It is challenging for decision-makers (DMs) to deal with uncertainties in multi-level agricultural water resource systems, where DMs independently make decisions but have different levels of power. In this paper, we model the multi-level agricultural water resources system under deep uncertainties as a Stackelberg game, use multi-level programming to solve equilibrium water allocation problems, and introduce robustness metrics into multi-level programming to balance solution feasibility and model optimality within uncertain environments. The approach is applied to a shallow groundwater area with three decision levels, pursuing, from the top level to the bottom one, high food production, fair water allocation, and increased economic benefit. The model generated a series of optimal equilibrium solutions with different robustness degrees. DMs can choose “rational” solutions according to their acceptable costs, oriented robustness degree, expected objective values, and advance risk assessment of uncertainties. Among these solutions, we capture a critical point with high objective values and strong robustness, where DMs can accomplish both objective optimality and solution robustness with a low cost. The proposed approach in this study provides a posterior decision support to consider solution robustness while designing policies in multi-level agricultural water resource systems under deep uncertainties.

中文翻译：

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浅层地下水区域鲁棒Stackelberg平衡水分配模式


对于决策者（DM）来说，处理多层次农业水资源系统中的不确定性是一项挑战，因为决策者独立做出决策，但拥有不同级别的权力。本文将深度不确定性下的多层次农业水资源系统建模为Stackelberg博弈，利用多层规划求解均衡水资源分配问题，并在多层规划中引入鲁棒性指标来平衡解决方案的可行性和模型的最优性在不确定的环境中。该方法适用于浅层地下水区，分三级决策，从上到下追求粮食高产、水资源分配公平、经济效益提高。该模型生成了一系列具有不同稳健程度的最优平衡解。决策者可以根据自己可接受的成本、导向的稳健程度、期望的目标值来选择“理性”的解决方案，并提前对不确定性进行风险评估。在这些解决方案中，我们抓住了一个目标值高、鲁棒性强的关键点，即决策者可以以较低的成本实现目标最优性和解决方案的鲁棒性。本研究提出的方法为在深度不确定性下设计多层次农业水资源系统政策时考虑解决方案的鲁棒性提供了后验决策支持。