Using Game Theory to Assign Groundwater Pumping Schedules

This paper deals with optimization of extracting groundwater by a number of users (stakeholders) from a common aquifer. The aim is to reduce their pumping cost and the respective energy consumption, taking into account the schedule preferences of the users (e.g. pumping during the day instead of during the night). Moreover, it is postulated that alternate pumping reduces pumping cost. To facilitate the participation of stakeholders in achieving the best alternate pumping schedule, the problem is formulated as an anti-coordination game. Using vertices to represent the players (users) and weighted edges to represent their interactions we have created an algorithm that can be used to get players’ payoffs. Then, assuming that the players are allowed to improve their payoffs by playing consecutive moves, we use our algorithm to find the Nash equilibria of the game. However, not all games converge to the same Nash equilibria, as changing the sequence of the players can result in different solutions. Therefore, we use Genetic Algorithms to find the sequence of the players that minimizes the overall pumping cost or the energy consumption, using the least possible game rounds. The algorithm proposed can be used by researchers and authorities to promote cooperation between well users, leading to financial and environmental benefit.