Groundwater exploitation and illegal behaviors in a differential game

This paper studies groundwater management through a leader-follower differential game between a water agency and farmers. The access to the common pool is not free and farmers have to pay a water tax to withdraw. To save this cost, we assume that farmers may not declare all the water pumped and face the risk of being sanctioned. The water agency, on the other hand, knows that unauthorized water extraction may occur and chooses the water tax that maximizes only the legal social welfare. The value of the farmers' evasion share is not knew ex-ante by the water agency. The game is solved by feedback Nash solution. To understand how the water agency may counter illegal behaviors, we perform numerical simulations based on the Western La Mancha (Spain) aquifer data. It emerges that the optimal path of the water table is always above the minimum level, although it is sensitive to the level of the ecosystem costs. Moreover, increasing the administrative sanction reduces the unauthorized water extraction and raises the social welfare.