The point of departure of this work is the situation occurring in the Crau area (South-East of France). In this region, organic farmers use surface water for irrigation and excess water percolates into an aquifer that is used as a source for local residents. In contrast to the standard framework, agricultural production thus increases groundwater levels. In this paper, using a dynamic model, we derive the myopic and socially optimal food and water consumption paths. The first aim is to bring to the fore that an intervention is needed and that, in such a specific case, the environment can be protected thanks to some "good" production incentives. We then analyze the problem of coordination that can occur when two distinct local authorities - an agricultural and a water one, optimize food production and water use. In order to do so, we use an open-loop Nash game. We furthermore add into the picture environmental externalities linked with irrigation water flows that can generate amenities when they replenish wetlands or negative externalities when they induce floods.