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

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.

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.

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.

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.