<p>As global climate change intensifies, the agricultural sector, responsible for over 30% of global greenhouse gas emissions, faces an urgent imperative to mitigate emissions and align with international climate commitments. Carbon sink trading, a market-based mechanism that incentivizes emission reductions through sequestration credits, has emerged as an important tool for accelerating carbon peaking and neutrality goals. This study investigates the influence of carbon sink trading on the strategic interactions between farmers and retailers in agricultural supply chains. Employing differential game theory, we construct three cooperative models: decentralized, Stackelberg leader-follower, and centralized, and derive equilibrium strategies for each using the Hamilton-Jacobi-Bellman framework. Through numerical simulations, we evaluate the influence of carbon sink trading on the emission reduction efforts of farmers and retailers, the extent of emission reductions in the supply chain, and the overall profits. Comparative analysis against baseline scenarios without carbon trading reveals that the integration of carbon sink markets enhances profit margins across all models and improves the level of emission reduction in the agricultural supply chain. In addition, our results show that the centralized model outperforms other configurations, followed by the Stackelberg model, with the decentralized model exhibiting the least effectiveness. These findings provide actionable insights for policymakers and supply chain managers to design carbon trading frameworks that harmonize economic incentives with ecological sustainability.</p>