With the continuous increase in greenhouse gas emissions in the world and the United States announcing withdrawal from the Paris Agreement, the conflicts between environmental protection and economic growth of developing and developed countries have become increasingly challenging. In this paper, following the principle of "common but differentiated responsibilities" specified in the Kyoto Protocol and the Paris Agreement, we develop an optimal pollution control model based on a dynamic system for both developing and developed countries. We analyze how different perspectives of the developing and developed countries affect their investments in pollution control and how to determine their responsibilities based on the principle of common but differentiated responsibilities. Our aim is to obtain a stable equilibrium mechanism to maximize the social welfare between the developing and developed countries and explore the optimal pollution control and economic growth path. Our results show that it is optimal for the developed countries to help developing countries with pollution control in their initial stage of economic growth. Once the developing countries reach a certain economic development level, they can contribute more to pollution control, while the developed countries can reduce their environmental investment. We show that by following this optimal path, the developing and developed countries can effectively control environment pollution without significant loss of social welfare.
Keywords: economic growth; environment protection; game theory; greenhouse gas emissions.