Study on the Pricing of Water Rights Transaction between Irrigation Water Users Based on Cooperative Game in China
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data Sources
2.1.1. Study Area
2.1.2. Data Sources
2.2. Methodology
2.2.1. Cost Price of Water Conservation in the Water Rights Transaction between Farmers
2.2.2. Earnings Price of Water Rights Transaction among Farmers Based on the Production Function of Crop Water and Cooperative Game Theory
Marginal Benefit of Crops
Determination of Reasonable Return Coefficient of Water Rights Transaction Based on Game Theory
2.2.3. Tradable Water Volume
2.2.4. Comprehensive Pricing
3. Results
3.1. The Relationship Between Irrigation Water Volume and Marginal Benefit
3.2. Tradeable Water Volume Among Farmers
3.3. Farmers’ Income Calculation Results
 (1)
 Farmers’ income after optimizing irrigation quota
 (2)
 Redistribution of farmers’ income based on Shapely Value
3.4. Water Rights Transaction Price
4. Discussion
4.1. Income Analysis Among Farmers
4.2. Analysis on the Price of Water Rights Transaction among Farmers
4.3. Limitation
5. Conclusions
 (1)
 Economically determined irrigation quotas and crop planting patterns can be used to optimize the allocation of water for each crop. If the initial allocation of water rights is inconsistent with the optimal allocation of water, the difference should theoretically be the volume of water to be traded.
 (2)
 The pricing model of water rights transaction proposed in this paper includes cost price and earnings price. The model is not only suitable for water rights transaction between farmers in waterdeficient areas, but also suitable for water rights transaction between different industries in waterdeficient areas.
 (3)
 The total revenue distribution based on the Shapley value method makes the revenue distribution under each alliance fairer and more reasonable, and the water rights pricing should also be acceptable to farmers, as undertaking a transaction will improve their income.
 (4)
 A reasonable price can encourage transactions, thereby improving the efficiency of the water rights market. The consideration of the earnings price makes the determined price closer to the real value of water resources, and has important theoretical significance for improving the water rights transaction price theory.
 (5)
 This paper mainly focuses on the study of water rights transaction between one buyer and two sellers, providing a basis for future transactions between multiple buyers and multiple sellers.
 (6)
 Because the price of water rights transaction is affected by many factors such as economy, society, and environment, the study of this paper on the price of water rights transaction based on the production function and Game Theory is only a theoretical discussion. In the practical work, it is necessary to determine the final price and tradable water volume of water right transaction based on this theory and considering various factors comprehensively, for example, the bargaining power of both parties to water rights transactions, supply and demand factors, and crop market prices.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Farmer  Crop  Total Water (10^{4} m^{3})  Irrigation Water Use Coefficient  Total Water for Irrigation (10^{4} m^{3})  Initial Water Rights (10^{4} m^{3})  Initial Irrigation Quota (m^{3}/hm^{2})  Crop Price ($/kg) 

N_{1}  Wheat  57  0.7  40  16.67 9.17 14.17  4168 4168 4168  0.264 
N_{2}  Maize  0.300  
N_{3}  Cotton  2.331 
Crop  Constant Term of Water Production Function  

a  b  c  
Wheat  −0.0059474  3.9260908  −197.94 
Maize  −0.0077347  4.7880120  −248.42 
Cotton  −0.0024283  1.9811347  −334.08 
Farmer  Crop  Initial Irrigation Quota (m^{3}/hm^{2})  Initial Allocation of Water (Ten Thousand m^{3})  Optimized Economic Irrigation Quota (m^{3}/hm^{2})  Water Demand after Optimization (Ten Thousand m^{3})  Water Savings (Ten Thousand m^{3}) 

N_{1}  wheat  4168  16.67  3267  13.07  3.6 
N_{2}  corn  4168  9.17  3502  7.7  +1.47 
N_{3}  cotton  4168  14.17  5651  19.21  −5.07 
Farmer  Revenue before Optimization (Thousand Dollars)  Revenue after Optimization (Thousand Dollars)  Revenue Per Unit Area before Optimization (1000 $/hm^{2})  Revenue Per Unit Area after Optimization (1000 $/hm^{2}) 

N_{1}  68.75  59.44  1.72  1.49 
N_{2}  47.97  44.32  2.18  2.01 
N_{3}  34.33  80.40  1.01  2.36 
No.  Alliance Form  Revenue 

1  ${N}_{1}$  68.75 
2  ${N}_{2}$  47.97 
3  ${N}_{3}$  34.33 
4  $\left\{{N}_{1},{N}_{2}\right\}$  116.72 
5  $\left\{{N}_{1},{N}_{3}\right\}$  134.37 
6  $\left\{{N}_{2},{N}_{3}\right\}$  106.64 
7  $\left\{{N}_{1},{N}_{2},{N}_{3}\right\}$  184.16 
S  ${\mathit{N}}_{1}$  $\left\{{\mathit{N}}_{1},{\mathit{N}}_{3}\right\}$ 

υ(S)  68.75  134.37 
υ(S\{M})  0  34.33 
υ(s) − υ(S\{M})  68.75  100.04 
S  1  2 
w(S)  1/2  1/2 
w(S)[υ(s) − υ(S\{M})]  34.37  50.02 
S  ${\mathit{N}}_{1}$  $\left\{{\mathit{N}}_{1},{\mathit{N}}_{2}\right\}$  $\left\{{\mathit{N}}_{1},{\mathit{N}}_{3}\right\}$  $\left\{{\mathit{N}}_{1},{\mathit{N}}_{2},{\mathit{N}}_{3}\right\}$ 

υ(S)  68.75  116.72  134.37  184.16 
υ(S\{M})  0  47.97  34.33  106.64 
υ(s) − υ(S\{M})  68.75  68.75  100.04  77.52 
S  1  2  2  3 
w(S)  1/3  1/6  1/6  1/3 
w(S)[υ(s) − υ(S\{M})]  22.92  11.46  16.67  25.84 
Strategy
$$\left({\mathit{N}}_{3}\right)$$
 Tradable Water (10^{4} m^{3})  Revenue under Alliances (Thousand Dollars)  Crop Revenue after Optimization (Thousand Dollars)  Increase Revenue Value (Thousand Dollars)  Pricing of Water Rights Transactions ($/m^{3})  

$${\mathit{N}}_{1}$$

$${\mathit{N}}_{2}$$

$${\mathit{N}}_{1}$$

$${\mathit{N}}_{2}$$

$${\mathit{N}}_{1}$$

$${\mathit{N}}_{2}$$

$${\mathit{N}}_{1}$$

$${\mathit{N}}_{2}$$
 N_{1}  N_{2}  
A1                     
A2  0  +3.65  0  60.14    33.24    +26.9    0.737 
A3  +4.76  0  84.40  0  55.01    +29.39  0.617    
A4  +3.60  +1.47  76.89  52.63  59.44  44.32  +17.45  +8.31  0.485  0.565 
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Guan, X.; Du, Q.; Zhang, W.; Wang, B. Study on the Pricing of Water Rights Transaction between Irrigation Water Users Based on Cooperative Game in China. Water 2021, 13, 1672. https://doi.org/10.3390/w13121672
Guan X, Du Q, Zhang W, Wang B. Study on the Pricing of Water Rights Transaction between Irrigation Water Users Based on Cooperative Game in China. Water. 2021; 13(12):1672. https://doi.org/10.3390/w13121672
Chicago/Turabian StyleGuan, Xinjian, Qiongying Du, Wenge Zhang, and Baoyong Wang. 2021. "Study on the Pricing of Water Rights Transaction between Irrigation Water Users Based on Cooperative Game in China" Water 13, no. 12: 1672. https://doi.org/10.3390/w13121672