Differential Game Analysis of Green Technology Investment in the Food Industry Under a Governmental Coordination Mechanism

This study constructs a Stackelberg differential game model for green technology invest-ment in the food industry under a governmental coordination mechanism. The optimal dynamic strategies for local governments and enterprises are derived using Pontryagin’s maximum principle. The backward differential equation method is employed in this study. It is used to analyze the impact of shadow prices on the optimal decisions of both parties. Furthermore, the study examines how social welfare benefits influence the food quality levels within the jurisdiction of local governments. Based on these findings, optimal strategy pathways are proposed to achieve social welfare and enterprise profit maximization in the green transition process of both government and enterprises. The results indicate that a local government’s investment in food quality improvement significantly enhances the food quality levels within their jurisdictions—greater government investment leads to higher food quality. At the same time, food quality levels are positively correlated with the enterprises’ green technology capital investment. Additionally, consumer price sensitivity and sensitivity to price differences have a notable impact on product pricing. As consumers become more price-sensitive, product prices decrease accordingly, which, in turn, helps increase the market share of the enterprises’ products.