the government efforts of tributary 1, tributary 2, and main stream under the Nash non-cooperative game model, are the optimal equilibrium solutions of the government revenue of tributary 1, tributary 2 and main stream under the Nash non-cooperative game model, q * is the pollutant emission reduction of the two tributaries under the Nash non-cooperative game model; The solution process of the Stackelberg master-slave game model is as follows: First, the mainstream government determines the pollution control efforts and the cost sharing ratios m and n for the governments of tributaries 1 and 2. Then the two tributary governments determine their own optimal strategies. Using the reverse induction method, we first find the optimal decisions of the governments of tributaries 1 and 2. The objective function satisfies the HJB equation: Formula 19: Formula 20: Solve the first-order conditions for maximizing A and B on the right side of Equation 19 and Equation 20, and substitute them into the HJB equation of the mainstream government to obtain: Formula 21: Assume that the function V i The expression of (q) is in linear form, and the Stackelberg equilibrium solution of the two tributaries and the main stream government under the cost sharing mechanism is: Formula 22: Formula 23: Formula 24: Formula 25: Formula 26: The optimal return for the three parties is: Formula 27: Formula 28: Formula 29: Among them A ** ,B ** ,Z ** are the optimal equilibrium solutions of the government efforts of tributary 1, tributary 2, and main stream in the Stackelberg master-slave game model, V1 ** ,V2 ** ,V3 ** are the optimal equilibrium solutions of the government revenues of tributary 1, tributary 2, and main stream in the Stackelberg master-slave game model, q ** It is the pollutant emission reduction of the two tributaries under the Stackelberg master-slave game model.

6. The method for sharing the cost of main and tributary water pollution control considering regional differences according to claim 1 is characterized in that: In step 4, an empirical analysis is conducted on the influence of various influencing factors on the game equilibrium in the study area.

7. A storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the steps of a method for sharing the cost of pollution control of main and tributary rivers considering regional differences as described in any one of claims 1 to 6 above are implemented.

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