*7.3. Influence of Changes in Government Subsidies and Fines on Evolution Results When Energy-Saving Benefits Outweigh Costs*

(1) When the benefits of energy-saving renovations are greater than the cost, the government subsidies increase. As shown in Figure 6, assuming that the initial state remains unchanged, the subsidies obtained by energy-saving service enterprises and rural residents voluntarily participating in the energy-saving renovations of existing rural residential buildings under the government's regulatory incentive policy are increased from *S*<sup>1</sup> = 30, *S*<sup>2</sup> = 5 to *S*<sup>1</sup> = 35, *S*<sup>2</sup> = 8. The ultimate behavior strategy of the three parties in the game is still H8 (1,1,1) (regulatory incentive, providing energy-saving services and performing energy-saving renovation). However, when comparing Figure 4 with Figure 6, due to the improvement in government subsidies, the energy-saving service enterprises and the rural residents can be fully mobilized to participate in energy-saving renovations of existing rural houses, and the benefits of both can be increased. Therefore, the rate at which an evolutionary stable equilibrium state is reached accelerates with the increase in the initial ratio. However, increasing government subsidies will increase the cost of supervision and the incentives for the government to participate in energy-saving renovations of existing

rural residential buildings. Therefore, by comparing Figures 4a and 6a, it can be found that no matter which initial state is chosen, the ultimate behavior strategy of the government is to implement supervision and incentive policies. However, in the same initial state, increasing subsidies will obviously slow down the process and bias the government's behavior strategy towards the implementation of supervision and incentive policies. The time needed for the system to evolve to an equilibrium and stable state is, therefore, also prolonged. By comparing Figure 4b with Figure 6b, it can be found that, in the same initial state, the curvatures of the three curves in Figure 4b are larger than the corresponding three curves in Figure 6b, and the trend rate of (1,1,1) is obviously larger. This conclusion can be verified again in conjunction with Figure 7. When the initial state is the same as (0.4, 0.5, 0.6), and when the government subsidy increases from *S*<sup>1</sup> = 30, *S*<sup>2</sup> = 5 to *S*<sup>1</sup> = 35, *S*<sup>2</sup> = 8, although the increase in the subsidy is moderate for energy-saving service enterprises and rural residents, their behavior strategies with regard to providing energy-saving services and performing energy-saving renovations are consistent, and the rate of the curve-biased cooperative strategy is also accelerated. However, raising subsidies has a significant impact on the government, which leads the three parties in the game taking more time to reach an evolutionary stable equilibrium state. The reason for this lies in the increase in subsidies, which increases the cost of government supervision.

**Figure 5.** System evolution results under different initial intentions when the cost of energy-saving renovations is greater than the benefit. (**a**) The time at which the system evolves to a stable state. (**b**) Evolution rate.

(2) When the income of energy-saving renovations is greater than the renovation costs, the government increases its fines. As shown in Figure 8a, when other conditions are unchanged, and the initial state is (0.4, 0.5, 0.6), government fines will increase from *F*<sup>1</sup> = 40 and *F*<sup>2</sup> = 10 to *F*<sup>1</sup> = 60 and *F*<sup>2</sup> = 15. The ultimate behavioral strategy of the three parties in the game is still H8 (1,1,1) (supervision and encouragement, providing energy-saving services and performing energy-saving transformations). However, it can also be seen from Figure 8 that when government fines increase, the time needed for the three parties in the game to reach an evolutionary stable equilibrium state is shortened on the premise that the income from energy-saving renovation is still greater than the renovation costs. At the same time, combined with Figure 8b, it can be seen that, when *F*<sup>1</sup> = 60, *F*<sup>2</sup> = 15, and the initial state increases from (0.2, 0.3, 0.4) to (0.5, 0.6, 0.7), the time needed for the three parties to reach an evolutionary stable equilibrium state is also shortened. When ensuring that the income created by energy-saving renovations is greater than the renovation costs, a moderate increase in government punishment will serve as a warning to energy-saving service enterprises providing standardized energy-saving services and rural residents

who refuse to perform energy-saving renovations. On the premise of the rational person, the energy-saving service enterprises and rural residents will choose to participate in the energy-saving renovations of existing rural residential buildings to ensure the maximization of their own interests after weighing the benefits and costs.

**Figure 6.** System evolution results under different initial intentions when subsidies are increased. (**a**) The time at which the system evolves to a stable state. (**b**) Evolution rate.

**Figure 7.** Evolution results of subsidy enhancement system under the same initial state.

**Figure 8.** System evolution results under different initial intentions when punishment is increased. (**a**) The time at which the system evolves to a stable state. (**b**) Evolution rate.

#### **8. Conclusions**

Energy-saving renovations of existing rural residential buildings is an important part of national energy-saving and emission-reduction work, which is of great significance for saving energy, improving the indoor thermal environment, reducing greenhouse gas emissions, and promoting the transformation of development mode in the field of housing, urban–rural construction, and sustainable economic and social development. In this paper, the evolutionary game theory of bounded rationality is used to analyze the evolution law of the behavior strategies of the main bodies involved in energy-saving renovations of existing rural residential buildings, and an evolutionary game model and dynamic decision equations of the three-party behavior bodies of the government, energy-saving service enterprises and rural residents are constructed. By solving the stability points of these dynamic equations, the stability strategies and influencing factors of tripartite actors in different situations are analyzed.

(1) In energy-saving renovations of existing rural residential buildings, as the decisionmaker and supervisor, the government's behavior strategies are mainly influenced by supervision cost and incentive policies. When the government does not supervise energy-saving service enterprises and rural residents, they have relatively low willingness to participate in existing rural buildings on the premise of limited rationality, and choose uncooperative behavioral strategies, that is, H1 (0,0,0) (laissez-faire, providing no energy-saving services, rejecting energy-saving renovations). However, in order to promote energy-saving renovations of existing rural residential buildings, and achieve energy conservation and emission reductions, the government tends to supervise the choice of behavior strategies. Therefore, in the process of supervision, the appropriate fines and subsidies provided by the government to energy-saving service enterprises and rural residents will help to mobilize their enthusiasm to participate in energy-saving transformations, and the behavior strategies of the three parties will tend towards H8 (1,1,1) (supervision incentives, providing energy-saving services and performing energy-saving transformations).

(2) The energy-saving service enterprises are the information-superior party, and they have complete information on energy-saving technologies. When participating in energysaving renovations of existing rural residential buildings, their behavior strategies are mainly affected by the benefits and costs of providing standardized energy-saving services, and the loss caused by providing unstandardized energy-saving services. Therefore, when the benefits of participating in energy-saving transformation outweigh the costs, the behavior strategy of the energy-saving service enterprises is to provide standardized energysaving services, regardless of whether the government subsidies or penalties are increased.

(3) As the inferior-information party, rural residents participate in energy-saving renovations of existing rural residential buildings in the hope of not only improving their living conditions, but also of obtaining certain government subsidies. The main influencing factors are the government subsidies, the loss caused by the unqualified energy-saving services provided by the energy-saving service enterprises and the extra economic expenses incurred during the energy-saving renovations. Hence, when the subsidies provided by the government are greater than the loss caused by unqualified energy-saving services provided by energy-saving service enterprises and the extra economic expenditure generated during the energy-saving transformation, the behavior strategy of rural residents is to carry out energy-saving transformations.

(4) The limitation of the research. The main limitation in this study is the research on the behavior strategy of market participants in energy-saving renovation of existing rural residential buildings only starts with three core participants, and the related auxiliary participants in energy-saving renovation of existing rural residential buildings have not been analyzed. That is because in the process of energy-saving renovation of existing rural residential buildings, the behaviors and strategies of the government, energy-saving service enterprises and rural residents have a relatively large mutual restriction and influence, while other related auxiliary participants may have an influence on a certain participant, but not all of them. For example, the bank's behavior strategy may have a greater impact

on the government and energy-saving service enterprises, but it has a less impact on rural residents. Therefore, the impact on the research results is not great, but it can be a direction for further research in the future.

Therefore, in the process of energy-saving renovations of existing rural residential buildings, the government, energy-saving service enterprises and rural residents, as the three main participants, will choose the most favorable behavior strategies, weighing the government subsidies and fines and the cost of their own participation to maximize their own interests under limited rationality. Therefore, in order to realize the energy-saving renovations of existing rural residential buildings, participants' cooperation is needed. In future research, we will further discuss the impact of increased stakeholder participation in energy-saving renovations of existing rural residential buildings, and analyze their development path, as influenced by various factors.

**Author Contributions:** Conceptualization, M.-Q.H. and R.-J.L.; methodology, M.-Q.H.; software, M.-Q.H.; validation, R.-J.L.; formal analysis, R.-J.L.; investigation, M.-Q.H. and R.-J.L.; data curation, M.-Q.H.; writing—original draft preparation, M.-Q.H. and R.-J.L.; writing—review and editing, M.-Q.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 71503224) and Fujian Natural Science Foundation (Grant No. 2019J01865). The work described in this paper was also funded by Fujian Social Natural Science Foundation (Grant No. FJ2015C110), University Outstanding Young Scientific Research Talent Cultivation Program Project in Fujian Province, Project of "Scientific Research Climbing Plan" of Xiamen University of Technology (Grant No. XPDKT20034), and China-APEC Cooperation Fund-Study and Training on Marine Spatial Planning in APEC Region (Grant No. 121170000000200012).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

