Water Allocation in Border River Basin with a Shared Vision, A Case Study: Harirod River

In the past few years, an increase in demand, a deficit in water resources and lack of
appropriate governance of water have forced many countries to exploit transboundary
rivers and shared water resources. This issue has led to a rise in water conflicts. Game
theory is one of the most substantial means of conflict resolution and reaching equilibrium
in a system. In the present study, conflict resolution in shared river Basin of Harirod was
approached through cooperative and non-cooperative game theory. In the first step,
considering the historical water right of players, the initial water allocation was done to
determine the profit in non-cooperative state. Then, in the second step, the players formed
crisp coalitions with fuzzy characteristic functions to increase their profit and the profit of
the system. At this stage, the players were uncertain about the expected payoffs in the
intended coalitions. To redistribute profit in crisp coalitions the Hukuhara–Shapley
function or fuzzy characterisc functions and also core methods were used. In the third step,
in order to increase the definitional domain of the players, a game with fuzzy coalitions
and fuzzy characteristic functions in the form of Choquet fuzzy Integral was used. At this
stage, after determining the participation rate of the players, the value of each coalition was
assessed through the fuzzy integral tool. The results showed that the cooperation of the
players in the grand coalition leads to an increase in the profit. That is to say based on
Shapley value, the profit for Iran has increased from 234 billion to 259 billion Rials.
Furthermore, using Gatley index, the players’ satisfaction rate of the profit redistribution in
grand coalition was studied. In addition, the Gatley index was less than 1 for all the three
countries and it confirmed the players’ satisfaction of the profit redistribution result. The
results obtained from games with fuzzy coalitions showed an increase in the profit of the
players compared to non-cooperative state and partial coalitions among the players; and the
best situation was attained when the players formed a grand coalition. Moreover, it was
also observed that the proposed methodologies are professionally appropriate to real-world
uncertain problems because the players would be able to investigate the problem by
changing the parameter 0,1 which is the degree of all the membership functions of the
fuzzy numbers involved in the games. After studying game in a cooperative state, it was
analyzed in a non-cooperative state. In this approach, after defining possible scenarios in
the basin, equilibrium in the behavior of the players was studied through the above
mentioned methods and its impact on the simulation model was detected. The results
showed that the percentage of agricultural water in the basin of the study area in scenario 1 was 53% and in scenario 2 was 37%. Furthermore, according to the results obtained from the simulation model, the aquifer of the study area in Iran’s basin would decrease from 244 million cubic meters to 175 million cubic meters a year. Investigating the equilibrium modes, it became clear that by paying motivation compensation to Afghanistan, Iran would be able to change the equilibrium to a cooperative mode and cause an increase in the profit of both countries.

Water Allocation in Border River Basin with a Shared Vision, A Case Study: Harirod River Keywords:

Water Allocation , Transboundary River , Cooperative and Non-Cooperative Game Theory , uncertainty , Conflict Resolution