The common property aquifer as a differential game

Abstract

Open‐loop and feedback equilibria are compared using a common property aquifer model. Open‐loop solutions correspond to assuming that participants commit themselves in the initial period to pumping rates in all future periods. Feedback solutions represent a more realistic assumption as farm operators adopt pumping strategies that depend on the reserve stock of water. Comparing the two equilibrium concepts reveals two sources of dynamic inefficiency in the common property aquifer: a pumping cost externality and a “strategic externality” that arises from the competition among users to capture the groundwater reserves. The qualitative results show that the open‐loop solution captures only the pumping cost externality. The feedback solution captures both externalities and exacerbates the over‐ exploitation of the commons compared to the open‐loop solution. Moreover, the dynamic inefficiency resulting from both externalities increases in the number of independent landowners with access to the aquifer.