Generalized Nash Equilibrium Seeking for Crop Mix Selection in Sustainable Agriculture

Since diversifying crop selection can significantly optimize resources, increase resilience to climate change, and contribute to sustainable development, decision-making tools are crucial to help farmers identify optimal crop cultivation strategies. This paper proposes a novel optimization framework for crop mix selection under the non-cooperative game-theoretical perspective, i.e., assuming that the agents (e.g., farmers and agriculture companies) behave selfishly. Such a perspective naturally arises when multiple agents are competing for shared resources, such as water, land, and carbon emissions quotas. First, we illustrate the system model, comprising both local and global resource constraints that the crop mix strategy of all agents must abide by. Then, we characterize the Generalized Nash Equilibrium problem stemming from such a formulation, providing an iterative equilibrium-seeking approach based on the consolidated operator splitting framework. Finally, we numerically test the proposed framework using real-world data.