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The work is devoted to the study of the impact of external control on the strategies of pollutant discharge enterprises and government regulators in the field of environmental protection. The authors construct a model of the relationship between these entities. It is an evolutionary game in which the players are entities that generate pollutants and the government departments that implement pollution supervision. The choice of strategies of both of these entities and the evolutionary stability of the system controlled by different regulatory efforts, i.e., a third party, are analyzed. The authors then verify the evolutionary paths and evolutionary results of the model under different conditions using simulation analysis based on this model. The conducted research shows that the weak power of third-party supervision is not enough to promote the evolution of the behavioral decisions of the government and enterprises. An appropriate increase in the power of third-party supervision will change the choice of the government and enterprises strategies in the short term; however, due to the mutual influence of the strategies between both sides of the game, in this situation, the evolutionary system does not pursue a stable state. The strong power of third-party supervision will push enterprises to choose a pollution control strategy, change the intensity of government supervision, and replace government supervision to a certain extent. It is an interesting example of modeling the relationship of this system on the basis of evolutionary game theory. The findings can be regarded as a theoretical reference for environmental pollution control of enterprises. [ABSTRACT FROM AUTHOR]