An Evolutionary Game Study of Clean Heating Promotion Mechanisms under the Policy Regulation in China

Recently, various Chinese provinces have greatly reduced their coal consumption due to new environmental protection policies. Because of these policies, the orderly development of the clean energy heating mode has been effectively promoted. As the problem of air pollution in the northern part of China is particularly prominent, adopting clean heating in winter is an important solution to control air pollution for those regions. However, there is a tricky balance to be struck between the government and the heating companies when it comes to using clean heating during winter. Therefore, it is crucial for the government and heating enterprises to research new strategies. Consequently, this paper carries out a comprehensive study on the multiple factors influencing the game relationship between the government and heating enterprises, and tries to set up a more general model for the theoretical analysis of mechanisms of clean heating promotion, as well as their numerical simulation. The research results show: (1) The initial possibilities available to government and heating enterprises have a significant impact on the final strategy choice for the heating system; (2) due to advantages such as increases in social benefits, subsidies, fines, and clean heating profits, as well as the lessening of traditional heating costs, and regardless of the decrease in traditional heating profits, it is possible for the government to adopt the promotion strategy; and (3) there are more opportunities for heating companies to pursue in order to implement clean heating strategies. In conclusion, this paper proposes valuable suggestions for the government and heating companies concerning clean heating in China.


Introduction
Recently, the Chinese government implemented the environmental protection supervision system. In response, the coal consumption of various provinces has greatly reduced, and clean energy heating systems have been effectively promoted. At the same time, the problem of air pollution in the northern part of China is particularly prominent. Due to large-scale winter heating, during the long heating period from October to April every year, the winter heating supply has a significant impact on the surrounding environment. Therefore, to further promote the issue of clean energy consumption, this paper discusses regional clean energy resources that could alleviate environmental pollution. For example, Beijing uses the surrounding wind energy, as well as electric heating technology, to solve the problem of winter heating [1]. At the same time, both the provincial and the municipal governments, as well as different heating companies, tend to pay attention to clean heating during the heating season. clean heating, and the other is to adopt traditional heating. This paper constructs an evolutionary game model of clean heating propulsion mechanisms, and conducts a theoretical analysis and numerical simulation on the basis of this model to provide useful suggestions for the government to assist in decision-making.
The paper consists of six parts: Section 1-an introduction to clean development and heating; Section 2-literature review; Section 3-building an evolution game model of the clean heating mechanism; Section 4-a discussion on the evolution game model; Section 5-the numerical simulation calculations; and Section 6-conclusions and future research directions.

Literature Review
Winter heating is one of the most significant sources of air pollution and has a significant impact on the environment. Clean heating can reduce pollutant emissions and improve air quality. Thus, clean heating plays an essential role in the heating industry, especially for winter heating of China. To solve the severe air pollution and smog problems in northern China, the Chinese government has introduced a series of clean heating policies. Options with respect to pricing policy have been proposed for clean heating in the northern region by the National Development and Reform Commission, for example, the winter clean heating plan for Northern China (2017-2021) and the Notice on Carrying out Central Financial Support for the Pilot Work of Winter Clean Heating in Northern Areas. It is necessary for heating companies to adopt clean heating while implementing a clean heating policy. Furthermore, due to the long cycle of heating in winter, it is necessary to carry out strategic selection research from the perspective of dynamic development.
Clean heating can improve air quality and save energy, and it has been widely used in many countries and regions. According to the census bureau, there are about 117 million households in the United States; 50% of households are heated by natural gas, 39% by electricity, and the rest by heating oil, propane, wood and other means. In Stockholm, the Swedish capital, there is a new way of heating the city's homes using the heat generated by data centers. In Austria, utility import waste from Rome, Italy has been used to generate electricity to supply the heating load. Power plant waste heating, natural gas and renewable energy supply three-quarters of Denmark's heating load. In Finland, almost all towns and cities have adopted waste heating from power plants to reduce environmental pollution. In Japan, heating products pay more attention to energy conservation and environmental protection, such as thermal power supply systems, heat storage tanks and urban waste heating, which can improve the efficiency of energy utilization.
Different countries and regions that promote clean heating have launched a variety of incentive policies, such as subsidies, tax incentives, and market access policies. Take Denmark's clean heating policy as an example. In 1990, to improve the environmental efficiency during the heating season, the government revised the heating act. On the one hand, it vigorously promoted the use of waste heat heating in power plants, and on the other hand, it increased the use of cleaner fuels, mainly natural gas. In addition to administratively promoting the use of clean heating and expanding the scale to reduce costs, the Danish government has also introduced various financial support policies to promote the efficient and clean transformation of heating through taxation, subsidies and other means. In terms of tax revenue, Denmark charges a corresponding tax on fossil fuels such as coal, oil and natural gas for heating, while there is no similar direct tax on the waste heat of power plants to reduce the tax payment. In terms of subsidies, all heating companies using natural gas and biomass fuels can enjoy different levels of subsidies. All these efforts are beginning to show results. Since 1998, Denmark has achieved self-sufficiency in energy, and the total amount of energy consumption remains unchanged despite the increase in gross domestic product year by year.
Policy regulation is a method of achieving goals by means that include incentives, punishments, and other policy measures [24][25][26][27], and many scholars have studied policy regulation in the environmental protection problem. For instance, Salomão and Rocha [28] used an evolutionary game model to study the interplay between corporate environmental compliance and enforcement promoted by the policymaker in a country facing a pollution trap. Achim and Jörg [29] found that management opportunities are more environmentally conscious than the government's economic activities. Taylor et al. [30] interviewed officials of the British government management department and analyzed the interview results to make recommendations for the government with respect to the formulation of regulatory policies. Cheng et al. [31] proposed countermeasures through statistical analysis from 30 Chinese provinces from 1997 to 2014, and provided a model for carrying out empirical research on impact reductions and technical progress under policy regulation. Jiang [32] constructed a multi-game subject evolution game model, including central and local governments, coal mining enterprises and miners, theoretical analysis and numerical simulation of the model.
The evolutionary game theory was proposed by the British scholar Smith [33]. As a new game theory research method, evolutionary game theory combines traditional game theory with animal evolution theory to analyze the game behavior of different participants [34]. In recent years, evolutionary games have found new applications and innovations in theory and applied research. For example, Kleshnina et al. [35] studied the problem of evolutionary stability strategy (ESS) under imperfect conditions and found that imperfections can change the outcome and dynamics of the game. Babu et al. [36] carried out a study based on evolutionary game theory in order to explain and predict the evolutionary game problem with respect to the social and economic sustainability of the public health insurance supply chain with random disturbances. Luo et al. [37] studied the co-evolution of resources and cooperation in the space evolution game. Kolokoltsov [38] studied the effects of interference, resistance, and cooperation on participants in evolutionary games. Hadzibeanovic et al. [39] studied the impact of enhanced cooperation mechanisms and signal guidance on the evolutionary game outcomes and their dynamics. Liu et al. [40] proposed a policy update rule driven by local information.
The advantages of using this evolutionary game rationality to study the mechanism of clean heating promotion are as follows: (1) Using evolutionary game theory can analyze the relationship between the choice strategies of two different stakeholders in local governments and heating companies over time, and avoid the static nature of traditional classical game analysis problems; (2) By constructing an evolutionary game model and using a theoretical solution and numerical simulation, it is possible to propose policy recommendations for the government to promote clean heating.

The Model
The research object of this paper is the clean heating promotion mechanism under the policy regulation in China. To improve the air quality, the government began to implement clean heating in winter to encourage the heating supply. The adoption of clean heating by heating companies is rewarded or punished through the adoption of policy regulations. There are two strategies for heating companies to make heating decisions, one is to adopt clean heating, and the other is to adopt traditional heating. For clean heating, due to the need to upgrade or replace new heating equipment, the cost will increase, and the revenue will decrease. At the same time, the use of clean heating will receive some government subsidies in order to reduce the operating costs. For traditional heating, the benefits are relatively high, due to the relatively low cost; however, environmental pollution is severe, so heating companies employing traditional heating will face penalties from the environmental protection department. The notation of the clean heating promotion mechanism under policy regulation is shown in Table 1. We assume that there are two players in the market: the government and the heating company. Then, we build the model in two steps: Step 1: The government's strategy can be either promotion or non-promotion. Therefore, the government's strategy can be as follows: (1) promote clean heating and subsidize companies that provide clean heating; or (2) adopt no promotion of clean heating, but give no subsidies to traditional heating companies.
The heating company has two pure strategies: clean heating and traditional heating. Therefore, the company's strategy can be as follows: (1) adopt clean heating of winter heating and receive subsidies from the government; or (2) adopt traditional heating and receive a substantial fine from the environmental protection department.
Step 2: Calculate the dynamic evolution system. In the model, x is the probability that the government will adopt the promotion clean heating strategy; thus, the probability of the government adopting no promotion clean heating behavior is 1 − x. Similarly, the probability of the heating company adopting a clean heating strategy is y, and the probability of adopting traditional heating behavior will be 1 − y. For governments and heating companies, as time goes on, they will adjust their strategies according to changes in income. The payoff matrix of governments and heating companies is shown in Table 2. For the government, when the heating company adopts the clean heating strategy, the benefit of the promotion strategy is Π g1 , and the benefit of the no promotion strategy is Π g3 . When the heating company adopts the traditional heating strategy, the benefit of the promotion strategy is Π g2 , and the benefit of the no promotion strategy is Π g4 .
Thus, when the government adopts the promotion strategy, the average revenue is When the government adopts the no promotion strategy, the average revenue is Similarly, for the heating company, when the government adopts the promotion strategy, the benefit of clean heating is Π h1 , and the benefit of traditional heating is Π h2 . When the government adopts the no promotion strategy, the benefit of clean heating is Π h3 ; and the benefit of traditional heating is Π h4 .
Thus, when the heating company adopts a clean heating strategy, the average revenue is When the heating company adopts a traditional heating strategy, the average revenue is For the government and heating company, the average revenues are Based on the classical theory of evolutionary games, the dynamic evolution equation of the government and heating company can be derived.
Next, by solving the equation, the equation can be represented by the parameters as follows:

Discussion
For the stability analysis of the evolutionary game model, the Jacobian matrix is used to find its value and trace, and the positive and negative is judged. The evolutionary game model between the government and the heating company's clean heating mechanism of the Jacobian matrix is Thus, the value of the matrix is Based on Equation (18), the trace of the matrix is Theorem 1. For the evolutionary game model between the government and the heating company's clean heating mechanism, when certain conditions are met, there are five equilibrium points (0,0), (0,1), (1,0), (1,1), and (x*,y*).
Proof. It is obvious that F(x) = dx dt = 0 and I(y) = dy dt = 0, (0,0), (0,1), (1,0), and (1,1) are equilibrium points when the evolutionary game replicates dynamic real estate satisfaction. The parameters meet It is easy to understand that if the value of x* or y* is greater than 1, the evolution game maximum will be exceeded. Due to space limitations, this paper only studies the evolutionary game process that satisfies the conditions 0 are satisfied, the evolutionary stable strategy (ESS) of the evolutionary game model between the government and the heating company's clean heating mechanism is only (0,0) and (1,1), and the unstable point is (0,1) and (1,0), the saddle point is (x * ,y * ).
can get values and traces of five state equilibrium points, as shown in Table 3. Table 3. Stability analysis.

Point det J tr J Stability
When social benefits and clean heating profit increases, and the cost of the traditional heating profit decreases, it is possible for the government and the heating company to adopt a promotion strategy.
To facilitate the analysis, the evolutionary game area is divided into two parts, named M and N, respectively, where M + N = 1. M represents a region consisting of four points (1,1), (0,1), (1,0), and (x*,y*), and the size of the area indicates the approaching point (1,1). N represents a region consisting of four points (0,0), (0,1), (1,0), and (x*,y*), the size of the area indicates the approach (0,0) point. Then, M can be expressed as a formula Proof. To study the influence of parameter changes on the evolutionary game process and solve the partial derivative of M, we can conclude that: We can get that M will increase when social benefits and clean heating profits increase. Therefore, when the social benefits and clean heating profits increase, it is more likely that the government will choose the promotion strategy and the heating enterprises will adopt a clean energy strategy.
(2) dM R 3 < 0. We can get an increase in promotion cost and the traditional heating profit. Therefore, when the promotion cost and the traditional heating profit increases, the chance that the government will choose the no promotion strategy will increase, and the chance that heating enterprises will adopt a traditional energy strategy will also increase.

Numerical Simulation
In this section, using the numerical software MATLAB2014b, the evolutionary game process is simulated, and the dynamic evolution process of different initial states and different parameter conditions is considered. Scenarios 1 to 3 consider the effects of low, medium and initial probability on the outcome of the evolutionary game process. Scenarios 4 to 9 consider the effects of social benefits, subsidy, promotion cost, fine, clean heating profit and traditional heating profit on the outcome of the evolutionary game process. The parameters have been set in different conditions, as described in Table 4.

Probability of X and Y Values
To study the influence of different initial probabilities on the evolutionary game results, the evolutionary game changes of the government and heating companies are considered in the three cases, including low initial probability, medium initial probability, and high initial probability. In the case of a low initial probability, it is unlikely that the government and heating company will initially adopt the promotion and clean heating strategies; therefore, the government will choose no promotion strategies, and the heating company will ultimately select traditional heating strategies. In the medium Sustainability 2019, 11, 3778 9 of 22 initial probability scenario, the government and heating company may initially adopt the promotion and clean heating strategies, so the government will ultimately choose promotion strategies, and the heating company will ultimately select clean heating strategies. In the high initial probability scenario, it is highly likely that the government and heating company will initially adopt the promotion and clean heating strategies, so the government will ultimately choose the promotion strategy, while the heating company will ultimately select clean heating strategies. In practice, due to the dangers of environmental pollution, the government is likely to adopt the promotion strategy at high initial probability in order to improve the environment. Then, heating enterprises will be affected by increased costs, and low initial probability will probably be adopted for traditional heating. Therefore, due to the government's high initial probability, the heating company likely has a low initial probability.
To study the low initial probability, medium initial probability, and high initial probability, the evolutionary game processes of the government and heating enterprises are shown in Figures 1-3. strategies, and the heating company will ultimately select clean heating strategies. In the high initial probability scenario, it is highly likely that the government and heating company will initially adopt the promotion and clean heating strategies, so the government will ultimately choose the promotion strategy, while the heating company will ultimately select clean heating strategies. In practice, due to the dangers of environmental pollution, the government is likely to adopt the promotion strategy at high initial probability in order to improve the environment. Then, heating enterprises will be affected by increased costs, and low initial probability will probably be adopted for traditional heating. Therefore, due to the government's high initial probability, the heating company likely has a low initial probability.
To study the low initial probability, medium initial probability, and high initial probability, the evolutionary game processes of the government and heating enterprises are shown in Figures 1-3. In Figure 1, the final result of the dynamic evolution of the system is (0,0), where the government will adopt the no promotion strategy, and the heating company will adopt the traditional heating strategies. From Figure 1, it can be seen that the heating company is evolving faster than the government. The main reason for this is that the heating company chooses a strategy for reaching 0, and it takes about time 1. Meanwhile, the government selects a strategy for reaching 0, and it takes about time 2. In Figure 2, the final result of the dynamic evolution of the system is (1,1), where the government will adopt promotion, and heating company will adopt clean heating strategies. From Figure 2, it can be seen that the government evolves faster than the heating company. The main reason for this is that the government chooses a strategy to reach 1, and it takes about time 3. Meanwhile, the heating  In Figure 2, the final result of the dynamic evolution of the system is (1,1), where the government will adopt promotion, and heating company will adopt clean heating strategies. From Figure 2, it can be seen that the government evolves faster than the heating company. The main reason for this is that the government chooses a strategy to reach 1, and it takes about time 3. Meanwhile, the heating company selects a strategy to reach 1, and it takes about time 8.  In Figure 1, the final result of the dynamic evolution of the system is (0,0), where the government will adopt the no promotion strategy, and the heating company will adopt the traditional heating strategies. From Figure 1, it can be seen that the heating company is evolving faster than the government. The main reason for this is that the heating company chooses a strategy for reaching 0, and it takes about time 1. Meanwhile, the government selects a strategy for reaching 0, and it takes about time 2.
In Figure 2, the final result of the dynamic evolution of the system is (1,1), where the government will adopt promotion, and heating company will adopt clean heating strategies. From Figure 2, it can be seen that the government evolves faster than the heating company. The main reason for this is that the government chooses a strategy to reach 1, and it takes about time 3. Meanwhile, the heating company selects a strategy to reach 1, and it takes about time 8.
In Figure 3, the final result of the dynamic evolution of the system is (1,1), where the government will adopt promotion, and the heating company will adopt clean heating strategies. From Figure 3, it can be seen that the government evolves faster than the heating company. The main reason for this is that the government chooses a strategy to reach 1, and it takes about time 1. Meanwhile, the heating company chooses a strategy to reach 1, and it takes about time 7.

Social Benefits
To study the influence of social benefits on the government choice of a promotion strategy, the parameter R 1 has a value range of (0, 40), and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 4 that, with the increase of social benefits, the government's final strategy gradually changes from adopting no promotion strategy to adopting the promotion strategy. When R 1 is very small in actual situations, the government will adopt a no promotion strategy. When R 1 is increased to a certain value, the government's strategy will change from the no promotion strategy to the promotion strategy. When social benefits are increased gradually, the speed of evolution becomes faster.
Similar change trends are also depicted in Figure 5 in order to study the influence of social benefits on the heating company's choice of clean heating strategy. It can be seen from Figure 5 that with the increase of social benefits, the heating company's final strategy gradually changes from adopting a traditional heating strategy to adopting a clean heating strategy. When R 1 is very small in actual situations, the heating company will opt for the traditional heating strategy. When R 1 is increased to a certain value, the heating company's strategy changes from the traditional heating strategy to the clean heating strategy. When social benefits are gradually increased, the speed of evolution becomes faster.
Based on the above, it may be concluded that the increased probability of social benefits can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent.
gradually, the speed of evolution becomes faster.
Similar change trends are also depicted in Figure 5 in order to study the influence of social benefits on the heating company's choice of clean heating strategy. It can be seen from Figure 5 that with the increase of social benefits, the heating company's final strategy gradually changes from adopting a traditional heating strategy to adopting a clean heating strategy. When R1 is very small in actual situations, the heating company will opt for the traditional heating strategy. When R1 is increased to a certain value, the heating company's strategy changes from the traditional heating strategy to the clean heating strategy. When social benefits are gradually increased, the speed of evolution becomes faster.
Based on the above, it may be concluded that the increased probability of social benefits can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent.

Subsidy
To study the influence of subsidy on the government's choice of a promotion strategy, the parameter U has a value range of (0,6), and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 6 that with the increase in subsidy, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When U is very small in actual situations, the government will adopt no promotion strategy.

Subsidy
To study the influence of subsidy on the government's choice of a promotion strategy, the parameter U has a value range of (0,6), and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 6 that with the increase in subsidy, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When U is very small in actual situations, the government will adopt no promotion strategy. When U increases to a certain value, the government's strategy changes from the no promotion strategy to the promotion strategy. When the subsidy is gradually increased, the speed of evolution becomes faster.  Similar change trends are also depicted in Figure 7, in order to study the influence of subsidy on the heating company's choice of clean heating strategy. It can be seen from Figure 7 that with the increase of subsidy, the heating company's final strategy gradually changes from adopting the traditional heating strategy to adopting the clean heating strategy. When U is very small in actual situations, the heating company will adopt the traditional heating strategy. When U is increased to a certain value, the Heating company's strategy changes from the traditional heating strategy to the clean heating strategy. When the subsidy is gradually increased, the speed of evolution becomes faster.  Based on the above, it may be concluded that the increased probability of subsidy can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent.

Promotion Cost
To study the influence of promotion costs on the government choice of a promotion strategy, the parameter C has a value range of (0,6), and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 8 that with a decrease in promotion cost, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When C is very small in actual situations, the government will adopt the no promotion strategy. When C is decreased to a certain value, the government's strategy changes from the no promotion strategy to the promotion strategy. When the promotion cost is gradually decreased, the speed of evolution becomes faster.
Similar change trends are also depicted in Figure 9, in order to study the influence of promotion cost on the heating company's choice of clean heating strategy. It can be seen from Figure 9 that, with a decrease in promotion cost, the heating company's final strategy gradually changes from adopting a traditional heating strategy to adopting a clean heating strategy. When C is very small in actual situations, the heating company will adopt the traditional heating strategy. When C is decreased to a certain value, the Heating company'sstrategy changes from traditional heating strategy to a clean heating strategy. While the promotion cost is gradually decreased, the speed of evolution becomes faster. a traditional heating strategy to adopting a clean heating strategy. When C is very small in actual situations, the heating company will adopt the traditional heating strategy. When C is decreased to a certain value, the Heating company'sstrategy changes from traditional heating strategy to a clean heating strategy. While the promotion cost is gradually decreased, the speed of evolution becomes faster.
Based on the above, it may be concluded that the decreased probability of promotion cost could effectively encourage heating companies to adopt clean heating strategies, and government will adopt the promotion strategy to some extent.

Fines
To study the influence of fines on the government choice of a promotion strategy, the parameter F has a value range of (0,6) and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 10 that with the increase of fines, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. Based on the above, it may be concluded that the decreased probability of promotion cost could effectively encourage heating companies to adopt clean heating strategies, and government will adopt the promotion strategy to some extent.

Fines
To study the influence of fines on the government choice of a promotion strategy, the parameter F has a value range of (0,6) and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 10 that with the increase of fines, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When F is very small in actual situations, the government will adopt the no promotion strategy. When F is increased to a certain value, the government's strategy changes from the no promotion strategy to the promotion strategy. When fines are gradually increased, the speed of evolution becomes faster.  Similar change trends are also depicted in Figure 11in order to study the influence of fines on the heating company's choice of clean heating strategy. It can be seen from Figure 11 that with the increase of the fine, the heating company's final strategy gradually changes from adopting a traditional heating strategy to adopting a clean heating strategy. When F is very small in actual situations, the heating company will adopt the traditional heating strategy. When F is increased to a certain value, the Heating company's strategy changes from the traditional heating strategy to the clean heating strategy. When the fine is gradually increased, the speed of evolution becomes faster.   Based on the above, it can be concluded that increased probability of fines can effectively encourage heating companies to adopt clean heating strategies, and the government will adopt the promotion strategy to some extent.

Clean Heating Profit
To study the influence of clean heating profit on the government's choice of a promotion strategy, the parameter R 2 has a value range of (0,20) and other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 12 that with the increase of clean heating profit, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When R 2 is very small in actual situations, the government will adopt the no promotion strategy. When R 2 is increased to a certain value, the government's strategy changes from the no promotion strategy to the promotion strategy. When clean heating profit is gradually increased, the speed of evolution becomes faster.
Similar change trends are also depicted in Figure 13 in order to study the influence of clean heating profits on the heating company's choice of clean heating strategy. It can be seen from Figure 13 that with the increase of clean heating profit, the heating company's final strategy gradually changes from adopting the traditional heating strategy to adopting the clean heating strategy. When R 2 is very small in actual situations, the heating company will adopt the traditional heating strategy. When R 2 is increased to a certain value, the Heating company'sstrategy changes from the traditional heating strategy to the clean heating strategy. When clean heating profit is gradually increased, the speed of evolution becomes faster.
heating strategy to the clean heating strategy. When clean heating profit is gradually increased, the speed of evolution becomes faster.
Based on the above, it can be concluded that the increased probability of clean heating profit can effectively encourage heating companies to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent.

Traditional Heating Profit
To study the influence of traditional heating profit on the government's choice of a promotion strategy, the parameter R3 has a value range of (0,30) and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 14 that with the decrease of traditional heating profit, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When R3 is very small in actual situations, the government will Based on the above, it can be concluded that the increased probability of clean heating profit can effectively encourage heating companies to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent.

Traditional Heating Profit
To study the influence of traditional heating profit on the government's choice of a promotion strategy, the parameter R 3 has a value range of (0,30) and the other parameters are fixed. The initial probability is set as (0.7, 0.3). It can be seen from Figure 14 that with the decrease of traditional heating profit, the government's final strategy gradually changes from adopting the no promotion strategy to adopting the promotion strategy. When R 3 is very small in actual situations, the government will adopt no promotion strategy. When R 3 is decreased to a certain value, the government's strategy changes from the no promotion strategy to the promotion strategy. When the traditional heating profit is gradually decreased, the speed of evolution becomes faster.  Similar change trends are also depicted in Figure 15 in order to study the influence of traditional heating profit on the heating company's choice of clean heating strategy. It can be seen from Figure 15 that with the decrease of traditional heating profit, the heating company's final strategy gradually changes from adopting the traditional heating strategy to adopting the clean heating strategy. When R 3 is very small in actual situations, the heating company will adopt the traditional heating strategy. When R 3 is decreased to a certain value, the Heating company's strategy changes from the traditional heating strategy to the clean heating strategy. While the traditional heating profit is gradually decreased, the speed of evolution becomes faster.  Based on the above, it can be concluded that a decrease of traditional heating profit can effectively encourage heating companies to adopt clean heating strategies, and the government will adopt the promotion strategy to some extent.
Through the above analysis, the scenario simulation results are extended to practical applications, and the specific analysis is as follows: From Figure 1 to Figure 3 in Scenarios 1 to 3, the initial probability has a significant impact on the evolutionary game results. Considering the actual situation of clean heating in China, the government has a high degree of enthusiasm for promotion, and enterprises are less motivated to adopt clean heating. Set x = 0.7, y = 0.3 in Scenarios 4 to 9.
From Figures 4 and 5 in Scenario 4, the increased probability of social benefits can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent. Therefore, the central government can strengthen the local government's clean heating promotion assessment to encourage local governments to promote the power of clean heating; local governments can recognize the company's clean heating behavior and improve social benefits in the future.
Form Figures 6 and 7 in Scenario 5, the increased probability of subsidy can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent. Therefore, local governments can increase financial subsidies to promote clean heating.
From Figures 8 and 9 in Scenario 6, the decreased probability of promotion cost can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent. Therefore, the reduction of promotion cost has an important impact on the heating company. The government should increase scientific, technological research and development support to reduce the purchase cost and operating cost of clean heating equipment.
From Figures 10 and 11 in Scenario 7, the increased probability of fines can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent. Therefore, the government can increase the fines for traditional heating, especially high-polluting heating equipment, and encourage heating companies to choose clean heating.
From Figures 12 and 13 in Scenario 8, the increased probability of clean heating profit can effectively encourage the heating company to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent. Therefore, the government can increase the profits of clean heating enterprises through measures such as tax reduction and preferential trading rights, and promote the promotion of clean heating. Heating companies can reduce costs and improve profits through measures such as technology and management.
From Figures 14 and 15 in Scenario 9, the decrease of traditional heating profit can effectively encourage heating companies to adopt the clean heating strategy, and the government will adopt the promotion strategy to some extent. Therefore, the government can reduce the profits of traditional heating companies by increasing taxes and sales controls, and then encourage heating companies to adopt clean heating.

Conclusions
This study focuses on clean heating promotion mechanisms during the heating season. Firstly, an evolutionary game model is constructed to analyze the promotion trend of the government and the clean heating trend of the heating company. Meanwhile, we analyze the game relationship between the government and the heating company. In this study, Firstly, social benefits, environmental benefits, subsidy, promotion cost, fine, clean heating profit, traditional heating profit, and other factors are considered. Secondly, we construct the evolutionary game matrix and solve the dynamic evolution process. Thirdly, we analyze the evolutionary game equilibrium points for the specific situation and their stability. Finally, a numerical simulation is carried out to verify the validity of the theoretical model. This paper focuses on the choice of strategy by governments and heating companies with respect to clean heating. By studying the different coefficient changes, it can be found that the reduction of heating costs will increase the probability of heating companies choosing clean heating. Meanwhile, while the subsidy for heating companies increases, it is possible for heating companies to choose clean heating. At the same time, research shows that the initial strategic choice probability of the government and heating companies has an important impact on the evolutionary game structure. Therefore, this paper proposes a long-term evolution model for promoting clean heating mechanisms, for the government to carry out clean heating promotion decisions, then improve policy recommendations and clean heating policy in evolution game simulation. On the basis of this study, we can also conclude that clean heating profit increases when social benefits, subsidies and fines increase. However, it will decrease if the cost and the traditional heating profit increase. As a result, it is likely that the government will adopt a promotion strategy and that the heating company will adopt a clean heating strategy.
This study can provide policy simulations and policy recommendations for government decision-making through clean heating. Also, there are some shortcomings in this paper, such as not considering the thermal efficiency of the heating equipment and the cost of purchasing the heating equipment. In future research, the main developments to be made are as follows. Firstly, considering more influencing factors to make the simulation more practical; secondly, conducting empirical research on the model to further improve the model through the promotion and practice of typical policies; thirdly, considering more game entities such as cleaning heating users.