Coevolution Mechanism of Remanufacturer–Construction Enterprise–Public in Construction and Demolition Waste Resource Utilization Projects under Green Value Co-Creation

Abstract

The utilization of resources plays a crucial role in mitigating the environmental pollution issue that improper disposal of construction and demolition waste (CDW) causes. However, the slow growth of the recycled building materials market limits the development of CDW resource utilization. Green value co-creation among remanufacturers, construction enterprises, and the public in CDW resource utilization projects is an effective way to address the issue. This study, based on the theory of value co-creation, uses the evolutionary game method to construct an evolutionary game model for CDW resource utilization projects. The main conclusions are as follows: (1) When the degree of green value co-creation is 0.1 or 0.5, the remanufacturer, the construction enterprise, and the public cannot maintain a state of green value co-creation; when the degree of green value co-creation is 0.9, the remanufacturer, the construction enterprise, and the public in the CDW resource utilization project finally reach a stable state of green value co-creation. (2) When the degree of green value co-creation is 0.5, enhancing the green value co-creation willingness of the remanufacturer or the public can lead other CDW resource utilization project stakeholders to participate in green value co-creation. This study contributes to the promotion of stakeholder cooperation in CDW resource utilization projects, thus providing implications for the promotion of CDW resources.

1. Introduction

The United Nations reports that global waste generation exceeds 10 billion tons annually [1]. As a major source of solid waste [2], improper disposal of construction and demolition waste (CDW) not only leads to increased costs, decreased profits, and overconsumption of raw materials for construction companies, but it also forces the public to face health issues and safety risks [3]. Therefore, how to efficiently handle the large amount of CDW generated has become an urgent problem.

Resource utilization is an effective way of dealing with the CDW [4]. Studies have confirmed the positive economic, social, and environmental effects of CDW resource utilization compared to landfills [5]. However, construction enterprises are reluctant to pay for reproductions due to issues such as low social acceptance and a lack of assurance of product quality [6]. This weakens the enthusiasm of remanufacturers and hinders the development of the CDW recycling market [2]. Therefore, it is necessary to take effective measures to improve the willingness of construction enterprises to pay for recycled building materials.

Green value co-creation improves product quality and customer acceptance through interactive feedback among CDW resource utilization project stakeholders [7], thus promoting the sustainable development of the CDW recycling market. Based on the participation of stakeholders in CDW resource utilization projects, green value co-creation incorporates environmental concepts and encompasses green co-production and green use value [8]. On the one hand, green innovation is the key to green co-production and affects product quality and the willingness of beneficiaries to engage in green value co-creation [9]. However, due to the complexity and uncertainty of innovation activities [10], remanufacturers, as the main body of innovation in CDW recycling, may not choose independent innovation. On the other hand, use is the premise of realizing green use value. However, construction enterprises, as the main users of recycled building materials, are reluctant to use recycled materials without significant advantages in quality and price [2]. Construction enterprises will only consider using recycled building materials for certain purposes, such as creating a green image for the enterprise or obtaining government incentives [2]. In addition, the public is an important driving force for enterprises to consider environmental concepts. Their environmental governance behavior can not only coordinate with the government’s environmental governance but also guide companies to regulate their behavior [11]. However, practical factors such as the difficulty of obtaining enterprise information and the high costs of participation continue to hinder public participation in environmental governance [12]. Therefore, further research is necessary to understand how the behaviors of remanufacturers, construction enterprises, and the public in CDW resource utilization projects affect green value co-creation.

Once remanufacturers, construction enterprises, and the public meet the basic requirements for participation, they can jointly create green value through interactive feedback at the stages of production and consumption [13]. The degree of those interactive feedback behaviors among remanufacturers, construction enterprises, and the public in CDW resource utilization projects is expressed as the degree of green value co-creation. The core of assessing the degree of green value co-creation is to evaluate the degree of active participation of project stakeholders in the creation process in terms of both green co-production and green use value. Re et al. assessed the degree of value co-creation using a questionnaire with several indicators, providing a methodology for quantitatively assessing the degree of green value co-creation [7]. The higher the degree of green value co-creation, the more outputs it generates [7]. Specifically, the richer, deeper, and more frequent the interactive feedback behaviors among remanufacturers, construction enterprises, and the public, the more benefits green value co-creation generates. However, the enhancement and deepening of interactive feedback behaviors mean an increase in associated costs. This could potentially impede or even undermine the green value co-creation behaviors of remanufacturers, construction enterprises, and the public in CDW resource utilization projects [14]. Research on green value co-creation primarily concentrates on its positive impact on green innovation [15], enterprise performance, and other aspects [16]. However, there is a dearth of research that delves into the impact of varying levels of green value co-creation on the behaviors of co-creation subjects. To encourage stable green value co-creation among remanufacturers, construction enterprises, and the public in CDW resource utilization projects, it is important to understand how different levels of green value co-creation change the ways that the three groups act.

To obtain green value co-creation for CDW resource utilization project stakeholders, the innovative choices of remanufacturers directly affect the quality and price of recycled building materials, thus influencing the choice of materials by construction enterprises. Construction enterprises’ use of materials reflects the market demand for recycled building materials, which in turn influences remanufacturers’ innovative choices. In addition, corporate behavior impacts the environment. The state of the environment influences public environmental governance behavior, which in turn shapes corporate behavior [17]. The decision making processes of remanufacturers, construction enterprises, and the public are interdependent and intertwined. Thus, exploring the evolution of the behaviors of remanufacturers, construction enterprises, and the public within the same framework is analyzing their coevolution, or dynamic interaction [18]. Clarifying the coevolution mechanism among remanufacturers, construction enterprises, and the public in CDW resource utilization projects is essential for facilitating CDW resource utilization [19]. However, the coevolution of remanufacturers, construction enterprises, and the public in CDW resource utilization projects under the green value co-creation perspective has not received enough attention. The evolutionary game approach is suitable for analyzing competition, learning, and adaptation among limited rational subjects and is widely used to study the evolution of stakeholder behavior in CDW resource utilization projects [20]. Therefore, the evolutionary game method can be used to explore the behavioral evolution among the three subjects.

Based on this, this paper aims to provide targeted suggestions for promoting CDW resource utilization by deepening the understanding of the coevolution among remanufacturers, construction enterprises, and the public in CDW resource utilization projects under green value co-creation. Specifically, this paper focuses on answering the following two scientific questions: First, what is the impact of the degree of green value co-creation among remanufacturers, construction enterprises, and the public in CDW resource utilization projects on realizing the green value co-creation steady state? Second, how does the willingness of remanufacturers, construction enterprises, and the public to participate in CDW resource utilization projects affect green value co-creation?

In addition, the contributions of this paper are as follows: (1) Innovatively consider the green value co-creation behavior of remanufacturers, construction enterprises, and the public in the adoption of CDW recycled building materials. This study not only enriches the research on green value co-creation but also establishes a theoretical foundation for encouraging green value co-creation among remanufacturers, construction enterprises, and the public. (2) This study introduces the theory of value co-creation into CDW resource utilization projects for the first time. It shows the mechanism of coevolution among remanufacturers, construction enterprises, and the public in CDW resource utilization projects under green value co-creation and provides new evidence to support the growth of CDW resource utilization.

The rest of the paper is structured as follows: Section 2 provides relevant literature reviews. Section 3 constructs a tripartite evolutionary game model of green value co-creation among a remanufacturer, a construction enterprise, and the public. Section 4 analyzes the asymptotic stability of the remanufacturer, the construction enterprise, and the public strategies, and it identifies the stability conditions for the different evolutionary stable strategies (ESSs). Section 5 carries out numerical simulations and discusses the effect of the relevant parameters on the evolutionary paths. Section 6 summarizes the conclusions and limitations of this paper.

2. Literature Review

This section reviews the literature from three aspects: CDW resource utilization projects, green value co-creation, and coevolution.

2.1. CDW Resource Utilization Projects

CDW resource utilization projects refer to using reasonable technology or management tools to recover useful substances in CDW [21]. Recycling CDW can reduce raw material consumption and conserve energy [22]. It can also effectively alleviate the problems of CDW occupying land resources and polluting the environment [23]. Therefore, many CDW resource utilization projects have emerged and received extensive attention from scholars.

Among them, the operation mode of CDW resource utilization projects and the coordination and cooperation of stakeholders have become research hotspots. On the one hand, the adoption of the public–private partnership (PPP) model, based on the characteristics of CDW resource utilization projects, can reduce the government’s financial pressure and, at the same time, enhance the investment willingness of enterprises [24]. Although CDW resource utilization PPP projects have the advantages mentioned above, the key to their success lies in reasonable risk and benefit allocation [25]. On the other hand, stakeholders’ coevolution will affect the smooth implementation of CDW resource utilization projects. The public, construction enterprises, and remanufacturers are the core stakeholders of the CDW resource utilization projects [26]. Previous research has used system dynamics models [27] and evolutionary game models [21] to examine the relationships among remanufacturers, construction companies, and the public in great detail. These analyses reveal that the interactions among the three, as well as their respective costs and benefits, all affect the CDW resource utilization effect.

Above all, an effective management solution is a way to promote CDW resource utilization. To foster coevolution among stakeholders in CDW resource utilization projects, they should pay particular attention to the distribution of costs and benefits. If the construction enterprises are reluctant to use the remanufactured products, then the remanufacturers’ resource behavior will lose motivation. Therefore, it is necessary to take valid measures to improve the willingness of construction enterprises to pay for recycled building materials. Unfortunately, the existing research mainly focuses on the generation and recycling stages of CDW. How to improve the willingness of construction enterprises to pay for recycled building materials has not received enough attention.

2.2. Green Value Co-Creation

Value co-creation is consumers’ active participation in cooperation and creating value with enterprises at one or more stages of production and consumption [28]. In recent years, research on value co-creation has gradually expanded from the dual value co-creation of enterprises and consumers to the multi-value co-creation among stakeholders [29]. In addition, green value co-creation has been proposed in the context of higher demands for green sustainability, that is, considering green concepts based on value co-creation [30].

There are two components of green value co-creation: green co-production and green value in use [30]. On the one hand, green co-production is a collaborative process among enterprises in green innovation, including three elements: knowledge sharing, equity, and interaction [30]. Voluntary interactive feedback among enterprises and stakeholders on demand and green awareness can help enterprises solve dynamic problems, clarify customer needs, and attract more customers [31]. On the other hand, green value in use refers to the customer’s experience in using, maintaining, and repairing green innovative products, including three elements: experience, personalization, and interpersonal relationships [32]. Feedback from customers provides enterprises with ideas for improving their products and opportunities to increase customer satisfaction. Based on the close relationship between green value co-creation and green innovation, green value co-creation is considered the decisive factor in green innovation [8]. Through quantitative analysis, the positive relationship between green value co-creation and green innovation has been confirmed by research [15]. Additionally, one study confirmed that green value co-creation positively affects enterprise performance, which further suggests that green value co-creation plays an important role in enterprise development [16].

Above all, in the process of green value co-creation, enterprises can not only promote enterprise innovation but also improve enterprise performance through interactive feedback with stakeholders. Unfortunately, research on green value co-creation is inadequate [33]. Green value co-creation, in particular, not only helps to improve product quality, but it can also promote consumer acceptance and adoption of products. While it effectively propels the growth of the market for recycled building materials, it remains unclear how to encourage stakeholders in the CDW resource utilization project to co-create green value.

2.3. Coevolution

Coevolution is a pattern of interactions between populations characterized by multilevelness, multidirectional causality, nonlinearity, feedback, and path dependence [34]. First, multilevelness shows that coevolution may occur between enterprises [35], between enterprises and consumers [36], and between enterprises and the social environment [37]. The analysis of coevolution should be integrated at the micro, meso, and macro levels, and one level should not be analyzed separately while ignoring the others [38]. Secondly, multidirectional causality refers to the change in organizations in the environment due to mutual influence. The change in one organization is the result of interactions among other organizations and environmental changes [39]. Thirdly, nonlinearity arises because the organization and the environment influence each other, and the environment is changeable. Therefore, the process of coevolution is complex and changeable. Fourthly, feedback is reflected in the interaction between the organization and the environment. Evolution is a result of feedback [40]. Finally, feedback determines the characteristics of coevolution path dependence. Path dependence reflects the system’s evolutionary tendencies under the feedback mechanism [40].

The concept of coevolution has been applied to the fields of ecological economy and organizational management. In the field of organizational management, coevolution provides a way to explore how organizations interact with each other, adapt to, and influence the environment [41]. To clarify how organizations adapt to and influence the environment, scholars have carried out a series of studies. On the one hand, the study of coevolution between enterprises confirms that the micro-behavior of enterprises will cause macro-changes in the relationship between enterprises [42]. On the other hand, the interaction between enterprise and consumer demonstrates that customer-based innovation can increase enterprises’ profits while facilitating market dominance development [36]. In addition, the coevolution of enterprises and the political environment shows not only that coevolution occurs in the subjects’ learning process but that power and influence also lead to coevolution [43].

Above all, a wealth of research has been conducted on the coevolution between the organization and the environment. It reveals the bidirectional relationship between the organization and the environment, which is significant for promoting organizational development. However, the majority of the existing studies concentrate on the coevolution of enterprise to enterprise, enterprise to consumer, or enterprise to environment, leaving a dearth of studies that simultaneously consider the coevolution of enterprise, consumer, and environment. Furthermore, the mutual influence of remanufacturers, construction enterprises, and the public under green value co-creation reflects the coevolution among enterprises, consumers, and the environment. No research has revealed the coevolution mechanism among the three under green value co-creation.

3. Methodology

3.1. Problem Description

To promote the development of CDW resource utilization, remanufacturers, construction enterprises, and other stakeholders in CDW resource utilization projects have started to participate in green value co-creation. For instance, a remanufacturer collaborated with a construction enterprise to carry out a CDW resource utilization project in Hangzhou, which further enhanced the market acceptance and recognition of recycled building materials by strengthening ties with the public [44]. To encourage green value co-creation among the stakeholders in CDW resource utilization projects, the government has implemented various incentives and constraints for enterprises and the public. These measures have motivated enterprises to participate in CDW resource utilization to a certain extent. However, economic incentives and constraints alone may not be sufficient to participate with a high degree of autonomy [21]. As the promoter of corporate green behavior, the public’s environmental governance behavior can motivate enterprises to implement green actions from a reputational perspective. Enterprises’ green actions can bring positive environmental benefits to the public. However, the cost of supervision and the difficulty of information acquisition hinder the public’s enthusiasm for environmental governance. As the main body of green use, the use behavior of construction enterprises reflects the demand for recycled building materials, which in turn influences the willingness of remanufacturers to innovate. Remanufacturers, the primary source of green innovation, can adopt different innovation strategies. Under different strategies, remanufacturers encounter different risks and costs, leading to variations in the quality and prices of recycled building materials, thereby influencing the willingness of construction enterprises to utilize these materials. Figure 1 illustrates the game relationship among the three players.

3.2. Model Assumption

Based on the analysis, this paper makes the following assumptions.

Table 1. Parameter settings and descriptions.

Unit	Parameter	Parameter Description
Government	$S_1$	Subsidies for the construction enterprise to positively use recycled building materials [45]
	$S_2$	Subsidies for the independent innovation of the remanufacturer [46]
	$Q$	Incentives for public participation in environmental governance [47]
	$T$	Resource taxes levied on the use of raw materials by the construction enterprise [2]
Remanufacturer	$C_1$	Independent innovation costs [48]
	$C_2$	Imitation innovation costs [49]
	$\Delta R$	The incremental benefits of independent innovation [50]
	$b_i$	The utilization rate of recycled building materials produced by independent innovation or imitation innovation, where $i=1$ denotes the utilization rate of recycled building materials produced by independent innovation and $i=2$ denotes the utilization rate of recycled building materials produced by imitation innovation [2] $(0<b_2<b_1<1)$
	$E_2$	The environmental benefits of independent innovation [51]
	$R_2$	The brand effect of independent innovation [52]
Construction enterprise	$P_1$	The price of purchasing raw materials [50]
	$P_2$	The price of purchasing recycled building materials [53]
	$\Delta C$	When the three parties join the green value co-creation, the communication costs between the construction enterprise and the remanufacturer [54]
	$R_1$	Image benefits for construction enterprises when positively using recycled building materials [55]
	$E_1$	The environmental benefits of positive use of recycled building materials [56]
Public	$C_p$	Total costs of participation in environmental governance [57]
	$\theta$	The degree of green value co-creation [7] $\left(0<\theta <1\right)$

describes the corresponding parameter settings and instructions.

Assumption 1. 

To promote CDW resource utilization, the government will guide enterprises and the public to positively participate in CDW resource utilization. At the enterprise level, on the one hand, the government encourages enterprises to make efforts to promote CDW resource utilization by providing them with subsidies. On the other hand, the government promotes the rational use of resources and encourages the use of recycled building materials by imposing taxes on resource products [2]. At the public level, the government points out that organizations and individuals have the right and duty to protect the environment. The government will encourage the public to participate in environmental governance through public opinion propaganda and other means [58].

Assumption 2. 

The remanufacturer has two innovation strategies: independent innovation and imitative innovation. Independent innovation is an autonomous enterprise activity for technological breakthroughs and new product development; imitation innovation generally manifests in the purchase of patents [49]. Independent and imitation innovation investments are C₁ and C₂, respectively. Compared with imitation innovation, although independent innovation is costly and risky [59], targeted innovation can improve product quality, reduce losses during the use of materials, and increase the utilization rate of recycled building materials b_i [2]. The utilization of recycled building materials b_i is relative to the utilization of raw materials. In addition, the enterprise that chooses independent innovation can convert its innovation activities into brand effects R₂ [60]. Moreover, the independent innovation of the enterprise can improve the waste recycling rate and save resources, thus bringing incremental benefits $\Delta R$ to the enterprise [50]. Due to the uncertainty and difficulty in quantifying the innovation risk of both independent and imitation innovation, this study does not consider the relevant risk parameters to simplify the model.

Assumption 3. 

After meeting the minimum use ratio, the construction enterprise can independently choose whether to continue to use recycled building materials, that is to say, it is up to the construction enterprise to decide whether to positively use recycled building materials. The construction enterprise’s attitude towards the use of materials directly determines its material procurement cost, where the raw materials’ procurement cost is P₁ and the recycled building materials’ procurement cost is P₂. To simplify the model, this study does not consider other green building techniques that the construction enterprise would adopt and only discusses the construction enterprise’s material use choices for sand, gravel, and clay. If the construction enterprise positively uses recycled building materials, it will not only receive government subsidies S₁ but also enhance its corporate image R₁ [61]. However, it is worth noting that the construction enterprise that positively uses recycled building materials needs to cope with the risks associated with material quality compared to negative use. While the construction enterprise that utilizes recycled building materials negatively does not face this risk, it must comply with government regulations by paying the resource tax T.

Assumption 4. 

The public has two strategies, including participating and not participating in environmental governance. The public with increasing concern about environmental issues may be willing to pay C_p to support construction and demolition waste separation and recycling programs, environmental education, and the promotion of recycled product consumption [62]. The public’s environmental governance behaviors have the potential to encourage enterprises to adopt green behaviors [63], thereby bringing environmental benefits E₁ and E₂ to the public. However, the public may still not choose the participation strategy due to constraints such as the difficulty of obtaining information about the enterprises and the cost of monitoring and reporting [12].

Assumption 5. 

When the remanufacturer innovates independently, the construction enterprise positively uses recycled building materials, and the public participates in environmental governance, the three parties reach a green value co-creation leading to additional benefits and costs. Both green value co-creation outcomes and costs are positively related to the degree of green value co-creation θ [7]. The degree of green value co-creation is a measure of the scope of green value co-creation based on the mechanism and form of green value co-creation that indicates the efforts made by the three parties for green value co-creation. The outputs of green value co-creation include improvement in product quality [64], attraction of new customers [65], and enhancement in brand loyalty [66]. The additional costs of green value co-creation include those related to incentives and feedback: specifically, the additional innovation costs θC₁ paid by the remanufacturer for targeted innovation by paying more attention to feedback during the innovation process; the costs $\theta \Delta C$ of positive feedback and communication between the construction enterprise and the remanufacturer; and the additional costs θC_p paid by the public for paying attention and feedback.

Assumption 6. 

It is supposed that the probability of the remanufacturer choosing independent innovation is x and the probability of imitating innovation is $1-x\left(0\le x\le 1\right)$; the probability of the construction enterprise choosing to use the recycled building materials positively is y and the probability of using the recycled building materials negatively is $1-y\left(0\le y\le 1\right)$; the probability of the public choosing to participate in the environmental governance is z and the probability of not participating in the environmental governance is $1-z\left(0\le z\le 1\right)$. Here, x, y, and z are functions of time.

Based on the research assumptions and model parameters, the benefits to the remanufacturer, the construction enterprise, and the public are calculated under different combinations of strategies. For example, when the remanufacturer innovates independently, the construction enterprise positively uses recycled building materials, and the public participates in environmental governance, $-\left(1+\theta \right)C_p+\left(1+\theta \right)E_1+\left(1+\theta \right)E_2+Q$ is the benefit equation for the public. That is, when three parties are involved in green value co-creation, the benefits to the public consist of the costs of public participation, the environmental benefits of corporate behavior, and government incentives.

Table 2. The payoff matrix of the three-party game.

Public	Construction Enterprise	Remanufacturer
		Independent Innovation (x)	Imitation Innovation (1 − x)
Participation $\left(z\right)$	Positive use $\left(y\right)$	$\begin{array}{l}-\left(1+\theta \right)C_1+P_2/(b_1+b_1\theta )+(1+\theta )R_2+S_2\\ +(1+\theta )\Delta R\end{array}$	$-C_2+P_2/b_2$
		$-P_2/(b_1+b_1\theta )-\theta \Delta C+(1+\theta )R_1+S_1$	$-P_2/b_2+R_1+S_1$
		$-\left(1+\theta \right)C_p+\left(1+\theta \right)E_1+\left(1+\theta \right)E_2+Q$	$-C_p+E_1+Q$
	Negative use $\left(1-y\right)$	$-C_1+S_2+R_2+\Delta R$	$-C_2$
		$-P_1-T$	$-P_1-T$
		$-C_p+E_2+Q$	$-C_p+Q$
Non-participation $\left(1-z\right)$	Positive use $\left(y\right)$	$-C_1+P_2/b_1+S_2+\Delta R$	$-C_2+P_2/b_2$
		$-P_2/b_1+S_1$	$-P_2/b_2+S_1$
		$E_1+E_2$	$E_1$
	Negative use $\left(1-y\right)$	$-C_1+S_2+\Delta R$	$-C_2$
		$-P_1-T$	$-P_1-T$
		$E_2$	$0$

describes the benefits for each stakeholder under the eight strategies.

4. Model Analysis

4.1. Replicated Dynamic Equations

4.1.1. The Replicated Dynamic Equation for the Remanufacturer, the Construction Enterprise, and the Public

According to the payoff matrix, the expected payoffs of the remanufacturer’s independent and imitative innovation strategies are shown in Equations (1) and (2), respectively, and the average expected payoff is shown in Equation (3):

$$U_{R0}=\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}+z\left(1+y\theta \right)R_2+S_2$$

(1)

$$U_{R1}={\displaystyle \frac{y{P}_2}{b_2}}-C_2$$

(2)

$$\overline{U_R}=x\left[\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}+z\left(1+y\theta \right)R_2+S_2\right]+\left(1-x\right)\left({\displaystyle \frac{y{P}_2}{b_2}}-C_2\right)$$

(3)

Based on Equations (1)–(3), the replicated dynamic equation of the remanufacturer is obtained as shown in Equation (4):

$$\begin{array}{l}F\left(x\right)={\displaystyle \frac{dx}{dt}}=x\left(U_{R0}-\overline{U_R}\right)\\ =\left(1-x\right)x\left[\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+C_2+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}-{\displaystyle \frac{y{P}_2}{b_2}}+z\left(1+y\theta \right)R_2+S_2\right]\end{array}$$

(4)

Based on the payoff matrix, the expected payoffs for the construction enterprise’s positive and negative use of recycled building material strategies are shown in Equations (5) and (6), respectively, and the average expected payoff is shown in Equation (7):

$$U_{E0}=-xz\theta \Delta C+{\displaystyle \frac{x\left[-1+\left(-1+z\right)\theta \right]P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1$$

(5)

$$U_{E1}=-T-P_1$$

(6)

$$\overline{U_E}=\mathrm{y}\left[-xz\theta \Delta C+{\displaystyle \frac{x\left(-1-\theta +\mathrm{z}\theta \right)P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1\right]+\left(1-y\right)\left(-T-P_1\right)$$

(7)

According to Equations (5)–(7), the replicated dynamic equation of the construction enterprise is obtained as shown in Equation (8):

$$\begin{array}{l}F\left(y\right)={\displaystyle \frac{dy}{dt}}=y\left(U_{E0}-\overline{U_E}\right)\\ =\left(1-y\right)y\left[T-xz\theta \Delta C+P_1+{\displaystyle \frac{x\left(-1-\theta +\mathrm{z}\theta \right)P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1\right]\end{array}$$

(8)

According to the payoff matrix, the expected payoffs for public participation in environmental governance and non-participation in environmental governance strategies are shown in Equations (9) and (10), respectively, and the average expected payoff is shown in Equation (11):

$$U_{P0}=Q-\left(1+xy\theta \right)C_P+y\left(1+x\theta \right)E_1+x\left(1+y\theta \right)E_2$$

(9)

$$U_{P1}=y{E}_1+x{E}_2$$

(10)

$$\overline{U_P}=Qz-\left(1+xy\theta \right)z{C}_P+y\left(1+zx\theta \right)E_1+x\left(1+yz\theta \right)E_2$$

(11)

According to Equations (9)–(11), the replicated dynamic equation of the public is obtained as shown in Equation (12):

$$\begin{array}{l}F\left(z\right)={\displaystyle \frac{dz}{dt}}=z\left(U_{P0}-\overline{U_P}\right)\\ =\left(1-z\right)z\left[Q-\left(1+xy\theta \right)C_P+xy\theta \left(E_1+E_2\right)\right]\end{array}$$

(12)

4.1.2. Analysis of the Replicated Dynamic Equation of the Remanufacturer

The derivation of the replicated dynamic equation of the remanufacturer, namely, Equation (4), yields:

$$F^{\prime }\left(x\right)=\left(1-2x\right)\left[\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+C_2+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}-{\displaystyle \frac{y{P}_2}{b_2}}+z\left(1+y\theta \right)R_2+S_2\right]$$

To facilitate the analysis of the stability of the remanufacturer, let $J\left(z\right)=\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+C_2+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}-{\displaystyle \frac{y{P}_2}{b_2}}+z\left(1+y\theta \right)R_2+S_2$. Let $J\left(z\right)=0$. Then, $z^{*}={\displaystyle \frac{-\Delta R+C_1-C_2-\frac{y{P}_2}{\left(1+\theta \right)b_1}-\frac{y\theta P_2}{\left(1+\theta \right)b_1}+\frac{y{P}_2}{b_2}-S_2}{y\Delta R\theta -y\theta C_1-\frac{y\theta P_2}{\left(1+\theta \right)b_1}+\left(1+y\theta \right)R_2}}$. Solve for the first-order partial derivative of $J\left(z\right)$ with respect to z, $J^{\prime }\left(z\right)=y\Delta R\theta -y\theta C_1-{\displaystyle \frac{y\theta P_2}{\left(1+\theta \right)b_1}}+\left(1+y\theta \right)R_2$. When $y\Delta R\theta -y\theta C_1-{\displaystyle \frac{y\theta P_2}{\left(1+\theta \right)b_1}}+\left(1+y\theta \right)R_2>0$, J(z) is an increasing function; otherwise, it is a decreasing function.

(1)

When J(z) is an increasing function:

If $z>z^{*}$, then $J\left(z\right)>0$, $F\left(1\right)=0$, $F^{\prime }\left(1\right)<0$, and the remanufacturer opts for the independent innovation strategy. If $z=z^{*}$, then $J\left(z\right)=0$, $F\left(x\right)\equiv 0$, $F^{\prime }\left(x\right)\equiv 0$, and any strategy of the remanufacturer is stable. If $z<z^{*}$, then $J\left(z\right)<0$, $F\left(0\right)=0$, $F^{\prime }\left(0\right)<0$, and the remanufacturer opts for the imitate innovation strategy.

(2)

When J(z) is a decreasing function:

If $z>z^{*}$, then $J\left(z\right)<0$, $F\left(0\right)=0$, $F^{\prime }\left(0\right)<0$, and the remanufacturer opts for the imitate innovation strategy. If $z=z^{*}$, then $J\left(z\right)=0$, $F\left(x\right)\equiv 0$, $F^{\prime }\left(x\right)\equiv 0$, and any strategy of the remanufacturer is stable. If $z<z^{*}$, then $J\left(z\right)>0$, $F\left(1\right)=0$, $F^{\prime }\left(1\right)<0$, and the remanufacturer opts for the independent innovation strategy.

Above all, the incremental revenue of independent innovation, the cost of independent innovation, the price of recycled building materials, the utilization rate of recycled building materials, the brand benefit of independent innovation, the degree of green value co-creation, and the probability of strategic choice of the public and construction enterprise also affect the innovation choice of the remanufacturer. Concretely speaking, when $y\Delta R\theta -y\theta C_1-{\displaystyle \frac{y\theta P_2}{\left(1+\theta \right)b_1}}+\left(1+y\theta \right)R_2>0$ and the public’s willingness to participate in environmental governance is high, the remanufacturer tends to independent innovation. When the public’s willingness to participate in environmental governance is low, the remanufacturer opts for imitation innovation. When the public’s willingness to participate in environmental governance is of critical value, the remanufacturer’s innovation choice is uncertain. When $y\Delta R\theta -y\theta C_1-{\displaystyle \frac{y\theta P_2}{\left(1+\theta \right)b_1}}+\left(1+y\theta \right)R_2<0$, the situation is the opposite.

4.1.3. Analysis of the Replicated Dynamic Equation of the Construction Enterprise

The derivation of the replicated dynamic equation of the construction enterprise, namely, Equation (8), yields:

$$F^{\prime }\left(y\right)=\left(1-2y\right)\left[T-xz\theta \Delta C+P_1+{\displaystyle \frac{x\left(-1-\theta +\mathrm{z}\theta \right)P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1\right]$$

For the purpose of analyzing the stability of the construction enterprise, let $L\left(x\right)=T-xz\theta \Delta C+P_1+{\displaystyle \frac{x\left(-1-\theta +\mathrm{z}\theta \right)P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1$. Let $L\left(x\right)=0$ to obtain $x^{*}={\displaystyle \frac{-T-P_1+\frac{P_2}{b_2}-z{R}_1-S_1}{-z\theta \Delta C-\frac{P_2}{b_1}+\frac{z\theta P_2}{\left(1+\theta \right)b_1}+\frac{P_2}{b_2}+z\theta R_1}}$.

The derivation of L(x) obtains $L^{\prime }\left(x\right)=-z\theta \Delta C-{\displaystyle \frac{P_2}{b_1}}+{\displaystyle \frac{z\theta P_2}{\left(1+\theta \right)b_1}}+{\displaystyle \frac{P_2}{b_2}}+z\theta R_1$. Thus, L(x) is an increasing function when $-z\theta \Delta C-{\displaystyle \frac{P_2}{b_1}}+{\displaystyle \frac{z\theta P_2}{\left(1+\theta \right)b_1}}+{\displaystyle \frac{P_2}{b_2}}+z\theta R_1>0$ and a decreasing function when the opposite is true.

(1)

When L(x) is an increasing function:

When $x>x^{*}$, we obtain $L\left(x\right)>0$, $F\left(1\right)=0$, $F^{\prime }\left(1\right)<0$, and at this time the stable strategy of the construction enterprise is to positively use recycled building materials. When $x=x^{*}$, we obtain $L\left(x\right)=0$, $F\left(y\right)\equiv 0$, $F^{\prime }\left(y\right)\equiv 0$, and then any strategy of the construction enterprise is stable. When $x<x^{*}$, we obtain $L\left(x\right)<0$, $F\left(0\right)=0$, $F^{\prime }\left(0\right)<0$, and then the stable strategy of the construction enterprise is to use recycled materials negatively.

(2)

When L(x) is a decreasing function:

When $x>x^{*}$, we obtain $L\left(x\right)<0$, $F\left(0\right)=0$, $F^{\prime }\left(0\right)<0$, and at this point, the construction enterprise’s stable strategy is to use recycled building materials negatively. When $x=x^{*}$, we obtain $L\left(x\right)=0$, $F\left(y\right)\equiv 0$, $F^{\prime }\left(y\right)\equiv 0$, and at this time any strategy of the construction enterprise is stable. When $x<x^{*}$, we obtain $L\left(x\right)>0$, $F\left(1\right)=0$, $F^{\prime }\left(1\right)<0$, and the stable strategy of the construction enterprise at this time is to use recycled building materials positively.

In summary, the decision making of the construction enterprise is influenced by the price of recycled building materials, the utilization rate of recycled building materials, the communication costs, the degree of green value co-creation, and the probability of strategic choices between the remanufacturer and the public. Specifically, when $-z\theta \Delta C-{\displaystyle \frac{P_2}{b_1}}+{\displaystyle \frac{z\theta P_2}{\left(1+\theta \right)b_1}}+{\displaystyle \frac{P_2}{b_2}}+z\theta R_1>0$ is satisfied and the remanufacturer’s willingness to innovate independently is high, the construction enterprise will choose to use the recycled building materials positively; on the contrary, when the remanufacturer’s willingness to innovate independently is low, the construction enterprise will choose to use the recycled building materials negatively; in particular, when the probability of the remanufacturer’s innovation independently is at a certain value, the construction enterprise’s choice is uncertain. The opposite is true when $-z\theta \Delta C-{\displaystyle \frac{P_2}{b_1}}+{\displaystyle \frac{z\theta P_2}{\left(1+\theta \right)b_1}}+{\displaystyle \frac{P_2}{b_2}}+z\theta R_1<0$.

4.1.4. Analysis of the Replicated Dynamic Equation of the Public

The derivation of the replicated dynamic equation of the public, namely, Equation (12), yields $F^{\prime }\left(z\right)=\left(1-2z\right)\left[Q-\left(1+xy\theta \right)C_P+xy\theta \left(E_1+E_2\right)\right]$. To facilitate the analysis of the stability of the public, let $Q\left(y\right)=Q-\left(1+xy\theta \right)C_P+xy\theta \left(E_1+E_2\right)$. Let $Q\left(y\right)=0$ to obtain $y^{*}={\displaystyle \frac{Q-C_P}{x\theta \left(C_P-E_1-E_2\right)}}$. The derivation of Q(y) yields $Q^{\prime }\left(y\right)=x\theta \left(E_1+E_2-C_P\right)$. It follows that Q(y) is an increasing function when $E_1+E_2-C_P>0$ and a decreasing function when the opposite is true.

(1)

When Q(y) is an increasing function:

When $y>y^{*}$, we obtain $Q\left(y\right)>0$, $F\left(1\right)=0$, $F^{\prime }\left(1\right)<0$, and the stable strategy of the public is to participate in environmental governance. When $y=y^{*}$, we obtain $Q\left(y\right)=0$, $F\left(z\right)\equiv 0$, $F^{\prime }\left(z\right)\equiv 0$, and at this point any strategy of the public is stable. When $y<y^{*}$, we obtain $Q\left(y\right)<0$, $F\left(0\right)=0$, $F^{\prime }\left(0\right)<0$, and at this time the public’s stable strategy is not to participate in environmental governance.

(2)

When Q(y) is a decreasing function:

When $y>y^{*}$, we obtain $Q\left(y\right)<0$, $F\left(0\right)=0$, $F^{\prime }\left(0\right)<0$, and at this time, the stable strategy of the public is not to participate in environmental governance. When $y=y^{*}$, we obtain $Q\left(y\right)=0$, $F\left(z\right)\equiv 0$, $F^{\prime }\left(z\right)\equiv 0$, and any strategy of the public is stable. When $y<y^{*}$, we obtain $Q\left(y\right)>0$, $F\left(1\right)=0$, $F^{\prime }\left(1\right)<0$, and at this point, the public’s stable strategy is to participate in environmental governance.

The analysis shows that the public’s participation behaviors are influenced by their participation costs and the behavior of the enterprises. When $E_1+E_2-C_P>0$ is satisfied and the willingness of the construction enterprise to positively use recycled building materials is not high enough, the public will choose not to participate regardless of the strategy chosen by the remanufacturer; on the contrary, if the willingness of the construction enterprise to positively use recycled building materials is high enough, the public will choose the participation strategy; when the probability of the construction enterprise positively using recycled building materials is at a certain value, the public’s decision making is uncertain. However, when $E_1+E_2-C_P<0$, the opposite is true.

The replicated dynamic system obtained from the analysis is shown in Equation (13).

$$\left\{\begin{array}{c}F\left(x\right)=\left(1-x\right)x\left[\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+C_2+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}-{\displaystyle \frac{y{P}_2}{b_2}}+z\left(1+y\theta \right)R_2+S_2\right]\\ F\left(y\right)=\left(1-y\right)y\left[T-xz\theta \Delta C+P_1+{\displaystyle \frac{x\left(-1-\theta +\mathrm{z}\theta \right)P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1\right]\\ F\left(z\right)=\left(1-z\right)z\left[Q-\left(1+xy\theta \right)C_P+xy\theta \left(E_1+E_2\right)\right]\end{array}\right.$$

(13)

4.2. Evolutionary Stable Strategy

The replicated dynamic equation reflects the changes in the direction and speed of the subjects’ behavioral choices. The equilibrium point is obtained when the replicated dynamic equations are equal to 0. It can be calculated according to Equation (14):

$$\left\{\begin{array}{c}F\left(x\right)=\left(1-x\right)x\left[\Delta R+yz\Delta R\theta -\left(1+yz\theta \right)C_1+C_2+{\displaystyle \frac{y\left(1+\theta -z\theta \right)P_2}{\left(1+\theta \right)b_1}}-{\displaystyle \frac{y{P}_2}{b_2}}+z\left(1+y\theta \right)R_2+S_2\right]=0\\ F\left(y\right)=\left(1-y\right)y\left[T-xz\theta \Delta C+P_1+{\displaystyle \frac{x\left(-1-\theta +\mathrm{z}\theta \right)P_2}{(1+\theta )b_1}}+{\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(1+x\theta \right)R_1+S_1\right]=0\\ F\left(z\right)=\left(1-z\right)z\left[Q-\left(1+xy\theta \right)C_P+xy\theta \left(E_1+E_2\right)\right]=0\end{array}\right.$$

(14)

By solving Equation (13), eight pure strategic equilibrium points, E₁ (0,0,0), E₂ (1,0,0), E₃ (0,1,0), E₄ (0,0,1), E₅ (0,1,1), E₆ (1,1,0), E₇ (1,0,1), and E₈ (1,1,1), are obtained.

Ritzberger and Weibull showed that it is the strict Nash equilibrium and the pure strategy Nash equilibrium that become asymptotically stable solutions to the evolving game system and therefore this paper did not consider mixed strategy solutions [67]. Thus, this section only analyzes eight pure strategy equilibrium points. According to the Friedman method, the stability of the equilibrium point of the evolutionary game can be judged by the local stability analysis method of the Jacobi matrix [68]. When all eigenvalues are negative, the point is ESS.

The Jacobi matrix of the tripartite evolutionary game system is shown in Equation (15):

$$J=\left[\begin{array}{ccc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}\end{array}\right]=\left[\begin{array}{ccc}\left(1-2x\right)\left[\begin{array}{l}{\displaystyle \frac{\left(1+\theta -\theta z\right)y{P}_2}{\left(1+\theta \right)b_1}}\\ -{\displaystyle \frac{y{P}_2}{b_2}}+\Delta R+\\ yz\Delta R\theta -\left(1+yz\theta \right)C_1\\ +C_2+z\left(1+y\theta \right)R_2+S_2\end{array}\right]& \left(1-x\right)x\left[\begin{array}{l}-z\theta C_1+z\theta \left(\begin{array}{l}\Delta R\\ +R_2\end{array}\right)\\ -{\displaystyle \frac{P_2}{b_2}}+{\displaystyle \frac{\left(1+\theta -\theta z\right)P_2}{\left(1+\theta \right)b_1}}\end{array}\right]& \left(1-x\right)x\left[\begin{array}{l}y\theta \Delta R+R_2+\\ y\theta \left(\begin{array}{l}-C_1-\\ {\displaystyle \frac{P_2}{b_1+\theta b_1}}\\ +R_2\end{array}\right)\end{array}\right]\\ \left(1-y\right)y\left[\begin{array}{l}-z\theta \Delta C+\\ {\displaystyle \frac{\left(-1-\theta +z\theta \right)P_2}{\left(1+\theta \right)b_1}}\\ +{\displaystyle \frac{P_2}{b_2}}+z\theta R_1\end{array}\right]& \left(1-2y\right)\left[\begin{array}{l}T-xz\theta \Delta C+P_1+\\ {\displaystyle \frac{x\left(-1-\theta +z\theta \right)P_2}{\left(1+\theta \right)b_1}}+\\ {\displaystyle \frac{(-1+x)P_2}{b_2}}+z\left(\begin{array}{l}1+\\ x\theta \end{array}\right)R_1\\ +S_1\end{array}\right]& \left(1-y\right)y\left[\begin{array}{l}-x\theta \Delta C+R_1+\\ x\theta \left(\begin{array}{l}{\displaystyle \frac{P_2}{b_1+\theta b_1}}\\ +R_1\end{array}\right)\end{array}\right]\\ \left(1-z\right)zy\theta \left(\begin{array}{l}-C_P+\\ E_1+E_2\end{array}\right)& \left(1-z\right)zx\theta \left(-C_P+E_1+E_2\right)& \left(1-2z\right)\left[\begin{array}{l}Q-\left(\begin{array}{l}1+\\ xy\theta \end{array}\right)C_P\\ +xy\theta \left(\begin{array}{l}{E}_1\\ +E_2\end{array}\right)\end{array}\right]\end{array}\right]$$

(15)

By putting the pure strategy equilibrium points into the Jacobi matrix, the eigenvalues can be obtained, as shown in

Table 3. Equilibrium points and Jacobi matrix eigenvalues.

Equilibrium Point	Eigenvalue
	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$
$E_1\left(0,0,0\right)$	$-C_1+C_2+S_2+\Delta R$	${\displaystyle \frac{-P_2+b_2\left(T+P_1+S_1\right)}{b_2}}$	$Q-C_p$
$E_2\left(1,0,0\right)$	$C_1-C_2-S_2-\Delta R$	${\displaystyle \frac{-P_2}{b_1}}+T+P_1+S_1$	$Q-C_p$
$E_3\left(0,1,0\right)$	${\displaystyle \frac{P_2}{b_1}}-{\displaystyle \frac{P_2}{b_2}}-C_1+C_2+S_2+\Delta R$	$-{\displaystyle \frac{-P_2+b_2\left(T+P_1+S_1\right)}{b_2}}$	$Q-C_p$
$E_4\left(0,0,1\right)$	$-C_1+C_2+S_2+R_2+\Delta R$	${\displaystyle \frac{-P_2+b_2\left(T+P_1+S_1+R_1\right)}{b_2}}$	$-Q+C_p$
$E_5\left(0,1,1\right)$	$\begin{array}{l}{\displaystyle \frac{P_2}{\left(1+\theta \right)b_1}}-{\displaystyle \frac{P_2}{b_2}}-\left(1+\theta \right)C_1\\ +C_2+S_2+\left(1+\theta \right)R_2+\left(1+\theta \right)\Delta R\end{array}$	${\displaystyle \frac{P_2}{b_2}}-T-P_1-S_1-R_1$	$-Q+C_p$
$E_6\left(1,1,0\right)$	$-{\displaystyle \frac{P_2}{b_1}}+{\displaystyle \frac{P_2}{b_2}}+C_1-C_2-S_2-\Delta R$	${\displaystyle \frac{P_2}{b_1}}-T-P_1-S_1$	$\begin{array}{l}Q-\left(1+\theta \right)C_p+\\ \theta \left(E_1+E_2\right)\end{array}$
$E_7\left(1,0,1\right)$	$C_1-C_2-S_2-R_2-\Delta R$	$\begin{array}{l}{\displaystyle \frac{-P_2}{\left(1+\theta \right)b_1}}+T+P_1+S_1\\ -\theta \Delta C+\left(1+\theta \right)R_1\end{array}$	$-Q+C_p$
$E_8\left(1,1,1\right)$	$\begin{array}{l}-{\displaystyle \frac{P_2}{\left(1+\theta \right)b_1}}+{\displaystyle \frac{P_2}{b_2}}+\left(1+\theta \right)C_1\\ -C_2-S_2-\left(1+\theta \right)R_2-\left(1+\theta \right)\Delta R\end{array}$	$\begin{array}{l}{\displaystyle \frac{P_2}{\left(1+\theta \right)b_1}}-T-P_1-S_1\\ +\theta \Delta C-\left(1+\theta \right)R_1\end{array}$	$\begin{array}{l}-Q+\left(1+\theta \right)C_p\\ -\theta \left(E_1+E_2\right)\end{array}$

.

This paper examines the equilibrium points and Jacobi matrix eigenvalues of the system in Table 3. Finding the positive and negative eigenvalues of each equilibrium point cannot be determined. It shows that the game’s strategy is constantly changing due to a variety of factors.

E₈ (1,1,1) is the most ideal result. In this situation, the remanufacturer opts for independent innovation, the construction enterprise opts for positively using recycled building materials, and the public opts for participating in environmental governance. This state can create more value for all parties while promoting the popularization and application of recycled building materials, thus promoting the development of CDW resource utilization.

To realize the stable state of E₈ (1,1,1), all its eigenvalues should be negative:

$$\left\{\begin{array}{c}-{\displaystyle \frac{P_2}{\left(1+\theta \right)b_1}}+{\displaystyle \frac{P_2}{b_2}}+\left(1+\theta \right)C_1-C_2-S_2-\left(1+\theta \right)R_2-\left(1+\theta \right)\Delta R<0\\ {\displaystyle \frac{P_2}{\left(1+\theta \right)b_1}}-T-P_1-S_1+\theta \Delta C-\left(1+\theta \right)R_1<0\\ -Q+\left(1+\theta \right)C_p-\theta \left(E_1+E_2\right)<0\end{array}\right.$$

That means when the other two parties are involved, the remanufacturer will choose to innovate independently if the benefits of independent innovation are higher than those of imitation. Similarly, the construction enterprise and the public will only choose the green value co-creation strategy, namely, using recycled building materials positively and taking part in environmental governance, if green value co-creation can bring higher benefits.

5. Numerical Simulation and Discussion

This paper focuses on how the three parties can achieve a steady state of green value co-creation through evolutionary game model analysis. The green value co-creation of the remanufacturer, the construction enterprise, and the public in the CDW resource utilization project are affected by the willingness of the parties and the degree of green value co-creation. This study uses MATLAB R2022b to numerically simulate and analyze the evolution of the system, making it easier to understand how the strategies of the remanufacturer, the construction enterprise, and the public worked together in the CDW resource utilization project.

Firstly, in Section 5.1, this paper considers the effects of different degrees of green value co-creation (θ) and initial willingness combinations of the remanufacturer, the construction enterprise, and the public on the steady state of system evolution. This helps to clarify the overall influence of multiple factors on the evolutionary trend of the system and provides a basis for further analysis on how to facilitate the evolution of the system to the desired state (1,1,1).

Secondly, in Section 5.2, this paper further analyzes how the degree of green value co-creation (θ) among the remanufacturer, the construction enterprise, and the public of the CDW resource utilization project affects the steady state of green value co-creation among the three. The optimal degree of green value co-creation to maintain green value co-creation homeostasis among the three is then obtained.

Finally, based on the analyses in Section 5.1 and Section 5.2, Section 5.3 aims to explore how the initial willingness of green value co-creation among the remanufacturer, the construction enterprise, and the public affects the state of green value co-creation among the three. Specifically, this paper explore the impact of changing the initial willingness of individual subjects on the system evolution outcome, particularly when the system evolution outcome is influenced by the combination of initial willingness but the degree of green value co-creation has not yet reached an optimal level. This helps to clarify which subject’s initial willingness enhancement is better suited to motivating other subjects to participate in green value co-creation. This provides ideas for promoting green value co-creation among remanufacturers, construction companies, and the public.

Based on this, this paper determines the initial values of the parameters through literature surveys and expert interviews, as shown in

Table 4. Initial parameter settings.

Parameters	Values	Parameters	Values
$S_1$	2 [56]	$C_2$	3 [49]
$S_2$	2 [69]	$\Delta \mathrm{R}$	6 [48]
$Q$	2 [47]	$b_1$	1.0 [2]
$C_P$	3 [70]	$E_2$	2.88 [71]
$P_1$	7 [50]	$T$	1
$P_2$	6 [50]	$E_1$	2.88
$\Delta C$	5 [54]	$b_2$	$0.55$
$R_1$	5 [55]	$R_2$	7
$C_1$	10 [51]

.

5.1. The Effect of the Degree of Green Value Co-Creation and the Combination of Initial Willingness on the Evolutionary Steady State of the System

In this section, θ = 0.1, 0.5, and 0.9 are used to denote the low, medium, and high degrees of green value co-creation, respectively [72]. And different initial willingness combinations are taken to evolve 50 times under low, medium, and high degrees [73], to explore the effect of the degree of green value co-creation θ and the combination of the initial willingness of the remanufacturer, the construction enterprise, and the public on the system evolution. Figure 2 describes how the degree of green value co-creation and the initial willingness combination affect the system’s evolutionary steady state.

As can be seen from Figure 2a, the system has no stable point, i.e., the system evolution cannot reach a steady state. As can be seen from Figure 2b,c, the system converges to a steady state (1,1,1) under some combinations of initial strategies, and the rest of the combinations have no steady state. This suggests that different combinations of the initial willingness of the remanufacturer, the construction enterprise, and the public lead to different evolutionary outcomes at medium and high levels of green value co-creation. This is consistent with the findings of Dou et al. [74], which together validate the butterfly effect in value co-creation [75]. Furthermore, as the degree of green value co-creation among the remanufacturer, the construction enterprise, and the public increases, the system transitions from a non-steady state to a steady state (1,1,1), and this motivates more initial willingness combinations to evolve towards (1,1,1). This means that the increase in the degree of green value co-creation among the stakeholders in the CDW resource utilization project helps the system reach the ideal state of three-party green value co-creation.

5.2. The Impact of the Degree of Green Value Co-Creation on the Evolutionary Steady State of the System

This section considers the effects of different degrees of green value co-creation on the evolutionary steady state of the system. The initial willingness of the game subjects is set to 0.5 to eliminate the influence of the subjects’ green value co-creation preference. Figure 3 describes the effect of the degree of green value co-creation on the evolution of the behavior of the remanufacturer, the construction enterprise, and the public.

As can be seen from Figure 3, when θ = 0.1 or θ = 0.5, x and y fail to reach a steady state, while z converges to 0; when θ = 0.9, x, y, and z all converge to 1. That is, under the medium and low degrees of green value co-creation, the strategic choices of the remanufacturer and the construction enterprise show cyclical oscillations, and the public will ultimately choose not to participate in the environmental governance; under the high degree of green value co-creation, the three main parties all choose green value co-creation behavior. This suggests that a high degree of green value co-creation is more conducive to a stable state of green value co-creation among the three parties, in line with the findings of Li et al. [76]. Li et al. stated that a high degree of value co-creation between manufacturers and retailers maximizes profits. The public’s consistent refusal to participate at medium and low levels may be due to their insufficient awareness of the environmental benefits and government incentives to offset their participation costs.

By analyzing Figure 3a,b, it is evident that the strategic choices of the remanufacturer and the construction enterprise are uncertain and show cyclical oscillations. This may be because when the remanufacturer shows a willingness to independently innovate, the construction enterprise will positively use recycled building materials to create a green corporate image. However, innovation is a long-term activity, and there is a lag in the construction enterprise’s recognition of the remanufacturer’s innovative activities. This largely affects the willingness of the remanufacturer to independently innovate, in turn affecting the willingness of the construction enterprise to use them.

5.3. The Impact of Initial Willingness on the Evolutionary Steady State of the System

In this section, three initial strategy scenarios of the subjects are considered at a medium degree of green value co-creation [77]. The initial state of each strategy is 0.1, 0.5, and 0.9, respectively.

5.3.1. The Impact of Changes in the Initial Willingness of the Remanufacturer on the Evolutionary Steady State of the System

The impact of the initial willingness of the remanufacturer to innovate independently on the strategic choices of the remanufacturer, the construction enterprise, and the public, respectively, is shown in Figure 4.

As can be seen from Figure 4, the change in the initial willingness of the remanufacturer has an effect on the evolution of the system. That is, when the remanufacturer’s willingness to innovate independently is 0.9, the remanufacturer, the construction enterprise, and the public all converge to the stable state of adopting green value co-creation behavior; when the remanufacturer’s initial willingness to innovate independently is 0.1 or 0.5, the decision making of the remanufacturer and the construction enterprise shows cyclical oscillations, and the higher the remanufacturer’s initial willingness to innovate independently, the slower the frequency of the oscillations. And eventually, the public converges on the stable state of not participating in environmental governance. This suggests that the increase in green value co-creation willingness of the remanufacturer can drive the construction enterprise and the public to participate in green value co-creation.

5.3.2. The Impact of Changes in the Initial Willingness of the Construction Enterprise on the Evolutionary Steady State of the System

The impact of the initial willingness of the construction enterprise to actively use recycled building materials on the strategic choices of the remanufacturer, the construction enterprise, and the public is shown in Figure 5.

In Figure 5, we see that the effect of changes in the initial willingness of the construction enterprise on the evolution of the system. Specifically, regardless of the initial willingness of the construction enterprise to use recycled building materials, the decisions of the remanufacturer and the construction enterprise always show periodic oscillations, and the public always converges to a steady state of non-participation in environmental governance. Moreover, the change in the initial willingness of the construction enterprise to positively use reproductions has little effect on the rate of system evolution. When the construction enterprise’s initial willingness to positively use recycled building materials is medium or high, the system evolution speed and trend are almost identical. This suggests that changing the green value co-creation willingness of the construction enterprise has little effect on the green value co-creation willingness of the remanufacturer and the public. This may be because the use behavior of the construction enterprise provides a free-rider opportunity for the remanufacturer and the public, and the remanufacturer and the public are more inclined to obtain something for nothing. Therefore, the willingness of the construction enterprise to use the product does not affect the decision making of the remanufacturer or the public.

5.3.3. The Impact of Changes in Initial Public Willingness on the Evolutionary Steady State of the System

The impact of the initial willingness of the public to participate in environmental governance on the strategic choices of the remanufacturer, the construction enterprise, and the public is shown in Figure 6.

As can be seen from Figure 6a,b, when the initial willingness of public participation is 0.1 or 0.5, the strategy choices of the remanufacturer and the construction enterprise show periodic oscillation, with the frequency of oscillation increasing with a lower initial willingness. When the initial willingness of public participation is 0.9, the strategies of both the remanufacturer and the construction enterprise change to adopt green value co-creation behaviors, i.e., independent innovation and positive use of recycled building materials. As can be seen from Figure 6c, when the initial willingness of public participation is 0.1 and 0.5, the public ultimately chooses the non-participation strategy, and when the initial willingness of public participation is 0.5, the convergence to the non-participation strategy is slower. In contrast, when the initial willingness of the public to participate is 0.9, the public strategy choice shifts to participation. This indicates that the change in public initial willingness can affect the strategy choices of the game subjects. Specifically, the higher the initial willingness of the public to participate, the more favorable it is for the three parties to reach a stable state of green value co-creation. In other words, the increase in the public’s willingness to participate in green value co-creation can lead to the participation of the remanufacturer and the construction enterprise in green value co-creation.

The results in Figure 4 and Figure 6 are mostly the same, which suggests that making the public and remanufacturer more willing to participate in green value co-creation has a positive effect on the system’s evolution to a steady state where all three parties opt for green value co-creation behaviors. That is, the selection of green value co-creation behaviors by the remanufacturer and the public can effectively promote the participation of other subjects in green value co-creation. This, together with the findings of Shi et al. [78], confirms the positive effect of the green value co-creation behavior of the remanufacturer on system evolution. On this basis, this study also highlights the positive effect of public green value co-creation behavior on system evolution. This may be because increased public green awareness can lead to enterprise transformation and green actions, which contribute to green value co-creation [79].

6. Conclusions and Limitations

Based on the theory of value co-creation, this paper constructs an evolutionary game model of the CDW resource utilization project among a remanufacturer, a construction enterprise, and the public using the evolutionary game method. The impacts of the degree of green value co-creation and the initial willingness combination of the remanufacturer, the construction enterprise, and the public on the evolutionary behavior of their collaborative governance of CDW are investigated. The main conclusions are as follows.

(1)

When the degree of green value co-creation is 0.1 or 0.5, the remanufacturer, the construction enterprise, and the public cannot maintain a state of green value co-creation. The decision making of the remanufacturer and the construction enterprise shows cyclical oscillations, and the public finally chooses not to participate in environmental governance. When the degree of green value co-creation is 0.9, the remanufacturer, the construction enterprise, and the public of the CDW resource utilization project finally reach a stable state of green value co-creation. Therefore, improving the degree of green value co-creation can help to achieve a stable state of green value co-creation among the remanufacturer, the construction enterprise, and the public.

(2)

When the degree of green value co-creation is 0.5, increasing the green value co-creation willingness of the remanufacturer or the public can lead other CDW resource utilization projects’ stakeholders to participate in green value co-creation. However, increasing the construction enterprise’s green value co-creation willingness has little effect on the system evolution trend and does not change the system evolution result. Therefore, it is a feasible way to encourage other stakeholders to participate in green value co-creation by increasing the green value co-creation willingness of remanufacturers or the public.

This paper, considering green value co-creation among remanufacturers, construction enterprises, and the public in CDW resource utilization projects for the first time, provides new evidence from CDW resource utilization for studies related to green value co-creation. Meanwhile, in the practical sense, the management insights of this paper are as follows:

(1)

Enhance the degree of green value co-creation among remanufacturers, construction enterprises, and the public in CDW resource utilization projects. For example, during the production stage, enterprises can strengthen their ties with stakeholders by distributing questionnaires or conducting interviews, thereby involving them in the product development stage and collaborating on the product’s design. During the consumption stage, enterprises can target product improvements by offering incentives or discounts to customers who provide feedback. A collaborative process at one or more stages of production or consumption would allow for a stronger green value co-creation relationship between remanufacturers, construction enterprises, and the public.

(2)

Enhance the positivity of remanufacturers and the public to co-create green value. At the remanufacturer level, on the one hand, the government should adopt a reasonable incentive model and policy guarantee for remanufacturers’ innovation. On the other hand, through a series of effective measures, the government can alleviate remanufacturers’ concerns about the failure of innovations related to CDW resource utilization. Specifically, the government should establish or improve the relevant technical standards and operational norms to ensure the innovations are measurable and comparable. This will not only improve the quality of innovative products but also increase market acceptance and reduce the losses suffered by remanufacturers due to the fear that innovation results will not meet the standards. Encourage research organizations to establish a close partnership with remanufacturers so that research results can be quickly transformed into practical applications. At the same time, remanufacturers can also provide feedback on market demand to scientific research institutes to guide the direction of scientific research to be closer to the actual demand. In the way, remanufacturers are encouraged to actively participate in independent innovation. At the public level, firstly, the education of the public should be strengthened to increase their awareness of environmental protection and encourage their participation in the supervision and management of CDW resources. Secondly, strengthen the disclosure of enterprise information, give full play to the role of various network platforms, and reduce the difficulty of public information access. In addition, the government should establish and improve the public supervision and reporting mechanism, increase the incentives for public participation in supervision, and reduce the cost of public participation in environmental governance.

The conclusions of this paper provide suggestions for promoting green value co-creation among the remanufacturer, the construction enterprise, and the public in CDW resource utilization projects, but this paper still suffers from the following limitations. Firstly, innovation risk is an important factor influencing enterprises’ innovation choices, but this paper only considers market risk and does not take into account risks such as innovation failure. Secondly, the data used in this study were taken from the relevant literature, and future research could draw from actual cases to obtain more realistic conclusions. Finally, this paper assumes that the influence of the degree of green value co-creation on both the costs and benefits of green value co-creation is linear, but the actual situation is more complicated. Future research can use non-linear regression, neural networks, and other methods to explore the relationship between the degree of green value co-creation and the costs and benefits of green value co-creation to more accurately understand the synergistic evolution mechanism of the stakeholders of CDW resource utilization projects under green value co-creation.