Robust Stackelberg equilibrium water allocation patterns in shallow groundwater areas

It is challenging for decision-makers (DM) 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 system 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.