A Multi-Objective Optimization for Determination of Sustainable Crop Pattern Using Game Theory

Amid growing concerns about environmental sustainability in agriculture, this study explores the potential of a game-theoretic approach to identify and implement sustainable crop patterns in the Marvdasht–Kherameh sub-basin, Iran. Employing a cooperative game-theoretic framework, the study considers farmers, environmental advocates and policymakers as stakeholders with distinct objectives: maximising profit, minimising environmental pollution and optimising water consumption. This research aims to develop and apply a comprehensive model that effectively integrates these diverse objectives, proposing practical, sustainable agricultural strategies for the region. The game-theoretic model is integrated with data analysis and optimization techniques to identify Pareto-optimal solutions that balance the competing objectives of stakeholders with vested interest. The advantage of this approach is its ability to produce a robust, spatially visualised solution using GIS-based mapping, which improves communication and aids in implementing sustainable crop patterns. Using regression models, an equilibrium point, defined as the intersection of the three polynomial regression models representing profit, nitrate fertiliser amount and water consumption objectives is identified. The optimised crop pattern corresponding to this equilibrium point is determined using a single-objective optimization model. Key findings include a 40% reduction in wheat cultivation and significant increases in barley (143%) and paddy rice (113%), leading to enhanced resource efficiency and sustainability by optimising water and nitrate fertiliser use. The results offer significant benefits, including detailed spatial visualisation and stakeholder-specific optimization for sustainable crop patterns, which can be adapted to other agricultural regions facing similar challenges.