Collaborative Evolution Mechanism and Simulation of Construction Waste Recycling Stakeholders Based on Social Network

Abstract

With the continuous advancement of urbanization, a huge amount of construction waste is generated in large-scale construction activities, which has aggravated the problems of environmental pollution, waste of resources and destruction of city appearance. Construction waste recycling can effectively solve these problems. However, the recycling rate of construction waste is low in China. Therefore, this paper, firstly through the way of literature analysis and questionnaire investigation, analyzes the factors that influence construction waste resource utilization, determines the key influence factors and the stakeholders in the process of construction waste resource utilization, and uses social network analysis method to identify core stakeholders. On this basis, this paper selects construction enterprises and recycling enterprises as the game subjects, and the government and the public as the external environment to explore the influence of the external environment on the cooperation behavior of the two stakeholders, and uses Matlab simulation to analyze the influence of external variables on the decision-making behavior evolution of the two stakeholders. The research results show that the government, construction enterprises, recycling enterprises and the public are the four core stakeholders of the construction waste recycling system, which have the power to control the information transmission among other stakeholders and play a great supporting role in the smooth implementation of the construction waste recycling project. Among them, the construction enterprise and recycling enterprise are the construction waste recycling system’s two stakeholders playing the pivotal role, and the government and the public are the external environment of the construction waste recycling system’s incentive and regulatory effect. The difference between the benefits and costs of the two stakeholders and the effect intensity of the external environment determines the stable state of the system, that is, the stronger the effect of the external environment and the larger the difference, the more the behavior of the two tends toward the recycling, on-site recycling strategy. Government penalties and rewards can effectively reduce the illegal dumping of construction waste, while excessive penalties and rewards have limitations in controlling illegal dumping. Public participation can effectively improve the efficiency of government supervision. The research results help to deeply understand the behavior, needs and cooperation of stakeholders in the construction waste recycling market, improve the efficiency of cooperation between construction enterprises and recycling enterprises, and provide management inspiration for the construction waste recycling practice.

1. Introduction

Massive greenhouse gas emissions have contributed to the “normalisation” of catastrophic weather occurrences in the complex international environment of today. This has increased instability and uncertainty and posed a significant threat to the advancement of the world’s economic and social systems [1]. A green, low-carbon and high-quality growth path is being opened by society in China around the “dual-carbon” goal and the “dual-cycle” development pattern in response to the complicated global environment that exists today [2]. The construction sector is growing rapidly due to increasing urbanization and rising infrastructure needs and is becoming one of the highest energy users and carbon emitters. A large amount of construction waste (CW) has been generated from new construction, reconstruction, expansion and demolition activities, which has aggravated the problems of resource waste, environmental pollution and destruction of city appearance [3]. The Ministry of Housing and Urban-Rural Development suggested on 8 May 2020, “Promoting the reduction of CW is a vital aspect of the CW management system and an important strategy to save resources and safeguard the environment.”. Construction waste recycling (CWR) has become an effective solution to save resources and protect the environment in China [4]. As the construction industry is in a period of rapid development, which is currently more focused on the construction stage than the disposal of CW, it has resulted in increasing CW year-by-year in China [5]. The total output of CW reached 3.209 billion tons in 2021, accounting for 30% to 40% of the total urban waste in China [6]. CWR technology is relatively backward compared with other developed countries, making the CWR rate still low in China [7]. At present, the recycling rate of CW is 5% in China, while developed countries such as Japan, South Korea and Germany have exceeded 90% [8]. Therefore, under the development pattern of ecological civilization construction and “dual-carbon” goals in China, how to comprehensively improve the efficiency of CWR and promote the sustainable development of the construction industry has become an important challenge that requires urgent resolution.

At present, CWR is regarded as an effective way to deal with CW in China [9]. However, CWR started late in China, and low resource technology, lack of resource awareness and low recognition of recycled products seriously hinder the development of CWR [10]. Meanwhile, as a complex engineering system, the process of CWR involves many stakeholders, and different stakeholders have different importance and influence on CWR. Whether the project can effectively make decisions and smoothly implement depends on the game results of the stakeholders of CWR [11]. Furthermore, the existing system does not consider the complexity of the stakeholder participation process and lacks effective management and guidance, which makes it impossible for stakeholders to cooperate, resulting in slow decision-making processes [12]. The treatment system with the government as the leader, enterprises as the main body and public participation should be built to realize the common governance, source prevention and efficient recycling of CW [13]. If the game relationship between the government, enterprises and the public in the collective action of CW treatment from “non-cooperation” to “cooperation” cannot be solved, the cooperative treatment system will not be able to realize the efficient utilization of resources and the implementation of recycling policies. Therefore, the implementation of a new era of ecological civilization construction and the double carbon targets in China, comprehensively improve the efficiency of resource utilization, establishing and perfecting the green, low-carbon-cycle economic development system, build the government as the leading factor, the enterprises as the main body and the public to participate in the work system, needs to identify the influencing factors of CW resource utilization, clear the responsibility of the different stakeholders in the process of CW resource utilization, and clarify the interaction between stakeholders.

Social network analysis (SNA) can visualize the relationship between various social subjects to form a social network diagram, analyze the strength of the association between each subject, explore the integrity of the network structure and reflect the role of each subject of position and degree of influence in the whole network, and then obtain the most influential stakeholders [14]. Evolutionary game originates from the study of biological evolutionary process in evolutionary theory. It is a combination of game theory and dynamic evolutionary process analysis and has been widely used in the study of strategy selection process [15]. Therefore, from the perspective of win–win cooperation among stakeholders, this paper conducts research on the development mechanism of CWR, defines the influencing factors of CWR, uses the social network analysis to identify the core stakeholders, and deeply analyzes the status, correlation and behavioral decisions of each stakeholder in the process of CWR, and uses the evolutionary game theory to build an evolutionary game model, explore a reasonable and efficient CWR operation model and management system, give full play to the role of various stakeholders, and promote the high-quality development of CWR.

2. Literature Review

With the increasing awareness of environmental protection and resource conservation, domestic and foreign scholars have conducted lots of research on CWR from different perspectives, mainly focusing on CWR technology, CWR management and the cooperative evolution mechanism of CWR.

2.1. Construction Waste Recycling Technology

Lots of research about CWR has been conducted by scholars from different perspectives with the increasing consciousness of environmental protection and resource conservation. In view of the CW treatment mode, beginners focus on the research of recycling technology of CW and believe that the government and enterprises should increase the research and development of technical equipment to improve the recycling rate of CW. Silva et al. used recycled aggregates in a variety of situations, and the study demonstrated the technical feasibility and appropriateness of using recycled aggregates in a variety of situations [16]. Tam et al. reviewed the literature on the production and utilization of recycled aggregates in concrete, concrete pavement and roads and systematically analyzed and evaluated the data on recycled aggregate standards (normative documents) published around the world, encouraging and further promoting recycling aggregates be used on a larger scale in civil engineering projects [17]. Akhtar et al. explored the properties of recycled concrete from a world perspective [18]. Ding et al. explored the situation, relevant laws and distribution characteristics of construction waste in eastern coastal cities of China and proposed new technologies for the resource utilization of construction waste [19]. Huang et al. summarized the mechanism and technical characteristics of urban waste recycling and proposed future research work to promote the efficient treatment of urban waste and realize urban green and sustainable development [20].

2.2. Construction Waste Recycling Management

However, the enhancement of the technical level has not significantly improved the recycling rate of CW [21]. Subsequently, scholars have refined the CW disposal model, arguing that it should shift to a government-led approach to improve the management of the CWR process and achieve diverse and diversified management. Bao et al. explored the on-site and off-site recycling management systems of construction waste in Hong Kong and proposed reasonable recycling strategies for construction waste [22]. Mohammed et al. reviewed the management of CW in Malaysia and implemented sustainable strategies based on the life-cycle theory to improve the 3R management principle and decrease the illegal disposal of CW [23]. Mak et al. used the theory of planned behavior to explore the key factors affecting the recycling behavior of CW of different stakeholders in Hong Kong [24]. Guerra et al. combined the time algorithm with 4D-BIM method to manage the reuse and recycling of CW, reduce the disposal of CW in landfills and improve the rate of CWR [25].

2.3. Cooperative Evolution Mechanism of CWR

Besides the macro research on the technology and management of CWR, scholars also study the cooperative mechanism of CWR from the micro perspective. Du et al. used evolutionary game theory to analyze the decision-making behavior among subjects of interest in the process of CWR, determined the influencing factors of CWR and explored the cooperation mechanism among subjects of interest [26]. Lu et al. used evolutionary game theory to explore the behavioral decision-making and management mechanism of CWR stakeholders under the PPP model [27]. Sun et al. was inspired by the sustainable development theory, established an evolutionary game model of the decision-making behavior among the government, recycling enterprises and production enterprises, and conducted numerical simulation analysis to explore the influence of the external environment on the decision behavior of participants [28]. Guo et al. developed a quadrilateral evolutionary game model of the government, construction enterprises, recycling enterprises and consumers, and analyzed the decision-making behaviors of the four parties in the recycling and sales stages, providing valuable management inspiration for the recycling practice of stakeholders [29].

In summary, the research of scholars on the recycling of CW is mainly analyzed from three aspects of the technology, management and collaboration mechanism, which provides a theoretical basis for the research in this paper. However, in terms of research content, the existing literature seldom defines the influencing factors and core stakeholders of CWR under bounded rationality. Meanwhile, the research method only uses the evolutionary game theory to study the specific stakeholders in the process of CWR, only explores the influence between the core stakeholders and rarely considers the influence of the external environment on the evolution behavior of the core stakeholders in CWR. Therefore, this paper first uses social network analysis to identify the influencing factors and stakeholders involved in the process of CWR based on the available research, then uses evolutionary game theory to analyze the behavior of core stakeholders and, through numerical simulation, explores the influence of each parameter change on the system evolution results, putting forward corresponding improvement strategies to promote the utilization of CW.

3. Analysis of Influencing Factors and Stakeholders of CWR

Under the “dual-carbon” goal and the development pattern of ecological civilization construction, the CWR rate is still low in China. To increase the rate of China’s CW resource utilization and promote sustainable development of the construction industry, this paper, on the basis of the existing literature research, according to the deductive logic structure, through the questionnaire, using simple random sampling method, semi-structured interviews, and using the SPSS data analysis software, summarizes factors affecting construction waste resource utilization and the influencing factors involved in the interest of the main body. On this basis, the social network analysis method is used to identify the core stakeholders. By summarizing the positioning of the core stakeholders and the influencing factors in the process of CWR, the dilemma faced by the recycling of CW is systematically explored, and the model decision body and parameter setting reference are provided for this paper.

3.1. Research Method

At present, there is minimal research literature on the factors affecting CWR, and it is not comprehensive enough to identify the factors affecting CWR only through literature analysis. In order to fully and accurately identify the influencing factors of CWR, this paper combines literature analysis and questionnaires to systematically analyze the factors affecting the development of CWR. This paper firstly obtains factors that affect CWR through existing literature [30,31,32] and then selects stakeholders involved in the recycling process of CW (such as the government, construction units, design units, construction enterprises, recycling enterprises and financial institutions), relevant experts in universities and the public as the objects of the questionnaire survey to determine the key factors that affect CWR. The paper adopts a semi-structured questionnaire type design and invites experts in this field to conduct a pre-survey before issuing the questionnaire to ensure the validity and completeness of the questionnaire. A total of 130 questionnaires were sent out online (114) and offline (16), 125 responses were received, and 120 effective questionnaires were received with effective recovery rate of 92.31%. The collected data were imported into SPSS23.0 for reliability and validity testing, with Alpha of 0.959 and KMO of 0.862, indicating good reliability and validity of the questionnaire. In order to better collect the basic information of interviewees, this paper imports the collected data into SPSS23.0 for descriptive analysis, and the results are shown in

Table 1. Basic information of interviewees.

Highest Degree	Junior College	Undergraduate	Master’s	Doctorate	Other
	12.31%	23.08%	46.92%	12.31%	5.38%
Work unit	Government	Construction unit	Design unit	Construction enterprise	Recycling enterprise
	16.15%	4.62%	3.08%	15.38%	13.85%
	Research institute	Colleges	Financial institution	Other
	7.69%	31.54%	3.85%	3.85%
Participate in the construction waste recycling project	0	1	2	3	4 or more
	7.69%	41.54%	23.08%	19.23%	8.46%

.

3.2. Influence Factors and Stakeholder Identification

The influencing factors of CWR were summarized, and the key factors affecting CWR were obtained by the questionnaire. Influencing factors of CWR and the current situation are shown in

Table 2. List of influence factors of CWR.

Number	Influence Factors	Current Situation
F1	Awareness of CWR	The main body has a relatively shallow understanding of CWR, lacks professional knowledge and has a low sense of identity, and it is difficult for it to fundamentally understand the meaning and benefits of CWR.
F2	Recycled product approval level	The main body has low recognition of recycled products and there are deviations, which makes it difficult to promote the recycled product market.
F3	Willingness of CWR	Driven by the maximization of interests, the willingness of the main body to participate in the CWR is low.
F4	Incentive policy	The government is the guiding force and driving force of CWR. Incentive policies such as government subsidies and tax incentives can help stimulate the enthusiasm of enterprises for recycling and promote the promotion of CWR.
F5	Supervision	As the main regulator of the CWR process, the government supervising construction enterprises can effectively inhibit the illegal disposal of CW and, at the same time, supervise recycled products to improve the quality of recycled products.
F6	Degree of publicity	The degree of publicity and popularity of the government directly affects the awareness of enterprises and the public on CWR, which in turn affects the enthusiasm of enterprises and the public to participate in recycling.
F7	Technological level of CWR	At present, CWR technology is backward in China, and there is a lack of technological innovation research, which makes CWR rate low.
F8	Research and investment in new technologies and equipment of CWR	The investment in research and development of new technologies and equipment will help improve the efficiency of CWR, reduce recycling costs, and promote the smooth implementation of CWR projects.
F9	Talent team training of CWR	Most technicians are relatively unfamiliar with CWR technology, lack professional skills and qualities, and the level of technical personnel is directly related to CWR efficiency and the quality of recycled products.
F10	Technical specifications and standards of CWR	The technical specifications and standards of CWR are the premise and core of the development of CWR. At present, the technical specifications and standards of CWR are not perfect, which increases the difficulty of the development of CWR.
F11	Cooperation benefits	The process of CWR involves multiple stakeholders, and its cooperation benefits directly affect the cooperative relationship between enterprises, which seriously hinders the virtuous circle of the system of CWR.
F12	The cost of CWR	Due to the complex process of CWR and the need for advanced technical equipment, the cost of CWR is relatively high.

. Friedman proposed that the relevant stakeholders of the incident can affect the process and results of the achievement of goals of the organization or the groups or individuals affected by the organization [33]. In order to break through the dilemma of CWR and improve the rate of CWR in China, the stakeholders involved in the influencing factors should be focused and fundamentally solve the factors that hinder the development of CWR. Through literature analysis, based on the recycling system of CWR, from the stage of CW generation, classification, recycling and reuse, the stakeholders involved mainly include the government (P₁), construction enterprise (P₂), construction unit (P₃), recycling enterprise (P₄), social public (P₅), research institute (P₆), college (P₇), financial institution (P₈), design unit (P₉), etc., the stakeholders involved in each influencing factor were identified, as shown in Figure 1.

3.3. Definition of Core Stakeholders

In the complex network environment of CWR, each stakeholder is interconnected and interacting to promote the cyclic operation of the CWR system. However, in this circulatory system, due to the different degrees of participation of different stakeholders, the depth of their impact on the network is different, and the roles and positions of various stakeholders in this system are also very different. Therefore, the paper adopts the social network analysis method to identify the core participants in the process of CWR.

3.3.1. Data Collection and Processing

According to the analysis and summary of the survey results in this paper, there are 9 stakeholders involved in the process of CWR. In order to clarify the strength of the relationship between the various stakeholders, this paper works through the questionnaire to rate the degree of the relationship between the two stakeholders and selects the “0–5” scale as the rating standard for the degree of relationship between the subjects. The stronger the association between the two subjects, the higher the number. That is, “0” means there is no relationship between the two factors, and “5” means the relationship between the two factors is strong. The evaluation results of each expert are sorted out by the average method, and the relationship strength matrix of the stakeholders of CWR is obtained, as shown in

Table 3. The strength matrix of the relationship between stakeholders of CWR.

Participating Subject	P1	P2	P3	P4	P5	P6	P7	P8	P9
P1	0	5	3	5	5	3	2	2	1
P2	5	0	3	5	5	1	1	3	1
P3	3	3	0	1	0	0	0	2	2
P4	5	5	1	0	5	3	2	3	0
P5	5	5	0	5	0	3	3	1	1
P6	3	1	0	3	3	0	2	0	0
P7	2	1	0	2	3	2	0	1	0
P8	2	3	2	3	1	0	1	0	1
P9	1	1	2	0	1	0	0	1	0

. It can be seen that in the process of CWR through Table 3, the degree of connection or interaction between various subjects of interest is different, resulting in different intensity of relationship between different subjects of interest. For instance, the relationship between the government and construction enterprises is 5, and that between the government and design units is 1, indicating that the government is in frequent contact with construction enterprises, and the interaction between the government and design units is weak in the process of CWR.

3.3.2. Social Network Model Development

In order to determine the core stakeholders in the process of CWR, the relationship strength matrix of CWR stakeholders was imported into UCINET software to form the social network visualization model of CWR stakeholders, as shown in Figure 2. It can be seen from the figure that the government, construction enterprises, the public and recycling enterprises are in the central position in the social network model, indicating that the four major subjects of interest have the most connections with other subjects of interest and the greatest influence and are the core subjects of interest in the process of CWR.

3.3.3. Analysis of Research Results

In order to make the results more convincing, more accurately determine the core subjects of interest of CWR, and explore the integrity and closeness of subjects of interest, this paper calculates the point centrality, middle centrality and proximity centrality of each subject of interest, as well as the middle center potential and density of the whole network through UCINET according to the social network model in Figure 2. The social network of CWR is systematically analyzed and the centrality of subjects of interest is analyzed, as shown in

Table 4. Stakeholder centrality analysis.

Participating Subject	Point Centrality	Betweenness Centrality	Closeness Centrality
Government	26.000	1.767	100.000
Construction enterprise	24.000	1.767	100.000
Construction unit	11.000	0.200	72.727
Recycling enterprise	24.000	0.983	88.889
Social public	23.000	0.983	88.889
Research institute	12.000	0.000	72.727
College	11.000	0.200	80.000
Financial institution	13.000	0.900	88.889
Design unit	6.000	0.200	72.727
Centralization	30.00%	3.97%	36.20%

. According to the calculation results, the highest scores are the government (26.000, 1.767, 100.000), construction enterprises (24.000, 1.767, 100.000), recycling enterprises (24.000, 0.983, 88.889), and social public (23.000, 0.983, 88.889). The quartet of stakeholders plays the pivotal role among other stakeholders and has a greater power to control the transmission of information among other stakeholders. Other stakeholders have lower centrality, weaker ability to transmit information resources, and lower status and less power in the process of CWR. Meanwhile, the central potential of the entire network is only 3.97%, indicating that the network tends to focus on one point less, the overall control and dominance of the network is relatively loose, and there is no absolute dominant main body leading the CWR system planning decisions. In addition, the density of the social network model of CWR stakeholders is 0.8056%, which indicates that the relationship between various stakeholders is not close enough and is less restricted by the influence of the overall network, and the degree of cooperation, information communication and connection between stakeholders is low, the integrity and cohesion of the social network are insufficient, and the cooperative behavior of stakeholders needs to be further improved. The alienation of their relationship makes it difficult for all parties to reach a consensus of interests, increases the difficulty of decision-making and implementation, affects the cooperation between the subjects, and hinders the development of CWR.

4. Model Construction

Through the above analysis, it is found that the four core stakeholders of the government, construction enterprises, recycling enterprises and social public have jointly built a CWR system. Among them, the government is the overall planner and policy maker in the process of CWR, publicizing and encouraging enterprises and the public to participate in CWR, guiding and promoting the smooth development of CWR, and promoting a virtuous cycle of the system. Construction enterprises are the producers of CW and play a source role in the process of CWR. Their participation will help improve the efficiency of CW treatment and promote the sustainable development of the construction industry. Recycling enterprises are producers of recycled products and play an important role in the process of CWR. The level of recycling technology determines the quality of recycled products, which in turn affects the market recognition of recycled products. The public plays a role of supervision and feedback in the process of CWR as the sufferer of environmental pollution and the recipient of recycled products, improving the quality of recycled products and promoting the sustainable development of CWR. The relationship between the four is shown in Figure 3. It can be seen that the four major stakeholders have a key position in the process of CWR, through Figure 3. This result is consistent with the social network map and centrality analysis of CWR stakeholders. Among them, construction enterprises and recycling enterprises, as the two main stakeholders of the CWR system, play the role of recycling hubs. As the external environment, the government and social public play an incentive and regulatory role in the recycling system of CWR. However, driven by the goal of maximizing profits, the willingness of construction enterprises and recycling enterprises to cooperate is not high, which seriously restricts the development of CWR. Therefore, how to strengthen the degree of collaboration between construction enterprises and recycling enterprises and promote the efficiency of CW treatment has become an important problem that needs to be solved urgently.

4.1. Behavior Analysis of Game Players

The decision facing construction enterprises is whether to recycle CW, that is, to recycle CW (referred to as recycling) or not to recycle CW and to illegally dispose of CW (referred to as non-recycling). For recycling enterprises, there are two ways of recycling at present, that is, recycling at the construction site (referred to as on-site recycling) and recycling at the recycling station (referred to as off-site recycling) [34]. Most recycling enterprises choose to recycle in the recycling station, which is a certain distance from the construction site, and the CW needs to be transported to the recycling station. However, on-site recycling can avoid the transfer of waste and the repeated classification of CW, so it can augment the income of recycling enterprises and construction enterprises to a certain degree, but on-site recycling equipment needs to involve additional costs. Therefore, recycling enterprises are also faced with two decisions, namely on-site recycling or recycling at the recycle station. Construction enterprises and recycling enterprises undertake the risk of costs caused by the choices of others, due to their profits depending on each other’s choices to a certain extent.

The game relationship among stakeholders should be defined before developing the model, as shown in Figure 4. In this cycle, the public and the government, as the external environment, supervise the illegal disposal of CW by construction enterprises and elevate the recycling rate of CW. The government will punish the illegal disposal of CW by construction enterprises, subsidize the recycling of construction enterprises, and subsidize the on-site recycling of recycling enterprises to elevate CWR and promote the sustainable development of the construction industry.

4.2. Model Assumptions

This paper puts forward 6 hypotheses to solve the above problems. Model parameters and expression meanings are shown in the figure below.

Assumption 1.

The government, construction enterprises, and recycling enterprises are all bounded and rational, have the ability to learn and adapt to environmental changes, and can adjust their own strategies in the recycling process.

Assumption 2.

If the construction enterprise selects “recycling”, the recycling cost is D_c. The profit of construction enterprises is influenced by the decision of recycling enterprises. If the recycling enterprise selects on-site recycling, the construction enterprise will receive E_c. If the recycling enterprise chooses off-site recycling, the income of construction enterprises is E_d. On the contrary, the cost of construction enterprise is D_d when choosing “non-recycling”.

Assumption 3.

If the recycling enterprise chooses “off-site recycling”, the recycling enterprise’s income is R_s, and the cost is C_s. If the recycling enterprise chooses “on-site recycling”, the income of recycling enterprise is R_r, and the incremental cost is C_r.

Assumption 4.

The possibility that construction enterprises choose “recycling” CW is x ($0\le x\le 1$

), and the possibility that they choose “non-recycling” CW is 1 − x. The possibility of “on-site recycling” is y ($0\le y\le 1$

), and the possibility of “off-site recycling” is 1 − y.

Assumption 5.

When the construction enterprise chooses “non-recycling”, it will incur transportation costs, which may be detected by the government or reported by the public. The probability is μ and ω, where 0 < μ < 1, 0 < ω < 1; the fine is F.

Assumption 6.

The government supervises the recycling process of CW and provides subsidies. The government will subsidize part of the recycling cost when construction enterprises recycle CW. We hypothesize that the subsidy rate is α₁, where 0 < α₁ < 1. In addition, the government rewards the partial costs when recycling enterprises choose “non-recycling”, and the reward rate is α₂, where 0 < α₂ < 1.

4.3. Model Analysis

The evolutionary game payoff matrix is developed by the above hypotheses. It is shown in

Table 5. The evolutionary game payoff matrix.

Construction Enterprises	Recycling Enterprises
	On-Site Recycling (y)	Off-Site Recycling (1 − y)
Recycling (x)	$(E_c-(1-{\alpha }_1)D_c$$,R_r-(1-{\alpha }_2)C_r-C_s$)	$(E_d-(1-{\alpha }_1)D_c$$,R_s-C_s$)
Non-recycling (1 − x)	$(-\left(\mu +\omega \right)F-D_d$$,{\alpha }_2{C}_r-C_r$)	$(-\left(\mu +\omega \right)F-D_d$, 0)

.

For construction enterprises, the anticipation of “recycling” is $E_x$, “non-recycling” is $E_{1-x}$, and the average anticipation is $\overline{E_x}$. For recycling enterprises, the anticipation of “on-site recycling” is $E_y$, the anticipation of “off-site recycling” is $E_{1-y}$, and the average anticipation is $\overline{E_y}$.

$$E_x=y\left[E_c-(1-{\alpha }_1)D_c\right]+(1-y)\left[E_d-(1-{\alpha }_1)D_c\right]$$

(1)

$$E_{1-}{}_x=y\left[-\left(\mu +\omega \right)F-D_d\right]+(1-y)\left[-\left(\mu +\omega \right)F-D_d\right]$$

(2)

$$\overline{E_x}=x{E}_x+(1-x)E_{1-}{}_x$$

(3)

$$E_y=x\left[R_r-(1-{\alpha }_2)C_r-C_s\right]+(1-x)({\alpha }_2{C}_r-C_r)$$

(4)

$$E_{1-y}=x(R_s-C_s)$$

(5)

$$\overline{E_y}=y{E}_y+(1-y)E_{1-}{}_y$$

(6)

According to the evolutionary game theory [35], the two-dimensional dynamic system of evolutionary game is:

$$\{\begin{array}{l}F\left(x,y\right)=x\left(1-x\right)\left[E_d-(1-{\alpha }_1)D_c+(\mu +\omega )F+D_d+y(E_c-E_d)\right]\\ Q\left(x,y\right)=y\left(1-y\right)\left[{\alpha }_2{C}_r-C_r+x(R_r-R_s)\right]\end{array}$$

(7)

According to $F\left(x,y\right)=0$ and $Q\left(x,y\right)=0$, it can be concluded that there are four dual population adopting pure strategy equilibrium points F (0,0), G (0,1), H (1,0), I (1,1), and one possible dual population adopting mixed strategy equilibrium point $(x^{*},y^{*})$, in which $x^{*}=\frac{C_r-{\alpha }_2{C}_r}{R_r-R_s}$, $y^{*}=\frac{(1-{\alpha }_1)D_c-D_d-(\mu +\omega )F-E_d}{E_c-E_d}$.

According to Friedman’s method [36], the determinant and trace of the system at each equilibrium point are shown in

Table 6. Determinant at the equilibrium point of the system.

Equilibrium Point	DetJ
F (0,0)	$\left[E_d-(1-{\alpha }_1)D_c+(\mu +\omega )F+D_d\right]({\alpha }_2{C}_r-C_r)$
G (0,1)	$\left[E_c-(1-{\alpha }_1)D_c+(\mu +\omega )F+D_d\right](C_r-{\alpha }_2{C}_r)$
H (1,0)	$\left[(1-{\alpha }_1)D_c-E_d-(\mu +\omega )F-D_d\right]({\alpha }_2{C}_r-C_r+R_r-R_s)$
I (1,1)	$\left[(1-{\alpha }_1)D_c-E_c-(\mu +\omega )F-D_d\right](C_r-{\alpha }_2{C}_r-R_r+R_s)$
$\mathrm{E}(x^{*},y^{*}$)	$\begin{array}{c}-\frac{(R_r-R_s-C_r+{\alpha }_2{C}_r)(C_r-{\alpha }_2{C}_r)}{R_r-R_s}\\ \times \frac{\left[E_c-(1-{\alpha }_1)D_c+D_d+(\mu +\omega )F\right]\left[(1-{\alpha }_1)D_c-D_d-(\mu +\omega )F-E_d\right]}{E_c-E_d}\end{array}$

and

Table 7. Traces of system equilibrium points.

Equilibrium Point	TrJ
F (0,0)	$\left[E_d-(1-{\alpha }_1)D_c+(\mu +\omega )F+D_d\right]+({\alpha }_2{C}_r-C_r)$
G (0,1)	$\left[E_c-(1-{\alpha }_1)D_c+(\mu +\omega )F+D_d\right]+(C_r-{\alpha }_2{C}_r)$
H (1,0)	$\left[(1-{\alpha }_1)D_c-E_d-(\mu +\omega )F-D_d\right]+({\alpha }_2{C}_r-C_r+R_r-R_s)$
I (1,1)	$\left[(1-{\alpha }_1)D_c-E_c-(\mu +\omega )F-D_d\right]+(C_r-{\alpha }_2{C}_r-R_r+R_s)$
$\mathrm{E}(x^{*},y^{*}$)	0

.

5. Numerical Simulation Analysis

5.1. The Stability Analysis of Equilibrium Strategy

When DetJ > 0 and TrJ < 0 are satisfied, the equilibrium point is the system evolution stable point (ESS). According to the equilibrium point of the evolution model and the analysis of its stability conditions, the evolution of the system is divided into four scenarios.

Scenario 1 When $1-{\alpha }_1{D}_c-E_c<\left(\mu +\omega \right)F+D_d<1-{\alpha }_1{D}_c-E_d$and ${\alpha }_2{C}_r-C_r<R_r+{\alpha }_2{C}_r-C_r$, $\left(\mu +\omega \right)F+D_d<1-{\alpha }_1{D}_c-E_d$ and ${\alpha }_2{C}_r-C_r<R_r+{\alpha }_2{C}_r-C_r$ or $R_r+{\alpha }_2{C}_r-C_r<R_s$, one of the conditions is satisfied, there is a unique ESS (0,0) in the system, and the evolution path of the system is shown in Figure 5. At this time, the recycling enterprise on-site recycling revenue is low, and the incremental cost paid is high. The evolutionary stabilization strategy of recycling enterprises has nothing to do with the choice of construction enterprises. Regardless of the proportion of the strategy of the construction enterprise, the off-site recycling strategy is always the evolution and stability strategy of recycling. The choice of the construction enterprise strategy is influenced by the choice of the recycling enterprise. When recycling enterprises choose on-site recycling, the recovery cost of construction enterprises is the lowest. When recycling enterprises choose off-site recycling, the recycling cost of construction enterprises is higher, and the income is lower. Therefore, the evolutionary stability strategy in this case is the non-recycling, off-site recycling strategy.

Scenario 2 When $\left(\mu +\omega \right)F+D_d>1-{\alpha }_1{D}_c-E_d$ and $R_r+{\alpha }_2{C}_r-C_r<R_s$ is satisfied, the system has a unique ESS (1,0), and the evolution path of the system is shown in Figure 6. The figure shows that the evolutionary stability strategies of the two service populations in the system do not affect each other. At this time, recycling enterprises choose on-site recycling to pay a higher incremental cost and obtain a moderate income but choose off-site recycling to obtain a high income. No matter what strategy the construction enterprise chooses, off-site recycling is always the evolution and stability strategy of the recycling enterprise. When recycling enterprises choose off-site recycling of CW, the cost of recycling is lower for construction enterprises, while the penalty cost of not recycling is higher. Therefore, the evolutionary stable strategy in this case is the recycling, off-site recycling strategy.

Scenario 3 When $\left(\mu +\omega \right)F+D_d>1-{\alpha }_1{D}_c-E_d$ and ${\alpha }_2{C}_r-C_r<R_s<R_r+{\alpha }_2{C}_r-C_r$ is satisfied, the system has a unique ESS (1,1), and the evolution path of the system is shown in Figure 7. At this time, the two sides of the service population in the system are less affected by the initial strategy selection. When the construction enterprise chooses non-recycling, the penalty cost is higher, and the fixed cost of recycling is lower, and the recycling income is general. No matter what strategy recycling enterprises choose, recycling will be the evolution of the stable strategy of construction enterprises. At the same time, the incremental cost of on-site recycling is normal, and the revenue is high, but the revenue of off-site recycling is normal. Therefore, no matter how the construction enterprise chooses the initial strategy and the proportion of the strategy, the evolution and stability strategy of the recycling enterprise will be the on-site recycling strategy. Therefore, the evolution stability strategy in this case is the recycling, on-site recycling strategy.

Scenario 4 When $1-{\alpha }_1{D}_c-E_c<\left(\mu +\omega \right)F+D_d<1-{\alpha }_1{D}_c-E_d$ and ${\alpha }_2{C}_r-C_r<R_s<R_r+{\alpha }_2{C}_r-C_r$ is satisfied, there are two ESS (0,0) and (1,1) simultaneously in the system, and the evolution path of the system is shown in Figure 8. At this time, the choice of the construction enterprise is seriously affected by the choice of the recycling enterprise. The penalty cost paid by the construction enterprises to choose the non-recycling strategy is general, while the benefits vary with the choice of recycling enterprises. Recycling enterprises choose the on-site recycling strategy to pay a low incremental cost and a high profit but choose the off-site recycling strategy to pay a moderate fixed cost. The figure shows that the evolutionary stability strategy of the system is affected by both sides. As long as the initial proportion of construction enterprises and recycling enterprises choosing on-site recycling cooperation strategy is higher than a certain proportion (x > 0.33, y > 0.33), the cooperative strategy is the stable equilibrium strategy of both parties. Otherwise, the stable equilibrium strategy of both parties is the non-cooperative strategy.

5.2. Model Parameter Analysis

The above research shows that only the evolutionary stability strategy of scenario 3 is a cooperation strategy of both parties, while the evolutionary stability strategy of scenario 4 may be a cooperation strategy of both parties. Matlab R2018b software will be used for numerical simulation, and a detailed analysis of the complex evolution of scenario 4 will be carried out to explore the impact of the external environment on the cooperative behavior of the two stakeholders and to promote the cooperation between the two stakeholders and improve the recycling rate of CW. Through on-the-spot research and reference to relevant literature, the initial value of the parameter is set as ${\alpha }_1=0.3$, ${\alpha }_2=0.4$, $\mu =0.2$, $\omega =0.3$, $F=1$, $D_c=4$, $D_d=0.5$, $E_c=5$, $E_d=1.5$, $C_r=2$, $R_s=2$, $R_r=4$ [37,38,39,40]. Except for the analysis object, the values of the other parameters remain unchanged in the process [41].

(1) The impact of the initial policy ratio on system evolution results

Let $x_0$, $y_0$, respectively, represent the initial proportion of cooperation strategies selected by construction enterprises and recycling enterprises, and the numerical simulation results can be obtained by changing the parameters of initial strategy proportion, as shown in Figure 9. As can be seen from Figure 9, the initial proportion of the two parties’ selection strategies has an impact on the convergence speed of the system, and the closer the initial proportion of the selection strategies is to the equilibrium point, the faster the convergence speed of the system. This indicates that the initial proportion of strategies is crucial to whether the two parties can start the cooperative symbiosis mode. Therefore, the cooperation intention of construction enterprises and recycling enterprises in the early stage of CWR is very important. Recycling enterprises tend to choose off-site recycling because of the high cost of on-site recycling. Therefore, aiming at the “on-site recycling” behavior of recycling enterprises is not positive; the next step is to focus on the analysis of $y_0$ = 0.1.

(2) The impact of government rewards and punishments on the system evolution results

As can be seen from Figure 10, Figure 11 and Figure 12, with the increase in government subsidies and penalties, construction enterprises and recycling enterprises change from non-recycling, off-site recycling to recycling, on-site recycling strategy. Therefore, by setting up reward and punishment mechanisms, strengthening supervision systems, improving relevant legal systems and other measures to increase the cost of punishment can promote the establishment and maintenance of a cooperative symbiosis state [42]. By comparing Figure 10 and Figure 12, it can be seen that government subsidies are sensitive to the change of the system evolution state of construction enterprises. Therefore, increasing the recycling subsidy of construction enterprises can improve their recycling willingness.

(3) The impact of government supervision on system evolution results

When the government supervision is adjusted downward to $\mu =0.1$ and upward to $\mu =0.4$, the result of system evolutions is shown as Figure 13. As can be seen from Figure 13, with the continuous increase in government supervision, the probability of construction enterprises choosing recycling strategy gradually increases, and the system tends toward the recycling, on-site recycling strategy. The higher the level of regulation there is, the higher the cost of regulation. In real life, due to the government’s limited manpower, material resources and financial resources, the supervision is insufficient, and most of the construction enterprises violating the regulations are easy to be ignored [43]. Therefore, government supervision should be strengthened, and the public should be called upon to assist the government in supervising the illegal disposal of CW.

(4)The impact of public participation on system evolution results

According to the simulation results in Figure 14, with the increase in public supervision, the tendency of the system toward the recycling, on-site recycling strategy will be greatly improved. Public supervision can effectively make up for the lack of government supervision, improve the efficiency of government supervision, restrain the illegal disposal of CW by construction enterprises, and promote the evolution of the system toward recycling, on-site recycling. Therefore, the government should make great efforts to publicize, formulate relevant laws and regulations, improve the public participation platform, increase public participation, and promote the utilization of CW.

6. Conclusions

In the context of the waste-free city (“Waste-free city” is new development of the innovation, coordination, green, open, sharing ideas as the lead, promoting green development way and way of life, advancing the solid waste source reduction and resource utilization, minimizing landfill, the solid waste to minimize environmental impact mode of city development; it is also a kind of advanced urban management concept.), to increase the rate of construction waste resource utilization, this paper use the social network analysis method to analyze the factors that influence construction waste resource utilization, determine the CWR process involving the core interests of the main body, and then using the evolutionary game theory to explore the game behavior of core stakeholders in order to promote efficient CWR. The results show that the initial intention of the behavior decision of the construction enterprise and the recycling enterprise has a great influence on the system evolution result. The government reward and punishment mechanism can effectively improve the willingness of efficient cooperation between construction enterprises and recycling enterprises, inhibit the illegal disposal of CW by construction enterprises, and promote the steady development of the CWR system. Meanwhile, public participation in the management and supervision of CW can effectively reduce the probability of illegal disposal of CW by construction enterprises, promote the formulation of efficient management strategies, improve government supervision, and promote sustainable production of construction enterprises. Therefore, in order to improve the efficiency of CW processing, promote the sustainable development of the construction industry, avoid environmental pollution and the resource waste problem, the government should establish close cooperation relations with the public, improve the efficiency of CW management strategy and regulation, improve the supervision of hotline and information platforms, increase R&D investment in the technology and equipment, set up the appropriate rewards and punishment mechanisms, and increase the willingness of construction enterprises and recycling enterprises to deal with CW efficiently.

There are many factors affecting the recycling of CW. This paper analyzes the main influencing factors involved in the recycling of CW and puts forward suggestions, while other related factors need to be further analyzed. Meanwhile, due to the limitations of data acquisition related to CW treatment, there may be some deviations from reality in game model assumptions, parameter settings and relationship determination, which need to be further improved. In addition, according to the suggestions put forward in this paper, the future should focus research on the reduction of CW and treatment of the source to reduce the production of CW.