The Application of Asymmetric Nash Solution in Optimal Allocation of Water Resources

Document Type : Complete scientific research article

Authors

1 Department of Agricultural Economics, Gorgan University of Agricultural Science And Natural Resources

2 , Faculty of Agricultural Science, Sari University of Agricultural Science and Natural Resources

3 Department of Agricultural Economics, Sari University of Agricultural Science And Natural Resources

Abstract

Background and objectives: The excessive use of water resources, particularly in areas where water resources are scarce and demand is much higher, has led to clashes between the various stakeholders that benefit from water extraction and water allocation. Most decision problems in natural resources management involve opposing objectives such as maximizing economic profit and minimizing negative environmental effects. Current research aims to find a compromise solution between economic and environmental objectives in Qarehsou reservoir basin.
Materials and methods: Qarehsou basin is an important agricultural center in Golestan Province. Assessment of changes in water levels indicates an increase in water extraction, especially groundwater in such basin. In order to achieve economic and environmental goals, five scenarios were analyzed, including 10%, 20%, 30%, 40%, and the maximum withdrawal of water. Then, optimal cropping pattern and optimum amount of water extraction were determined, using positive mathematical programming model and asymmetric Nash solution, respectively. In this research, the two primary stakeholders, or players, are economic benefit, whose payoff goes to the local farmers (player 1), and the reduction of water resources, whose payoff goes to the community residents (player 2). The total water extraction volume is the decision variable.
Results: The result of applying positive mathematical programming indicate that the cropping pattern has changed toward more profitable crops. According to our results from a game theory application, we observe that the optimal decision will depend on the relative importance weights assigned to the conflicting objectives. When economic benefit is considered as the only objective, the optimal groundwater withdrawal is at its maximum level. On the opposite extreme, when only the environment is considered, the optimal groundwater withdrawal decision is to extract the minimum volume of groundwater. Given the equal weights for economics and environmental goals, the optimal extraction of water resources is 175 million cubic meters. Accordingly, the amount of water extraction can be reduced by 27% to achieve environmental goals.
Conclusion: This study illustrates how game theory can be used to obtain tradeoffs in a straightforward and understandable manner to facilitate an objective assessment of benefits to the various stakeholders and decision makers. Based on the results from our game theory application, in a case of equal weights which are given to both economic and environmental impacts, the optimal withdrawal of water resources is less than the current withdrawal. Therefore, the economic benefits should be balanced with associated negative environmental impact of water withdrawal.

Keywords

References

1.Abdoli, Gh. 2007. Game theory and its applications static and dynamic games of complete information. Tehran University Press, 454p. (In Persian)
2.Asadi, E., Keramatzadeh, A., and Eshraghi, F. 2018. Determining the optimal exploitation of groundwater resources by using Game Theory (Case study: Gorgan County). J. of Waterand Soil Conservation, 25: 3. 129-144.(In Persian)
3.Gleick, P.H., and Palaniappan, M.2010. Peak Water Limits to Freshwater with Drawl and Use. Proceedings of
the National Academy of Sciencesof the United States of America,107: 11155-11162.
4.Gong, X., Zhang, H., Ren, C., Dongyong, S., and Yanga, J. 2020. Optimization allocation of irrigation water resources based on crop water requirement under considering effective precipitation and uncertainty. Agricultural Water Management, 239: 106264.
5.Harsanyi, J.C., and Selten, R. 1972. A generalized Nash solution for two-person bargaining games with incomplete information. Management Science,18: 80-106.
6.Howitt, R.E. 1995. Positive Mathematical Programming. American Journal of Agricultural Economics, 77: 329-342.
7.Jalili Kamjou, P., and Khoshakhlagh, R. 2016. Using the Game Theory in Optimal Allocation of Water in Zayandehrud. Iranian, J. of Applied Economic Studies. 18: 5. 53-80. (In Persian)
8.Jury, W.A., and Vaux, Jr. 2005. TheRole of Science in Solving the World’s Emerging Water Problems, Proc. Natl. Acad. Sci. 102: 15715-15720.
9.Kalbali, E., Ziaee, S., Mardani Najafabadi, M., and Zakerinia, M. 2021. Approches to adapting the impacts of climate change in northern Iran: The Application of a Hydrology-Economics model. Journal of cleaner production. 280: 124067.
10.Kiani, Gh., Khoshakhlagh, R., and Kamal, M. 2019. Optimal Allocation of Zayanderood River among Chaharmahal &Bakhtiary, Yazd and Isfahan Provinces. Applied Theories of Economics. 6: 3. 165-188. (In Persian)
11.Klozen, W.H., and Garces, R.C. 1998. Assessing irrigation performance with competitive indicators: the case of
the Alto Rio Lerma irrigationdistrict, Mexico. International Water Management Institute, Research Report No. 22.
12.Madani, K. 2010. Game Theory and Water Resources. Journal of hydrology, 381: 225-238.
13.Meftah Halaghi, M., Abareshi, F., Ghorbani, Kh., and Dehghani, A. 2018. Assessment of aquifer performance affected by different climate scenarios (Case study: Qareso basin). Iran. J. Irrig. Drain. 12: 5. 1140-1153. (In Persian)
14.Meftah Halaghi, M., Ghorhabi, Kh., Keramatzadeh, A., and Salarijazi, M. 2021. Application of Game Theory to Determining Optimal Harvesting of Water Resources and Determination of Optimal cropping pattern (Case study: Qarehsou basin). Journal of Waterand Soil Conservation. 27: 5. 69-87.(In Persian)
15.Meteorological Organization in Golestan Province. 2020. (In Persian)
16.Mohammadi Soleimani, E., Ahmadian, M., Keramatzadeh, A., Shokat Fadaei, M., and Mahmoodi, A. 2020. Application of Non-symmetric Nash solution to determine the Optimal Extraction of Groundwater Aquifers in Jiroft Plain of Iran. Agricultural economics and Development. 27: 107. 181-234.(In Persian)
17.Mushtaq, S., and Moghaddasi, M. 2011. Evaluating the Potentials of Deficit Irrigation as an Adaptive Response to Climate Change and Environmental Demand. Environmental science and policy, Australia College of Agriculture, 14: 1139-1150.
18.Nakao, M.D., Wichelns, D., and Montgomery, I. 2002. Game theory analysis of competition for groundwater involving El Paso, Texas and Ciudad Juarez, Mexico. Annual meeting, July 28-31, Long Beach, CA from American Agricultural Economics Association.pp. 18-33.
19.Nash, J. 1950a. The bargaining problem. Econometrica, 18: 155-162.
20.Nash, J. 1950b. Equilibrium points in N-person games. Proceeding of the national Academy of science, 36: 48-69.
21.Nash, J. 1951. Non-cooperative games. Annals of Mathematics, 54: 286-295.
22.Nash, J. 1953. Two- person cooperative games. Econometrica, 2: 128-140.
23.Paris, Q., and Howitt, R.E. 1998. An Analysis of Ill- Posed Production Problems Using Maximum Entropy. American Journal of Agricultural Economics, 8: 124-138.
24.Pongkijvorasin, S. 2007. Stock-to-Stock Externalities Resources in Renewable Resource Economics: Watersheds, Conjunctive Water Use, and Mud. Ph.D. Dissertation in Economics, University of Hawaii.
25.Poorzand, F., and Zibaei, M. 2011. Application of Game Theory for the Optimal Groundwater Extraction in Firouzabad Plain. 5: 4. 1-24. (In Persian)
26.Rahmani, A., and Sedehi, M. 2005. Predication of Groundwater Level Changes in the Plain of Hamedan-Bahar Using Time Series Model. Journal of Water and Wastewater. 15: 3. 42-49.(In Persian)
27.Regional Water Company of Golestan. 2020. Report on water resources of Golestan County, Gorgan. (In Persian)
28.Salazar, R., Szidarovszhy, F., Coppola, E., and Rajano, A. 2007. Application of game theory for a groundwater conflict in Mexico. Journal of Environmental Management, 54: 560-571.
29.Shannon, C.E. 1948. A Mathematical Theory of Communications. Journal of Bell System Technical, 27: 37-94.
30.Sheng Lee, C. 2012. Multi-objective game theory models for conflict analysis in reservoir watershed management. Chemosphere, 87: 608-613.
31.Wang, X., Zhang, Y., Zeng, Y., and Liu, C. 2013. Resolving Trans-jurisdictional Water Conflicts by the Nash Bargaining Method: A Case Study in Zhangweinan Canal Basin in North China, water resources management, 27: 1235-1247.
32.Xianchi, L. 2017. Research on water resources management based on game model. Procedia Computer Science,
107: 262-267.
33.Yuan, L., He, W., Degefu, M., Liao, Z., Wu, X., An, M., Zhang, Z., and Ramsey, T.S. 2020. Transboundary water sharing problem; a theoretical analysis using evolutionary game and system dynamics, Journal of Hydrology. 582:124521. 1-10.
34.Zeng, Y., Li, J., Cai, Y., Tan, Q., and Dai, C. 2019. A hybrid game theory and mathematical programming model for solving trans-boundary water conflicts. Journal of Hydrology, 570: 666-681.
35.Ziolkowska, J.R. 2015. Shadow Price of Water for Irrigation: A Case of the High Plains. Agricultural Water Management, 153: 20-31.
Journal of Water and Soil Conservation
Volume 28, Issue 2
October 2021
Pages 43-62

Files

Share

How to cite

Statistics