# Behavioral Game Theory Model in Pollution Control with Additional Supervision
## 2 Related Work  
The research on environmental pollution control of enterprises mainly focused on formulating and revising environmental protection policies and regulations, pollutant discharge supervision, and third-party pollution control. Environmental protection policies and regulations are important rules to restrict behaviors of enterprises and an important basis for the government regulators to exercise their regulatory responsibilities. From the perspective of the impact of government policies on enterprise behavior, some scholars found that reasonable and effective environmental protection policies [26; 27; 28] can guide enterprises to control pollution actively and reduce environmental pollution; however, in the long-term communication process, enterprises update their strategies to deal with environmental policies [29]. In December 2014, the general office of the State Council issued the opinions on promoting the third-party governance of environmental pollution to promote the establishment of the third-party governance mechanism and improve the third-party governance market. However, this model encountered many problems in the process of practice, such as the failure to establish cooperative relationships between pollutant discharge enterprises and third-party governance enterprises due to unclear responsibility boundaries, with the high cost of technological innovation causing the third-party pollution governance enterprises to bear high market risks. In order to seek scientific decisions to break through the dilemma, the authors of [30] constructed an interest game model between the entrusting party and the entrusted party from the perspective of the third-party pollution control mode, to analyze the main influencing factors of the provision of third-party governance services; they provided policy suggestions for improving the third-party pollution control mechanism. The authors of [31] analyzed the stochastic differential cooperative game model between pollutants discharge enterprises and third-party governance enterprises, and they found that government regulators could guide third-party governance enterprises to actively enter the pollution control market and carry out technology research through balanced regulation and incentive measures. [PERSON] et al. [32] studied the third-party governance of environmental pollution from the principal-agent perspective. [PERSON] et al. [33] explored the rules of communication and the evolutionary law of system formation between the government and third-party pollution governance enterprises. Pollution discharge is an external behavior of enterprises, which requires government supervision and guidance. Although local governments are more capable of controlling environmental pollution than the central government, local governments alone cannot solve the problem of environmental pollution [34]. Pollutant discharge enterprises and government regulators are the two basic related subjects in the problem of enterprise pollution control. Many scholars have carried out a series of studies on the mutual driving relationship between the two. [PERSON] [35] used game theory to explore the strategic interaction between enterprises and government regulators, and found that government regulatory behavior and environmental awareness education can lead to an increase in green production behavior. Using a noncooperative game model, [PERSON] [36] found that increasing fines of enterprise violations would reduce the frequency of law enforcement; The author of [37] used the tool of evolutionary game analysis to demonstrate the important role of government regulation in corporate environmental governance, and the research showed that the government's moderate punishment and maintaining a certain probability of government regulation would promote enterprises to form a stable environmental protection strategy. Therefore, the active supervision strategy of government regulators is in favor of the environmental quality.