A Game Theory Approach for Conjunctive Use Optimization Model Based on Virtual Water Concept

In this study to allocate the agricultural and environmental water, considering virtual water concept, a multi-objective optimization model based on NSGA-II is developed. The objectives consist of equity maximization, agricultural benefit maximization for each region, maximization of green water utilization and finally minimization of environmental shortage. Then a cooperative game (Grand Coalition) model is presented by forming all possible coalitions. By the game model including Nucleolus, Proportional Nucleolus, Normal Nucleolus and Shapley methods, the benefit is reallocated based on all Pareto optimal solutions obtained from multi-objective optimization model. Then using two famous fallback bargaining methods, Unanimity and q-Approval, preferable alternative (solution) for each of the cooperative games is determined. Finally, based on the obtained benefit for each selected alternatives, the two most beneficial alternatives are chosen. The proposed methodology applied for water allocation of Minoo-Dasht, Azad-Shahr and Gonbad-Kavoos cities in Golestan province, Iran for a 3-year period as a case study. Also, eight crops including Wheat, Alfalfa, Barley, Bean, Rice, Corn, Soya, and Cotton are selected based on local experts’ recommendations. The models’ results indicated no significant difference between the grand coalition model and the multi-objective optimization model in terms of the average cultivation area (a relative change of 2.1%), while lower agricultural water allocation occurred for the grand coalition model (about 10.35 percent average) compared with the multi-objective optimization model. It is also observed that more agricultural benefit gained by the grand coalition model (32 percent average). Finally, it is found that Wheat and Corn hold the most rates of import and export, respectively, and Rice was the crop which has the least shortage of production to supply food demand.

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