Marine Construction Waste Recycling Mechanism Considering Public Participation and Carbon Trading: A Study on Dynamic Modeling and Simulation Based on Sustainability Policy

Abstract

The classification and recycling of construction waste is important for reducing waste emissions, preventing marine pollution, and protecting the natural environment, which can promote carbon trading and carbon sink cycles. Based on the evolutionary game theory, this paper investigated the evolutionary decision-making process and stable strategies of three stakeholders in the construction waste recycling system, namely, the Department of Environment Regulation (DER), the Construction Waste Recycler (CWR), and the Construction Project Contractor (CPC), and analyzed the main factors affecting the stakeholders’ strategies, the evolutionary stable strategies and stable conditions from the perspective of public participation and carbon trading. Then, a DER-CWR-CPC benefit matrix and a replicator dynamics equation representing strategy selection were constructed, in which parameters represent the interest relationship of the three parties, and evolutionary stable strategy (ESS) points were obtained by solving the Jacobian matrix. Finally, the validity of the model was verified by taking the actual values into the simulation. The results showed that DER needs to actively participate in the early stage of the development of the construction waste classification and recycling system, but with the increase of enterprises choosing to recycle construction waste, DER can gradually reduce its intervention in these enterprises. Setting reasonable incentives and penalties, mobilizing public participation, and developing cleaner construction waste sorting equipment to obtain more carbon emission trading targets can facilitate the development of construction waste recycling systems.

1. Introduction

China has witnessed accelerated urbanization and further population growth, so its demand for construction is further increasing, with the coastal areas seeing a second urbanization. Since 2013, China has built more than four billion square meters of buildings per year, which construction rate is expected to continue in the coming decades, adding thirty-three billion square meters by 2040 [1]. New construction projects consume a large quantity of raw materials and generate quantities of construction waste, which will lead to a shortage of natural resources. Moreover, construction waste has the greatest environmental impact on the ocean and can incur the destruction of ecological balance [2,3]. In order to reduce the consumption of natural materials and to avoid pollution of the marine environment, the recycling of construction engineering waste is considered to be one of the most effective and sustainable methods for social development and environmental protection [4,5].

At present, China’s construction waste recycling mechanism mainly focuses on waste generated during the engineering projects, the recycling mechanism of which can be divided mainly into three categories. The first is the producers of construction waste, namely, contractors of construction projects or contractors of engineering projects responsible for renovation and demolition of old buildings. The second category is the recyclers of recyclable waste materials, and the third is the policy makers dedicated to the sustainable development of the country, that is, environmental protection departments at all levels [6]. Different recycling methods can be found for various types of construction waste, such as wood and plastic products, which can be recycled to factories for secondary processing if not corroded or polluted by the environment. But when dealing with construction engineering waste that cannot be processed, such as excess prefabricated floor slabs or concrete blocks already in production, they can be crushed for paving suburban roads to level the terrain [7,8,9]. In China, there are usually two ways to deal with construction waste. One is that the contractor pays for the removal and transportation of construction waste, and it is handed over to the construction waste disposal yard set up by the local government for treatment; the other is that recyclers and contractors cooperate to recycle construction waste [6].

China’s existing construction waste recycling system still needs to be improved. And according to the Chinese government’s 14th Five-Year Plan and China’s visionary development goals for 2035, China needs to strongly support assembly-type construction, reduce the resource consumption and environmental damage of traditional construction models, and establish Hainan self-trade province to comprehensively develop coastal infrastructure projects. Therefore, it has become a matter of urgency to improve China’s existing construction waste recycling regulatory system and protect the marine environment to achieve sustainable development. In the existing construction waste recycling system, the government controls the enterprises merely by the reward and punishment system, to achieve the goal through financial incentives and penalties [10]. However, such a method has great defects and cannot mobilize the subjective willingness of the project parties, and in the case of lax supervision, they are likely to dispose of construction waste without following the regulations in order to save labor and time.

Environmental pollution infringes on the interests of the public. The current policies for construction waste disposal around the world only consider the mutual influence between the construction project party and the government, while ignoring the role of third parties, including the influence factors of public participation and the current carbon emission trading mechanism. Moreover, the environmental cost of illegal disposal of construction waste is partly paid by the public [11], and the carbon dioxide emissions and carbon sink indexes brought by construction waste resourceization are huge. Therefore, it is necessary to study the strategies of the three stakeholders involved in the process of construction waste resourceization in the context of carbon trading and considering the public participation [12,13,14].

In summary, for DER, environmental pollution is detrimental to the long-term development of the country, the consequences of which are to be borne by the public [15]. However, relying only on government regulation will waste a lot of financial and human resources, and command-and-control type instructions to regulate the related waste manufacturers is not a strategy for the long-term development of society. Policies should be developed so that DER, CPC, and CWR can achieve positive feedback on the public regulation and carbon trading platform, forming a combination of incentives and voluntary behavior. In this paper, a tripartite evolutionary game study was conducted on DER, CPC, and CWR from the perspective of public regulation and carbon trading. The established model revealed the interaction mechanism of different parties under various chosen strategies. Subsequently, numerical simulations were conducted using MATLAB R2021b software, and the effects of parameter changes on the strategic choices of each party were discussed based on the simulated data results. Meanwhile, feasible suggestions were made for each party to protect the ecological environment and improve the level of carbon trading in the Chinese market.

2. Literature Review

2.1. Recycling and Resourcing of Construction Waste

Construction waste refers to the residual mud, sediment, slurry, broken materials, and other polluting waste generated during construction, demolition, and renovation by construction units or residents [16]. Tirth pointed out that, sustainable construction practices in the construction industry include three main areas: conservation and optimization of resources, waste management, and reduction of energy and water footprints [17]. In coastal regions such as Hainan, China, construction companies often evade government regulation to dump construction waste into the ocean, which causes irreversible and lasting impacts on the marine aquatic environment through biological and chemical effects.

Construction waste resourceization means the adoption of management and technology to recover useful materials and energy from construction waste, which includes material recovery, material conversion, and energy conversion. Liu [18] studied how to achieve sustainable development of construction waste industrialization based on a system dynamics model and made valuable suggestions for upstream and downstream enterprises in the industry chain and government making policies respectively. Liu [19] used system dynamics software to analyze the public-private partnership project risk of the construction waste recycling industry, the result of which shows that the cooperation environment risk has the greatest impact on the bidding risk, and that the greatest risk during the construction process comes from cost, schedule delay, and design defects [16].

In addition, how to use specific technical measures to recycle garbage is also a hot topic. Ulsen and Liu et al. [20,21,22] proposed the use of new mechanical equipment to recycle construction waste to produce high quality reclaimed sand, which can be used for the reuse of resources for other construction projects. Based on computer vision technology and path planning algorithms by designing intelligent devices, Wang et al. produced a waste recycling robot that can quickly find loose nails on site and automatically recycle them, saving costs for the next project [23]. Rautkoski commercialized broken soft building materials, such as broken wood and plastic, by making recycled materials through physical and chemical treatments [24]. Waskow [25] processed excess construction waste from construction projects by means of high pressure, yielding construction materials of the same quality as unprocessed materials, which avoided dust pollution due to physical damage. Vegas [26] used infrared radiation classification of waste construction materials to improve the efficiency of screening non-recyclable waste. Sarkar [27] studied the technology of recycling fly ash and suggested that the use of sintered fly ash added to alkaline activator can develop composite materials with higher mechanical strength and durability. Tirth pointed to one of the most effective ways to recycle wastewater, which is by using air conditioning condensate and using it for sanitation without any purification or filtration [28].

To sum up, the study of construction waste recycling is of great theoretical and practical significance, from the perspective of both macro economy and micro technology. The existing technology has proved that resourceization is achievable and conducive to sustainable economic development. How to combine government and enterprises to create a sustainable waste recycling industry chain to realize construction waste resourceization is a very important research subject.

2.2. Carbon Trading Game

Carbon credits are carbon emission allowances allocated to key emitters for a specified period. Carbon emission trading, also known as “carbon trading”, is an important approach for global climate governance. Carbon trading is a systematic innovation as well as an important policy tool to implement the national carbon peak target and carbon neutrality vision. The Chinese government has introduced this mechanism to regulate the recycling of construction waste. The most commonly used analytical tool for studying such problems is game theory.

Compared with classical game theory, evolutionary game theory only requires that the participants are finitely rational. It can explain the phenomenon of mutual learning, competition, and adaptation during biological evolution [29]. Moreover, it emphasizes the dynamic evolutionary equilibrium of strategic changes.

It has been used widely to explore the interaction of strategic choices of different parties in the process of construction waste recycling. For example, Du constructed an evolutionary game model between real estate developers and property owners to investigate whether the implementation of a carbon tax would affect their choice of low-carbon buildings. Xia [30] identified the impact of carbon trading on the low carbon supply chain in any case by constructing a two-sided game model of low carbon products and conventional products. Due to the uncertainty of the market for low-carbon products and waste products, Sun [31] and Liu [32] explored measures to effectively manage construction waste recycling by developing a stochastic game model among government agencies, construction waste producers, and construction waste recyclers.

Based on the carbon and trading mechanism, Wang [33] analyzed the carbon reduction effect of non-cooperative upstream and downstream enterprises with game theory and discussed the carbon reduction decision of upstream and downstream enterprises in the supply chain and the choice strategy of the government carbon emission allowance allocation scheme under the government carbon emission constraint. Yu [34] constructed an investment game model based on cost allocation and coordination under the cost subsidy of manufacturers and retailers and found that the cost subsidy policy under the carbon trading system has a regulatory effect on corporate emission reduction investment and corporate profits. Zhang [35] established an evolutionary game model between the government and manufacturers and found that dynamic carbon trading pricing policies are effective in accelerating carbon emission reductions. Furthermore, the likelihood of manufacturers introducing green technologies is negatively related to the cost of government intervention. However, all the current studies only consider the interaction between enterprises and government in the waste recycling chain, while ignoring the participation of the public, the broadest group.

Therefore, it is necessary to investigate the strategies of the three stakeholders involved in the process of recycling and resource utilization of construction waste in the context of carbon trading and considering public participation behavior. In addition to considering the command-and-control policies of government departments, this study also introduces the influencing factors of public participation action and carbon emission trading mechanism. If the construction waste recycler can work out the recycling of construction waste, it can reduce carbon emissions and obtain corresponding carbon emission allowance [12,13].

3. Problem Description and Model Framework

3.1. Problem Description

According to the construction waste recycling mechanism, the construction materials are first transported to the construction project for construction. Then the generated building engineering waste and various types of waste are sorted and encapsulated. The non-recyclable waste will be selected according to whether it will pollute the marine environment or whether it will be directly reclaimed or discharged. The recyclable waste will be classified into combustible and recycled waste. The combustible waste will be used as energy material for energy production, while the recycled waste can be recycled and remade into another product according to the relevant technology, and the government environmental protection department will play a management role in the whole process of waste recycling. The relationship between the construction waste recycling process and the parties in China’s marine environment is shown in Figure 1.

3.2. Problem Explanation

In the construction waste recycling system, DER not only reviews the recording of waste disposal records and business credentials of enterprises, but also supervises the specific disposal methods. However, the completion of these tasks requires more human resources, the problems within often cannot be found and dealt with in time. When the construction waste is recycled, CPC can sort it to produce renewable construction materials, but when they do not, CPC has to dispose of the construction waste whether it sorts the waste or not. Construction waste not recycled or disposed of may be illegally dumped to pollute the ocean or burned randomly to pollute the atmosphere [36], which can seriously damage the level of environmental health [37] and affect the quality of the public’s living environment [38], thus leading to public complaining against the government and reporting the companies. Considering the complaint rate of the public combined with the correlations shown in Figure 1, this paper focuses on the following three questions. Firstly, in response to the current low recycling rate of construction waste, what measures can DER take to make all enterprises in the coastal construction waste recycling system take the initiative to sort and recycle construction waste, and reduce the pollution caused by illegal disposal of polluting waste to the marine environment? Secondly, how can public complaints and reports affect the relevant strategies of DER and CPC? Thirdly, does the current carbon trading mechanism influence the choices of enterprises?

In conclusion, the game model constructed in this paper is shown in Figure 2 below.

3.3. Model Establishment

By sorting out the research results of many scholars and conducting interviews with relevant practitioners and government departments in China’s construction industry, it emerged that it is more of a logical relationship about qualification. In order to clarify the qualification of this study, it was explained in the form of a hypothesis. To build a game model for a construction waste recycling system of various stakeholders and study the regulatory strategy of construction waste dumped into the marine under the background of public complaints and carbon trading, we proposed the following hypotheses:

Hypothesis 1 (H1).

There are three game subjects in this model, DER is the first game party to boost the share of companies in the market who are willing to recycle construction waste, to achieve the utilization of construction waste materials, and to reduce the environmental carbon emissions. As the remaining parties, the main purpose of construction waste generators and recyclers is to maximize their profits. The strategy that the three parties can take are, respectively: DER (positive regulation, negative regulation), construction waste generators and recyclers (recycling, no recycling).

Hypothesis 2 (H2).

Descriptions of public participation parameters. The inactions of both DER and enterprises will harm public environmental quality, resulting in their complaints and report. ${\beta }_1$is the probability of complaining about the inaction of DER.$L_1$is the demand compensation, and the average loss of the government is${\beta }_1\ast L_1$;${\beta }_2$is the probability of complaining about the inaction of the enterprise,$L_2$is the demand compensation, and the average loss of the enterprise is${\beta }_2\ast L_2$. Referring to the research of previous scholars [39], damage claims sought from businesses by the public will eventually be transferred to businesses through the government.

Hypothesis 3 (H3).

Strategic assumptions of DER. In this paper, we take administrative regulators related to the public and the environment into consideration. Revenue part: $H$is a good social reputation the governmental environmental regulators gained with implement active regulation, even though they fail to curb construction waste discharge.$Q$is the social benefits of recycling construction waste of all enterprises, (including social reputation, economic benefits, etc.)$A$is the fine for enterprises who refused to recycle their construction waste under the government’s active regulation. Their risk of being discovered is$\xi$, and their average benefit is$\xi \ast A$; Expenditure part:$C_1$is the additional regulatory cost besides DER’s positive regulations,$E_g$is the cost of environmental governance caused by enterprises not recycling construction waste. In addition, government should offer subsidies$S$to enterprises acting in line with their regulations and claim${\beta }_1\ast L_1$if they take negative regulation.

Hypothesis 4 (H4).

Strategic assumptions of CWR. Revenue part: Through the recycling of classified construction waste, the CWR makes a profit by producing renewable construction materials, which is $\lambda \ast \left(P_1+\mu P_{Cq}\right)$($\lambda$is the profit-sharing ratio defined by the contract between the generator and the recycler when recycling construction waste,$P_1$is the profit from production,$P_{Cq}$is the carbon trading price, and$\mu$is the carbon trading index brought by the production of renewable construction materials).$P_2$is the profit of construction materials made by natural materials.$S$is the subsidy head out to enterprises for construction waste recycling when they are actively regulated by DER. Expenditure part: the total cost of recycling construction waste from sorting to remanufacturing is C. Fines from the government in case of non-recycling is$\xi \ast A$and compensation for public losses is${\beta }_2\ast L_2$. $P_3$is the loss when the construction waste generator adopts a “no-recycling” strategy while CWR adopts a “recycling” strategy (such as investment in technology research or equipment replacement, etc.).

Hypothesis 5 (H5).

Strategic assumptions of CPC. Revenue part: construction waste recyclers make a profit from producing renewable construction materials, their profit is $\left(1-\lambda \right)\ast \left(P_1+\mu P_{Cq}\right)$. $S$is the subsidy given out to enterprises for construction waste recycling when they are actively regulated by DER. Expenditure part:$C_2$refers to the cost of transporting construction waste to a landfill if it is not recycled, and$C_3\ast \eta$refers to the cost of construction waste classification if it is sorted ($\eta$indicates the level of sorting, and the finer the sorting, the higher the cost). In the case of non-recycling, the government will impose a fine, that is$\xi \ast A$and the compensation for the public losses is${\beta }_2\ast L_2$. The tripartite game matrix of construction waste recycling incentives considering the public participation mechanism is shown in

Table 1. Payoff matrix between DER–CWR–CPC.

CPC	DER’s Active Regulation(x)		DER’s Negative Regulation(1 − x)
	Recycle of CWR(y)	Non-Recycle of CWR(1 − y)	Recycle of CWR(y)	Non-Recycle of CWR(1 − y)
recycling(z)	${\mathrm{Q}-\mathrm{C}}_1-2\mathrm{S}$ ${\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right)+\mathrm{S}$ $\left(1-\lambda \right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)-\mathsf{\eta }\mathrm{C}}_3+\mathrm{S}$	$\mathrm{H}+\mathsf{\xi }{\mathrm{A}+\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{C}}_1{-\mathrm{S}-\mathrm{E}}_{\mathrm{g}}$ ${\mathrm{P}}_2-\mathsf{\xi }{\mathrm{A}-\mathsf{\beta }}_2{\mathrm{L}}_2$ ${\mathrm{S}-\mathsf{\eta }\mathrm{C}}_3{-\mathrm{C}}_2$	${\mathrm{Q}-\mathsf{\beta }}_1{\mathrm{L}}_1$ ${\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right)$ $\left(1-\lambda \right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)-\mathsf{\eta }\mathrm{C}}_3$	${\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\beta }}_1{\mathrm{L}}_1{-\mathrm{E}}_{\mathrm{g}}$ ${\mathrm{P}}_2{-\mathsf{\beta }}_2{\mathrm{L}}_2$ ${-\mathrm{C}}_3{\mathsf{\eta }-\mathrm{C}}_2$
Non- recycling (1 − z)	$\mathrm{H}+\mathsf{\xi }{\mathrm{A}+\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{C}}_1{-\mathrm{S}-\mathrm{E}}_{\mathrm{g}}$ ${\mathrm{P}}_2{-\mathrm{P}}_3+\mathrm{S}$ ${-\mathrm{C}}_2-\mathsf{\xi }{\mathrm{A}-\mathsf{\beta }}_2{\mathrm{L}}_2$	$\mathrm{H}+2\mathsf{\xi }{\mathrm{A}+2\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{C}}_1{-\mathrm{E}}_{\mathrm{g}}$ ${\mathrm{P}}_2-\mathsf{\xi }{\mathrm{A}-\mathsf{\beta }}_2{\mathrm{L}}_2$ ${-\mathrm{C}}_2-\mathsf{\xi }{\mathrm{A}-\mathsf{\beta }}_2{\mathrm{L}}_2$	${\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\beta }}_1{\mathrm{L}}_1{-\mathrm{E}}_{\mathrm{g}}$ ${\mathrm{P}}_2{-\mathrm{P}}_3$ ${-\mathrm{C}}_2{-\mathsf{\beta }}_2{\ast \mathrm{L}}_2$	${2\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\beta }}_1{\mathrm{L}}_1{-\mathrm{E}}_{\mathrm{g}}$ ${\mathrm{P}}_2{-\mathsf{\beta }}_2{\mathrm{L}}_2$ ${-\mathrm{C}}_2{-\mathsf{\beta }}_2{\mathrm{L}}_2$

.

4. Model Analysis

4.1. Stability Analysis of DER’s Strategies

The expected benefits of active regulation or negative regulation by government environmental regulators and the average expected benefits are (${\mathrm{E}}_{11},{\mathrm{E}}_{12},\overline{{\mathrm{E}}_1}$) respectively:

$$\left\{\begin{array}{c}{\mathrm{E}}_{11}{=\mathrm{H}+2\mathsf{\xi }\mathrm{A}+2\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{C}}_1{-\mathrm{E}}_{\mathrm{g}}\\ +(\mathrm{y}+\mathrm{z})\left({-\mathrm{S}-\mathsf{\xi }\mathrm{A}-\mathsf{\beta }}_2{\mathrm{L}}_2\right){+\mathrm{yz}(\mathrm{Q}-\mathrm{H}+\mathrm{E}}_{\mathrm{g}})\\ {\mathrm{E}}_{12}{=2\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\beta }}_1{\mathrm{L}}_1{-\mathrm{E}}_{\mathrm{g}}+(\mathrm{y}+\mathrm{z})\left({-\mathsf{\beta }}_2{\mathrm{L}}_2\right){+\mathrm{yz}(\mathrm{Q}+\mathrm{E}}_{\mathrm{g}})\\ \overline{{\mathrm{E}}_1 }{=\mathrm{xE}}_{11}{+(1-\mathrm{x})\mathrm{E}}_{12}\end{array}\right.$$

(1)

The replication dynamic equation for the choice of planning strategy of the government environmental protection regulation department is obtained as:

$$\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{dx}}{\mathrm{dt}}{=\mathrm{x}(\mathrm{E}}_{11}-\overline{{\mathrm{E}}_1}{)=\mathrm{x}(1-\mathrm{x}\left)\right[\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1+\left(\mathrm{y}+\mathrm{z}\right)\left(-\mathrm{S}-\mathsf{\xi }\mathrm{A}\right)+\mathrm{yz}(-\mathrm{H})]$$

(2)

The derivative of the above formula with respect to x and the set “G(y)” is:

$$\frac{\mathrm{dF}\left(\mathrm{x}\right)}{\mathrm{dx}}=\left(2\mathrm{x}-1\right){[\mathrm{C}}_1{+\mathsf{\beta }}_1{\mathrm{L}}_1+\left(\mathrm{y}+\mathrm{z}\right)\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)+\mathrm{yzH}-\mathrm{H}-2\mathsf{\xi }\mathrm{A}]$$

(3)

$${\mathrm{G}\left(\mathrm{y}\right)=[\mathrm{C}}_1{+\mathsf{\beta }}_1{\mathrm{L}}_1+\left(\mathrm{y}+\mathrm{z}\right)\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)+\mathrm{yzH}-\mathrm{H}-2\mathsf{\xi }\mathrm{A}]$$

(4)

According to relevant research [40], when DER chooses active regulation the probability of state stability must satisfy: $\mathrm{F}\left(\mathrm{x}\right)=0$ and $\mathrm{dF}\left(\mathrm{x}\right)/\mathrm{dx}<0$. As $\partial \mathrm{g}\left(\mathrm{y}\right)/\partial \mathrm{y}>0$, thus $\mathrm{g}\left(\mathrm{y}\right)$ is increasing with the increase of y. When ${\mathrm{y}=\mathrm{y}}^{\ast }=\left[\mathrm{H}+2\mathsf{\xi }\mathrm{A}-{\mathrm{C}}_1-{\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{z}\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)\right]/[\mathrm{S}+\mathsf{\xi }\mathrm{A}+\mathrm{zH}]$, $\mathrm{g}\left(\mathrm{y}\right)=0$, $\mathrm{dF}\left(\mathrm{x}\right)/\mathrm{dx}=0$. It is hard to determine the stabilization strategy of DER. When ${\mathrm{y}>\mathrm{y}}^{\ast }$, $\mathrm{g}\left(\mathrm{y}\right)>0$. $\mathrm{x}=0$, $\mathrm{dF}\left(\mathrm{x}\right)/\mathrm{dx}<0$, and X equals to zero makes the Evolutionarily Stable Strategy (ESS) of the government environmental regulator; on the contrary situation, if x = 1, it makes the ESS. The phase diagram of regulatory strategy evolution of DER is shown in Figure 3.

From Figure 2, it can be seen that the tangent plane cross the point ${(0,0,(\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1)/(\mathrm{S}+\mathsf{\xi }\mathrm{A}\left)\right)$, the probability that DER takes positive regulation is $A_1$, and its volume is $V_{A_1}$, the probability of negative regulation is $A_2$ and its volume is $V_{A_2}$. The calculation is obtained by using Formulas (5) and (6):

$$\begin{array}{ll}{\mathrm{V}}_{{\mathrm{A}}_1}& ={{\displaystyle \int }}_0^1{{\displaystyle \int }}_0^{\frac{{\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1}{\mathrm{S}+\mathsf{\xi }\mathrm{A}}}\frac{{\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{z}\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)}{\mathrm{S}+\mathsf{\xi }\mathrm{A}+\mathrm{zH}}\mathrm{dzdx}\\ & =[\frac{{\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1}{\mathrm{H}}+(\frac{\mathrm{S}+\mathsf{\xi }\mathrm{A}}{\mathrm{H}}{)}^2]\ln \left(1+\frac{\mathrm{H}}{\mathrm{S}+\mathsf{\xi }\mathrm{A}}\right)-1-\frac{{2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1}{\mathrm{H}}\end{array}$$

(5)

$${\mathrm{V}}_{{\mathrm{A}}_2}{=1-\mathrm{V}}_{{\mathrm{A}}_2}=2+\frac{{2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1}{\mathrm{H}}-[\frac{{\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1}{\mathrm{H}}+(\frac{\mathrm{S}+\mathsf{\xi }\mathrm{A}}{\mathrm{H}}{)}^2]\ln \left(1+\frac{\mathrm{H}}{\mathrm{S}+\mathsf{\xi }\mathrm{A}}\right)$$

(6)

Proposition 1.

During the evolution of the model, the probability that DER adopts an aggressive regulatory strategy decreases as the probability that firms choose to recycle construction waste increases.

Proof. 

From the stability of DER’s strategy, we can see that when ${\mathrm{y}<\mathrm{y}}^{\ast }{,\mathrm{z}<\mathrm{z}}^{\ast }=\left[{\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\right]/(\mathsf{\xi }\mathrm{A}+\mathrm{S})$, X = 1 makes ESS; and when ${\mathrm{y}>\mathrm{y}}^{\ast }{,\mathrm{z}>\mathrm{z}}^{\ast }$, X = 0 achieves ESS. DER’s strategy will change with the other two parties, and x will move to 1 as y and z rise. □

Proposition 1 indicates that DER’s active regulatory role of the bunker depends on the strategic choice of the bunker and the waste collector. When DER believes that CPC and waste collectors have a higher probability of actively recycling construction waste, it will not regulate the situation, and then public complaints will easily occur.

Proposition 2.

The relationship between the strategy probability of DER choosing active regulation and various parameters cannot be simply judged. This is because although the government’s active regulation will improve its reputation, it will pay additional supervision costs. Although the public will complain about the negative regulation, it will charge the compensation paid by the enterprise. Therefore, it cannot simply see the relationship between parameters and strategy choice.

Proof. 

The partial derivatives of each parameter in ${\mathrm{V}}_{{\mathrm{A}}_1}$ are found to be uncertain. For example, $\partial {\mathrm{V}}_{{\mathrm{A}}_1}/\partial {\mathrm{C}}_1=\frac{1}{\mathrm{H}}-\frac{1}{\mathrm{H}}\ln [\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}+\mathrm{H}\right)/\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)]$ means the strategy taken by DER is influenced by multiple factors. □

The proposition 2 shows DER needs to consider the numerical relationship between all the factors to figure out the influence of each factor on their strategy choice, thus decide the best strategy, and there are many influences on the strategy choice of the government administration. In the section on numerical simulation below, the authors use real survey data to analyze the changes in the influence parameters of DER.

4.2. Stability Analysis of CWR’s Strategies

The expected revenue of CWR for recycling construction waste or not recycling construction waste and the average expected revenue are ${(\mathrm{E}}_{21}{,\mathrm{E}}_{22},\overline{{\mathrm{E}}_2})$ respectively:

$$\begin{array}{c}{\mathrm{E}}_{21}{=\mathrm{P}}_2{-\mathrm{P}}_3{+\mathrm{xS}+\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\\ {\mathrm{E}}_{22}{=\mathrm{P}}_2{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{x}\mathsf{\xi }\mathrm{A}\\ \overline{{\mathrm{E}}_2}{=\mathrm{yE}}_{21}{+(1-\mathrm{y})\mathrm{E}}_{22}\end{array}$$

(7)

Therefore, the replicated dynamic equation for the strategic choice of the construction waste recycler is:

$$\mathrm{F}\left(\mathrm{y}\right)=\frac{\mathrm{dy}}{\mathrm{dt}}{=\mathrm{y}(\mathrm{E}}_{21}-\overline{{\mathrm{E}}_2}{)=\mathrm{y}(1-\mathrm{y})\text{{}\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{P}}_3{+\mathrm{x}(\mathsf{\xi }\mathrm{A}+\mathrm{S})+\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\text{}}$$

(8)

The derivative of the above formula with respect to y and the set “J(x)” are respectively:

$$\frac{\mathrm{dF}\left(\mathrm{y}\right)}{\mathrm{dy}}=\left(1-2\mathrm{y}\right){\text{{}\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{P}}_3{+\mathrm{x}(\mathsf{\xi }\mathrm{A}+\mathrm{S})+\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\text{}}$$

(9)

$${\mathrm{J}\left(\mathrm{x}\right)=\text{{}\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{P}}_3{+\mathrm{x}(\mathsf{\xi }\mathrm{A}+\mathrm{S})+\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\text{}}$$

(10)

When the recycler chooses to recycle the garbage the probability state stability must satisfy: $\mathrm{F}\left(\mathrm{y}\right)=0$ and $\mathrm{dF}\left(\mathrm{y}\right)/\mathrm{dy}<0$. Since $\partial \mathrm{J}\left(\mathrm{x}\right)/\partial \mathrm{x}>0$, so “J(x)” increases as x increases. When ${\mathrm{x}=\mathrm{x}}^{\ast }=\left[{\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\right]/(\mathsf{\xi }\mathrm{A}+\mathrm{S})$, $\mathrm{J}\left(\mathrm{x}\right)=0$ and $\mathrm{dF}\left(\mathrm{y}\right)/\mathrm{dy}=0$. It is hard to determine the stabilization strategy of the government environmental regulator at this point. When ${\mathrm{x}>\mathrm{x}}^{\ast }$, $\mathrm{J}\left(\mathrm{z}\right)>0$. $\mathrm{y}=1$, $\mathrm{dF}\left(\mathrm{y}\right)/\mathrm{dy}<0$, if y equals to 1, it can achieve the ESS of DER; on the contrary situation, if y=0, it makes ESS. The evolutionary phase diagram of the recycling strategy of CWR is shown in Figure 4.

From Figure 4, it can be seen that the tangent plane cross the point ${(0,0,(\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{)/[\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right])$, and to make the paper more concise, we make ${\mathsf{\tau }=\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]$. The probability that CWR chooses sorting and recycling is $B_1$, and its volume is $V_{B_1}$, the probability that it chooses negative regulation is $B_2$ and its volume is $V_{B_2}$. The calculation is obtained by using Formulas (11) and (12):

$${\mathrm{V}}_{{\mathrm{B}}_2}={{\displaystyle \int }}_0^1{{\displaystyle \int }}_0^{\frac{{\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2}{\mathsf{\tau }}}\frac{\left[{\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{z}\mathsf{\tau }\right]}{(\mathsf{\xi }\mathrm{A}+\mathrm{S})}\mathrm{dzdy}=\frac{{\left({\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2\right)}^2}{{2\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)-\mathrm{C}+\mathsf{\eta }\mathrm{C}}_3{-\mathrm{P}}_2+{\mathrm{P}}_3\left]\right(\mathsf{\xi }\mathrm{A}+\mathrm{S})}$$

(11)

$${\mathrm{V}}_{{\mathrm{B}}_1}{=1-\mathrm{V}}_{{\mathrm{B}}_2}$$

(12)

Proposition 3.

The probability that CWR chooses to recycle construction waste is positively correlated with the sales proceeds from the production of recyclable materials and carbon emissions trading proceeds, the CPC’s expenditure on construction waste sorting, the amount of rewards and penalties from the government environmental regulator, and the public’s compensation for complaints, and is negatively correlated with the total cost of sorting and recycling to remanufacturing, the proceeds from the production of construction materials using natural materials, and it is not easy to judge the correlation of equipment replacement costs incurred when CPC “do not recycle” construction waste.

Proof. 

Take the first partial derivative of each element in ${\mathrm{V}}_{{\mathrm{B}}_1}$, we can know that $\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathrm{C}<0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial {\mathrm{P}}_2<0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial {\mathsf{\beta }}_2>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial {\mathrm{L}}_2>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathsf{\lambda }>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial {\mathrm{P}}_1>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathsf{\mu }>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}$ $/\partial {\mathrm{P}}_{\mathrm{Cq}}>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathsf{\eta }>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial {\mathrm{C}}_3>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathsf{\xi }>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathrm{A}>0,\partial {\mathrm{V}}_{{\mathrm{B}}_1}/\partial \mathrm{S}>0$. □

Therefore, the decrease of ${\mathrm{C},\mathrm{P}}_2$, or the increase of ${\mathsf{\beta }}_2{,\mathrm{L}}_2{,\mathsf{\lambda },\mathrm{P}}_1{,\mathsf{\mu },\mathrm{P}}_{\mathrm{Cq}}{,\mathsf{\eta },\mathrm{C}}_3,\mathsf{\xi },\mathrm{A},\mathrm{S}$ will increase the probability of recycling construction waste by CWR.

The proposition 3 shows that the choice of recyclers to recycle construction waste can also be promoted through increased public participation and carbon trading revenues. When the cost of breaking down construction waste into recyclable building materials is too high, and the profit of using natural materials to produce building materials is too high, the Building DER should adopt an active regulatory strategy to regulate recyclers.

Proposition 4.

In the process of evolution, the probability of recycling construction waste by CWR will increase with the positive planning rate of DER and the probability of classifying and recycling construction waste by CPC.

Proof. 

From the strategy stability of the construction waste recycler side, if ${\mathrm{x}<\mathrm{x}}^{\ast }{,\mathrm{z}<\mathrm{z}}^{\ast \ast }=\left[{\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2 {-\mathrm{P}}_3\left)\right]\right]/(\mathsf{\xi }\mathrm{A}+\mathrm{S})$ “y = 0” achieves the ESS; while ${\mathrm{x}>\mathrm{x}}^{\ast }{,\mathrm{z}>\mathrm{z}}^{\ast }$, “y = 1” achieves ESS. Obviously, the strategy of CER will change with the remaining two parties, and y will move to 1 as z and x rise. □

The proposition 4 shows, the government’s proactive regulation and CPC’s strategy of separating and recycling construction waste can promote the recyclers’ choice of producing renewable construction materials from construction waste. Whether DER actively regulates and whether CPC classify and recycle construction waste will affect the strategy of CWR. Thus, to promote construction waste recycling and to ensure that recyclers will recycle waste requires active regulation by the government administration and the initiative behavior of CPC to separate construction waste and motivate them to be environmentally conscious.

4.3. Stability Analysis of Construction Waste Generators’ Strategies

The expected benefits for CPC to separate and recycle construction waste or not and the average expected benefits are ${(\mathrm{E}}_{31}{,\mathrm{E}}_{32},\overline{{\mathrm{E}}_3})$ respectively:

$$\left\{\begin{array}{c}{\mathrm{E}}_{31}{=-\mathsf{\eta }\mathrm{C}}_3{-\mathrm{C}}_2+\mathrm{xS}+\mathrm{y}[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2]\\ {\mathrm{E}}_{32}{=-\mathrm{C}}_2{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{x}\mathsf{\xi }\mathrm{A}\\ \overline{{\mathrm{E}}_3 }{=\mathrm{zE}}_{31}{+(1-\mathrm{z})\mathrm{E}}_{32}\end{array}\right.$$

(13)

Therefore, the replication dynamic equation for the selection of CPC is obtained as Formula (14). The derivative of the above equation with respect to z and the set “K(y)” is Formula (15):

$$\frac{\mathrm{dF}\left(\mathrm{z}\right)}{\mathrm{dz}}=\left(1-2\mathrm{z}\right){\text{{}-\mathsf{\eta }\mathrm{C}}_3+\mathrm{x}(\mathrm{S}+\mathsf{\xi }\mathrm{A})+\mathrm{y}[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{]+\mathsf{\beta }}_2{\mathrm{L}}_2\text{}}$$

(14)

$${\mathrm{K}\left(\mathrm{y}\right)=\text{{}-\mathsf{\eta }\mathrm{C}}_3+\mathrm{x}(\mathrm{S}+\mathsf{\xi }\mathrm{A})+\mathrm{y}[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{]+\mathsf{\beta }}_2{\mathrm{L}}_2\text{}}$$

(15)

CPC of the construction project chooses the probabilistic stabilization of the sorted recycling waste must satisfy:$\mathrm{F}\left(\mathrm{z}\right)=0$ and $\mathrm{dF}\left(\mathrm{z}\right)/\mathrm{dz}<0$. Since $\partial \mathrm{K}\left(\mathrm{y}\right)/\partial \mathrm{y}>0$, So “J(y)” increases as y increases. When ${\mathrm{y}=\mathrm{y}}^{\ast \ast }=\left[{\mathsf{\eta }\mathrm{C}}_3{-\mathrm{x}(\mathrm{S}+\mathsf{\xi }\mathrm{A})-\mathsf{\beta }}_2{\mathrm{L}}_2\right]/[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2]$, $\mathrm{K}\left(\mathrm{y}\right)=0$, $\mathrm{dF}\left(\mathrm{z}\right)/\mathrm{dz}=0$. It is not easy to determine the stabilization strategy of the construction project contractor at this point. When ${\mathrm{y}>\mathrm{y}}^{\ast }$, $\mathrm{K}\left(\mathrm{y}\right)>0$. $\mathrm{z}=1$, $\mathrm{dF}\left(\mathrm{y}\right)/\mathrm{dy}<0$, then “z = 1” is the ESS of the construction project contractor; on the contrary, “y = 0” is the ESS. The evolutionary phase diagram of the recovery strategy of the construction project contractor is shown in Figure 5.

From Figure 5, it can be seen that the tangent plane crosses the point ${\left(\right(\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2)/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),0,0)$, the probability of CWR’s classification and recycling is ${\mathrm{C}}_1$ represented as the volume ${\mathrm{V}}_{{\mathrm{C}}_1}$, and the probability of choosing negative regulation is ${\mathrm{C}}_2$ represented as the volume ${\mathrm{V}}_{{\mathrm{C}}_2}$. The calculation is obtained by using Formulas (16) and (17).

$${\mathrm{V}}_{{\mathrm{C}}_2}={{\displaystyle \int }}_0^1{{\displaystyle \int }}_0^{\frac{{\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2}{\mathrm{S}+\mathsf{\xi }\mathrm{A}}}\frac{{\mathsf{\eta }\mathrm{C}}_3{-\mathrm{x}(\mathrm{S}+\mathsf{\xi }\mathrm{A})-\mathsf{\beta }}_2{\mathrm{L}}_2}{\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2}\mathrm{dxdz}=\frac{{\left({\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2\right)}^2}{2(\mathrm{S}+\mathsf{\xi }\mathrm{A})[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2]}$$

(16)

$${\mathrm{V}}_{{\mathrm{C}}_1}{=1-\mathrm{V}}_{{\mathrm{C}}_2}$$

(17)

Proposition 5.

The probability of CPC’s classification and recycling of construction waste.There is a positive correlation between the sale proceeds from recyclable material production and the revenues from carbon emissions trading, the amount of incentives and penalties from DER, the compensation for complaints from the public as well as the cost of transporting construction waste to landfills. In addition, there is a negative correlation between the construction waste classification cost paid by CPC and the profit distribution rate negotiated with the recyclers.

Proof. 

The first-order partial derivative of each element in ${\mathrm{V}}_{{\mathrm{C}}_1}$ is obtained as $\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial \mathsf{\eta }<0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial {\mathrm{C}}_3<0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial \mathsf{\lambda }<0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial {\mathsf{\beta }}_2>0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial {\mathrm{L}}_2>0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial {\mathrm{P}}_1>0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial \mathsf{\mu }>0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial \mathsf{\xi }>0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial \mathrm{A}>0,\partial {\mathrm{V}}_{{\mathrm{C}}_1}/\partial \mathrm{S}>0$. Therefore, a decrease in ${\mathsf{\eta },\mathsf{\lambda },\mathrm{C}}_3$ and an increase in ${\mathsf{\beta }}_2{,\mathrm{L}}_2{,\mathrm{P}}_1{,\mathsf{\mu },\mathrm{P}}_{\mathrm{Cq}}{,\mathsf{\xi },\mathrm{A},\mathrm{S},\mathrm{C}}_2$ will all raise the probability of CWR recycling construction waste. □

Proposition 5 shows the CPC has invested too much in the classification of construction waste, and DER should adopt an active regulatory strategy, promote the classification and resource use of construction waste by increasing public participation, revenue from carbon emissions, and government incentives and penalties.

Proposition 6.

During the evolution, with the active planning rate of DER and the probability of waste recyclers recycling construction waste going up, the probability of CPC classifying and recycling such waste will increase as well.

Proof. 

In accordance with the strategy stability of CPC, when ${\mathrm{y}<\mathrm{y}}^{\ast \ast }{,\mathrm{x}<\mathrm{x}}^{\ast \ast }{=\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2/(\mathrm{S}+\mathsf{\xi }\mathrm{A})$, $\mathrm{z}=0$ is ESS; when ${\mathrm{y}>\mathrm{y}}^{\ast \ast }{,\mathrm{x}>\mathrm{x}}^{\ast \ast }$, $\mathrm{z}=1$ is ESS. Clearly, CPC’s strategies will change as the remaining two parties change, and z will move to 1 as x and y rise. □

The proposition 6 shows that whether CPC take the initiative to classify and recycle construction waste is influenced by whether DER actively regulates and whether CWR recycle. The government’s advanced positive regulation and construction waste recycling done by the recyclers can promote CPC’s initiative to classify and recycle.

4.4. Stability Analysis of the Equilibrium Point of the Game Model System

If $\mathrm{F}\left(\mathrm{x}\right)=0,\mathrm{F}\left(\mathrm{y}\right)=0,\mathrm{F}\left(\mathrm{z}\right)=0$, the equilibrium stability point of the model can be obtained:

$${\mathrm{E}}_1\left(0,0,0\right){,\mathrm{E}}_2\left(1,0,0\right){,\mathrm{E}}_3\left(0,1,0\right){,\mathrm{E}}_4\left(0,0,1\right){,\mathrm{E}}_5\left(1,0,1\right){,\mathrm{E}}_6\left(1,1,0\right){,\mathrm{E}}_7\left(0,1,1\right){,\mathrm{E}}_8\left(1,1,1\right),$$

$${\mathrm{E}}_9\left({0,(\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2)/[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{],(\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{)/[\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\right),$$

$${\mathrm{E}}_{10}\left({(\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{)/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),0,(\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1)/(\mathrm{S}+\mathsf{\xi }\mathrm{A})\right),$$

$${\mathrm{E}}_{11}\left({(\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{)/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),(\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1)/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),0\right),$$

$${\mathrm{E}}_{12}\left({1,(\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{S}-\mathsf{\xi }\mathrm{A})/[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{],(\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\xi }\mathrm{A}-\mathrm{S})/[\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\right),$$

$${\mathrm{E}}_{13}\left({\text{{}\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{]\text{}}/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),1,(\mathrm{H}+\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{S})/(\mathrm{S}+\mathsf{\xi }\mathrm{A}+\mathrm{H})\right),$$

$${\mathrm{E}}_{14}\left({\text{{}\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3{\left)\right]\text{}}/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),(\mathrm{H}+\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathrm{s}\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{S})/(\mathrm{S}+\mathsf{\xi }\mathrm{A}),1\right)$$

Since $\mathrm{x},\mathrm{y},\mathrm{z}\mathsf{ϵ}$[0, 1], the stable point ${\mathrm{E}}_9{\text{~}\mathrm{E}}_{14}$ would be meaningful if given certain circumstances. It is shown through observation that ${\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{]<0,\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\xi }\mathrm{A}-\mathrm{S}<0,\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1)/(\mathrm{S}+\mathsf{\xi }\mathrm{A})>1$, so ${\mathrm{E}}_{10}{\text{~}\mathrm{E}}_{13}$ is meaningless. The Jacobian matrix of the model is obtained in Formula (18).

$$\begin{gathered} \mathrm{J}=\left[\begin{array}{ccc}{\mathrm{J}}_1& {\mathrm{J}}_2& {\mathrm{J}}_3\\ {\mathrm{J}}_4& {\mathrm{J}}_5& {\mathrm{J}}_6\\ {\mathrm{J}}_7& {\mathrm{J}}_8& {\mathrm{J}}_9\end{array}\right]=\left[\begin{array}{ccc}\partial \mathrm{F}\left(\mathrm{x}\right)/\partial \mathrm{x}& \partial \mathrm{F}\left(\mathrm{x}\right)/\partial \mathrm{y}& \partial \mathrm{F}\left(\mathrm{x}\right)/\partial \mathrm{z}\\ \partial \mathrm{F}\left(\mathrm{y}\right)/\partial \mathrm{x}& \partial \mathrm{F}\left(\mathrm{x}\right)/\partial \mathrm{y}& \partial \mathrm{F}\left(\mathrm{x}\right)/\partial \mathrm{z}\\ \partial \mathrm{F}\left(\mathrm{z}\right)/\partial \mathrm{x}& \partial \mathrm{F}\left(\mathrm{z}\right)/\partial \mathrm{y}& \partial \mathrm{F}\left(\mathrm{z}\right)/\partial \mathrm{z}\end{array}\right] \\ \begin{array}{c}=\left[\begin{array}{ccc}{(1-2\mathrm{x})[\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\left(\mathrm{y}+\mathrm{z}\right)\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)-\mathrm{yz}\left(\mathrm{H}\right)]& \mathrm{x}(1-\mathrm{x})[-\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)-\mathrm{z}\left(\mathrm{H}\right)]& \mathrm{x}(1-\mathrm{x})[-\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right)-\mathrm{y}\left(\mathrm{H}\right)]\\ \mathrm{y}(1-\mathrm{y})(\mathsf{\xi }\mathrm{A}+\mathrm{S})& {(1-2\mathrm{y})\text{{}\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{P}}_3{+\mathrm{x}(\mathsf{\xi }\mathrm{A}+\mathrm{S})+\mathrm{z}\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\text{}}& {\mathrm{y}(1-\mathrm{y})\left[\mathsf{\lambda }\right(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-(\mathrm{P}}_2{-\mathrm{P}}_3\left)\right]\\ \mathrm{z}(1-\mathrm{z})(\mathrm{S}+\mathsf{\xi }\mathrm{A})& \mathrm{z}(1-\mathrm{z})[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2]& {(1-2\mathrm{z})\text{{}-\mathsf{\eta }\mathrm{C}}_3+\mathrm{x}(\mathrm{S}+\mathsf{\xi }\mathrm{A})+\mathrm{y}[\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2{]+\mathsf{\beta }}_2{\mathrm{L}}_2\text{}}\end{array}\right]\end{array} \end{gathered}$$

(18)

According to the first principle of Lyapunov, if all the Jacobian matrix eigenvalues are negative numbers, it is the asymptotic stability point; if there is at least one integer, it is the instability point (IP); if all of them are negative numbers except zero, it is in a critical state and the stability cannot be determined by symbols. By substituting the values of each equilibrium point, the results after analysis are shown in

Table 2. Equilibrium point stability analysis.

Equilibrium Points	Jacobian Matrix Eigenvalues		Stability Conclusions	Conditions
	${\mathsf{\lambda }}_1{,\mathsf{\lambda }}_2{,\mathsf{\lambda }}_3$	Symbols
${\mathrm{E}}_1\left(0,0,0\right)$	${\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{P}}_3$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\eta }\mathrm{C}}_3$	(+,−,−)	IP
${\mathrm{E}}_2\left(1,0,0\right)$	${\mathrm{C}}_1{+\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{H}-2\mathsf{\xi }\mathrm{A}$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathrm{P}}_3+\mathsf{\xi }\mathrm{A}+\mathrm{S}$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{+\mathrm{S}+\mathsf{\xi }\mathrm{A}-\mathsf{\eta }\mathrm{C}}_3$	(−,−,−)	ESS	➀
${\mathrm{E}}_3\left(0,1,0\right)$	${\mathrm{H}+\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{S}$, ${\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\eta }\mathrm{C}}_3+\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2$	(+,+,+)	IP
${\mathrm{E}}_4\left(0,0,1\right)$	${\mathrm{H}+\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{S}$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{+\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-\mathrm{P}}_2{,\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2$	(+,−,+)	IP
${\mathrm{E}}_5\left(1,0,1\right)$	${\mathrm{C}}_1{+\mathsf{\beta }}_1{\mathrm{L}}_1+\mathrm{S}-\mathrm{H}-\mathsf{\xi }\mathrm{A}$, ${\mathsf{\beta }}_2{\mathrm{L}}_2{+\mathsf{\xi }\mathrm{A}+\mathrm{S}+\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})-\left({\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3\right){-\mathrm{P}}_2$, ${\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{S}-\mathsf{\xi }\mathrm{A}$	(−,−,−)	ESS	➁
${\mathrm{E}}_6\left(1,1,0\right)$	${\mathrm{C}}_1{+\mathsf{\beta }}_1{\mathrm{L}}_1+\mathrm{S}-\mathrm{H}-\mathsf{\xi }\mathrm{A}$, ${\mathrm{P}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathsf{\xi }\mathrm{A}-\mathrm{S}$, ${-\mathsf{\eta }\mathrm{C}}_3{+\mathsf{\beta }}_2{\mathrm{L}}_2+\mathrm{S}+\mathsf{\xi }\mathrm{A}+\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)+\mathrm{C}}_2$	(−,−,+)	IP
${\mathrm{E}}_7\left(0,1,1\right)$	${\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\mathrm{S}$, ${\mathrm{C}-\mathsf{\eta }\mathrm{C}}_3{+\mathrm{P}}_2{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})$, ${\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)-\mathrm{C}}_2$	(−,−,−)	ESS
${\mathrm{E}}_8\left(1,1,1\right)$	${\mathrm{C}}_1{+\mathsf{\beta }}_1{\mathrm{L}}_1{+2\mathrm{S},\mathrm{C}+\mathrm{P}}_2{-\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2{-\mathsf{\xi }\mathrm{A}-\mathrm{S}-\mathsf{\lambda }(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}})$, ${\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{S}-\mathsf{\xi }\mathrm{A}-\left(1-\mathsf{\lambda }\right){(\mathrm{P}}_1{+\mathsf{\mu }\mathrm{P}}_{\mathrm{Cq}}{)-\mathrm{C}}_2$	(+,−,−)	IP
${\mathrm{E}}_9(0,y_1,z_1$)	${[\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\left({\mathrm{y}}_1{+\mathrm{z}}_1\right)\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right){-\mathrm{y}}_1{\mathrm{z}}_1\left(\mathrm{H}\right)]$,0,0	(−,$0$,0)	IP	➂
${\mathrm{E}}_{14}\left(x_1,y_2,1\right)$	$a_1,a_2,a_3$	($\times$, $\times$,−)	IP	➃ ➄

Notes: x in the table indicates whether the symbol is positive or negative is uncertain, and ${\mathrm{x}}_1{,\mathrm{x}}_2{,\mathrm{y}}_1{,\mathrm{y}}_2{,\mathrm{z}}_1{,\mathrm{z}}_2$ are the corresponding coordinates of each point. If each point does not meet the corresponding conditions, then the point is unstable or meaningless. ①: ${\mathsf{\beta }}_2{\mathrm{L}}_2{+\mathsf{\xi }\mathrm{A}+\mathrm{S}-\mathrm{P}}_3<0$; ②: ${\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{S}-\mathsf{\xi }\mathrm{A}<0$; ③: ${\mathrm{H}+2\mathsf{\xi }\mathrm{A}-\mathrm{C}}_1{-\mathsf{\beta }}_1{\mathrm{L}}_1-\left({\mathrm{y}}_1{+\mathrm{z}}_1\right)\left(\mathrm{S}+\mathsf{\xi }\mathrm{A}\right){-\mathrm{y}}_1{\mathrm{z}}_1\left(\mathrm{H}\right)<0$; ④: ${\mathrm{A}}_1<0$; ⑤: ${\mathrm{A}}_2<0$.

:

Proposition 7.

There is a stable point$E_2\left(1,0,0\right)$in the system if the equipment renewal cost to be paid by CWR is greater than the sum of incentives and penalties from DER and public compensation.

Proof. 

As can be seen form Table 2, when ${\mathsf{\beta }}_2{\mathrm{L}}_2{+\mathsf{\xi }\mathrm{A}+\mathrm{S}-\mathrm{P}}_3<0$, the real part symbols are all negative numbers under the status of ${\mathrm{E}}_2\left(1,0,0\right)$, which is a stability strategy. □

Proposition 7 shows that government’s active planning and the reluctance of enterprises to take the initiative to recycle construction waste are in line with the current situation of this field in China. CWR are unwilling to spend extra money on equipment renewal for construction waste recycling while CPC are also reluctant to pay for its classification and recycling. For the recyclers, if they upgrade the equipment while CPC incinerate or landfill the construction waste, they have no opportunity to produce recyclable construction materials; for CPC, landfill and incineration is more convenient and less expensive compared with classification and recycling. This requires the joint efforts of both DER and the public to make some changes.

Proposition 8.

There is a stable point$E_5\left(1,0,1\right)$in the system if the construction waste classification cost paid by CPC is less than the sum of incentives and penalties from DER and public compensation.

Proof. 

As can be seen from Table 2, when ${\mathsf{\eta }\mathrm{C}}_3{-\mathsf{\beta }}_2{\mathrm{L}}_2-\mathrm{S}-\mathsf{\xi }\mathrm{A}<0$, the real part symbols are all negative numbers under the status of ${\mathrm{E}}_5\left(1,0,1\right)$, which is a stability strategy. □

Proposition 8 shows that after a period of the government’s active planning, CPC begin to classify and recycle construction waste, which indicates that efforts paid by DER and the public are effective. Influenced by these two parties, CPC can generally become environmentally conscious and change their original disposal methods to cleaner production methods.

Proposition 9.

There is at least one stable point$E_7\left(0,1,1\right)$in the system.

Proof. 

As can be seen from Table 2, according to the numerical analysis of the actual production process, the real part symbols are all negative numbers under the status of ${\mathrm{E}}_7\left(0,1,1\right)$, which is a stability strategy. □

Proposition 9 shows that after a period of the government’s active planning, the recyclers and CPC start the classification and recycling of construction waste; while enterprises take action on the recycling, there is no need for government regulation. This demonstrates that DER does not participate in the construction waste recycling system when a high percentage of enterprises do the recycling, but rather regulates carbon trading price and promotes public participation, which stabilizes such a system.

Stable points of ${\mathrm{E}}_9{(0,\mathrm{y}}_1{,\mathrm{z}}_1)$ and ${\mathrm{E}}_{14}\left({\mathrm{x}}_1{,\mathrm{y}}_2,1\right)$ are special cases and will not be analyzed separately. Moving from stable point ${\mathrm{E}}_2\left(1,0,0\right)$ to stable point ${\mathrm{E}}_5\left(1,0,1\right)$ and then to stable point ${\mathrm{E}}_7\left(0,1,1\right)$ is the path for China’s construction waste recycling system to improve from the status quo to the optimal situation. DER’s high incentives and penalties promote the participation of enterprises, and then enterprises generally carry out spontaneous cooperation in construction waste recycling and the production of recyclable construction materials. In this way, the government can also reduce intervention with no subsidies but only regulatory penalties.

5. Numerical Simulation Analysis

In order to verify the rationality of the above analysis, the value is assigned based on previous studies [41,42,43] and actual engineering project investigation, and MATLAB2021b software was used for simulation. Array 1: ${\mathrm{H}=15,\mathrm{S}=5,\mathrm{A}=10,\mathrm{Q}=30,\mathsf{\xi }=30\%,\mathsf{\beta }}_1{=4\%,\mathrm{L}}_1=5,$ ${\mathsf{\beta }}_2{=8\%,\mathrm{L}}_2=3,\mathsf{\lambda }=0{.6,\mathsf{\mu }=100,\mathrm{P}}_{\mathrm{Cq}}=0{.05,\mathrm{C}=30,\mathrm{C}}_1=5$, ${\mathrm{C}}_2{=10,\mathrm{C}}_3=20,\mathsf{\eta }=0{.7,\mathrm{P}}_1{=40,\mathrm{P}}_2{=10,\mathrm{P}}_3=8$, on the basis of this data, the influence of $\mathsf{\xi }$, ${\mathrm{S},\mathsf{\beta }}_1,{\mathsf{\beta }}_2,{\mathrm{C}}_3,{\mathrm{P}}_3,\mathsf{\lambda },{\mathrm{P}}_{\mathrm{Cq}}$ on the evolution process and results is analyzed.

First of all, in order to analyze the impact of government reward and punishment mechanism on enterprises’ construction waste recycling, making $\mathsf{\xi }$ be 0.3, 0.5, 0.8 respectively, the simulation result is shown in Figure 6 and making $\mathrm{S}$ be 5, 8, 10 respectively, the simulation result is shown in Figure 7.

As can be seen from Figure 6 of the numerical simulation results above, with the regulator success rate of DER increasing, the probability of its active planning will also increase. After all enterprises selecting construction waste recycling, the probability of DER’s active planning will slowly decline towards zero. Figure 6 shows that incentives are more conducive to promoting enterprises’ construction waste recycling, but if it is excessive, it is unfavorable for DER’s regulation and could reduce the probability of active planning. Therefore, a reasonable reward and punishment mechanism as well as supervision means can make enterprises work together with DER in the construction waste recycling system.

Secondly, for the purpose of analyzing the impact of public participation on enterprises and DER’s strategies, making ${\mathsf{\beta }}_1$ be 0.04, 0.44, 0.84 respectively, then the simulation result is shown in Figure 8; making ${\mathsf{\beta }}_2$ be 0.08, 0.48, 0.88 respectively, then the simulation result is shown in Figure 9.

From the above, it is clearly that public participation has a positive impact on DER and enterprises. Figure 8 shows that when the success rate of public complaints against DER’s inaction increases, this department will speed up its strategies adjustment and its active planning for construction waste recycling. Figure 9 shows that when the success rate of the public reporting the failure of enterprises increases, enterprises will be more proactive in construction waste recycling, and DER can reduce intervention to allow the market’s free development. Therefore, DER should engage the public in participation through the improvement of the protection and rewards for informants.

Finally, in order to analyze the influence enterprises’ extra expenditure and income on their construction waste recycling, making ${\mathrm{C}}_3$ be 20, 25, 30, ${\mathrm{P}}_3\mathrm{be}8,16,24$ and ${\mathrm{P}}_{\mathrm{Cq}}\mathrm{be}0.05,0.15,0.25$ respectively, the simulation results are shown in Figure 10, Figure 11, Figure 12 and Figure 13.

Figure 10 indicates that the higher the cost of classifying and recycling construction waste is, the less the contractor will take the initiative to do it, although the proactivity of the recyclers will be mobilized. Figure 11 and Figure 12 show that show that as the profit distribution ratio and carbon emissions trading price grow, the enthusiasm of CWR will increase and the initiative of CPC’s classification and recycling of construction waste will rise even faster. This proves that it is also an alternative to bring CWR into the carbon emissions trading market and regulate its strategies by controlling the carbon trading price. Figure 13 shows that when the equipment renewal cost is too high, enterprises will not recycle construction waste even if DER takes active planning measures, which proves that there are two stability strategies ESS, namely ${\mathrm{E}}_2\left(1,0,0\right)$ and ${\mathrm{E}}_7\left(0,1,1\right)$. In terms of the issue of excessive equipment renewal cost, DER needs to be proactive in strengthening the cooperation between enterprises and universities for the development of more efficient construction waste classification equipment.

6. Discussion and Limitation

6.1. Discussion

The numerical simulations above show that there are three stable scenarios in the evolutionary process, which are:

(1)

Government chooses to specify positive incentive rules to promote marine environmental construction waste disposal and carbon trading. Under this strategy choice, it is generally the government that uses coercive measures to build the market framework and encourages all parties to participate in the policy construction by adopting the development of incentive regulations to promote the construction waste treatment and carbon sink cycle. For the other two parties, since they are all capitalists, they tend to choose the strategy that is favorable to them. With various forms of incentives from the government, such as construction qualification incentives, land tax exemptions, environmental protection qualification ratings [42], etc. The whole industry will be stimulated to generate internal healthy competition, and more project contractors and construction waste recyclers will participate in the process of construction waste sorting and recycling, which will greatly stimulate the market share of carbon trading. This will greatly stimulate the market share of carbon trading and increase the carbon sink space [12], which is the early development stage of the whole construction waste disposal system.

(2)

The second one is a scenario in which the government chooses incentive policies and construction waste recyclers can take the initiative to recycle construction waste. This scenario, according to the simulated values of this study, will exist after the policy is formulated, and the government’s stimulus incentive behavior has been carried out for some time [44]. At this point, after a period of development of the construction waste disposal and carbon trading platform in the marine environment, each entity has already built the relevant responsible department or institution. In particular, the construction waste recyclers will gradually move towards the industrialized and mature stage under the development of the large market of carbon trading for waste recycling, with industrial assembly lines and skilled workers with relevant skills, which can greatly reduce the cost of recycling. After the cost is reduced, construction waste recyclers will compete within the industry to improve technical productivity to expand profit margins. They will also optimize the disposal methods and technologies of non-recyclable waste [36] and expand the business of land reclamation for the disposal of non-polluting building materials waste, earning more room for development of their industry.

${\mathrm{E}}_7\left(0,1,1\right)$ means that the government has formulated relevant policies on marine garbage treatment with no incentives or subsides for project contractors and the recyclers, and CPC can take the initiative to carry out classified transportation processing while CWR can classify and reuse the construction waste. The emergence of such stable point demonstrates that with the establishment of public supervision and a carbon trading platform, the development of a marine environmental construction waste disposal system is nearing completion. At this time, the government no longer needs to reward the other two parties in order to promote social sustainable development and environmental protection. CPC will reach a consensus with the recyclers on its own and actively provide them with recyclable construction waste and classify the polluting waste to reduce the human resources input of the recyclers in exchange for the discount of recycled construction materials. Meanwhile, the public participation also greatly reduces the manpower input of the relevant government departments and puts the corresponding fines for violations into public undertakings and expands the welfare of the public [6].

The development mechanism of construction waste recycling in the marine environment considering public participation and carbon trading in this research system is shown in Figure 14.

Most developed countries have a high recycling rate of construction waste, and only need to develop recycled goods with high recovery rate to obtain a considerable amount of renewable economy; For most developing countries, however, they do not attach importance to the recycling of construction waste, and China is the representative of developing countries. Taking China as an example, the policy suggestions put forward in this paper can provide some reference for other developing countries, and urge developing countries to establish a recycling mechanism of marine construction waste resources suitable for their own national conditions.

6.2. Limitations

The biggest limitation of this article is that it does not consider the influence of public behavior and mood changes on government policy-making. In this study, if construction waste is dumped into the sea illegally or incinerated without decontamination, the public’s living environment and the carbon sink reserve in the marine environment will be affected, so that the public will definitely participate in this system. However, in practice the public may be less involved due to fears of excessive time costs or retaliation. In addition, the effect of game order is not considered in this paper.

7. Conclusions

In view of the current situation of low recycling rate of construction waste and untreated polluting waste in China’s marine environment, combined with the current carbon emission trading market and public participation behavior, this paper constructs an evolutionary game model among DER, CWR, and construction waste generator (CPC), analyzes the stability of the strategy choices of these three parties, the stability of the equilibrium strategy combination of the game system and the influence of each factor. The validity of the conclusion is verified by real data simulation analysis, and the conditions that when all enterprises choose the strategy of construction waste recycling are obtained. According to the influence relationship of factors, relevant suggestions are put forward for proving departments.

The main conclusions include:

• In the early stages, the planning policies of DER were crucial in increasing the proportion of enterprises recycling construction waste. Appropriate incentive policies should be formulated to establish the processing and recycling system of waste in the marine environment and the platform of carbon sink reserve and carbon trading.
• With the gradual maturation of the construction waste recycling industry, it is profitable for enterprises to recycle such waste. When a high percentage of enterprises do this, DER will gradually reduce their intervention in them, eventually evolving into no regulation. Setting a reasonable reward and punishment mechanism is conducive to promoting enterprises’ construction waste recycling and motivating DER to fulfill its responsibilities, however, excessive incentive money could discourage it from actively planning.
• The public is a significant participant in the construction waste recycling system, and whether to classify and recycle such waste could affect the living environment of the public. It is an effective method to promote construction waste recycling to mobilize public participation and increase informants’ protection and rewards. Certain profits could be brought by the current carbon emissions trading market for enterprises producing renewable construction materials. DER could take the lead to accelerate the cooperation between enterprises and universities to develop more efficient and cleaner construction waste sorting equipment to bring more carbon emission trading indexes for enterprises, which can also promote enterprises to recycle construction waste.

A future research direction will be to build a four-way game model of DER–CWR–CPC–the public by introducing the public’s participation selection strategies and DER’s incentives and protections for them. With the development of time and technology, each country will pay more attention to the resources under the ocean. Therefore, such research will promote environmental sustainability.