Managing a Common Pool Resource: Real Time Decision-Making in a Groundwater Aquifer

In a Common Pool Resource (CPR) such as a groundwater aquifer, multiple landowners (agents) are competing for a limited resource of water. Landowners pump out the water to grow their own crops. Such problems can be posed as differential games, with agents all trying to control the behavior of the shared dynamic system. Each agent aims to maximize his/her own personal objective like agriculture yield, being aware that the action of every other agent collectively influences the behavior of the shared aquifer. The agents therefore choose a subgame perfect Nash equilibrium strategy that derives an optimal action for each agent based on the current state of the aquifer and assumes perfect information of every other agents' objective function. Furthermore, using an Iterated Best Response approach and interpolating techniques, an optimal pumping strategy can be computed for a more-realistic description of the groundwater model under certain assumptions. The numerical implementation of dynamic optimization techniques for a relevant description of the physical system yields results qualitatively different from the previous solutions obtained from simple abstractions.This work aims to bridge the gap between extensive modeling approaches in hydrology and competitive solution strategies in differential game theory.