Water price evolution method and terminal device based on multi-agent game of water supply project

Abstract

The application discloses a water price evolution method and terminal equipment based on a multi-agent game of a water supply project, belongs to the technical field of intelligent optimization, and can solve the problem that existing technologies cannot provide dynamic and quantitative strategy support, resulting in that the formulation of core clauses of a concession contract is highly dependent on subjective experience and static judgment and is difficult to adapt to negotiation requirements of a water supply project. The method comprises the following steps: S1, determining a full-cost water price prediction interval of a target region according to multi-dimensional basic data of the target region; S2, determining each agent in the water supply project and a corresponding strategy set of the agent, and determining a payment function of each agent under different strategy combinations according to the corresponding strategy set of the agent; S3, constructing a replicator dynamic equation of the corresponding agent according to the payment function of each agent; and S4, determining a water price evolution stable interval of the target region according to the full-cost water price prediction interval and the replicator dynamic equation of all agents. The application is used for water price evolution of a water supply project.

Description

Technical Field

[0001] This invention relates to a water price evolution method and terminal equipment based on multi-stakeholder game theory in water supply projects, belonging to the field of intelligent optimization technology. Background Technology

[0002] Water supply infrastructure concession contracts typically last 20 to 30 years. Current technologies for water price forecasting primarily employ full-cost water pricing models or long-term marginal cost methods for static or semi-static calculations, lacking the ability to dynamically predict water price trends during the contract period. This makes it difficult to quantify the long-term impact of uncertainties such as policy, inflation, and demand fluctuations. Regarding game theory analysis, while some studies have introduced evolutionary game models to analyze the behavioral strategies of governments, water supply companies, and water users, the payment matrix parameters are often subjectively assigned by researchers, lacking a coupling mechanism with objective cost and price data. Furthermore, the formulation of core clauses in concession contracts, such as price adjustment mechanisms, risk sharing, and revenue guarantees, mainly relies on the experience and judgment of project financing, legal advisors, and negotiation experts, failing to develop systematic quantitative decision-making tools.

[0003] In summary, existing technologies suffer from three main shortcomings: first, they lack scientific forecasting tools capable of generating dynamic water price sequences throughout the contract period; second, game theory analysis remains theoretical, with parameters artificially set and lacking objective coupling with cost and price data; and third, they fail to systematically integrate water price forecasting, tripartite game theory, and contract strategy generation. Therefore, existing technologies cannot provide dynamic and quantitative strategic support for negotiating parties (especially private capital parties), leading to a high reliance on subjective experience and static judgment in the formulation of core concession agreement terms, making it difficult to adapt to the negotiation needs of long-term, highly uncertain water supply projects. Summary of the Invention

[0004] This invention provides a water price evolution method and terminal equipment based on multi-party game theory in water supply projects. It can solve the problem that existing technologies cannot provide dynamic and quantitative strategy support, which leads to the formulation of core terms of concession contracts relying heavily on subjective experience and static judgment, making it difficult to adapt to the negotiation needs of long-term and highly uncertain water supply projects.

[0005] On the one hand, this invention provides a water price evolution method based on multi-stakeholder game theory in water supply projects, the method comprising: S1. Determine the full-cost water price prediction range for the target area based on multi-dimensional basic data of the target area; S2. Determine the entities in the water supply project and their corresponding strategy sets, and determine the payoff function for each entity under different strategy combinations based on the strategy sets corresponding to each entity. S3. Construct the corresponding replication dynamic equation for each entity based on its payment function; S4. Based on the full-cost water price prediction range and the replication dynamic equations of all subjects, determine the stable range of water price evolution in the target area.

[0006] Optionally, after S4, the method further includes: Based on the total cost water price prediction range and the water price evolution stability range, the pricing potential coefficient of the target area is determined; The water price in the target area is assessed based on the pricing potential coefficient.

[0007] Optionally, S1 specifically includes: Based on multi-dimensional basic data of the target area, a full-cost water price prediction model for the target area is constructed. Determine the water price sensitive parameters, and based on the water price sensitive parameters and the full-cost water price prediction model, determine the full-cost water price prediction range for the target area.

[0008] Optionally, the multi-dimensional basic data includes engineering economic data, resource and environmental data, and socio-economic forecast data; Based on multi-dimensional basic data of the target area, a full-cost water price prediction model for the target area is constructed, specifically including: The static full-cost water price for the target area is determined based on the engineering economic data and the resource and environmental data. Based on the static full-cost water price and the socio-economic forecast data, a full-cost water price prediction model for the target area is constructed.

[0009] Optionally, based on the static full-cost water price and the socio-economic forecast data, a full-cost water price prediction model for the target area is constructed, specifically including: Based on the static full-cost water price and the socio-economic forecast data, resource water price prediction sub-model, engineering water price prediction sub-model, environmental water price prediction model and water-saving water price prediction model are constructed respectively. The resource water price prediction sub-model, the engineering water price prediction sub-model, the environmental water price prediction sub-model, and the water-saving water price prediction sub-model are summed to obtain the full-cost water price prediction model for the target area.

[0010] Optionally, based on the water price sensitivity parameter and the full-cost water price prediction model, the full-cost water price prediction range for the target area is determined, specifically including: The water price sensitive parameters are used to drive the full-cost water price prediction model to perform multiple simulations, resulting in multiple simulation results. Calculate the 90% confidence intervals for all simulation results, and use the 90% confidence intervals as the full-cost water price prediction intervals for the target area.

[0011] Optionally, S4 specifically includes: Determine the replication dynamic equations of all subjects corresponding to the minimum value of the full-cost water price prediction interval, form the first dynamic equation set, and solve the first dynamic equation set to obtain the stable minimum value of water price evolution. The replication dynamic equations of all subjects corresponding to the maximum value of the full-cost water price prediction interval are determined to form a second dynamic equation set, and the second dynamic equation set is solved to obtain the maximum stable value of water price evolution; the minimum stable value of water price evolution and the maximum stable value of water price evolution constitute the stable water price evolution interval of the target area.

[0012] Optionally, based on the full-cost water price prediction range and the water price evolution stability range, the pricing potential coefficient of the target area is determined, specifically including: Calculate the ratio of the median of the stable water price evolution interval to the median of the full-cost water price prediction interval, and use the ratio as the pricing potential coefficient of the target area.

[0013] Optionally, the water price sensitive parameters include the per capita GDP growth rate, the labor cost growth rate, the electricity cost growth rate, and the water demand price elasticity coefficient.

[0014] On the other hand, the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the water price evolution method based on multi-agent evolutionary game of water supply engineering as described above.

[0015] The beneficial effects that this invention can produce include: This invention provides a water price evolution method based on multi-party game theory in water supply projects, constructing a three-party evolutionary game model with the government, water supply companies, and water users as the main participants. Unlike traditional game models, the payoff function in this invention's game model is not artificially set, but directly derived from the calculation results and full-cost water price prediction range of the full-cost water price prediction model. This parameter coupling mechanism ensures that the input of the game model has an objective data basis, rather than relying on subjective assignment, thereby enhancing the credibility and scientific rigor of the game analysis results.

[0016] The water price evolution method based on multi-party game theory in water supply projects provided by this invention transforms the game equilibrium result into a market pricing potential coefficient. The stable water price evolution range obtained by solving the three-party evolutionary game is... This is transformed into a pricing potential coefficient λ, which serves as a key parameter for subsequent strategy optimization models. Attached Figure Description

[0017] Figure 1A flowchart of a water price evolution method based on multi-stakeholder game theory in water supply projects, provided for embodiments of the present invention. Detailed Implementation

[0018] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0019] This invention provides a water price evolution method based on multi-stakeholder game theory in water supply projects, such as... Figure 1 As shown, the method includes: S1. Determine the full-cost water price prediction range for the target area based on multi-dimensional basic data of the target area.

[0020] Specifically, it includes: (1) Based on the multi-dimensional basic data of the target area, construct a full-cost water price prediction model for the target area; among which, the multi-dimensional basic data includes engineering economic data, resource and environmental data, and socio-economic prediction data.

[0021] In this embodiment, multi-dimensional basic data of the target area is obtained, including: the original value of fixed assets of water supply projects, depreciation period, annual operating costs (labor, electricity, chemicals), annual water supply, comprehensive tax rate, social discount rate, per capita water resources, water quality standards, water resources development and utilization rate, ecological environment water demand satisfaction, unit sewage treatment cost, sewage discharge rate, residential water quota, per capita comprehensive water consumption, residential water consumption, industrial water consumption, agricultural water consumption, ecological water consumption, water demand price elasticity coefficient, water demand income elasticity coefficient, and the region's total population forecast, per capita GDP growth rate, and per capita disposable income forecast for urban residents for the next 5-30 years.

[0022] Specifically: 1) Determine the static full-cost water price for the target area based on engineering economic data and resource and environmental data.

[0023] Based on engineering economic data and resource and environmental data, calculate the static resource water price, static engineering water price, static environmental water price, and static water-saving water price respectively. Then, sum these four to obtain the static full-cost water price for the target area.

[0024] Among them, the static resource water price, static engineering water price, static environmental water price, and static water-saving water price can be calculated using existing methods, and this invention does not limit them.

[0025] 2) Based on static full-cost water price and socio-economic forecast data, construct a full-cost water price forecast model for the target area.

[0026] In this invention, firstly, based on static full-cost water price and socio-economic forecast data, resource water price prediction sub-models, engineering water price prediction sub-models, environmental water price prediction sub-models, and water-saving water price prediction sub-models are constructed respectively; then, the resource water price prediction sub-models, engineering water price prediction sub-models, environmental water price prediction sub-models, and water-saving water price prediction sub-models are summed to obtain the full-cost water price prediction model for the target area.

[0027] The static full-cost water price calculated in the preceding steps is combined with the obtained socio-economic forecast data to dynamically calculate the predicted water price for each year during the concession period, and a reasonable fluctuation range is proposed. The full-cost water price is decomposed into four dynamic components: resource water price, engineering water price, environmental water price, and water-saving water price. Each component has its own prediction sub-model, which are then combined into a comprehensive full-cost water price.

[0028] a) Construct a sub-model for predicting water prices for resources.

[0029] Water resource prices are mainly affected by the scarcity of water resources, the level of economic development, and population density, and their predictive sub-models... The expression is as follows: ; in, This is the static water resource price, also known as the water resource price for the initial year; This is an adjustment coefficient for water resource scarcity. This refers to the GDP growth rate per capita. The population density elasticity coefficient, with an empirical value range of 0.2-0.5, reflects the amplifying effect of population agglomeration on resource scarcity; For predicting the year (i.e., the year) t Population in (year), This represents the population in the initial year.

[0030] Water resource scarcity adjustment coefficient It is related to the changing trends of per capita water resources and water resources development and utilization rate, and its expression is as follows: ; in, and The per capita water resources for the predicted year and the initial year are respectively; and These represent the water resource development and utilization rates for the predicted year and the initial year, respectively.

[0031] b) Construct a sub-model for predicting water prices for engineering projects.

[0032] The project water price consists of fixed asset depreciation, major repair costs, operating costs, profit, and taxes. Among these, operating costs (labor, electricity, chemicals, maintenance, etc.) are the most dynamic, while depreciation and major repair costs are relatively fixed financially (unless large-scale upgrades or renovations occur). Project Water Price Prediction Sub-model The expression is as follows: ; in, Depreciation expense for fixed assets; Major repair costs for buildings or equipment; For the predicted annual operating costs; To predict profits for the year; Forecast taxes for the year; To predict the annual water supply for a given year.

[0033] The dynamic prediction of each component is described below.

[0034] Annual operating costs for the forecast year The expression is as follows: ; in, The annual operating cost for the initial year; , , , These represent the percentages of labor costs, electricity costs, pharmaceutical costs, and maintenance costs to operating costs in the initial year, and... ; , , , These are the projected growth rates for labor costs, electricity costs, pharmaceutical costs, and maintenance costs for the respective years.

[0035] Annual water supply for the predicted year The expression is as follows: ; in, The annual water supply for the initial year, also known as the baseline annual water supply; This is the price elasticity coefficient of water demand; To predict the terminal water price of the previous year; This represents the initial year's terminal water price.

[0036] Profit forecast for the year using the cost-plus method. and taxes As the cost base increases linearly, its expression is as follows: ; ; in, Cost-profit margin; This is the combined tax rate.

[0037] c) Construct a sub-model for predicting environmental water prices.

[0038] Environmental water pricing includes wastewater treatment fees, ecological water pricing, and water quality maintenance fees. Its changes are primarily influenced by environmental policies, emission standards, and unit treatment costs. Environmental water pricing prediction sub-model. The expression is as follows: ; in, Wastewater treatment costs for the predicted year; To predict the ecological water price for a given year; Forecast water quality maintenance costs for the year.

[0039] Wastewater treatment fees for the forecast year The expression is as follows: ; in, Wastewater treatment fees for the initial year; This represents the growth rate of environmental governance costs. The cost elasticity coefficient for raising emission standards; A 0-1 variable, representing the first... t Will new emission standards be implemented in the current year (i.e., the predicted year)?

[0040] Ecological water price for the predicted year The expression is as follows: ; in, The ecological water price for the initial year; and These represent the total ecological water deficit for the predicted year and the initial year, respectively. and These represent the unit value of ecological loss for the predicted year and the initial year (linked to GDP growth).

[0041] Predicted annual water quality maintenance costs The expression is as follows: ; in, Water quality maintenance fee for the initial year; This is the penalty coefficient adjustment factor. This indicates whether stricter penalties for exceeding limits will be introduced in the predicted year.

[0042] d) Construct a water-saving price prediction sub-model.

[0043] Water conservation pricing reflects the value of the total social cost invested in achieving water conservation goals, allocated to a unit of water volume. Its dynamic changes are influenced by multiple factors, including advancements in water-saving technologies, policy intensity, and residents' behavioral responses.

[0044] The water price for water conservation will be broken down into five components: direct water conservation costs, residential water conservation costs, water supply enterprise water conservation costs, environmental and social water conservation benefits, and incremental costs over the entire life cycle.

[0045] Direct water savings for the forecast year The portion of the end-user water price used to incentivize water conservation is expressed as follows: ; in, It is the predicted terminal water price for the year (requires iterative calculation); It predicts the amount of water to be saved in a given year; T For the franchise period.

[0046] Predicted residential water saving costs for the year The expression is as follows: ; in, Water savings costs for residents in the initial year; The annual growth rate of investment in water-saving equipment; This is the water conservation policy intensity index.

[0047] The cost of water conservation for residents mainly includes the expenditure on purchasing water-saving appliances, which increases with income growth and policy incentives.

[0048] Water saving costs for water supply companies in the forecast year The expression is as follows: ; in, This will save water costs for water supply companies in the initial year. The proportion of water saved by water supply companies.

[0049] Water supply companies' water-saving costs include investments in pipeline leakage control, zoned metering, and the construction of smart water systems. While unit water-saving costs may decrease with technological advancements, total investment increases as leakage control targets rise.

[0050] Predicted Environmental and Social Water Conservation Benefits for the Year The negative cost, i.e., the positive benefit of water conservation, is expressed as follows: ; in, For the environmental and social water-saving benefits in the initial year; This represents the water savings in the initial year.

[0051] Water conservation reduces wastewater treatment volume and pollutant emissions, thereby lowering environmental governance costs. It is a negative value.

[0052] Predicted annual lifecycle incremental cost The expression is as follows: ; in, The total lifecycle incremental cost for the initial year; The rate of decrease in water-saving technology costs.

[0053] After synthesizing the above prediction components, the water-saving price prediction sub-model is obtained as follows: ; in, This is the total water supply (or total water consumption) for the predicted year.

[0054] f) The full-cost water price prediction model is obtained by combining the results. Its expression is as follows: .

[0055] (2) Determine the water price sensitive parameters, and based on the water price sensitive parameters and the full-cost water price prediction model, determine the full-cost water price prediction range for the target area.

[0056] Among them, water price-sensitive parameters include per capita GDP growth rate, labor cost growth rate, electricity cost growth rate, and water demand price elasticity coefficient.

[0057] Specifically: First, the full-cost water price prediction model is driven by water price sensitive parameters to perform multiple simulations and obtain multiple simulation results; then, the 90% confidence interval of all simulation results is calculated, and the 90% confidence interval is used as the full-cost water price prediction interval for the target area.

[0058] In practical applications, due to the uncertainty of economic forecasting (high, medium, and low scenarios), and the fluctuation range of the growth rate of cost drivers, it is necessary to... Interval estimation is performed. Therefore, three typical scenarios are set up, as shown in Table 1.

[0059] Table 1 Three typical scenarios

[0060] The Monte Carlo simulation method was used to generate the full-cost water price prediction range.

[0061] The key parameters most sensitive to the impact on water prices were selected as random variables, including: GDP growth rate per capita. Assuming a triangular distribution, the minimum, most likely, and maximum values ​​correspond to low, medium, and high scenario growth rates, respectively; labor cost growth rate. :and Highly correlated, with a correlation coefficient of 0.8; electricity price growth rate Water demand price elasticity coefficient follows a triangular distribution with a fluctuation range of ±30%. : Follows a normal distribution, with a mean of -0.2 and a standard deviation of 0.05.

[0062] Using water price-sensitive parameters to drive a full-cost water price prediction model The simulation ( ≥1000): No. In this simulation, the values ​​of each parameter for the current year are randomly selected; the results of this simulation are calculated. And store the simulation results.

[0063] Statistical interval: for each forecast year t ,calculate N 5th percentile of the simulation results and 95th percentile ; We obtained a 90% confidence interval for the future full-cost water price: Simultaneously record the median. Used as a baseline forecast value.

[0064] S2. Determine the entities in the water supply project and their corresponding strategy sets, and based on the strategy sets corresponding to each entity, determine the payoff function for each entity under different strategy combinations.

[0065] The static total cost water price calculated in step 1 and the predicted total cost water price range are combined. As input parameters, an evolutionary game model involving the government, water supply companies, and water users is constructed.

[0066] (1) Basic model settings.

[0067] First, the game players are selected, and their core interests are shown in Table 2.

[0068] Table 2 Core Interests of Each Entity

[0069] Each player has a finite set of possible strategies, as shown in Table 3. The strategy space is designed based on real-world behavioral possibilities.

[0070] Table 3. Strategy Sets of Each Entity

[0071] (2) Construct the payment functions for each subject.

[0072] Quantify the gains (or costs) each entity receives under different strategy combinations. The cost parameters in all payoff functions are derived from the preceding steps.

[0073] 1) Constructing government payment functions .

[0074] The government's benefits are comprehensively considered, including: total social welfare (resident satisfaction, water supply stability), fiscal subsidy expenditures, and political reputation (fairness of price adjustments). The expression for its payoff function is as follows: ; in, This is the water price welfare coefficient; This represents the total amount of government subsidies. = (Considering changes in water consumption due to demand elasticity) The subsidy amount is per unit of water volume. Annual water sales volume This is the price elasticity coefficient of water demand. This represents the relative rate of change in water prices. The subsidy aversion coefficient; If the government adopts weak regulation ( However, the high standards of corporate operations lead to a loss of fairness; This reflects the government's level of attention to social equity. The reputation gained from strong regulation and reasonable price adjustments; This reflects the degree to which the government values ​​its political reputation.

[0075] 2) Construct the payment function for water supply companies .

[0076] ; in, The final water price will be determined by government regulation. ( (Allowing reasonable profits), if regulation is weak... (Possibly below cost); If the price of water at the point of sale is lower than the total cost, the government will provide a subsidy. Operating costs are higher at higher standards and lower at lower standards; For annual investments (such as pipeline renovation), additional investment is required for higher standards.

[0077] 3) Construct the user payment function .

[0078] ; in, The amount of water a user consumes depends on the water price and their willingness to conserve water: if they conserve water... ,otherwise , This represents the actual water sales volume for the current year. Water saving rate; Costs incurred for water conservation (such as purchasing water-saving appliances) only occur when water conservation is chosen. This represents an individual's preference coefficient for environmental protection. The environmental improvement value perceived by users due to water-saving behaviors.

[0079] S3. Construct the corresponding replication dynamic equations for each subject based on the payment function of each subject.

[0080] set up The proportion of governments choosing a "strong regulation" strategy, then It is considered "weak regulation"; set up The proportion of water supply companies selected for "high-standard operation" is... "Low-standard operation"; set up If water users choose a "water-saving" percentage, then This is considered "not conserving water".

[0081] The replication dynamic equations of the three parties are as follows: 1) Construct the replication dynamic equation of the government group.

[0082] Expected benefits of the government choosing strong regulation The expression is as follows: ; Expected benefits of the government choosing weak regulation The expression is as follows: ; Average expected returns of the government group The expression is as follows: ; Then the government's replication dynamic equation The expression is as follows: ; 2) Construct a replication dynamic equation for the water supply enterprise group.

[0083] Define the expected benefits of water supply companies choosing high-standard operations. Choose a lower standard of expected return Average return The replication dynamic equation of the water supply company is obtained. The expression is as follows: ; 3) Construct a replication dynamic equation for the water user group.

[0084] Replication dynamic equations of water users The expression is as follows: ; in, To allow water users to choose their expected benefits from water conservation. To allow water users to choose the expected benefits of not conserving water, This represents the average revenue per water user.

[0085] S4. Based on the full-cost water price forecast range and the replication dynamic equations of all subjects, determine the stable range of water price evolution in the target area.

[0086] Specifically, it includes: First, determine the replication dynamic equations of all subjects corresponding to the minimum value of the full-cost water price prediction interval, form the first dynamic equation set, and solve the first dynamic equation set to obtain the stable minimum value of water price evolution. Then, the replication dynamic equations of all subjects corresponding to the maximum value of the full-cost water price prediction interval are determined to form the second dynamic equation set. The second dynamic equation set is then solved to obtain the maximum stable value of water price evolution. The minimum stable value of water price evolution and the maximum stable value of water price evolution constitute the stable water price evolution interval of the target area.

[0087] 1) Solving for the equilibrium point.

[0088] make This yields the system's equilibrium points. These equilibrium points include eight pure strategy equilibrium points: Several hybrid strategy equilibrium points (satisfying) ).

[0089] By analyzing the local stability of the Jacobian matrix, the stability of each equilibrium point is determined, and the evolutionary stable strategy (ESS) is obtained.

[0090] 2) Stable range of water price evolution The determination.

[0091] The distribution of terminal water prices at stable evolution under different scenarios was obtained through simulation: (The following is a list of parameters, not a direct translation) 5th percentile (i.e. (Low-cost scenario), simulation results ;Pick 50th percentile (i.e. (Base scenario), simulation results ;Pick 95th percentile (i.e. (High-cost scenario), simulation results .

[0092] The final stable range of water price evolution: ; This range reflects the reasonable range within which water prices may stabilize under the influence of market forces.

[0093] Furthermore, after S4, the method further includes: The pricing potential coefficient for the target area is determined based on the full-cost water price forecast range and the stable water price evolution range. Water prices in the target area are assessed based on the pricing potential coefficient.

[0094] Specifically: calculate the ratio of the median of the stable water price evolution range to the median of the full-cost water price prediction range, and use this ratio as the pricing potential coefficient for the target area.

[0095] Will Range and full-cost water price forecast range By comparison, a pricing potential coefficient is defined: ; like This indicates that the equilibrium water price is higher than the full-cost water price, suggesting that the market has strong pricing potential and that private capital can negotiate higher price adjustment coefficients; if This indicates that market forces suppressing water price increases necessitate reliance on government subsidies or extended franchise periods to guarantee revenue; if Market equilibrium and costs are basically consistent, so the strategy should focus on risk control.

[0096] Another embodiment of the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the water price evolution method based on multi-agent evolutionary game of water supply engineering as described above.

[0097] The above descriptions are merely a few embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any modifications or alterations made by those skilled in the art without departing from the scope of the technical solution of the present invention using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for water price evolution based on multi-stakeholder game theory in water supply projects, characterized in that, The method includes: S1. Determine the full-cost water price prediction range for the target area based on multi-dimensional basic data of the target area; S2. Determine the entities in the water supply project and their corresponding strategy sets, and determine the payoff function for each entity under different strategy combinations based on the strategy sets corresponding to each entity. S3. Construct the corresponding replication dynamic equation for each entity based on its payment function; S4. Based on the full-cost water price prediction range and the replication dynamic equations of all subjects, determine the stable range of water price evolution in the target area.

2. The method according to claim 1, characterized in that, Following S4, the method further includes: Based on the total cost water price prediction range and the water price evolution stability range, the pricing potential coefficient of the target area is determined; The water price in the target area is assessed based on the pricing potential coefficient.

3. The method according to claim 1, characterized in that, S1 specifically includes: Based on multi-dimensional basic data of the target area, a full-cost water price prediction model for the target area is constructed. Determine the water price sensitive parameters, and based on the water price sensitive parameters and the full-cost water price prediction model, determine the full-cost water price prediction range for the target area.

4. The method according to claim 3, characterized in that, The multi-dimensional basic data includes engineering economic data, resource and environmental data, and socio-economic forecast data. Based on multi-dimensional basic data of the target area, a full-cost water price prediction model for the target area is constructed, specifically including: The static full-cost water price for the target area is determined based on the engineering economic data and the resource and environmental data. Based on the static full-cost water price and the socio-economic forecast data, a full-cost water price prediction model for the target area is constructed.

5. The method according to claim 4, characterized in that, Based on the static full-cost water price and the socio-economic forecast data, a full-cost water price prediction model for the target area is constructed, specifically including: Based on the static full-cost water price and the socio-economic forecast data, resource water price prediction sub-model, engineering water price prediction sub-model, environmental water price prediction model and water-saving water price prediction model are constructed respectively. The resource water price prediction sub-model, the engineering water price prediction sub-model, the environmental water price prediction sub-model, and the water-saving water price prediction sub-model are summed to obtain the full-cost water price prediction model for the target area.

6. The method according to claim 3, characterized in that, Based on the water price sensitivity parameters and the full-cost water price prediction model, the full-cost water price prediction range for the target area is determined, specifically including: The water price sensitive parameters are used to drive the full-cost water price prediction model to perform multiple simulations, resulting in multiple simulation results. Calculate the 90% confidence intervals for all simulation results, and use the 90% confidence intervals as the full-cost water price prediction intervals for the target area.

7. The method according to claim 1, characterized in that, S4 specifically includes: Determine the replication dynamic equations of all subjects corresponding to the minimum value of the full-cost water price prediction interval, form the first dynamic equation set, and solve the first dynamic equation set to obtain the stable minimum value of water price evolution. The replication dynamic equations of all subjects corresponding to the maximum value of the full-cost water price prediction interval are determined to form a second dynamic equation set, and the second dynamic equation set is solved to obtain the maximum stable value of water price evolution; the minimum stable value of water price evolution and the maximum stable value of water price evolution constitute the stable water price evolution interval of the target area.

8. The method according to claim 2, characterized in that, Based on the total cost water price prediction range and the water price evolution stability range, the pricing potential coefficient of the target area is determined, specifically including: Calculate the ratio of the median of the stable water price evolution interval to the median of the full-cost water price prediction interval, and use the ratio as the pricing potential coefficient of the target area.

9. The method according to claim 3, characterized in that, The water price sensitive parameters include the per capita GDP growth rate, the labor cost growth rate, the electricity cost growth rate, and the water demand price elasticity coefficient.

10. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the water price evolution method based on multi-agent evolutionary game theory in water supply engineering as described in any one of claims 1 to 9.

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