A sizable part of the water extracted is unauthorized. This phenomenon may contribute to exacerbate the problem of groundwater over-exploitation. To consider both issues, we study the interaction between the water agency and farmers through a leader–follower differential game in which both agents are perfect foresight. Since the farmers have to pay a tax on individual withdrawals imposed by the water agency to manage the groundwater, illegal behaviors may arise to save this cost. However, if discovered, the farmers are punished with an administrative sanction. The game is solved using feedback Stackelberg solution. Moreover, to enrich the model’s policy suggestions, we also consider an alternative context in which farmers can adopt a trigger strategy. Finally, we perform numerical simulations based on the western La Mancha (Spain) aquifer data to better understand both the analytical results and the effects of the sanction mechanism on non-compliant behaviors.

相当一部分提取的水未经授权。这种现象可能会加剧地下水过度开采的问题。为了考虑这两个问题，我们通过领导者 - 跟随者差异博弈研究水机构和农民之间的互动，其中两个代理人都是完美的远见卓识。由于农民必须对水务机构为管理地下水而征收的个人取水缴税，因此可能会出现非法行为以节省这笔费用。但是，一经发现，农民将受到行政处罚。该游戏使用反馈 Stackelberg 解决方案来解决。此外，为了丰富模型的政策建议，我们还考虑了农民可以采用触发策略的替代背景。最后，