Optimization of Water Allocation using Cooperative Game Theory Case Study: Zayandehrud Basin

Document Type : Research Paper


1 Master of Science, Department of Environmnetal Engineering, Faculty of Environment, University of Tehran

2 Assistant Professor, Department of Environmnetal Engineering, Faculty of Environment, University of Tehran,

3 Associate Professor, Department of Environmnetal Engineering, Faculty of Environment, University of Tehran,


When there is no determined value for water (as a public asset) by its trustees and beneficiaries and its allocation method is more dependent on the requirements of water consumers than comparing water affairs benefits with its real value, decision making on which interested group, when and to what extent can use water is a game. This study is aimed to determine sustainable policies for water allocation to interested groups such that high quality sufficient water is available to survive water bodies and economic purposes of interested groups are satisfied by sustainability agreement with the environment. For this, the environment is recognized as an independent water user in optimization model and as an independent player in the game theory. Thereby, Zayandehrud basin has been studied as a case study.
Materials and Methods:
In this study was first dealt with optimizing the allocation of water output from the reservoir to consumptions including drinking, agriculture, industry and environment by means of genetic algorithm. To get the most desirable possible state of water provision for consumptions, 4 approaches have been considered, as described briefly below.
The first includes providing biological current for the river which is in an equilibrium using Tenant (Montana) method and available data (providing 2.06 (MCM) for each month in the cold season and 6.18 (MCM) for each month in the warm season). The second has been formulated by providing minimum water requirement for lagoon survival and considering protection and provision of minimum survival requirements for this valuable water ecosystem in the area. Continuity of natural life in the swamp depends completely on water depth. The lowest possible depth for vital activities is in about depth of 15cm. This depth can be achieved by importing 75 MCM per year water to the swamp. Benthos is hardly survived in this depth. The third includes providing desirable quality for the lagoon based on TDS such that the water requirements for TDS dilution have been assumed as a biological requirement. In the fourth, provision of minimum water requirement for the lagoon is considered and with regard to the studies on Gavkhoony swamp, desirable performance occurs with provision of 140MCM per year water. This amount provides depth of 30cm for the swamp. Then, having estimated benefits of each beneficiary, their interactions in the basin have economically investigated by cooperative games. The percentages of requirement provision for beneficiaries and annual water allocations have presented in Table 1 for different approaches. The benefits of each beneficiary and the results of cooperative game have been provided in Figure 1.
Tabel - Gross profit of water user in each approach

4th approache

3rd approache

2nd approache

1st approache


Benefit ($)

Water use (MCM)

Benefit ($)

Water use (MCM)

Benefit ($)

Water use (MCM)

Benefit ($)

Water use (MCM)






























2nd Approach

1st Approach


4th Approach

3rd Approach

Figure 1. Results of cooperative games in different approaches
Discussion and Conclusion:
With regard to data from the studied area, in spite of various managerial plans to increase water provision for the basin, it no longer satisfies the requirements of water consumers. Specially, it is the case in the environmental sector where because of ignorance and devoting water allocation priorities in the recent years, it has been deficient in its life and is completely dependent on seasonal currents and rainfalls. According to the designed approaches in the environmental sector of this study, more than 85% of its requirements can be eliminated in allocations. With water provision approach for environment sector, 3-8% of agricultural and 8% of industrial requirements are deficient. From environmental requirement provision point of view which has been distinctively defined in every approach, the model has shown the best performance in the first approach such that 100% of environmental requirements are satisfied. Of course, considering that this approach has accounted minimum requirements for the environment, minimum deficiencies in agricultural and industrial allocations have been observed. Maximum water requirement has been considered in the fourth approach in which optimization model can allocate 87% of environmental requirements. The fourth approach, from water allocation to the environment view point, is the best approach because of water allocation to the environment with regard to water content as well as positioning the lagoon in a desirable state for survival.
It can be concluded from economic analyses of model approaches that the industry has the same benefit in all approaches despite 8% change in water allocation respect to unfair allocation and low or high environmental utility in different approaches has no influence on economic performance of the industry. The second approach has the most benefit in agricultural sector and it has the best performance in environmental sector because of the most desirable state for the river and lagoon survival. Economic analysis shows that agricultural sector has more benefit in second approach than other states. From model allocations, it can be said monthly allocation and distribution model has impressive effect in agricultural sector. With constant optimization procedure in allocations, agricultural sector incurs severe pressures but considering allocated water and benefits in the agricultural sector, first, second and fourth approaches have little differences because of monthly water distribution procedure in firth and third approaches.
From game theory, benefits from player cooperation in agricultural and environmental sector have been more than no cooperation. The industry earns the same benefit from both states, except for third approach. Proportional Nucleolus game has maximum benefit in agricultural sector, except in the first approach. Weak Nucleolus has shown better performance in benefit calculation in the environmental sector, except for fourth approach. Therefore, there is no specified procedure for games but because of more benefit from cooperation in agricultural and environmental sectors than no cooperation both sectors will get more benefits from cooperation beside water requirement provision. Best benefit allocation has respectively occurred in fourth, second, third and first approaches.
Finally, it is clear that considering the environment as a beneficiary of basins and planning for water resource management makes always more benefit the system, although less water allocation to consumers makes less benefit. Because of no profit in environment sector and no protest except in critical conditions, there is ignorance in this sector while water ecosystems are most valuable resources that their economic value estimation is complicated and far from reality but with these economic methods it is seen that the aggregate benefit and profit is in the environment protection and survival.


Main Subjects

سلطانی، س. 1388. تعیین حداقل آب مورد نیاز (حقابه) باتلاق گاوخونی، مطالعات مشترک دانشگاه صنعتی اصفهان و محیط‌زیست استان اصفهان، چاپ‌نشده.
کریمی، ا. نیکو، م. کراچیان، ر. شیرنگی، ا. 1391. ارزیابی قابلیت تأمین بلندمدت آب در حوضة آبریز زاینده‌رود تحت تأثیر طرح‌های انتقال آب با بهینه‌سازی چنددوره‌ای، پژوهش آب ایران، سال ششم، شمارة 11.
مهندسین مشاور یکم. 1382. مطالعات بهنگام‌سازی طرح جامع آب کشور- حوضة گاوخونی.
نیک‌سخن، م. کراچیان، ر. 1387. مدیریت کیفیت آب رودخانة مبتنی بر مدل تصمیم‌گیری مجوز تخلیۀ بار آلودگی، رسالة دکتری دانشکدة فنی، دانشگاه تهران.
Abrishamchi, A., Danesh-Yazdi, M., Tajrish, M. 2011. Conflict Resolution of Water Resources Allocation Using Game Theoretic Approach: the case of orumieh river basin in Iran, AWRA Summer Specialty Conference
Ardakanian, R. 2005. Optimization the coordination of hydro and thermal plant: the HTCOM model. The International Journal on Hydropower & Dams.
Coad, B.W. 2010. Xeric Freshwaters and Endorheic (Closed) Basins. Freshwater Ecoregions of the Words (FWOW) Site.
Dinar, A., and Wolf, A. T. 1994. International Markets for Water and the Potential for Regional Cooperation: Economic and Political Perspectives in the Western Middle East, Economic Development and Cultural Change.
Dufournaud, C. 1982. On the Mutually Beneficial Cooperative Scheme: Dynamic Change in the Payoff Matrix of International River Basin Schemes, Water Resources Research.
Ganji, A., Karamouz, M. and Khalili, D. 2007. Development of stochastic dynamic Nash game model for reservoir operation.I. The symmetric stochastic model with perfect information, Advances in Water Resources
Gohari, A., Eslamian, S., Abedi, J., Massah, A., Wang, D., and Madani, K. 2013. Climate change impacts on crop production in Iran's Zayandeh-Rud River Basin. Science of The Total Environment.
Goldberg, D. E. 1989. A comparative Analysis of selection Scheme Used in Genetic Algorithms, Foundation of Genetic Algorithms, morgan Kaufman, San Mateo, Calif.
Haab, T. C., and McConnell, K. E. 2002. Valuing Environmental and Natural Resources. Edward Elgar Publishing Limited, Cheltenham, UK.
Lejano, R. P., and Davos, C. A. 1995. Cost Allocation of Multiagency Water Resource Projects: Game-Theoretic Approaches and Case Study, Water Resources Research.
Madani, K. 2010. Game theory and water resources, Journal of Hydrology.
Madani, K. 2011. Hydropower licensing and climate change: Insights from cooperative game theory, Advances in Water Resources.
Mahboubi Sufiani, N. 1996. Liminological study and environmental balance of interior water of the Gaw Khuni swamp, Esfahan Environment Authority.
Mansoori, J. 1997. Ramsar Report for Gavkhouni Lake and Marshes of the Lower Zaindeh Rud. The Ramsar Sites Database.
Michalewics, Z. 1992. Genetic Algorithms + Data Structures=Evolution Programs, Springer.
Moeinian, M. T. 2000. The impact of drought on ecological factors of the Gaw-Khuni swamp, Esfahan Environment Authority.
Morid, S., and Massah, A. R. 2004. Modeling Zayandeh Rud basin under climate change. Proceeding of Conference on Hydrology: Science and practice for the 21st century London, UK.
Nikouei, A., Zibai, M., Ward, F. 2012. Incentives to adopt irrigation water saving measures for wetlands preservation: An integrated basin scale analysis, Journal of Hydrology.
Roe, T., and Diao, X. 1997. The Strategic Interdependence of a Shared Water Aquifer: A General Equilibrium Analysis, Dordecht: Kluwer Academic Publishers.
Rogers, P. 1969. A Game Theory Approach to the Problems of International River Basins, Water Resources Research
Salemi, H. R., and Murray-Rust, H. 2002. Water Supply and Demand Forecasting in the Zayandeh Rud basin. Iran. IAERI-IWMI Research Reports.
Vakil, H. A. 2006. Gavkhooni Swamp to Turn into an International Tourism Destination. Skyscrapercity: Tourism Infrastructure, Development and News.
Wang, L., Fang, L., Hipel, K.W. 2008. Basin-wide Cooperative Resources Allocation, European Journal of Operational Research.
Wardlaw, R., and Sharif, M. 1999. Evaluation of Genetic Algorithms for Optimal Reservoir System Operation, Journal of Water Resources Planning and Management.