# Behavioral Game Theory Model in Pollution Control with Additional Supervision
## 6 Conclusions  
### Research Findings  
From the perspective of evolutionary game theory, this paper constructed a game model between pollutant discharge enterprises and government regulators subject to the influence of third-party supervision, analyzed the impact of different degrees of third-party supervision on the evolutionary stability of government-enterprise strategies, and simulated the theoretical analysis with MATLAB. The results show that the strategy selection of the pollutant discharge enterprises influences that of the government. Moreover, third-party supervision will change the strategy choice of enterprises, as well as have an impact on the supervision behavior of the government. To a certain extent, it will also play a substitute role for government supervision. The findings are summarized below.  
The first conclusion was obtained from Corollary 1 and the simulation results in Figure 6. When the power of third-party supervision is weak, the probability of pollutant discharge enterprises and the government bearing losses due to third-party supervision is very small; thus, it is impossible to change the strategy selection of the enterprises and the government.  
The second conclusion was obtained from Corollary 2 and the simulation results in Figure 7. Appropriately increasing the power of third-party supervision will affect the behavior choice of pollutant discharge enterprises or the government in a short period of  
Figure 8: Simulation results of government–enterprise strategies. (**a**) Results after increasing the power of third-party supervision, where the increase is higher than that in Figure 7. The corresponding value range of \(\mu\) is \((\frac{C_{1}}{W_{1}},\frac{C_{2}}{H+W_{2}})\). (**b**) Results of the strong power of third-party supervision. The corresponding value range of \(\mu\) is \((\max(\frac{C_{2}}{W_{1}},\frac{C_{3}}{H+W_{2}}),1)\).  
time. If the enterprises have a lower cost of pollution control, higher penalties from the government for no control pollution strategy, or a greater loss after the discovery of no control pollution behavior by the third-party, third-party supervision will promote the enterprises to evolve into a pollution control strategy; otherwise, third-party supervision will not play a role. If the supervision cost of the government is small, the government attaches great importance to reputation benefits, or the loss after the discovery of no supervision behavior by the third-party is large, the government will tend to choose a supervision strategy under the influence of third-party supervision; otherwise, third-party supervision is ineffective for government regulators. In this situation, the strategy selection of the pollutant discharge enterprises follows that of government regulators; thus, there is no evolutionary stability strategy between the government and enterprises under the third-party supervision.  
The third conclusion was obtained from Corollaries 3 and 4 and the simulation results in Figure 8. The strong power of third-party supervision will promote the pollutant discharge enterprises to evolve into a pollution control strategy, even if the government chooses no supervision strategy, and the third party can also replace the government in playing a regulatory role. A stronger power of third-party supervision accelerates the evolutions of enterprises into a pollution control strategy.