Dynamic Subsidy Design for Sustainable Fresh Agricultural Supply Chains: A Differential Game Approach

Fresh agricultural products are highly perishable, and inadequate preservation leads to food loss and supply chain inefficiency, undermining sustainability. This study develops a continuous-time differential game model to analyze dynamic pricing and cold-chain investment decisions in a two-echelon fresh agricultural produce supply chain under government intervention. Two subsidy regimes are examined: one targeting suppliers’ cold-chain investments and another supporting the retailer based on sales volume. By explicitly modeling the dynamic evolution of product freshness, we analyze how subsidy intensity and allocation influence firms’ strategies, market outcomes, and social welfare over time. The results show that when initial freshness is low, firms consistently adopt a penetration pricing strategy and increase cold-chain investment irrespective of subsidy intensity. In contrast, when initial freshness is high, a critical subsidy threshold emerges: Below this threshold, firms employ skimming pricing and reduce investment, whereas above it, they switch to penetration pricing and raise investment. Under equal government expenditure, supplier subsidies achieve higher product freshness but raise retail prices, while retailer subsidies lower prices and stimulate demand, albeit with more modest freshness improvements. Welfare effects are non-linear: supplier subsidies are more effective at low intensities, whereas retailer subsidies become superior beyond a specific threshold. These findings provide actionable insights for designing sustainable, targeted subsidy policies in fresh agricultural supply chains.