Sharing a groundwater resource in a context of regime shifts

Abstract

We study the occurrence of shocks in a common groundwater resource problem using a differential game. In particular, we use Rubio and Casino's adaptation of the Gisser and Sánchez model where we introduce a sudden change in the dynamics of the resource, namely a decrease in the recharge rate of the aquifer. We compare the pareto optimal solution with open-loop and feedback equilibria. First, we show analytically how different solutions, at the steady state, depend on the intensity of the shock. Moreover, we show that the cost and the strategic effects are decreasing functions of the intensity of the shock, i.e. that all the solutions get closer at the steady state for more intense shocks. We finally apply the game to the particular case of the Western La Mancha aquifer. The aim of this application is to estimate how shocks influence the inefficiency of open loop and feedback strategies in terms of welfare. We show that this inefficiency decreases the earlier the shock occurs or the higher the intensity of the shock.