Differential Game Analysis of Transboundary Pollution Based on Competitive Pricing

Considering the mutual influence of product prices in adjacent regions on demand, in this paper, we develop a differential game model of transboundary pollution that incorporates emission reduction technologies. By applying optimal control theory, we derive the optimal strategies and pollution stock emission paths for two regions in both non-cooperative and cooperative game scenarios. A comparative analysis of the optimal results and an examination of parameter impacts are conducted for these two scenarios. The research results demonstrate that under cooperative game theory, product prices are lower, optimal production is higher, pollution levels in the air are lower, and social welfare is higher. Furthermore, as price competition intensifies, product prices exhibit a downward trend, while pollution stocks have increased accordingly. Conversely, advancements in emission reduction technology lead to increased regional benefits and a corresponding decrease in pollution stocks.