Standard economic models of groundwater management assume perfect transmissivity (i.e., the aquifer behaves as a bathtub), no external effects of groundwater stocks, and/or homogenous agents. In this article, we develop a model relaxing these assumptions. Although our model generalizes to an arbitrary number of cells, we are able to obtain key insights with a two-cell finite-horizon differential game. We find a simple linear mechanism that induces the socially optimal extraction path in Markov-perfect equilibrium. Moreover, implementation requires that the regulator need only monitor the state of the resource (e.g., depth of the aquifer), not individual extraction rates. We illustrate the mechanism with a simulation based on data from the Indian state of Andhra Pradesh. The simulation suggests that significant welfare loss may occur if the regulator disregards physical and economic complexity.