A water resource allocation scheme decision method and system based on multi-agent game

Abstract

The application discloses a water resource allocation scheme decision method and system based on multi-agent game, and relates to the technical and method fields of water resource management. The method comprises the following steps: acquiring a set of water resource allocation schemes of a research area; calculating water use benefits of multi-agents; calculating water use fairness of the multi-agents; determining an allocation scheme preference matrix of the multi-agents; analyzing allocation scheme negotiation spaces of the multi-agents; carrying out multi-agent negotiation based on group decision game; and determining a water resource allocation scheme under game equilibrium. The application is helpful for considering reasonable utilization appeals of each agent, and giving consideration to the distribution fairness of interests and the water resource allocation efficiency in decision making.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical and method field of water resource management, and particularly relates to a water resource allocation scheme decision method and system based on multi-agent game. BACKGROUND

[0002] Water resource allocation is a complex system involving multiple regions, multiple industries and multiple users. Current research on multi-objective optimization of water resource allocation focuses on how to achieve the overall Pareto optimal solution. The influence of competition and cooperation between different regions and different water users on water resource optimization allocation still needs to be further studied. The difference between the theoretical optimal solution of water resource allocation and the actual allocation needs to be bridged. Therefore, solving the problem of water resource allocation needs to fully respect and value all interest demands and strategic interaction characteristics, avoid water-related conflicts through scientific and reasonable institutional arrangements, and realize sustainable development of water resources.

[0003] The present application introduces group decision game method into water resource allocation decision, and proposes a water resource allocation scheme decision method and system based on multi-agent game. From the perspective of game equilibrium of all parties, the greatest common divisor of water resource allocation scheme that meets the interests of all parties is found, and the practicality and feasibility of the final decision scheme are increased.

[0004] The ultimate goal of water resource optimization allocation is to realize the sustainable development of the region, and the game theory provides tools and means for it. The study of the decision-making process of each game agent can reveal the stability and dynamic evolution law, which is crucial for realizing the sustainability and benefit maximization of the allocation result. However, each game agent has different goals and interest preferences, and other external factors (enterprise strategy, political factors, public interest demands, etc.) also affect the game pattern and final decision.

[0005] Therefore, a water resource allocation scheme decision method and system based on multi-agent game is proposed, which considers the reasonable use of demands of each agent in decision-making, and takes into account the fairness of interest distribution and the efficiency of water resource allocation, which is a problem that needs to be solved by those skilled in the art. SUMMARY

[0006] Therefore, the present application provides a water resource allocation scheme decision method and system based on multi-agent game, which helps to take into account the fairness of interest distribution and the efficiency of water resource allocation.

[0007] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0008] A water resource allocation scheme decision method based on multi-agent game comprises the following steps:

[0009] S1, obtaining a set of water resource allocation schemes of a research region to obtain a configuration scheme matrix of the research region;

[0010] S2, based on the use of water revenue maximization as one of the conditions for making configuration scheme decision, the use of water revenue of multi-agent under different configuration scheme is calculated, and then the total water use revenue target is obtained;

[0011] S3, based on the fairness of water use optimization as one of the conditions for making configuration scheme decision, the water use fairness of multi-agent under different configuration scheme is calculated by using the minimum water shortage rate in multi-agent, and then the total water use fairness optimization target is obtained;

[0012] S4, a water resource configuration scheme preference matrix of multi-agent is constructed;

[0013] S5, the water use revenue negotiation space of each agent is determined;

[0014] S6, multi-agent water use revenue negotiation is carried out based on group decision game;

[0015] S7, the water resource configuration scheme under game equilibrium is determined.

[0016] The above method, optionally, the specific content of S1 is: calling the water resource configuration model of the research area, forming different configuration scheme set, and the configuration scheme matrix of the research area is:

[0017]

[0018] Wherein, D N×K is the water resource configuration scheme matrix of the calculation area; d i,k is the water use of agent i under water resource configuration scheme k, wherein: i=1, 2,...N, k=1, 2,...K, N is the total number of agents, K is the total number of schemes.

[0019] The above method, optionally, the total water use revenue target in S2 is:

[0020]

[0021] Wherein,

[0022] v i,j =w i,j ×p i,j

[0023] Wherein, v i is the water use revenue target of agent i; w i,j is the water supply of j department / industry of agent i; p i,j is the single party benefit of water use of j department / industry of agent i; j=1, 2,...M, M is the total number of departments / industries in the agent;

[0024] Then the water use revenue matrix of water resource configuration scheme is:

[0025]

[0026] wherein, V N×K is the benefit matrix of water resources allocation scheme of the calculation area; v i,k is the water use benefit of subject i under water resources allocation scheme k.

[0027] The above method, optionally, the total water use fairness optimal target in S3 is expressed as:

[0028]

[0029] wherein,

[0030]

[0031] wherein, s i is the water use fairness target of subject i; s i,j is the water shortage rate of subject i under water resources allocation scheme j. is the water demand of j department / industry of subject i, respectively;

[0032] The water use fairness matrix of water resources allocation scheme is:

[0033]

[0034] wherein, S N×K is the water use fairness matrix of water resources allocation scheme of the calculation area; s i,k is the water use fairness index of subject i under water resources allocation scheme k.

[0035] The above method, optionally, the water use benefit and water use fairness demand in S4 are standardized, and the specific method is:

[0036]

[0037] wherein, n i,k is the value of water use evaluation index of subject i to the kth scheme; N i,k is the standardized attribute value;

[0038] A weighted index evaluation matrix is constructed according to the preferences of each subject, and the weighting method is:

[0039] wn i,k =N i,k 0ω i,j

[0040] wherein, wn i,k is the weighted attribute value, and ω i,j is the weight value of subject i to industry j;

[0041] Further determine the positive and negative ideal solution of each subject and The method is:

[0042]

[0043] Wherein:

[0044]

[0045] Wherein, and The positive and negative ideal solution of subject i to the kth scheme respectively;

[0046] Calculate the distance between each configuration scheme and the positive and negative ideal solution, as follows:

[0047]

[0048] Wherein: The Euclidean distance between scheme k and the positive ideal solution under the preference of subject i; The Euclidean distance between scheme k and the negative ideal solution under the preference of subject i;

[0049] The degree of conformity of each configuration scheme to the ideal method is represented by the following formula:

[0050]

[0051] Wherein, The degree of conformity of scheme k to the ideal scheme under the preference of subject i;

[0052] The greater the value, the higher the degree of preference of subject i to scheme k. The preference matrix of each subject to each scheme is obtained by sorting from large to small as follows:

[0053]

[0054] Wherein, r i,k The preference order of subject i to scheme j according to the value of

[0055] The above method, optionally, the set of all stable schemes of cooperation game in S5 is represented as:

[0056]

[0057] Wherein, The comprehensive benefit obtained by subject i in cooperation, i is a positive integer greater than 1; u i ​The comprehensive benefit obtained by the main body i in the non-cooperation; S and N respectively represent a local cooperation set and a global cooperation set, v(s) represents the benefit when the local cooperation s; v(N) is the benefit of global cooperation.

[0058] The above method, optionally, the negotiation decision method used in S6 includes a plurality of voting method PV, Hall system method HS, Borda voting method BC, pair comparison method PC and approval voting method AV.

[0059] The above method, optionally, the final decision scheme in S7 is expressed as:

[0060] BEST=Max{PV,HS,BC,PC,AV}

[0061] Wherein, BEST is the optimal solution of the lower group decision game model.

[0062] A water resource allocation scheme decision system based on multi-agent game, executes any one of the water resource allocation scheme decision methods based on multi-agent game, comprising: a memory, a processor, a calling interface and an output interface;

[0063] The memory is in communication connection with the processor, and the processor is in communication connection with the calling interface and the output interface respectively;

[0064] The memory is used for storing and calling the data required by the model;

[0065] The processor is used for realizing the functions of calling data, running model program and inputting and outputting calculation results;

[0066] The calling interface is used for calling the water resource allocation model and obtaining the water resource allocation scheme set under different scenes;

[0067] The output interface is used for outputting the standardized decision result data.

[0068] According to the above technical solution, compared with the prior art, the present application provides a water resource allocation scheme decision method and system based on multi-agent game, which has the following beneficial effects:

[0069] The method proposes a multi-agent decision preference recognition method based on TOPSIS and a multi-agent negotiation and decision method based on group decision game, thereby obtaining a water resource allocation scheme decision method system considering multi-agent game, and proposes a corresponding system; The method can provide scientific basis for solving the water use conflicts between different regions and different water users, and realizing water resource allocation scheme considering water use benefit and fairness. BRIEF DESCRIPTION OF DRAWINGS

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0071] Figure 1 This is a flowchart of a water resource allocation scheme decision-making method based on multi-agent game theory disclosed in this invention;

[0072] Figure 2 This is a flowchart illustrating the calculation process of the water resource allocation scheme decision-making method based on multi-agent game theory disclosed in this invention.

[0073] Figure 3 This is a structural diagram of a water resource allocation scheme decision system based on multi-agent game theory disclosed in this invention. Detailed Implementation

[0074] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0076] The purpose of this invention is to provide a multi-scheme decision-making method for water resource allocation based on multi-agent group decision-making game, and to form a practical system to solve water use conflicts among different regions and water users, achieving water resource allocation that balances water use equity, water use efficiency, and the economic demands of all parties. The computational flowchart of the technology involved in this invention is shown below. Figure 2 As shown. Based on Figure 2 The present invention discloses a specific solution for the described process, as follows:

[0077] Referring to Figure 1 As shown in the figure, the application discloses a water resource allocation scheme decision-making method based on multi-agent game, comprising the following steps:

[0078] S1, obtaining a set of water resource allocation schemes of a research area to obtain an allocation scheme matrix of the research area;

[0079] S2, based on maximizing the water use benefit as one of the conditions for making the allocation scheme decision, calculating the water use benefits of the multi-agents under different allocation schemes, and then obtaining a total water use benefit target;

[0080] S3, based on the optimal fairness of water use as one of the conditions for making the allocation scheme decision, using the minimum water shortage rate in the multi-agent to calculate the water use fairness of the multi-agents under different allocation schemes, and then obtaining an optimal total water use fairness target;

[0081] S4, constructing a water resource allocation scheme preference matrix of the multi-agent;

[0082] S5, determining the water use benefit negotiation space of each agent;

[0083] S6, carrying out multi-agent water use benefit negotiation based on group decision game;

[0084] S7, determining the water resource allocation scheme under game equilibrium.

[0085] Further, referring to Figure 3 As shown in the figure, the specific content of S1 is: calling a water resource allocation model of the research area to form a set of different allocation schemes, and the allocation scheme matrix of the research area is:

[0086]

[0087] Wherein, D N×K is the water resource allocation scheme matrix of the calculation area; d i,k is the water use amount (10,000 m 3 ) of the agent i under the water resource allocation scheme k, wherein: i=1, 2,...N, k=1, 2,...K, N is the total number of agents, and K is the total number of schemes.

[0088] Specifically, under different allocation schemes, after each agent obtains the corresponding allocation water amount, the agent further carries out water resource allocation among different departments / industries to maximize the water use effect considering the benefits and fairness. Therefore, corresponding objective functions need to be set up from two dimensions of water use benefit and water use fairness.

[0089] Further, the total water use benefit target in S2 is:

[0090]

[0091] wherein,

[0092] v i,j = w i,j × p i,j

[0093] wherein, v i is the water use benefit target of subject i; w i,j is the water supply of j department / industry of subject i; p i,j is the unit benefit of water use of j department / industry of subject i; j = 1, 2,... M, M is the total number of departments / industries within the subject;

[0094] The water use benefit matrix of the water resources allocation scheme is:

[0095]

[0096] wherein, V N×K is the benefit matrix of the water resources allocation scheme of the calculation area; v i,k is the water use benefit of subject i under water resources allocation scheme k.

[0097] Specifically, the water use benefits of the multi-subjects under different allocation schemes are evaluated, and the maximization of water use benefit is taken as one of the basic bases for decision-making of the allocation scheme. For the water use subject, there can be multiple water use departments / industries (for example: agriculture, industry, life, etc.) inside, and the water use demands of each department / industry are different. The maximization of overall water use benefit is taken as one of the allocation targets of the subject.

[0098] Further, the total water use fairness optimal target in S3 can be expressed as:

[0099]

[0100] wherein,

[0101]

[0102] wherein, s i is the water use fairness target of subject i; s i,j is the water shortage rate of subject i under water resources allocation scheme j; is the water use demand of j department / industry of subject i, respectively;

[0103] Then the water use fairness matrix of the water resources allocation scheme is:

[0104]

[0105] wherein, S N×K is the water use fairness matrix of the water resources allocation scheme of the calculation area; si,k is the water use fairness index of subject i under water resource allocation scheme k.

[0106] Specifically, the water use fairness of multiple subjects under different allocation schemes is evaluated, and the optimal water use fairness is taken as one of the basis for decision-making of allocation schemes. The minimum water shortage rate of each water use department / industry in the subject is taken as the index for examining fairness.

[0107] Further, in S4, the water use benefits and water use fairness demands are standardized, and the specific method is:

[0108]

[0109] wherein, n i,k is the value of the water use evaluation index of subject i for the kth scheme; N i,k is the standardized attribute value;

[0110] Considering the preference differences of different subjects, a weighted index evaluation matrix is constructed according to the preferences of each subject, and the weighting method is:

[0111] wn i,k =N i,k ·ω i,j

[0112] wherein, wn i,k is the weighted attribute value, and ω i,j is the weight value of subject i for industry j;

[0113] Further determine the positive ideal solution and negative ideal solution of each subject and The method is:

[0114]

[0115] wherein:

[0116]

[0117] wherein, and are the positive ideal solution and negative ideal solution of subject i for the kth scheme, respectively;

[0118] Calculate the distance of each allocation scheme from the positive ideal solution and the negative ideal solution, and the method is as follows:

[0119]

[0120] wherein: is the Euclidean distance between scheme k and the positive ideal solution under the preference of subject i; is the Euclidean distance between scheme k and the negative ideal solution under the preference of subject i;

[0121] The degree of compliance of each configuration scheme with the ideal method is represented by the following formula:

[0122]

[0123] Wherein, is the degree of compliance of the scheme k preferred by the subject i with the ideal scheme;

[0124] The greater the value, the higher the degree of preference of the subject i for the scheme k. The schemes are ranked from large to small, and the preference matrix of the subject i for each scheme is as follows:

[0125]

[0126] Wherein, r i,k is the preference order of the subject i for the scheme j according to the value of

[0127] Specifically, since each participating subject has different interest demands for different allocation schemes, and the differences in different regions (hydrological conditions, cultural factors, political factors, historical factors, etc.) will also affect the game pattern and the final decision. Therefore, first of all, the preference matrix of each participating subject needs to be clarified. In group decision-making, the subject will preferentially select the schemes ranked at the top according to its own preference.

[0128] Further, all the schemes that can keep the cooperation stable in the cooperative game in S5 are represented as:

[0129]

[0130] Wherein, is the comprehensive benefit obtained by the subject i in cooperation, i is a positive integer greater than 1; u i is the comprehensive benefit obtained by the subject i in non-cooperation; S and N represent the set of local cooperation and the set of global cooperation, v(s) represents the benefit when cooperating locally; v(N) is the benefit of global cooperation.

[0131] ​Specifically, in order to realize the rational allocation of regional water resources and find a balanced solution that meets the interests of all parties, the patent introduces the cooperation game method into the decision of water resources allocation scheme. Cooperation Game Theory (CGT) is an important branch of Game Theory, mainly used to solve the problem of reasonable distribution of interests among different game subjects. Its biggest feature is that the participating subjects participate in multi-party cooperation based on the principle of individual rationality, and on the premise of maximizing the total benefit of cooperation, they make their own interests meet according to certain strategies, so as to achieve the balance of interests of all parties. Cooperation Game focuses on the fair and effective distribution of the benefits obtained through cooperation, and evaluates the acceptable degree of each participant in different distribution schemes, which has a good supporting role for forming a win-win cooperation pattern.

[0132] In order to realize the cooperation game of all parties, it is necessary to first find the "core" of the cooperation game, that is, the outer boundary of all distribution methods that all participants can accept, that is, the set of all stable schemes that can cooperate. The scheme in the core needs to meet the condition that each game subject will not benefit from leaving the cooperation body (adopting an uncooperative way). The "core" of the cooperation game is used as the negotiation space of each water resources allocation participant, that is, if the water resources allocation scheme belongs to the "core", it is considered that the scheme has feasible conditions.

[0133] Further, the negotiation and decision-making method used in S6 includes multiple voting method PV, Hal system method HS, Borda voting method BC, pairwise comparison method PC and approval voting method AV.

[0134] Multiple voting method PV is one of the widely used decision-making methods. The "winning" scheme of this method is the scheme most favored by all parties:

[0135]

[0136] The number of votes obtained by the alternative scheme j is:

[0137]

[0138] Under the PV method, the scheme with the most total votes wins.

[0139] Hal system method HS designs a multi-round elimination mechanism. In each round of voting, the worst alternative scheme is eliminated, and the remaining scheme is the "winning" scheme. For a decision-making scene with m alternative schemes, Hal system method needs at most m-1 rounds of voting.

[0140] The eliminated scheme in each round of voting is:

[0141] P j* =Min{P j

[0142] where P is the number of participants, m is the number of alternatives, and b is the score of alternative j given by participant i. j The definition of P is the same as in PV.

[0143] The final "winning" alternative is:

[0144]

[0145] where m' is the number of alternatives remaining in the last round of voting.

[0146] In Borda Count (BC), each participant ranks the alternatives in order of preference, and the alternative with the highest score is the "winning" alternative.

[0147] The score of alternative j can be expressed as:

[0148]

[0149] where n is the number of participants and m is the number of alternatives.

[0150] Finally, the alternative with the highest score wins.

[0151] In Pairwise Comparison (PC), participants compare each pair of alternatives and score them. The winning alternative gets 1 point, a tie gets 0.5 points each, and the losing alternative gets 0 points:

[0152]

[0153] where g≠h and g, h∈{1,2,...m}

[0154] where b g,h is the score of alternative g compared to alternative h; N(i g ,j h ) is the sum of all participants' scores based on their preferences for the comparison between alternatives g and h.

[0155] In the PC scenario with m alternatives, the pairwise comparison matrix P m×m can be constructed as

[0156]

[0157] For any b g,h +b h,g =1

[0158] The final score for alternative j is:

[0159]

[0160] Finally, the alternative with the highest score wins.

[0161] In the AV method, the participants can vote for multiple schemes at the same time, and the scheme with the most votes is the "winning" scheme:

[0162]

[0163] In the formula, p is the number of votes each participant can cast, 1 < p < m;

[0164] The final score of the alternative scheme j is:

[0165] Further, the final decision scheme in S7 is expressed as:

[0166] BEST=Max{PV,HS,BC,PC,AV}

[0167] BEST is the optimal solution of the lower group decision game model.

[0168] With Figure 1 The method corresponds to the application also discloses a water resource allocation scheme decision system based on multi-agent game, executes any one of the water resource allocation scheme decision methods based on multi-agent game, and the specific structure refers to Figure 3 As shown in the figure, it comprises a memory, a processor, a calling interface and an output interface.

[0169] The memory is in communication connection with the processor, and the processor is in communication connection with the calling interface and the output interface respectively;

[0170] The memory is used for storing and calling the data required by the model;

[0171] The processor is used for realizing the functions of calling data, running the model program, inputting and outputting the calculation results;

[0172] The calling interface is used for calling the water resource allocation model and obtaining the water resource allocation scheme set under different scenes;

[0173] The output interface is used for outputting the standardized decision result data.

[0174] Specifically, the memory mainly serves as a database of the model, and undertakes the functions of storage and calling of required data. The memory contains various data types such as local water source data, water demand data of various industries, economic and social data, reservoir information data, and engineering node topology data, and the storage file can be in a database format such as.db,.sqlite,.dmp, or in a readable file format such as.scv. The processor provides a calculation platform for the model, and undertakes the functions of calling data, running the model program, and inputting and outputting the calculation results. The professional models in the processor are developed by using FORTRAN or Python, and mainly include a generalization module, a water use benefit analysis module, a negotiation space analysis module, a subject preference calculation module, and a group decision game module, and different functional modules are called according to different calculation requirements.

[0175] Each of the embodiments in the specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other. Each of the embodiments mainly describes the difference from other embodiments. Especially, the system or the system embodiment is described simply because it is basically similar to the method embodiment. The related parts can be referred to the part of the description of the method embodiment. The system and the system embodiment described above are only illustrative, and the units described as separate components can be or can not be physically separated, and the components shown as units can be or can not be physical units, that is, they can be located in one place or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment according to the actual needs. Those skilled in the art can understand and implement it without creative labor.

[0176] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A water resources allocation scheme decision-making method based on multi-agent game, characterized in that, The method comprises the following steps: S1, obtaining a set of water resource allocation schemes of a research area to obtain an allocation scheme matrix of the research area; S2, based on maximizing water use benefits as one of the conditions for making allocation scheme decisions, calculating the water use benefits of multiple subjects under different allocation schemes, and then obtaining a total water use benefit target; S3, based on optimizing water use fairness as one of the conditions for making allocation scheme decisions, using the minimum water shortage rate within the multiple subjects to calculate the water use fairness of the multiple subjects under different allocation schemes, and then obtaining a total water use fairness optimization target; S4, constructing a water resource allocation scheme preference matrix of the multiple subjects; S5, determining the water use benefit negotiation space of each subject; S6, negotiating the water use benefits of the multiple subjects based on group decision-making games; S7, determining a water resource allocation scheme under game equilibrium; The specific content of S1 is: calling a water resource allocation model of the research area to form a set of different allocation schemes, and the allocation scheme matrix of the research area is: wherein, is a water resource allocation scheme matrix for a calculation region; is a water consumption of the subject i under the water resource allocation scheme k, wherein: , N is the total number of subjects, and K is the total number of schemes. The total water use fairness optimization target in S3 is expressed as: Wherein, wherein, is the water equity objective for the agent i; is the water deficit rate for the agent i under the water resources allocation scheme j; is the water demand of the jth sector / industry of the agent i, respectively; The water use fairness matrix of the water resource allocation scheme is: wherein, is a water use fairness matrix for a water resources allocation scheme for a region; is a water use fairness index for subject i under water resources allocation scheme k. In S4, the water use benefit and water use fairness claims are standardized, and the specific method is: wherein, is the value of the water evaluation index for the i-th subject for the k-th scenario; is the normalized attribute value; According to the preference of each subject, a weighted index evaluation matrix is constructed, and the weighting method is: wherein, is the weighted attribute value, is the weight value of the subject i for the industry j; S5 determines the water use benefit negotiation space of each subject based on the 'kernel' of cooperative game, and the negotiation space is all the scheme sets that can keep cooperation stable, which is expressed as: wherein, S is the overall benefit obtained by the subject i in cooperation, i being a positive integer greater than 1; S is the overall benefit obtained by the subject i in cooperation, i being a positive integer greater than 1; ; S is the overall benefit obtained by the subject i in cooperation, i being a positive integer greater than 1; S is the overall benefit obtained by the subject i in cooperation, i being a positive integer greater than 1; 2. The water resource allocation scheme decision-making method based on multi-agent game according to claim 1, wherein, The total water use benefit target in S2 is: Wherein, wherein, is the water use benefit target for subject i; is the water supply for j sector / industry of subject i; is the one-sided benefit of water use for j sector / industry of subject i; M is the total number of sectors / industries within the subject. The water use benefit matrix of the water resource allocation scheme is: wherein, is the payoff matrix of the water resources allocation scheme for the region; is the water use payoff of agent i under water resources allocation scheme k.

3. The water resource allocation scheme decision-making method based on multi-agent game according to claim 1, wherein, S4 further comprises: further determining the positive understanding and the negative ideal solution of each subject and The method is: Wherein: wherein, and are the positive and negative ideal solutions of the i-th subject to the k-th problem, respectively. The distance of each allocation scheme from the positive ideal solution and the negative ideal solution is calculated, and the method is as follows: wherein: is the Euclidean distance between solution k and the positive ideal solution under the preferences of agent i; is the Euclidean distance between solution k and the negative ideal solution under the preferences of agent i. The degree of conformity of each allocation scheme to the ideal method is expressed by the following formula: wherein, is the degree of agreement of the solution k with the ideal solution for the subject i preferences; The greater the value, the higher the degree of preference of the subject i for the scheme k. The preference matrix of the subject i for each scheme is obtained by ranking each scheme from large to small, as follows: wherein, is the value of the preference of the subject i for the scheme j. is the value of the preference of the subject i for the scheme j.

4. The water resource allocation scheme decision-making method based on multi-agent game according to claim 1, wherein, The negotiation decision-making method used in S6 includes the plurality of voting method PV, the Hal system method HS, the Borda voting method BC, the pair-wise comparison method PC, and the approval voting method AV.

5. The water resource allocation scheme decision-making method based on multi-agent game according to claim 4, wherein, The final decision scheme in S7 is expressed as: wherein, is the optimal solution of the lower-level group decision game model.

6. A water resources allocation scheme decision system based on multi-agent game, characterized in that, The water resource allocation scheme decision-making method based on multi-agent game according to any one of claims 1-5 comprises: a memory, a processor, a calling interface, and an output interface; The memory is in communication connection with the processor, and the processor is in communication connection with the calling interface and the output interface respectively; The memory is used to store and call the data required by the model; The processor is used to realize the functions of calling data, running model programs, and inputting and outputting calculation results; The calling interface is used to call the water resource allocation model to obtain a set of water resource allocation schemes under different scenarios; The output interface is used to output the standardized decision-making result data.

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