Game-Theoretic Analysis of Grain Sales Strategies: Nash Equilibrium and Cooperative Bargaining

Abstract

This study uses game-theoretic models, including Nash equilibrium and Rubinstein bargaining theory, to analyze the strategic interactions between grain farmers and enterprises in Heilongjiang, China. A mathematical framework was developed to incorporate moisture content, discount factors, and threat points to derive equilibrium conditions with a focus on profit distribution under price mechanisms. The analysis reveals that farmers face a trade-off between higher profits from enterprise cooperation, which emphasizes grain quality, and lower-risk market sales, while enterprises balance procurement costs against resale premiums. Through Python simulations with real data, the analysis suggests that smallholders tend to prefer direct market sales due to quality-related risks, whereas large-scale farmers benefit more from cooperative agreements. The bargaining model further identifies Pareto-optimal solutions under dynamic negotiations, and highlights how first-mover advantages and discount factors shape outcomes. The findings suggest policy interventions to better align incentives, reduce negative-sum scenarios, and promote sustainable farmer-enterprise partnerships. This study has significant practical and theoretical implications.