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We study a problem of exploitation of a groundwater resource, mainly used for irrigation, in which a water agency is needed to manage an exceptional and priority extraction of water for an alternative/new use. To this goal, we build a two-stage discrete Stackelberg game in which the leader (the water agency) just intervenes when the new use takes place (in the second stage) and the follower is a representative agent of the regular users of the aquifer. We study two types of Stackelberg equilibrium, namely open-loop (commitment) equilibrium and feedback (non-commitment) equilibrium. Theoretical results show that commitment strategies lead to higher stock levels than non-commitment strategies. However, performing numerical simulations relaxing previous economic assumptions, we show that there are situations in which non-commitment strategies could be more favorable than commitment strategies not only in terms of final stock of the resource but also in terms of regular users' profits.
(with Guiomar Martín-Herrán and Mabel Tidball)