Impacts of Foresight Among Competitive Groundwater Users: An investigation through Receding Horizon Games

Groundwater is a shared (common-pool) resource and, as such, is vulnerable to individual users making decisions that benefit themselves but degrade the aggregate welfare of all users. However, past theoretical and empirical studies have shown mixed results regarding whether competition among individuals actually does degrade aggregate welfare in the groundwater context. Here, we help to clarify this discord by illustrating the relationship between (1) the length of a competitive groundwater user’s foresight for the impact of their present decision on their own future costs and (2) the externalities of a competitive groundwater user’s decision on the costs of other users in other locations. Toward this end, and whereas prior work in this area often treats competitive behavior as exclusively myopic or analyzes steady state outcomes, we deploy a novel framework where user foresight is a tunable parameter and where user decisions and their environment are dynamic. In our framework, groundwater users are participants in a Receding Horizon Game where at each time step of simulation (1) a generalized game is solved to obtain the optimal (open loop) pumping sequence of all users during a given foresight horizon, (2) each user plays only their first pumping decision, and (3) the procedure is repeated from the next time step with updated state information. We compare outcomes from different foresight lengths to the maximum social welfare solution and illustrate how longer foresight for individual groundwater users decreases the negative externalities of their decisions. We also illustrate how foresight (a temporal dimension) and distance between wells (a spatial dimension) interact to shape externalities. Further, this study demonstrates the suitability of the Receding Horizon Game approach, an emerging tool in the optimization and control community, to model and optimize dynamic behavior of competitive agents in other water resources systems.