We consider the exploitation of a common groundwater resource for irrigation as a differential game. In particular, we use the Rubio and Casino 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 then compare the socially optimal solution with Open-loop and feedback equilibrium. First, we show analytically that different solutions (at the steady state) do not depend on the intensity of the shock, but on the value of the recharge rate upon occurrence of the shock. Moreover, we show that solutions get closer at the steady state for lower values of recharge rates. We finally apply the game to the particular case of the Western La Mancha aquifer. The aim of this application is to estimate (in terms of welfare) the inefficiency of open loop and feedback strategies with regards to the characteristics of the shock. We show that the loss of welfare due to private exploitation is maximal for low-intense or later shocks and can reach important values of 40 million of euros.