Trans-boundary water resource pollution cooperative treatment method based on dynamic game theory

Abstract

The invention discloses a cross-boundary water resource pollution cooperative treatment method based on a dynamic game theory, and the method comprises the steps: S1, constructing a dynamic game model, and defining a revenue function, a strategy set and a pollution diffusion matrix of a treatment subject; s2, optimizing an income distribution and strategy adjustment path based on a dynamic game algorithm; s3, introducing a dynamic fracture-reconstruction game algorithm, monitoring income imbalance, pollution diffusion overrun or strategy stagnation, triggering fracture and freezing a strategy; s4, after fracture triggering, reconfiguring income distribution and a strategy set, optimizing governance responsibility and resource configuration, and forming a cooperation framework; s5, in combination with pollution diffusion dynamic change, optimizing a treatment strategy, and dynamically adjusting a strategy evolution path; and S6, judging the convergence state of the governance strategy, and if the governance strategy is not balanced, returning to the fracture reconstruction stage for iterative optimization. According to the invention, the problems of unstable cooperation, non-uniform income distribution and low treatment efficiency of trans-boundary water pollution treatment are effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of water resources, and in particular to a collaborative governance method for cross-border water resource pollution based on dynamic game theory. Background Art

[0002] In modern water resource management, transboundary water pollution has become one of the global challenges. The traditional transboundary water pollution control model mainly relies on fixed responsibility sharing. However, this governance model often lacks dynamic adaptability and is difficult to effectively respond to the temporal and spatial changes in pollution loads. At the same time, due to differences among regional governance entities in economic development, environmental protection and governance costs, cross-border governance agreements are difficult to implement continuously, and there may even be a "free-rider" phenomenon, that is, some regions reduce governance investment and transfer pollution control responsibilities to downstream areas, weakening the overall governance effect.

[0003] Existing methods for transboundary water pollution control lack dynamic optimization capabilities. In traditional methods, governance decisions are usually based on historical data and empirical rules, and fail to fully consider the nonlinear dynamic changes of pollution diffusion and the strategic game relationship between governance entities. Some studies have attempted to introduce pollution emission rights trading and economic incentive mechanisms to encourage regional entities to reduce emissions and optimize governance strategies. However, these methods usually rely on preset economic models and fixed game rules, and cannot effectively respond to environmental changes, differences in governance capabilities, and dynamic governance needs over long time dimensions.

[0004] Existing pollution diffusion control methods often use static optimization methods, such as total pollution control (TMDL) or regional water quality assessment (WQAA). Although these methods can provide pollution load management solutions in the short term, in the long-term governance process, due to changes in hydrological conditions, pollution source emissions and governance technologies, static optimization methods are prone to failure and cannot dynamically adjust governance plans. In addition, some studies have attempted to use machine learning or big data analysis technology to predict pollution diffusion and optimize governance, but these methods lack strategic interaction analysis between governance entities and are difficult to solve the problem of cooperative stability under multi-agent games.

[0005] In summary, the existing transboundary water pollution control methods have problems such as unstable governance cooperation, low pollution diffusion control efficiency, and insufficient strategy optimization capabilities. Therefore, how to provide a transboundary water pollution collaborative governance method based on a dynamic game algorithm is an urgent problem that technicians in this field need to solve. Summary of the invention

[0006] One purpose of the present invention is to propose a collaborative governance method for cross-border water resource pollution based on dynamic game theory. The present invention makes full use of dynamic game algorithms, fracture-reconstruction game mechanisms and dynamic optimization strategies for pollution diffusion, and describes in detail an intelligent collaborative mechanism for benefit distribution, responsibility distribution and governance strategy optimization among cross-regional water pollution governance entities. It has the advantages of high governance efficiency, strong cooperation stability and optimized pollution control effects.

[0007] The collaborative governance method for transboundary water resource pollution based on dynamic game theory according to an embodiment of the present invention comprises the following steps: S1. Construct a dynamic game model, define the benefit function, strategy set and pollution diffusion matrix of the governance subject, and describe the dynamic behavior relationship and cooperation constraints between subjects; S2. Based on the dynamic game algorithm, establish a strategy evolution mechanism, dynamically calculate the impact of pollution diffusion on governance benefits and costs, and optimize the benefit distribution and strategy adjustment path; S3. Introduce a dynamic break-reconstruction game algorithm and set a break trigger mechanism to determine the conditions for cooperation break and freeze the existing strategy by monitoring the imbalance of income distribution, excessive pollution diffusion or stagnation of strategy evolution; S4. After the fracture state is triggered, by reconstructing the benefit distribution and strategy set, based on the pollution diffusion matrix and governance costs, the responsibility distribution and resource allocation of each governance subject are optimized to form a new cooperation framework; S5. Combine the reconstructed cooperation model and the dynamic changes of pollution diffusion to optimize and adjust the governance strategy and dynamically update the strategy evolution path; S6. Determine the dynamic convergence state of the governance strategy, and adjust the benefits and strategies to see whether a stable equilibrium has been achieved. If not, return to the fracture reconstruction stage and continue to optimize the model and strategy until dynamic equilibrium and governance goals are achieved.

[0008] Optionally, the S1 includes the following steps: S11. Determine the number of governance entities within the governance area and define the governance entity set in Indicates the total number of governance entities; S12. Define the benefit function for each governance entity ; S13. Define the policy set of governance entities , the strategy set includes pollution reduction efforts , Resource Allocation Priority and other governance-related strategies; S14. Constructing a pollution diffusion matrix in Indicates time Internal pollutants from the main governance The region to the governance body The diffusion effect of the region, the matrix elements satisfy and ; S15. Profit function The pollution diffusion effect in is expressed as ,in, From the main body To the subject The impact of pollution diffusion, Main body A collection of governance policies; S16. Set up cooperation constraints between governance entities and allocate responsibility through the cooperation responsibility matrix Represents that the matrix element satisfy and , used to define the governance resource allocation relationship between entities; S17. Complete the initialization of the multi-agent dynamic game model through the joint description of the profit function, strategy set, pollution diffusion matrix and cooperation constraint matrix.

[0009] Optionally, S2 includes the following steps: S21. Based on the dynamic game algorithm, a dynamic evolution model of the governance subject's benefits is constructed. The dynamic formula of benefits is: ; in, Representing the subject In time of income, and are the input and output weights of pollution diffusion, For governance strategies, For governance costs, and is the income adjustment factor; S22. Based on the dynamic evolution model of returns, a strategy evolution mechanism is constructed. The strategy update formula is: ; in, As the main In time The strategy value of is the revenue-driven adjustment factor, is the diffusion weight influencing factor, As the main The gradient of the reward function, represents the interactive impact of strategies on the returns of other entities; S23, dynamically adjust the pollution diffusion matrix and update the diffusion weight; S24. Based on the dynamic evolution of strategies and benefits, combined with the time adjustment of the diffusion matrix, the benefit distribution path between governance entities is optimized to dynamically reduce the negative impact of pollution diffusion on benefits; S25. Dynamically balance the distribution relationship between benefits and costs by adjusting the strategy set and diffusion weights through multi-stage iterations; S26. Determine the convergence state of governance benefits and strategy paths. If the preset equilibrium conditions are met, stop the evolution process and output the optimization results. S27. Complete the dynamic adjustment of strategy evolution and benefit distribution, and optimize the impact of pollution diffusion on governance benefits.

[0010] Optionally, S3 includes the following steps: S31. Based on the dynamic fracture-reconstruction game algorithm, define the trigger conditions for income imbalance, combine the dynamic evolution of income and distribution differences, and establish an income imbalance model: ; in, Represents the income imbalance, As the main of income, Representing the subject With the subject The cooperation weight, is the total number of subjects, is the income imbalance threshold, which indicates the maximum income deviation that the system can tolerate; the threshold calculation formula is: ; is the adjustment coefficient, obtained by fitting historical data, which indicates the tolerance range of the governance system to uneven distribution of benefits; is the standard deviation of the return, reflecting the degree of dispersion of the global return distribution; when When , the income imbalance break condition is triggered; S32. Combined with the time dynamic characteristics of the pollution diffusion matrix, define the diffusion over-limit triggering conditions, and construct the diffusion over-limit model through the change of diffusion intensity between subjects: ; in, Indicates time main body To the subject The pollution diffusion weight, and is the policy value of the subject, is the diffusion dynamic adjustment factor, is the diffusion excess dynamic intensity, is the diffusion limit threshold, which indicates the maximum tolerable intensity of pollution diffusion; the threshold calculation formula is: ; is the adjustment coefficient, is the maximum value of the pollution diffusion matrix; when When , the diffusion over-limit fracture condition is triggered; S33. Define the triggering condition of strategy evolution stagnation. By monitoring the time change of the strategy gradient, determine whether there is a phenomenon of strategy adjustment stagnation. The strategy evolution stagnation model is: ; in, Indicates time The mean of the dynamic adjustment of the strategy, As the main The temporal gradient of the policy, is the strategy evolution stagnation threshold, which indicates the minimum dynamic change range of strategy adjustment; the threshold calculation formula is: ; is the adjustment coefficient, represents the time average of the policy gradient; when When , the strategy evolution stagnation fracture condition is triggered; S34. Construct a comprehensive fracture trigger model, combining the multi-dimensional impact of return imbalance, diffusion overlimit and strategy evolution stagnation, and the comprehensive trigger function is: ; in, Indicates the comprehensive fracture trigger value, , , are the weight factors of return imbalance, diffusion excess and strategy stagnation, is the comprehensive trigger threshold, which indicates the critical value of the comprehensive fracture condition; the threshold calculation formula is: ; is the comprehensive regulatory factor; When the fracture mechanism is triggered; S35, freeze the current state, record the strategy set, pollution diffusion matrix and benefit distribution matrix, and define the frozen matrix as ;in, The state of the frozen moment, is a set of strategies, is the diffusion matrix, is the profit allocation matrix; S36, based on the frozen state, restructure the benefits and redistribute the benefits of the subject to restore the cooperative balance; S37. Based on the state after the profit reconstruction, dynamically optimize the strategy set and adjust the optimization strategy path according to the gradient.

[0011] Optionally, S4 includes the following steps: S41. Freeze the current cooperation status and record the freeze matrix , freeze strategy set Pollution Diffusion Matrix and income collection ; S42, Freezing-based Pollution Diffusion Matrix and governance cost matrix , define the reconstruction income distribution model, optimize the main income through the dynamic adjustment mechanism, and reconstruct the income distribution model as follows: ; in, As the main The post-reconstruction benefit is is the income adjustment factor, is the governance cost adjustment coefficient, and are the output and input weights of pollution diffusion, As the main To the subject allocation of governance costs; S43. Constructing a responsibility allocation matrix Based on the pollution diffusion matrix and the benefit reconstruction results, the responsibility allocation is dynamically optimized. The calculation formula of the responsibility allocation matrix is: ; in, Representing the subject To the subject The proportion of responsibility distribution, Dynamic adjustment factors for responsibility allocation, Ensure that the total allocation is 1; S44. Re-optimize the resource allocation matrix , combined with the distribution of governance costs and benefits, dynamically adjust the resource allocation path, and the calculation formula of the resource allocation matrix is: ; in, Representing the subject Assign to subject The proportion of resources S45. Combine the responsibility allocation matrix and resource allocation matrix to form a new cooperation framework, and dynamically adjust the cooperation strategy through the strategy set update formula; S46. Through strategy set , Responsibility Allocation Matrix and resource allocation matrix to form a new framework for cooperation.

[0012] Optionally, S5 includes the following steps: S51, based on the reconstructed pollution diffusion matrix , Responsibility Allocation Matrix and resource allocation matrix , comprehensively analyze the distribution of benefits, responsibility and resource utilization of the governance subject, and determine the starting point for optimization; S52. Strategy set reconstructed through analysis , combined with the dynamic income change model , evaluate the impact of existing strategies on returns and diffusion control, and generate strategy optimization parameters; S53. Build a governance efficiency improvement model by dynamically adjusting the strategy set Optimize governance efficiency by combining the various components of the , including pollution reduction efforts and resource allocation priorities; S54. Based on the responsibility allocation matrix and resource allocation matrix , adjust the intensity of collaboration between entities, dynamically allocate governance resources, and optimize the inhibitory effect of governance strategies on pollution spread; S55. Combined with the strategy evolution mechanism of the dynamic game algorithm, the strategy set of the subject is updated, and the new strategy set Optimize and adjust by comprehensively considering the dynamic changes of pollution diffusion, the results of benefit reconstruction and the cost of governance; S56. Dynamically monitor the optimized policy path and determine whether the policy adjustment achieves the expected goal through the governance efficiency evaluation index. If not, iteratively update the policy path and continuously optimize the governance model. S57. After the strategy path reaches a dynamic balance, solidify the optimization results to form a stable governance framework, and record the optimized pollution diffusion matrix , income collection and policy set .

[0013] Optionally, the S6 includes the following steps: S61. Based on the optimized benefit set, strategy set and pollution diffusion matrix, analyze the dynamic change trend of the current governance status and determine the key indicators of whether the governance goals have been achieved; S62. By comparing the time series changes of the income set, evaluate the stability of income distribution and determine whether there is significant income fluctuation; S63, analyzing the time evolution path of the strategy set, and determining whether the strategy set has reached a stable state based on the dynamic gradient of the strategy adjustment; S64. Combined with the dynamic adjustment characteristics of the pollution diffusion matrix, evaluate the changes in the pollution diffusion weight in the time dimension and determine whether the pollution control has achieved the predetermined goal; S65. If the dynamic changes of the benefit set, strategy set or pollution diffusion matrix have not reached a stable state, return to the fracture reconstruction stage to iteratively optimize the benefit distribution, strategy path and pollution diffusion model; S66. After completing the optimization adjustment after each fracture reconstruction, re-evaluate the governance status and determine whether dynamic equilibrium has been achieved through convergence conditions, including the stability of income distribution, the asymptotic nature of strategy adjustment, and the control effect of pollution diffusion; S67. When the governance state reaches dynamic equilibrium, the final benefit set, strategy set and pollution diffusion matrix are solidified, and the convergence results of the governance model are recorded to provide a basis for the subsequent adjustment of dynamically changing governance objectives.

[0014] The beneficial effects of the present invention are: This paper proposes a collaborative governance method for cross-border water resource pollution based on dynamic game theory. By building a dynamic game model, defining the benefit function, strategy set and pollution diffusion matrix of the governance subject, and using a dynamic game algorithm to optimize the benefit distribution and strategy adjustment path. This method can dynamically respond to the spatiotemporal changes of pollution diffusion, achieve fair cooperation among cross-regional governance subjects, avoid the rupture of cooperation caused by imbalance of benefits in the traditional governance model, and improve governance stability.

[0015] The present invention introduces a dynamic rupture-reconstruction game algorithm, sets a rupture trigger mechanism, monitors the imbalance of income distribution, the excessive pollution diffusion or the stagnant state of strategy evolution in real time, and triggers the rupture mechanism when the cooperation is unbalanced, freezes the existing strategy, and re-optimizes the income distribution and governance strategy. Through this method, the free-riding phenomenon in cross-border governance can be effectively suppressed, the continuous investment of governance entities can be promoted, and the overall pollution control effect can be improved.

[0016] The present invention constructs a pollution diffusion matrix, a responsibility allocation matrix and a resource allocation matrix, and dynamically adjusts them through a governance cost optimization mechanism to achieve a reasonable allocation of responsibilities and resources. Compared with traditional static pollution control methods, this method can dynamically adjust governance responsibilities and resource flows, improve the accuracy of pollution diffusion suppression, and enhance the coordination of cross-border governance.

[0017] The present invention adopts a dynamic update mechanism for the strategy evolution path, performs iterative optimization based on the dynamic changes of pollution diffusion, the results of benefit reconstruction and the governance cost, and ensures the dynamic convergence of the governance strategy. By combining the feedback mechanism with the dynamic optimization model, the pollution control plan can gradually approach the optimal in a complex environment, improving the adaptability and long-term stability of the governance strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings: Figure 1 This is a flow chart of the collaborative governance method for transboundary water resource pollution based on dynamic game theory proposed by the present invention; Figure 2 A schematic diagram of the construction of a dynamic game model in the present invention; Figure 3 This is a logical diagram of the dynamic fracture-reconstruction game algorithm adopted by the present invention. DETAILED DESCRIPTION

[0019] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0020] refer to Figure 1-3 , a collaborative governance method for transboundary water pollution based on dynamic game theory includes the following steps: S1. Construct a dynamic game model, define the benefit function, strategy set and pollution diffusion matrix of the governance subject, and describe the dynamic behavior relationship and cooperation constraints between subjects; S2. Based on the dynamic game algorithm, establish a strategy evolution mechanism, dynamically calculate the impact of pollution diffusion on governance benefits and costs, and optimize the benefit distribution and strategy adjustment path; S3. Introduce a dynamic break-reconstruction game algorithm and set a break trigger mechanism to determine the conditions for cooperation break and freeze the existing strategy by monitoring the imbalance of income distribution, excessive pollution diffusion or stagnation of strategy evolution; S4. After the fracture state is triggered, by reconstructing the benefit distribution and strategy set, based on the pollution diffusion matrix and governance costs, the responsibility distribution and resource allocation of each governance subject are optimized to form a new cooperation framework; S5. Combine the reconstructed cooperation model and the dynamic changes of pollution diffusion to optimize and adjust the governance strategy and dynamically update the strategy evolution path; S6. Determine the dynamic convergence state of the governance strategy, and adjust the benefits and strategies to see whether a stable equilibrium has been achieved. If not, return to the fracture reconstruction stage and continue to optimize the model and strategy until dynamic equilibrium and governance goals are achieved.

[0021] In this implementation, S1 includes the following steps: S11. Determine the number of governance entities within the governance area and define the governance entity set in Indicates the total number of governance entities; S12. Define the benefit function for each governance entity ; S13. Define the policy set of governance entities , the strategy set includes pollution reduction efforts , Resource Allocation Priority and other governance-related strategies; S14. Constructing a pollution diffusion matrix in Indicates time Internal pollutants from the main governance The region to the governance body The diffusion effect of the region, the matrix elements satisfy and ; S15. Profit function The pollution diffusion effect in is expressed as ,in, From the main body To the subject The impact of pollution diffusion, As the main A collection of governance policies; S16. Set up cooperation constraints between governance entities and allocate responsibility through the cooperation responsibility matrix Represents that the matrix element satisfy and , used to define the governance resource allocation relationship between entities; S17. Complete the initialization of the multi-agent dynamic game model through the joint description of the profit function, strategy set, pollution diffusion matrix and cooperation constraint matrix.

[0022] In this implementation, S2 includes the following steps: S21. Based on the dynamic game algorithm, a dynamic evolution model of the governance subject's benefits is constructed. The dynamic formula of benefits is: ; in, Representing the subject In time of income, and are the input and output weights of pollution diffusion, For governance strategies, For governance costs, and is the income adjustment factor; S22. Based on the dynamic evolution model of returns, a strategy evolution mechanism is constructed. The strategy update formula is: ; in, As the main In time The strategy value of is the revenue-driven adjustment factor, is the diffusion weight influencing factor, As the main The gradient of the reward function, represents the interactive impact of strategies on the returns of other entities; S23, dynamically adjust the pollution diffusion matrix and update the diffusion weight; S24. Based on the dynamic evolution of strategies and benefits, combined with the time adjustment of the diffusion matrix, the benefit distribution path between governance entities is optimized to dynamically reduce the negative impact of pollution diffusion on benefits; S25. Dynamically balance the distribution relationship between benefits and costs by adjusting the strategy set and diffusion weights through multi-stage iterations; S26. Determine the convergence state of governance benefits and strategy paths. If the preset equilibrium conditions are met, stop the evolution process and output the optimization results. S27. Complete the dynamic adjustment of strategy evolution and benefit distribution, and optimize the impact of pollution diffusion on governance benefits.

[0023] In this implementation, S3 includes the following steps: S31. Based on the dynamic fracture-reconstruction game algorithm, define the trigger conditions for income imbalance, combine the dynamic evolution of income and distribution differences, and establish an income imbalance model: ; in, Represents the income imbalance, As the main of income, Representing the subject With the subject The cooperation weight, is the total number of subjects, is the income imbalance threshold, which indicates the maximum income deviation that the system can tolerate; the threshold calculation formula is: ; is the adjustment coefficient, obtained by fitting historical data, which indicates the tolerance range of the governance system to uneven distribution of benefits; is the standard deviation of the return, reflecting the degree of dispersion of the global return distribution; when When , the income imbalance break condition is triggered; S32. Combined with the time dynamic characteristics of the pollution diffusion matrix, define the diffusion over-limit triggering conditions, and construct the diffusion over-limit model through the change of diffusion intensity between subjects: ; in, Indicates time main body To the subject The pollution diffusion weight, and is the policy value of the subject, is the diffusion dynamic adjustment factor, is the diffusion excess dynamic intensity, is the diffusion limit threshold, which indicates the maximum tolerable intensity of pollution diffusion; the threshold calculation formula is: ; is the adjustment coefficient, is the maximum value of the pollution diffusion matrix; when When , the diffusion over-limit fracture condition is triggered; S33. Define the triggering condition of strategy evolution stagnation. By monitoring the time change of the strategy gradient, determine whether there is a phenomenon of strategy adjustment stagnation. The strategy evolution stagnation model is: ; in, Indicates time The mean of the dynamic adjustment of the strategy, As the main The temporal gradient of the policy, is the strategy evolution stagnation threshold, which indicates the minimum dynamic change range of strategy adjustment; the threshold calculation formula is: ; is the adjustment coefficient, represents the time average of the policy gradient; when When , the strategy evolution stagnation fracture condition is triggered; S34. Construct a comprehensive fracture trigger model, combining the multi-dimensional impact of return imbalance, diffusion overlimit and strategy evolution stagnation, and the comprehensive trigger function is: ; in, Indicates the comprehensive fracture trigger value, , , are the weight factors of return imbalance, diffusion excess and strategy stagnation, is the comprehensive trigger threshold, which indicates the critical value of the comprehensive fracture condition; the threshold calculation formula is: ; is the comprehensive regulatory factor; When the fracture mechanism is triggered; S35, freeze the current state, record the strategy set, pollution diffusion matrix and benefit distribution matrix, and define the frozen matrix as ;in, The state of the frozen moment, is a set of strategies, is the diffusion matrix, is the profit allocation matrix; S36, based on the frozen state, restructure the benefits and redistribute the benefits of the subject to restore the cooperative balance; S37. Based on the state after the profit reconstruction, dynamically optimize the strategy set and adjust the optimization strategy path according to the gradient.

[0024] In this implementation, S4 includes the following steps: S41. Freeze the current cooperation status and record the freeze matrix , freeze strategy set Pollution Diffusion Matrix and income collection ; S42, Freezing-based Pollution Diffusion Matrix and governance cost matrix , define the reconstruction income distribution model, optimize the main income through the dynamic adjustment mechanism, and reconstruct the income distribution model as follows: ; in, As the main The post-reconstruction benefit is is the income adjustment factor, is the governance cost adjustment coefficient, and are the output and input weights of pollution diffusion, As the main To the subject allocation of governance costs; S43. Constructing a responsibility allocation matrix Based on the pollution diffusion matrix and the benefit reconstruction results, the responsibility allocation is dynamically optimized. The calculation formula of the responsibility allocation matrix is: ; in, Representing the subject To the subject The proportion of responsibility distribution, Dynamic adjustment factors for responsibility allocation, Ensure that the total allocation is 1; S44. Re-optimize the resource allocation matrix , combined with the distribution of governance costs and benefits, dynamically adjust the resource allocation path, and the calculation formula of the resource allocation matrix is: ; in, Representing the subject Assign to subject The proportion of resources S45. Combine the responsibility allocation matrix and resource allocation matrix to form a new cooperation framework, and dynamically adjust the cooperation strategy through the strategy set update formula; S46. Through strategy set , Responsibility Allocation Matrix and resource allocation matrix to form a new framework for cooperation.

[0025] In this implementation, S5 includes the following steps: S51, based on the reconstructed pollution diffusion matrix , Responsibility Allocation Matrix and resource allocation matrix , comprehensively analyze the distribution of benefits, responsibility and resource utilization of the governance subject, and determine the starting point for optimization; S52. Strategy set reconstructed through analysis , combined with the dynamic income change model , evaluate the impact of existing strategies on returns and diffusion control, and generate strategy optimization parameters; S53. Build a governance efficiency improvement model by dynamically adjusting the strategy set Optimize governance efficiency by combining the various components of the , including pollution reduction efforts and resource allocation priorities; S54. Based on the responsibility allocation matrix and resource allocation matrix , adjust the intensity of collaboration between entities, dynamically allocate governance resources, and optimize the inhibitory effect of governance strategies on pollution spread; S55. Combined with the strategy evolution mechanism of the dynamic game algorithm, the strategy set of the subject is updated, and the new strategy set Optimize and adjust by comprehensively considering the dynamic changes of pollution diffusion, the results of benefit reconstruction and the cost of governance; S56. Dynamically monitor the optimized policy path and determine whether the policy adjustment achieves the expected goal through the governance efficiency evaluation index. If not, iteratively update the policy path and continuously optimize the governance model. S57. After the strategy path reaches a dynamic balance, solidify the optimization results to form a stable governance framework, and record the optimized pollution diffusion matrix , income collection and policy set .

[0026] In this implementation, S6 includes the following steps: S61. Based on the optimized benefit set, strategy set and pollution diffusion matrix, analyze the dynamic change trend of the current governance status and determine the key indicators of whether the governance goals have been achieved; S62. By comparing the time series changes of the income set, evaluate the stability of income distribution and determine whether there is significant income fluctuation; S63, analyzing the time evolution path of the strategy set, and determining whether the strategy set has reached a stable state based on the dynamic gradient of the strategy adjustment; S64. Combined with the dynamic adjustment characteristics of the pollution diffusion matrix, evaluate the changes in the pollution diffusion weight in the time dimension and determine whether the pollution control has achieved the predetermined goal; S65. If the dynamic changes of the benefit set, strategy set or pollution diffusion matrix have not reached a stable state, return to the fracture reconstruction stage to iteratively optimize the benefit distribution, strategy path and pollution diffusion model; S66. After completing the optimization adjustment after each fracture reconstruction, re-evaluate the governance status and determine whether dynamic equilibrium has been achieved through convergence conditions, including the stability of income distribution, the asymptotic nature of strategy adjustment, and the control effect of pollution diffusion; S67. When the governance state reaches dynamic equilibrium, the final benefit set, strategy set and pollution diffusion matrix are solidified, and the convergence results of the governance model are recorded to provide a basis for the subsequent adjustment of dynamically changing governance objectives.

[0027] Embodiment 1: This method first constructs a pollution diffusion model and uses hydrological monitoring data to establish a pollution diffusion matrix to truly reflect the diffusion of pollutants. Through years of water quality monitoring data, it is found that pollutants discharged from upstream city A have a certain hysteresis effect and cumulative effect in the water body. It takes 3-5 days for the pollution load to be transmitted to downstream city B, and 7-9 days to reach city C. In addition, different pollutants have different diffusion rates. For example, the degradation cycle of ammonia nitrogen is about 7 days, while total phosphorus may remain in sediments for several months or even longer due to its strong adsorption.

[0028] In terms of the allocation of governance responsibilities, traditional methods often only apportion the total amount of pollution emissions, while the present invention adopts a dynamic game optimization strategy to construct a benefit function between governance entities to achieve the economic feasibility and balance of pollution control. According to the optimization calculation of this method, the governance cost borne by City A is 52% of the total pollution control cost, City B is 30%, and City C is 18%. Compared with the traditional static governance scheme, this method makes the distribution of governance costs more fair and avoids the problem of downstream areas unilaterally bearing high governance costs.

[0029] The introduction of the dynamic fracture-reconstruction game algorithm enables the governance strategy to automatically trigger the fracture mechanism and adjust the cooperation model when the pollution diffusion intensity exceeds the threshold, the benefit distribution is unbalanced, or the strategy adjustment is stagnant. For example, in the first governance cycle (6 months), City A originally planned to reduce pollution emissions by 20%, but because some companies failed to strictly implement emission reduction measures, the pollution spread exceeded expectations, triggering the fracture mechanism. After the fracture is triggered, the system automatically adjusts the pollution control responsibility. City A increases its governance investment to reduce pollution by 30%. At the same time, City B and City C provide technical support and optimize the ecological restoration measures of downstream water bodies.

[0030] In terms of optimizing the strategy evolution path, this method combines the dynamic optimization algorithm to monitor the strategy convergence in real time. The experimental results show that after the third fracture-reconstruction adjustment, the governance strategies of each region tend to be stable, the pollutant reduction rate reaches the target requirement, and the governance cost is reduced by 12.5% ​​compared with the traditional model. In addition, through dynamic optimization of resource allocation, the operating efficiency of the newly added sewage treatment plant in City A has increased by 18%, and the water quality compliance rate in City B and City C has increased by 22%.

[0031] Concrete data demonstrating beneficial effects During the application of this invention, we monitored the changes in multiple water quality indicators and collected key data such as treatment costs and pollution load reduction rates. The following table shows the changes in key indicators at different treatment stages: Table 1 Water quality changes (mg / L)

[0032] Table 2 Distribution of governance costs (unit: 10,000 yuan)

[0033] Table 3 Pollutant reduction rate (%)

[0034] The application of the present invention shows that by optimizing the cross-border water pollution control strategy through dynamic game theory, the control efficiency has been significantly improved, and the water quality has been significantly improved. Compared with the traditional control model, this method reduces the control cost, improves the fairness of benefit distribution, and enhances the dynamic adaptability of the control plan to environmental changes. The pollutant concentration has decreased, and the water quality has returned to the Class III water standard. At the same time, the control cost distribution of each region is more reasonable, and the stability of cross-regional cooperation has been significantly improved.

[0035] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A collaborative governance method for transboundary water resource pollution based on dynamic game theory, characterized by: The following steps are involved: S1. Construct a dynamic game model, define the benefit function, strategy set and pollution diffusion matrix of the governance subject, and describe the dynamic behavior relationship and cooperation constraints between subjects; S2. Based on the dynamic game algorithm, establish a strategy evolution mechanism, dynamically calculate the impact of pollution diffusion on governance benefits and costs, and optimize the benefit distribution and strategy adjustment path; S3. Introduce a dynamic break-reconstruction game algorithm and set a break trigger mechanism to determine the conditions for cooperation break and freeze the existing strategy by monitoring the imbalance of income distribution, excessive pollution diffusion or stagnation of strategy evolution; S4. After the fracture state is triggered, by reconstructing the benefit distribution and strategy set, based on the pollution diffusion matrix and governance costs, the responsibility distribution and resource allocation of each governance subject are optimized to form a new cooperation framework; S5. Combine the reconstructed cooperation model and the dynamic changes of pollution diffusion to optimize and adjust the governance strategy and dynamically update the strategy evolution path; S6. Determine the dynamic convergence state of the governance strategy, and adjust the benefits and strategies to see whether a stable equilibrium has been achieved. If not, return to the fracture reconstruction stage and continue to optimize the model and strategy until dynamic equilibrium and governance goals are achieved.

2. The collaborative management method for transboundary water resource pollution based on dynamic game theory according to claim 1 is characterized in that: The S1 comprises the following steps: S11. Determine the number of governance entities within the governance area and define the governance entity set in Indicates the total number of governance entities; S12. Define a benefit function for each governance entity ; S13. Define the policy set of governance entities , the strategy set includes pollution reduction efforts , Resource Allocation Priority and other governance-related strategies; S14. Constructing a pollution diffusion matrix in Indicates time Internal pollutants from the main governance The region to the governance body The diffusion effect of the region, the matrix elements satisfy and ; S15. Profit function The pollution diffusion effect in is expressed as ,in, From the main body To the subject The impact of pollution diffusion, Main body A collection of governance policies; S16. Set up cooperation constraints between governance entities and allocate responsibility through the cooperation responsibility matrix Represents that the matrix element satisfy and , used to define the governance resource allocation relationship between entities; S17. Complete the initialization of the multi-agent dynamic game model through the joint description of the profit function, strategy set, pollution diffusion matrix and cooperation constraint matrix.

3. The collaborative management method for transboundary water resource pollution based on dynamic game theory according to claim 1 is characterized in that: The S2 comprises the following steps: S21. Based on the dynamic game algorithm, a dynamic evolution model of the governance subject's benefits is constructed. The dynamic formula of benefits is: ； in, Representation subject In time of income, and are the input and output weights of pollution diffusion, For governance strategies, For governance costs, and is the income adjustment factor; S22. Based on the dynamic evolution model of returns, a strategy evolution mechanism is constructed. The strategy update formula is: ； in, Main body In time The strategy value of is the revenue-driven adjustment factor, is the diffusion weight influencing factor, Main body The gradient of the reward function, represents the interactive impact of strategies on the returns of other entities; S23, dynamically adjust the pollution diffusion matrix and update the diffusion weight; S24. Based on the dynamic evolution of strategies and benefits, combined with the time adjustment of the diffusion matrix, the benefit distribution path between governance entities is optimized to dynamically reduce the negative impact of pollution diffusion on benefits; S25. Dynamically balance the distribution relationship between benefits and costs by adjusting the strategy set and diffusion weights through multi-stage iterations; S26. Determine the convergence state of governance benefits and strategy paths. If the preset equilibrium conditions are met, stop the evolution process and output the optimization results. S27. Complete the dynamic adjustment of strategy evolution and benefit distribution, and optimize the impact of pollution diffusion on governance benefits.

4. The collaborative management method for transboundary water resource pollution based on dynamic game theory according to claim 1 is characterized in that: The S3 comprises the following steps: S31. Based on the dynamic fracture-reconstruction game algorithm, define the trigger conditions for income imbalance, combine the dynamic evolution of income and distribution differences, and establish an income imbalance model: ； in, Represents the income imbalance, Main body of income, Representation subject With the subject The cooperation weight, is the total number of subjects, is the income imbalance threshold, which indicates the maximum income deviation that the system can tolerate; the threshold calculation formula is: ; is the adjustment coefficient, obtained by fitting historical data, which indicates the tolerance range of the governance system to uneven distribution of benefits; is the standard deviation of the return, reflecting the degree of dispersion of the global return distribution; when When , the income imbalance break condition is triggered; S32. Combined with the time dynamic characteristics of the pollution diffusion matrix, define the diffusion over-limit triggering conditions, and construct the diffusion over-limit model through the change of diffusion intensity between the subjects: ； in, Indicates time main body To the subject The pollution diffusion weight, and is the policy value of the subject, is the diffusion dynamic adjustment factor, is the diffusion excess dynamic intensity, is the diffusion limit threshold, which indicates the maximum tolerable intensity of pollution diffusion; the threshold calculation formula is: ; is the adjustment coefficient, is the maximum value of the pollution diffusion matrix; when When , the diffusion over-limit fracture condition is triggered; S33. Define the triggering condition of strategy evolution stagnation. By monitoring the time change of the strategy gradient, determine whether there is a phenomenon of strategy adjustment stagnation. The strategy evolution stagnation model is: ； in, Indicates time The mean of the dynamic adjustment of the strategy, Main body The temporal gradient of the policy, is the strategy evolution stagnation threshold, which indicates the minimum dynamic change range of strategy adjustment; the threshold calculation formula is: ; is the adjustment coefficient, represents the time average of the policy gradient; when When , the strategy evolution stagnation fracture condition is triggered; S34. Construct a comprehensive fracture trigger model, combining the multi-dimensional impact of return imbalance, diffusion overlimit and strategy evolution stagnation, and the comprehensive trigger function is: ； in, Indicates the comprehensive fracture trigger value, , , are the weight factors of return imbalance, diffusion excess and strategy stagnation, is the comprehensive trigger threshold, which indicates the critical value of the comprehensive fracture condition; the threshold calculation formula is: ; is the comprehensive regulatory factor; When the fracture mechanism is triggered; S35, freeze the current state, record the strategy set, pollution diffusion matrix and benefit distribution matrix, and define the frozen matrix as ;in, The state of the frozen moment, is a set of strategies, is the diffusion matrix, is the profit allocation matrix; S36, based on the frozen state, restructure the benefits and redistribute the benefits of the subject to restore the cooperative balance; S37. Based on the state after the profit reconstruction, dynamically optimize the strategy set and adjust the optimization strategy path according to the gradient.

5. The collaborative management method for transboundary water resource pollution based on dynamic game theory according to claim 1 is characterized in that: The S4 comprises the following steps: S41. Freeze the current cooperation status and record the freeze matrix , freeze strategy set Pollution Diffusion Matrix and income collection ; S42. Freezing-based pollution diffusion matrix and governance cost matrix , define the reconstruction income distribution model, optimize the main income through the dynamic adjustment mechanism, and reconstruct the income distribution model as follows: ； in, Main body The post-reconstruction benefit is is the income adjustment factor, is the governance cost adjustment coefficient, and are the output and input weights of pollution diffusion, Main body To the subject allocation of governance costs; S43. Constructing a responsibility allocation matrix Based on the pollution diffusion matrix and the benefit reconstruction results, the responsibility allocation is dynamically optimized. The calculation formula of the responsibility allocation matrix is: ； in, Representation subject To the subject The proportion of responsibility distribution, Dynamic adjustment factors for responsibility allocation, Ensure that the total allocation is 1; S44. Re-optimize the resource allocation matrix , combined with the distribution of governance costs and benefits, dynamically adjust the resource allocation path, and the calculation formula of the resource allocation matrix is: ； in, Representation subject Assign to subject The proportion of resources S45. Combine the responsibility allocation matrix and resource allocation matrix to form a new cooperation framework, and dynamically adjust the cooperation strategy through the strategy set update formula; S46. Through strategy set , Responsibility Allocation Matrix and resource allocation matrix to form a new framework for cooperation.

6. The collaborative management method for transboundary water resource pollution based on dynamic game theory according to claim 1 is characterized in that: The S5 comprises the following steps: S51, based on the reconstructed pollution diffusion matrix , Responsibility Allocation Matrix and resource allocation matrix , comprehensively analyze the distribution of benefits, responsibility and resource utilization of the governance subject, and determine the starting point for optimization; S52. Strategy set reconstructed through analysis , combined with the dynamic income change model , evaluate the impact of existing strategies on returns and diffusion control, and generate strategy optimization parameters; S53. Build a governance efficiency improvement model by dynamically adjusting the strategy set Optimize governance efficiency by combining the various components of the , including pollution reduction efforts and resource allocation priorities; S54. Based on the responsibility allocation matrix and resource allocation matrix , adjust the intensity of collaboration between entities, dynamically allocate governance resources, and optimize the inhibitory effect of governance strategies on pollution spread; S55. Combined with the strategy evolution mechanism of the dynamic game algorithm, the strategy set of the subject is updated, and the new strategy set Optimize and adjust by comprehensively considering the dynamic changes of pollution diffusion, the results of benefit reconstruction and the cost of governance; S56. Dynamically monitor the optimized policy path and determine whether the policy adjustment achieves the expected goal through the governance efficiency evaluation index. If not, iteratively update the policy path and continuously optimize the governance model. S57. After the strategy path reaches a dynamic balance, solidify the optimization results to form a stable governance framework, and record the optimized pollution diffusion matrix , income collection and strategy set .

7. The collaborative management method for transboundary water resource pollution based on dynamic game theory according to claim 1 is characterized in that: The S6 comprises the following steps: S61. Based on the optimized benefit set, strategy set and pollution diffusion matrix, analyze the dynamic change trend of the current governance status and determine the key indicators of whether the governance goals have been achieved; S62. By comparing the time series changes of the income set, evaluate the stability of income distribution and determine whether there is significant income fluctuation; S63, analyzing the time evolution path of the strategy set, and determining whether the strategy set has reached a stable state based on the dynamic gradient of the strategy adjustment; S64. Combined with the dynamic adjustment characteristics of the pollution diffusion matrix, evaluate the changes in the pollution diffusion weight in the time dimension and determine whether the pollution control has achieved the predetermined goal; S65. If the dynamic changes of the benefit set, strategy set or pollution diffusion matrix have not reached a stable state, return to the fracture reconstruction stage to iteratively optimize the benefit distribution, strategy path and pollution diffusion model; S66. After completing the optimization adjustment after each fracture reconstruction, re-evaluate the governance status and determine whether dynamic equilibrium has been achieved through convergence conditions, including the stability of income distribution, the asymptotic nature of strategy adjustment, and the control effect of pollution diffusion; S67. When the governance state reaches dynamic equilibrium, the final benefit set, strategy set and pollution diffusion matrix are solidified, and the convergence results of the governance model are recorded to provide a basis for the subsequent adjustment of dynamically changing governance objectives.

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