A local public-good game played on directed networks is analyzed. The model is motivated by one-way flows of hydrological influence between cities of a river basin that may shape the level of their contribution to the conservation of wetlands. It is shown that in many (but not all) directed networks, there exists an equilibrium, sometimes socially desirable, in which some stakeholders exert maximal effort and the others free ride. It is also shown that more directed links are not always better. Finally, the model is applied to the conservation of wetlands in the Gironde estuary (France).