A Water Agency faced with quantity-quality management of a groundwater resource

We consider a problem of groundwater management in which a group of farmers over- exploits a groundwater stock and causes excessive pollution. A Water Agency wishes to regulate the farmer's activity, in order to reach a minimum quantity and quality level but it is subject to a budget constraint and cannot credibly commit to time-dependent optimal policies. We construct a Stackelberg game to determine a set of constant policies that brings the groundwater resource back to the desired state. We define a set of conditions for which constant policies exist and compute the amount of these instruments in an example.