Bilevel optimisation as a solution method for an agri-environmental principal-agent problem

Abstract

Recent computational advances in environmental modelling have enabled modellers to predict the impacts of spatially distributed management practices on environmental quality throughout agricultural, forested, urban, and mixed-use watersheds. In addition, real and hypothetical incentive policies- A s well as the interactions between policymakers and policy followers-have been simulated using agent-based modelling techniques as well as optimisation and multi-criteria decision-making methods. In this paper, we use bilevel optimisation as a solution method for solving an agri-environmental principal-agent problem-that is, to create spatially targeted environmental incentive policies to improve water quality. In constructing the problem and solution framework, we draw parallels between agent-based and bilevel approaches as means to simultaneously consider both the objectives of the policymakers and policy followers. Our case study investigates the Tully catchment, which is dominated by sugar cane farming and a major contributor of nutrient runoff from northeastern Australia to the Great Barrier Reef Lagoon. We compare uniform and spatially targeted policies that offer payments for agricultural producers to implement discrete reductions in fertilizer application rates, and the resulting policy solutions highlight the optimal trade-offs between policy cost and nutrient reductions. In addition, we show that targeting policy incentives based on soil type achieves greater efficiencies (i.e., less policy cost, and less nutrient runoff) than simply offering different incentives for each fertilizer reduction. By leveraging knowledge of the spatial distribution of soil type throughout the catchment, our results suggest that policymakers can construct more efficient policies that will ensure adoption and achieve considerable nutrient load reductions at feasible costs. This framework for optimizing incentive policies could be extended to include more complicated and realistic policy options, and it could also be applied in other watersheds dominated by agricultural, forested, urban, and mixed land uses.