Developing a non-cooperative optimization model for water and crop area allocation based on leader-follower game

In this paper, a mathematical model for conflict resolution among a diverse set of agricultural water users in Golestan province, Iran, is developed. Given the bi-level nature of the distribution of power in the current problem, a combination of Leader–Follower game and Nash–Harsanyi bargaining solution method is employed to find optimal water and crop area allocations. The Golestan Regional Water Authority is the leader in this setting, controlling the total water allocations; and the agricultural sectors are the followers, competing over the allocated water. Two objectives for the leader are (i) maximizing profits, and (ii) maximizing share of green water in total agricultural production through selecting more efficient crop patterns. The followers’ objective is merely maximizing obtained benefits for the selected crop patterns. Virtual water concept is also factored into the related objective functions, and the water allocation problem is solved considering spatio-temporal crop pattern along with a dynamic water pricing system. This involves using a hybrid optimization structure as a new approach to solving two level optimization problems. The results show that the leader's income is independent of total water allocation and is only affected by crop pattern and crop area, two factors which drive water price too. The followers’ benefit also depends on crop pattern and crop area, as they influence the crop yield, cost and water price. Finally, green water plays a key role in selecting the optimal crop pattern and crop area.