Evolutionary Game Analysis for Promoting the Realization of Construction Waste Recycling and Resource Utilization: Based on a Multi-Agent Collaboration Perspective

Abstract

Excessive growth or improper disposal of construction waste can lead to negative consequences such as environmental destruction and waste of resources. The policy practice of construction waste reduction and resource utilization is facing challenging issues. Construction enterprises (also constructors of construction waste) and building material manufacturers (also recyclers of construction waste) play significant roles in the system of construction waste recycling and resource utilization. However, they are often absent or out of position in most cases. Therefore, this study constructs an evolutionary game model and conducts numerical simulation analysis, aiming to clarify the interactive relationship between their interests and government policy implementation, promote the formation of a cooperative system for construction waste management, and facilitate the achievement of ultimate governance objectives. The research results show that: (1) Current collaboration in construction waste management has fallen into a dilemma of relying solely on government efforts, resulting in inefficient or ineffective policy implementation. (2) The government can change the current situation and achieve better policy outcomes by taking measures such as increasing the income of recycled construction waste products, increasing fines for violations, and lowering industry entry barriers. (3) Different optimization measures vary in the speed at which they promote the evolutionary game system to evolve into a stable and ideal strategic combination. In comparison, increasing the market price of recycled products and increasing their sales volume are more effective optimization strategies. The process and conclusions of this study provide valuable reference and inspiration for the government to formulate construction waste management policies and optimize their policy implementation plans.

1. Introduction

Undoubtedly, the construction industry, amidst its vital contributions towards global economic growth and modernization, has also emerged as the principal generator of solid waste, particularly construction waste (Ruiz LL et al., 2020) [1]. Distinct from domestic waste, the excessive and illicit disposal of construction waste not only negatively impacts the ecological and living environments, leading to the degradation of air, water, and soil quality (Kama A A L, 2001) [2], but also poses a serious threat to the overall reserves of non-renewable resources, including limestone, clay, and iron ore (Su Y, 2020) [3]. Consequently, this results in significant resource wastage and depletion. The report “Building Materials and the Climate: Constructing a New Future”, jointly issued by the United Nations Environment Program and the Yale Center for Ecology and Architecture, underscores a critical issue: the construction industry has emerged as the foremost contributor to greenhouse gas emissions, accounting for a staggering 37 percent of global carbon emissions. Within this sector, a significant portion of the so-called “hidden” carbon footprint stems from the unchecked emissions of construction waste. Alarmingly, much of this waste, which primarily comprises renewable natural materials, is neither recycled nor properly disposed of, thereby leaving a substantial carbon footprint. Consequently, the failure to implement effective strategies to mitigate the generation and improper disposal of construction waste poses a significant obstacle to our efforts to mitigate climate change, safeguard the ecological environment, and conserve resources. Such inaction is diametrically opposed to the Sustainable Development Goals that humanity has set for itself.

In response to the pressing environmental challenges posed by construction waste, governments worldwide have embarked on concerted efforts towards its treatment and resource utilization (Kabirifar K et al., 2020) [4]. These endeavors aim to mitigate environmental degradation and resource depletion by establishing comprehensive recycling systems. Through these systems, governments strive to transform construction waste into reusable materials, thereby promoting sustainable development and adhering to the principles of environmental stewardship. Among the various strategies employed, the most fundamental approach involves enacting pertinent laws and regulations that directly oversee the waste discharge practices of construction enterprises, thereby compelling them to minimize the generation of construction waste (Kelly D L, 2006) [5]. As an illustrative example, the Chinese government has promulgated the “Regulations on the Management of Urban Construction Waste”, which unequivocally defines the unlawful disposal of construction waste and establishes clear-cut forms of punishment as well as specific standards for enforcement. Simultaneously, utilizing market and economic mechanisms to regulate the waste disposal behavior of construction enterprises is recognized as an effective intervention strategy. The sewage fee and subsidy system, which is rooted in the Pigou tax and Coase theorem, stands as the most archetypal form of economic incentive-based environmental regulation (Mankiw N G, 2012) [6], and it is extensively employed in the management of construction waste. For instance, in China, measures such as imposing fees for construction waste disposal and promoting clean freight have been implemented, aiming to increase the cost of disposing of construction waste, thereby motivating construction enterprises to minimize waste generation. Italy, for instance, provides subsidies to companies that engage in recycling and reusing solid waste. The government prioritizes those enterprises that optimize their construction or production processes in order to minimize waste generation. In Germany, subsidies are preferentially awarded to small and medium-sized enterprises that encounter financial challenges due to their efforts in waste reduction (Kama A A L et al., 2001) [2].

Despite these efforts, the global recycling rate of construction waste remains at a disappointingly low level. According to studies, the average annual total amount of construction waste generated in each country worldwide exceeds 2 billion tons, yet only a fraction, ranging from 20% to 30%, of this waste is recycled (Kim J, 2021) [7]. This is a significant shortfall in meeting the demands of environmental protection and resource conservation. In the midst of the evident mismatch between policy investments and their corresponding outcomes, scholars have increasingly turned their focus toward the intricate interplay of interests underlying the recycling and disposal of construction waste. This effort is aimed at unpacking the reasons for the current inefficiencies or failures in policy implementation, thereby informing future strategies and enhancing the overall management of this crucial resource. The research by Kularatne R. K. A. (2015) [8] indicates that the increased cost due to compliant disposal of construction waste is the main reason why construction enterprises are reluctant to implement policy requirements. Insufficient funding and decreasing profits hinder their participation in the recycling of construction waste. Nuria C., Laura, V. C., and Isabel N. C. (2014) [9] believe that the reduction and recycling of construction waste contradicts the goal of maximizing profits pursued by enterprises. This is the reason why enterprises ignore government initiatives and requirements. At the same time, government supervision cannot cover all construction enterprises and projects, and the illegal costs faced by enterprises are not high, which can easily lead to policy suspension. Ma M et al. (2020) [10] point out that the insufficient governance capabilities of the government are also the reason for the failure to achieve policy objectives. He believes that the government should take the lead in establishing a sound guidance mechanism and interest coordination model in public affairs management to promote relevant enterprises to fulfill their environmental and social responsibilities. Obviously, many government departments have overlooked this aspect. Xia B., Ding, T., and Xiao J. (2020) [11] focus on the differences in policy effectiveness caused by different policy contents and implementation strategies. He points out that different policy tools, such as fines, subsidies, and taxes, often have limited effects when used alone. However, combining several different policy tools can enhance policy effectiveness. The research by Ma and L Z L. (2020) [12] indicates that the integrity of the construction waste recycling industry chain is crucial for achieving the goal of construction waste management. The study believes that the key to achieving the recycling of construction waste lies in gaining consumer market recognition for recycled building materials and enabling recycling enterprises to obtain profits. Unfortunately, in most countries, construction waste recycling enterprises often face survival crises due to difficulties in product sales. The absence of recycling enterprises disrupts the recycling chain of construction waste, discouraging relevant parties from participating.

Through a review of the literature, it can be seen that the construction waste management system mainly involves three entities: construction enterprises, construction waste recycling enterprises, and the government. In the recycling of construction waste, these three entities play the roles of waste producer, recycler, and manager, respectively. However, to pursue maximum economic interests, both manufacturers and recyclers are unwilling to make efforts to assume the responsibility of construction waste management. Even worse, the “free-rider” behavior is prevalent, with all parties expecting to reap benefits from each other’s environmental governance efforts (Zhang Y et al., 2020) [13]. Specifically, the relevant responsible parties for construction waste are unwilling to invest human and material resources in environmental protection disposal (Duan H et al., 2016) [14], and they do not want to change the current traditional production process that can create considerable economic benefits (Zhang F et al., 2020) [15]. The ultimate result is bound to be the outbreak of environmental protection issues of construction waste, causing damage to land, blue sky, air, and other resources, leading to the “tragedy of the commons”. From this perspective, the key to solving the problem lies in transforming the externalities of construction waste emission and illegal disposal into internal issues, thereby stimulating the motivation of relevant enterprises to participate from internal demand. And this requires the government to play the role of the “visible hand” to guide and intervene (Jiang H et al., 2017) [16]. The phenomenon of failure in collaborative environmental protection governance caused by the withdrawal of stakeholders can be explained by the theory of property rights. The theory of property rights proposed by economist Ronald Coase (1972) [17] argues that the main reason for relevant responsible parties to withdraw from environmental protection cooperation is that they cannot obtain equal compensation for their efforts or that there is no corresponding cost for evasion behavior. It also points out that establishing a trading mechanism that clarifies the responsibilities and rights of all parties while making environmental protection collaboration “reward and punishment clear, more work more reward” will help achieve public governance goals.

Evolutionary game theory has advantages in revealing the mechanism of agent cooperation. Evolutionary game theory does not mandate that agents possess complete rationality, believing instead that agents will continuously alter their strategies through learning and modeling. This makes it more aligned with the behavioral characteristics of organizations and individuals in the field of environmental protection [18]. Simultaneously, evolutionary game models can explain the formation and evolution of group behaviors in the environmental protection field [19], such as the enhancement of public environmental awareness [20] and the selection of corporate environmental strategies [21]. By analyzing the dissemination and adaptation processes of different strategies within groups, we can uncover the underlying reasons for the formation of pro-environmental behaviors, which will serve as supportive evidence for government policy formulation and governance goal achievement [22]. Thus, evolutionary game models are frequently applied to behavioral research in the field of environmental protection due to their advantages of high theoretical fit, high interpretability, and high guidance.

In the intersection of building and environmental protection, evolutionary game models are frequently mentioned as a technique to reveal the decision-making mechanisms of agents and solve collaboration challenges among stakeholders in the building sector. Yuan M, Li Z, Li X, et al. constructed a tripartite evolutionary game model consisting of the government, home buyers, and real estate developers to analyze the reasons behind the obstacles faced by prefabricated and assembled housing in China [23]. They believed that the government’s low subsidy and low penalty regulatory policies are not conducive to promoting the adoption of prefabricated and assembled housing by businesses and home buyers, hindering the sustainable development of China’s construction industry. A L C, A X G, B C H A, et al. established a tripartite evolutionary game model to address the issue of promoting green building technology [24]. Green building technology has the advantage of reducing material and resource consumption but also increases construction costs, thus exhibiting externality characteristics. The authors compared the effectiveness of subsidy and penalty policy tools and concluded that strong government regulatory policies could more effectively urge enterprises to introduce and apply green building technologies. To promote the expansion of the green building market, Liu Y, Zuo J, Pan M, et al. established an evolutionary game model involving the government, suppliers, and developers [25]. Their research indicated that excessive subsidies and penalty amounts are not conducive to generating green behaviors among collaborating entities, and high costs are the primary reason why suppliers and developers are reluctant to participate in green building projects. It is worth noting that while the introduction of public supervision can enhance green behaviors among construction parties and developers to some extent, it can also easily lead to confusion in government regulation and increased governance costs. Therefore, it should receive attention in government policy formulation. It can be seen that in the research fields of green building and low-carbon building, evolutionary game models provide theoretical insights and explanatory tools for achieving collaboration among entities and are widely applied in various areas such as building consumption, construction technology application, and construction market development.

Therefore, many scholars have been dedicated to building evolutionary game models for construction waste management and recycling, aiming to verify the feasibility and effectiveness of the aforementioned potential paths. Hong S., Ying P., and Chun X. G. (2018) [26] proposed a dual-agent evolutionary game model for construction waste management, analyzing the cooperative behavior between construction material suppliers and demanders. The research indicates that the construction waste management system is likely to evolve towards an ideal state only when at least one party perceives significantly higher benefits from cooperation than from non-cooperation. Ma and LZ L. (2020) [12] explored and analyzed the evolutionary trajectory of symbiotic behavior between construction waste producers and recyclers, as well as the impact of government incentives on these trajectories. This study believes that the existence of government incentives can accelerate the evolution process toward cooperation between the two agents. Chen J., Hua C., and Liu C. (2019) [27] directly included government agencies as the participants in the game, analyzing the evolution of the relationship between policy executors and actors between the government and construction enterprises. The research shows that strict supervision and severe fines have a significant restrictive effect on enterprises’ construction waste discharge behavior. Su Y. (2020) [3] further established a tripartite evolutionary game model to analyze the behavioral decisions and stable strategic combinations of government agencies, construction waste producers, and recyclers in collaboration for construction waste management. The study points out that the government should adopt different levels of intervention strategies and means at different stages of system evolution to converge the system evolution towards an ideal state. Li M, Han C, Shao Z, et al. (2024) established an evolutionary game model from the perspective of cooperation among construction waste recycling enterprises, incorporating profit distribution coefficients and synergistic benefits as new factors into the model [28]. The study analyzed the behavior of commercial enterprises cooperating to increase the revenue of construction waste recycling, with the government subsidy mechanism as the background, thereby promoting the efficiency of construction waste management from another perspective. Wang Y, Wang C, Deng X, Wu Z (2023) combined prospect theory with an evolutionary game model for construction waste management, focusing on the role of the public in collaborative governance [29]. The research indicated that the supervisory behavior of the public based on social responsibility can promote tripartite cooperation towards a satisfactory solution, but resource investments from the government and enterprises play a decisive role. Therefore, construction waste management is not an environmental issue that can be achieved through the efforts of a single entity. Long H, Liu H, Li X, et al. (2020) explained the reasons for the low efficiency of the construction waste recycling chain from a supply chain perspective, arguing that the “free-riding” behavior of construction waste producers and recyclers hinders the emergence of cooperative behavior between them [30]. Increasing the government’s subsidy probability and regulatory probability for construction waste recycling can significantly inhibit such “free-riding” behavior and motivate both parties to actively participate in construction waste recycling.

In summary, the research method of evolutionary game theory has gained favor among scholars in both the field of construction research and environmental protection behavior research, becoming an important method for constructing and analyzing the internal mechanisms of collaborative governance and driving theoretical and practical progress in related disciplines. Construction waste recycling and resource disposal are no exception, but in comparison, there is still considerable room for further research and expansion. Upon reviewing the literature, the research finds that the existing research system still has some shortcomings. These research deficiencies have resulted in a gap between the theoretical analysis results and the actual resolution of real-world problems and challenges. First, in the study of evolutionary games, most scholars quantify the benefits or costs of related enterprises into a single variable or indicator in a general way. However, in the practice of construction waste management, factors such as the amount of construction waste disposed, unit disposal cost, sales volume of building materials, and sales price may independently change as the strategies of the agents change. Simplifying them into a comprehensive indicator cannot reflect the subtle interactive relationship and precise changes in benefits in the evolutionary game model, which may easily lead to biases in the evolution results and research conclusions of the system. Second, existing evolutionary game studies assume that construction waste recyclers can recover all the construction waste generated by construction enterprises. However, the fact is that the current market for the resource utilization of construction waste is still in its infancy, with low recycling capacity and remanufacturing capacity, and can only recycle and reuse a portion of the construction waste. Such assumptions can lead to distortions in theoretical models and a loss of research significance.

Therefore, this paper aims to introduce more parameters and set a recoverable proportion θ for construction waste recyclers to represent their recycling capacity and degree. By doing so, a new evolutionary game model, including construction enterprises, construction waste recycling and utilization enterprises, and the government, will be constructed to analyze the changes in benefits and strategic choices of the three parties in the construction waste management and reuse system.

Ultimately, the study establishes a tripartite cooperation governance model for construction waste and conducts numerical simulation verification on its effectiveness and sensitivity. The results reveal that factors such as the amount of construction waste generated (Q) and the disposal fee (f) have an impact on the probability of behavioral choices of various participants, which in turn affects the equilibrium and stability of the tripartite cooperation system. The aforementioned findings not only validate the previous research that advocates for increasing disposal fees for construction waste generators but also further elaborate on how to enhance these fees and the subsequent effects of such changes on the behaviors of other participants. Consequently, the strength of this paper lies in its more thorough revelation of the inherent mechanisms of cooperative governance of construction waste, shedding light on numerous perplexing issues faced by governments and enterprises in reality and deepening the research. Given that the mathematical model constructed in this paper profoundly reflects objective realities, governments can obtain detailed operational measures rather than directional policy recommendations, which is also one of the innovative aspects of this paper.

2. Model Construction

Furthermore, Actor-Network Theory (ANT) [31] provides a feasible solution to the above problems. According to ANT, the emergence of any social phenomenon or the resolution of social issues cannot be avoided, considering the role of relevant actors and the network relationships they construct. Although actors have different behavioral motivations, they can transform their respective intentions, interests, knowledge, etc., into a process of common understanding and action through communication and interaction under the guidance of key actors, ultimately promoting the achievement of macro goals. Given the advantages of ANT in constructing multi-agent collaboration relationships and exploring the interactive relationship of actors’ interests, the research will use this theory as a guide to constructing an evolutionary game model.

The Actor-Network Theory constructs a multi-agent transaction mechanism with actors, heterogeneity, and translation as its core components and processes (Callon, M, 1986) [31].

Actors: construction enterprises (producers), manufacturers of building materials (recyclers), and the government (leader and supervisor).

Heterogeneous demands for interests: The producers and recyclers of construction waste aim to maximize economic profits and minimize costs while the government takes into consideration economic benefits, environmental benefits, and social benefits.

Translation is a crucial process that connects loose stakeholders into an interactive network of actors. It involves identifying key actors, establishing choke points, stimulating willingness, recruiting, mobilizing, and other steps.

In the theory of actor-network theory, the key actor is not only the proposer of common goals and choke points but also the mediator of conflicts in the interests of various parties in practice, the builder of collaborative networks, and the regulator of the actions of these parties. In the recycling and resource utilization of construction waste, the government, as the executive body of state power and the representative of citizens’ interests, has both governance capabilities and motivations. It can provide policies, resources, services, and other means to ensure that the process of achieving governance goals remains on track. Therefore, the government plays the role of a key actor in the collaborative network aimed at reducing, recycling, and harmlessly disposing of construction waste. The comparison between the collaborative model of construction waste recycling and resource utilization based on ANT theory and the traditional model can be seen in Figure 1.

Based on the perspective of property rights theory and combined with the implementation practice of China’s construction waste policies, it is believed that the current main challenges are reconciling the conflicts between enterprise costs and benefits and improving the effectiveness and efficiency of policy implementation. Therefore, the forced-crossing point proposed by the key actor is a multi-stakeholder collaborative governance model for construction waste under the leadership of the government, with the deep participation of construction waste producers and recyclers. Specifically, the choke points emphasize that construction waste producers should minimize the generation of waste such as concrete, silt, mortar, glass, wood, and various metal products during the demolition and construction process and adopt proper disposal methods for the already-formed construction waste, including collection, classification, stacking, transportation, etc. (Purushothaman M B et al., 2024) [32]. Meanwhile, recyclers should dismantle and pre-classify the collected construction waste without causing harm to the environment in order to eliminate materials irrelevant to the reuse process. After that, the obtained renewable construction waste undergoes fine screening, crushing, remanufacturing, and other processes to recycle waste concrete blocks, bricks, silt, and other materials, ultimately producing building materials that can be redistributed to the market and sold (Meshref A N et al., 2023) [33].

However, based on the perspective of property rights theory, construction enterprises and building material manufacturers do not inherently have the motivation to fulfill their responsibilities for environmentally friendly disposal of construction waste. The government needs to stimulate interest through mechanism establishment and policy design to recruit and mobilize relevant actors (Wahi N et al., 2016) [34]. The interest stimulation process aims to enhance the willingness of construction waste producers and recyclers to support the government’s proposed choke points, and it also includes the government’s efforts to increase social attention and influence of the policies. Recruitment and mobilization refer to the government as the leader of this actor-network, providing necessary support and incentives for other actors to participate and maintain their actions, as well as the stability and efficiency of the network. China is one of the countries that proposed the vision of domestic waste sorting as the earliest and has the longest history of policy evolution. It has accumulated a large number of legal, economic, and market-based policy tools in this area, which will all have an impact on the construction of the evolutionary game model in this paper.

2.1. Model Assumptions

Based on the above analysis, the research proposes six assumptions to make the constructed evolutionary game model as close to the real world as possible.

Assumption 1. 

Construction enterprises, resource utilization enterprises and government are all bounded rationality. And each subject can constantly adjust the strategy through self-learning and adaptation.

Assumption 2. 

The strategic space of the construction enterprise is “compliance disposal or illegal dumping”, and the probability of adopting the two strategies is x (0 ≤ x ≤ 1) and (1 − x) respectively. The strategy space of resource utilization is ‘investment participation or traditional production’, and the probability of adopting two strategies is y (0 ≤ y ≤ 1) and (1 − y), respectively. The policy space of the government is “incentive constraint or deregulation”, and the probability of adopting the two strategies is z (0 ≤ z ≤ 1) and (1 − z) respectively.

Assumption 3. 

Construction enterprises in compliance with the disposal of construction waste should pay the disposal fee “on time and according to the amount”, recorded as the product of f and Q. Where f is the unit disposal fee, Q is the total amount of construction waste generated. Construction companies illegally dumping construction waste face fines, marked as F.

Assumption 4. 

The fixed investment of the construction material production enterprise participating in the construction waste resource utilization project is denoted as C, and the variable cost is the unit transportation cost (denoted as V) and unit production cost (denoted as N) of the construction waste recycling. The unit price of recycled building materials is denoted as p, and its market share is denoted as d. Due to the active participation in the recycling and resource utilization of construction waste, the government granted the franchise sales share to the construction waste recycling enterprise, recorded as U. Building material manufacturers insist on using natural raw materials for production, unit production cost is recorded as M, unit sales price of traditional products is recorded as P (P > p), and market share is recorded as D (D > d).

Assumption 5. 

If construction waste is not properly disposed of, the government needs to bear the after-treatment cost, which is denoted as E. There are regulatory costs in government active regulation, which are denoted as S. Negative government regulation will suffer a loss of prestige, denoted L. The active participation of construction enterprises and recyclers in the recycling of construction waste can be attributed to their efforts to reduce the cost of post-event environmental treatment borne by the government, respectively, and the reduction coefficients are denoted as η and θ. When both are active effort strategies, E = 0.

Assumption 6. 

As an innovation point in the establishment of evolutionary game model in this study, the recycling capacity coefficient of building material remanufacturing enterprises is denoted as θ (0 < θ < 1) to represent the proportion of total construction waste recyclers can recycle. At the same time, the income distribution coefficient of construction waste recycling set by research innovation is denoted as α. This coefficient is used to reflect the distribution of additional revenue when the construction enterprise and the recycler realize the cooperation (0 < α < 1). The existence of the regulatory factor θ can make the evolutionary game model more realistic. The role of α is to explore a new incentive mechanism to promote the realization of tripartite cooperation.

2.2. Model Analysis

2.2.1. Constructing an Evolutionary Game Revenue Matrix

In this evolutionary game, the form and content of each subject’s payoff function are influenced by its own behavior and the strategic choices of other subjects. This implies that there exists a complex interaction among construction enterprises, building material manufacturers, and the government, such that any change in the strategy of one subject can have an impact on the payoffs of other subjects and the stability of the system’s evolution. Consequently, the payoff function matrices for each subject are constructed as follows.

2.2.2. Evolutionary Game Model Analysis

According to the contents listed in

Table 1. The payoff matrix.

Construction Enterprises	Manufacturer	Government: Incentive Constraint	Government: Deregulation
Compliance Disposal	Investment Participation	$\alpha pU-f(1-\theta )Q$	$-f(1-\theta )Q$
		$pd+(1-\alpha )pU-C-\theta QM+B$	$pd-C-\theta QM$
		$-S-B$	$-L$
	No Investment	$-fQ$	$-fQ$
		$Pd-Nd$	$PD-ND$
		$-(1-\eta )E-S$	$-(1-\eta )E-L$
Illegal Dumping	Investment Participation	$-F$	$0$
		$p(d+U)-C-\theta QV-\theta QM+B$	$pd-C-\theta QV-\theta QM$
		$F-(1-\theta )E-S-B$	$-(1-\theta )E-L$
	No Investment	$-F$	$0$
		$Pd-Nd$	$PD-ND$
		$F-E-S$	$-E-L$

, the following expected return function can be obtained where π₁₁ refers to the expected return when the construction enterprise chooses the compliance disposal strategy, while π₁₂ refers to the expected return when it chooses the random dumping strategy. Similarly, π₂₁ and π_22, respectively, refer to the expected returns of building material manufacturers when they choose investment participation and non-investment strategies. π₃₁ and π₃₂ refer to the expected returns when the government chooses the strict strategy and the laissez-faire strategy, respectively.

$$\begin{array}{c}{\pi }_{11}=yz(\alpha pU-f(1-\theta )Q)+y(1-z)(-f(1-\theta )Q)\\ \hspace{1em} +z(1-y)(-fQ)+(1-y)(1-z)(-fQ)\hfill \end{array}$$

(1)

$${\pi }_{12}=yz(-F)+y(1-z)(0)+z(1-y)(-F)+(1-y)(1-z)(0)$$

(2)

$$\begin{array}{c}{\pi }_{21}=xz(pd+(1-\alpha )pU-C-\theta QM+B)+x(1-z)(pd-C-\theta QM)\\ \hspace{1em} +z(1-x)(p(d+U)-C-\theta QV-\theta QM+B)\hfill \\ \hspace{1em} +(1-x)(1-z)(pd-C-\theta QV-\theta QM)\hfill \end{array}$$

(3)

$$\begin{array}{c}{\pi }_{22}=xz(Pd-Nd)+x(1-z)(PD-ND)+z(1-x)(Pd-Nd)\\ \hspace{1em} +(1-x)(1-z)(PD-ND)\hfill \end{array}$$

(4)

$$\begin{array}{c}{\pi }_{31}=xy(-B-S)+x(1-y)(-(1-\eta )E-S)\hfill \\ \hspace{1em} +y(1-x)(F-(1-\theta )E-S-B)+(1-x)(1-y)(F-E-S)\hfill \end{array}$$

(5)

$$\begin{array}{c}{\pi }_{32}=xy(-L)+x(1-y)(-(1-\eta )E-L)+y(1-x)(-(1-\theta )E-L)\\ \hspace{1em} +(1-x)(1-y)(-E-L)\hfill \end{array}$$

(6)

According to Formulas (1)–(6), the average expected income of construction enterprises, construction material manufacturers, and the government can be calculated as follows:

$${\pi }_1=x{\pi }_{11}+(1-x){\pi }_{12}$$

(7)

$${\pi }_2=x{\pi }_{21}+(1-x){\pi }_{22}$$

(8)

$${\pi }_3=x{\pi }_{31}+(1-x){\pi }_{32}$$

(9)

Further, the replication dynamic equation of each subject in the evolutionary game model of construction waste treatment and resource utilization can be calculated as follows.

$$\begin{array}{c}F(x)={\displaystyle \frac{dx}{dt}}=x({\pi }_{11}-{\pi }_1)=x(1-x)({\pi }_{11}-{\pi }_{12})\hfill \\ \hspace{1em} =x(1-x)\left[yz(\alpha pU)+y(f\theta Q)+z(F)-fQ\right]\hfill \end{array}$$

(10)

$$\begin{array}{c}F(y)={\displaystyle \frac{dy}{dt}}=x({\pi }_{21}-{\pi }_2)=y(1-y)({\pi }_{21}-{\pi }_{22})\hfill \\ \hspace{1em} =y(1-y)\left[\begin{array}{l}xz(-\alpha pU)+x(\theta QV)+z(pU+B-Pd+PD+Nd-ND)\\ +pd-PD+ND-C-\theta QV-\theta QM\end{array}\right]\hfill \end{array}$$

(11)

$$\begin{array}{c}F(z)={\displaystyle \frac{dz}{dt}}=x({\pi }_{31}-{\pi }_3)=z(1-z)({\pi }_{31}-{\pi }_{32})\hfill \\ \hspace{1em} =z(1-z)\left[x(-F)+y(-B)+F+L-S\right]\hfill \end{array}$$

(12)

Further calculation of Formula (11) shows that:

When $y=y^{\ast }={\displaystyle \frac{fQ-zF}{z\alpha pU+\theta fQ}}$, $F(x)\equiv 0$. Under this condition, the game system is stable for any value of x. In other words, the strategic choice of construction enterprises does not change with the evolution of time.

When $y\ne y^{\ast }={\displaystyle \frac{fQ-zF}{z\alpha pU+\theta fQ}}$, x = 0 and x = 1 are two possible equilibrium stable states. It is necessary to discuss the stability strategy of construction enterprises in different situations further. When $y>{\displaystyle \frac{fQ-zF}{z\alpha pU+\theta fQ}}$, $F^{\prime }(x){|}_{x=0}<0 \& F^{\prime }(x){|}_{x=1}>0$ achieved. In this case, x = 1 is the stable point, and construction enterprises choose compliance disposal as an ESS. Conversely, when $y<{\displaystyle \frac{fQ-zF}{z\alpha pU+\theta fQ}}$, $F^{\prime }(x){|}_{x=0}>0 \& F^{\prime }(x){|}_{x=1}<0$ achieved. Under this combination of conditions, x = 0 is the stable point, and construction enterprises choose illegal dumping as an ESS.

It can be seen that whether a construction enterprise chooses to dispose of construction waste in the standardized way required by the policy depends on the equation composed of the parameters that can affect its own income function and the probability of the other two entities choosing the cooperation strategy. Important parameters include the disposal fee of construction waste units, the production volume of construction waste, the amount of fines to be borne by illegal dumping, the distribution income obtained by participation, and the recycling proportion of Q by construction waste recyclers.

Further calculation of Formula (12) shows that:

When $x=x^{\ast }={\displaystyle \frac{pd-C-\theta QV-\theta QM-PD+ND+z(pU+B-Pd+PD+Nd-ND)}{z\alpha pU-\theta QV}}$, $F(y)\equiv 0$. Under this condition, the game system is stable for any value of x. In other words, the strategic choice of construction waste recycler does not change with the evolution of time.

When $x\ne x^{\ast }={\displaystyle \frac{pd-C-\theta QV-\theta QM-PD+ND+z(pU+B-Pd+PD+Nd-ND)}{z\alpha pU-\theta QV}}$, y = 0 and y = 1 are two possible equilibrium stable states. It is necessary to discuss the stability strategy of construction waste recyclers in different situations further. When $x>x^{\ast }$ and $z\alpha pU-\theta QV>0$, or in condition $x<x^{\ast }$ and $z\alpha pU-\theta QV<0$, $F^{\prime }(y){|}_{y=0}>0 \& F^{\prime }(y){|}_{y=1}<0$ achieved. Under this combination of conditions, y = 1 is the stable point, and it is ESS that construction waste recyclers choose to invest and participate in resource utilization projects. When $x>x^{\ast }$ and $z\alpha pU-\theta QV<0$, or in condition $x<x^{\ast }$ and $z\alpha pU-\theta QV>0$, $F^{\prime }(y){|}_{y=0}<0 \& F^{\prime }(y){|}_{y=1}>0$ achieved. Under this combination of conditions, y = 0 is the stable point, and the construction waste recyclers choose not to participate in their ESS.

It can be seen that whether a building material manufacturer invests in the production of construction waste recycling products depends on an equation composed of parameters that can affect its own income function and the probability of the other two entities choosing a cooperation strategy. There are many relevant parameters, which are summarized as follows: the price and market share of reused products, the price and market share of traditional products, the total production cost of reused products, the total production cost of traditional products, the economic income formed by the transformation of market share given by the government, the proportion of additional income allocated to construction enterprises α, and the recycling capacity θ.

Further calculation of Formula (13) shows that:

When $x=x^{\ast }={\displaystyle \frac{(F+L-S)-yB}{F}}$, $F(z)\equiv 0$. Under this condition, the game system is stable for any value of z. In other words, the strategic choice of government does not change with the evolution of time.

When $x\ne x^{\ast }={\displaystyle \frac{(F+L-S)-yB}{F}}$, z = 0 and z = 1 are two possible equilibrium stable states. It is necessary to discuss the stability strategy of the government in different situations further. When $x>{\displaystyle \frac{(F+L-S)-yB}{F}}$, $F^{\prime }(z){|}_{z=0}>0 \& F^{\prime }(z){|}_{z=1}<0$ achieved. At this time, z = 1 is the stable point, and the government chooses the incentive constraint as the ESS. When $x<{\displaystyle \frac{(F+L-S)-yB}{F}}$, $F^{\prime }(\mathrm{z}){|}_{\mathrm{z}=0}<0 \& F^{\prime }(\mathrm{z}){|}_{\mathrm{z}=1}>0$ achieved. At this time, z = 0 is the stable point, and the government chooses passive intervention as the ESS.

It can be seen that whether the government adopts the proactive incentive and constraint strategy depends on the equation composed of the parameters that can affect its own income function and the probability that the other two entities choose the cooperation strategy. Relevant parameters include fines to construction companies, reputational damage value, regulatory costs, and the amount of subsidies to recyclers.

2.2.3. Strategy Stability Analysis of Model Evolution

Based on the Lyapunov stability theory, the asymptotic stability of the system at its equilibrium point can be determined by analyzing the eigenvalues of the game system’s Jacobian matrix (Xinhan L et al., 2020) [35]. The calculation of the system’s Jacobian matrix is demonstrated in Equation (13):

$$J=\left[\begin{array}{ccc}{J}_{11}& J_{12}& J_{13}\\ J_{21}& J_{22}& J_{23}\\ J_{31}& J_{32}& J_{33}\end{array}\right]=\left[\begin{array}{ccc}{\displaystyle \frac{\partial F(x)}{\partial x}}& {\displaystyle \frac{\partial F(x)}{\partial y}}& {\displaystyle \frac{\partial F(x)}{\partial z}}\\ {\displaystyle \frac{\partial F(y)}{\partial x}}& {\displaystyle \frac{\partial F(y)}{\partial y}}& {\displaystyle \frac{\partial F(y)}{\partial z}}\\ {\displaystyle \frac{\partial F(z)}{\partial x}}& {\displaystyle \frac{\partial F(z)}{\partial y}}& {\displaystyle \frac{\partial F(z)}{\partial z}}\end{array}\right]$$

(13)

And:

$${\displaystyle \frac{\partial F(x)}{\partial x}}=(1-2x)\left[yz(\alpha pU)+y(f\theta Q)+z(F)-fQ\right]$$

$${\displaystyle \frac{\partial F(x)}{\partial y}}=x(1-x)\left[z(\alpha pU)+f\theta Q\right]$$

$${\displaystyle \frac{\partial F(x)}{\partial z}}=x(1-x)\left[z(\alpha pU)+F\right]$$

$${\displaystyle \frac{\partial F(y)}{\partial x}}=y(1-y)\left[z(-\alpha pU)+\theta QV\right]$$

$${\displaystyle \frac{\partial F(y)}{\partial y}}=(1-2y)\left[\begin{array}{l}xz(-\alpha pU)+x(\theta QV)+z(pU+B-Pd+PD+Nd-ND)\\ +pd-PD+ND-C-\theta QV-\theta QM\end{array}\right]$$

$${\displaystyle \frac{\partial F(y)}{\partial z}}=y(1-y)\left[x(-\alpha pU)+pU+B-Pd+PD+Nd-ND\right]$$

$${\displaystyle \frac{\partial F(z)}{\partial x}}=z(1-z)\left[-F\right]$$

$${\displaystyle \frac{\partial F(z)}{\partial y}}=z(1-z)\left[-B\right]$$

$${\displaystyle \frac{\partial F(z)}{\partial z}}=(1-2z)\left[x(-F)+y(-B)+F+L-S\right]$$

Since the asymptotically stable solution of a multi-agent evolutionary game system must be a strict Nash equilibrium; this paper only considers the possibility of the pure strategy equilibrium solution becoming an ESS. The possible equilibrium points of mixed strategies are not considered.

Lyapunov’s first method proposes if all the eigenvalues of the Jacobian matrix have negative real parts, then the equilibrium point is asymptotically stable. If at least one of the eigenvalues of the Jacobian matrix has a positive real part, the equilibrium point is an unstable point. If the Jacobian matrix has negative real parts except the eigenvalues with zero real parts, then the equilibrium point is in a critical state, and the stability cannot be determined by the eigenvalue sign. Therefore, this study calculates the eigenvalues of the Jacobian matrix at each pure strategy equilibrium point based on Formula (14), which are shown in

Table 2. Stability analysis of equilibrium points.

Point of Equilibrium	The Eigenvalue of a Jacobian Matrix				Stability
	λ1	λ2	λ3	±
O1 (1,1,1)	$-\left[\alpha pU+F-(1-\theta )fQ\right]$	$-\left[pU-\alpha pU+pd+B-C-\theta QM-(Pd-Nd)\right]$	$-\left[L-B-S\right]$	(⊗,⊗,⊗)	unknown
O2 (1,1,0)	$(1-\theta )fQ$	$-\left[pd-C-\theta QM-(PD-ND)\right]$	$L-B-S$	(+,⊗,⊗)	unstable
O3 (1,0,1)	$-\left[F-fQ\right]$	$pU-\alpha pU+pd+B-C-\theta QM-(Pd-Nd)$	$-\left[L-S\right]$	(⊗,⊗,⊗)	unknown
O4 (0,1,1)	$\alpha pU+F-(1-\theta )fQ$	$-\left[pU+pd+B-C-\theta QV-\theta QM-(Pd-Nd)\right]$	$-\left[F+L-B-S\right]$	(⊗,⊗,⊗)	unknown
O5 (1,0,0)	$fQ$	$pd-C-\theta QM-(PD-ND)$	$L-S$	(+,⊗,⊗)	unstable
O6 (0,1,0)	$-(1-\theta )fQ$	$-\left[pd-C-\theta QV-\theta QM-(PD-ND)\right]$	$F-B+L-S$	(−,⊗,⊗)	unknown
O7 (0,0,1)	$F-fQ$	$pU+pd+B-C-\theta QV-\theta QM-(Pd-Nd)$	$-\left[F+L-S\right]$	(⊗,⊗,⊗)	unknown
O8 (0,0,0)	$-fQ$	$pd-C-\theta QV-\theta QM-(PD-ND)$	$F+L-S$	(−,⊗,⊗)	unknown

Note: The “+” in parentheses after the eigenvalue expression means that the eigenvalue is positive. The “ − ” indicates that the eigenvalue is negative. The “⊗” indicates that the eigenvalue is positive or negative.

, and determines the asymptotic stability of each equilibrium point according to Lyapunov’s first method.

In the solution domain V = {(x,y,z)|0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1} from O₈ (0,0,0) to O₁ (1,1,1), combined with the parameter assumption conditions of p < P and d < D, it can be seen that the introduction of adjustment factors θ, α, etc., complicates the interactive relationship of interests among construction enterprises, construction waste recyclers, and the government. The determination of ESS also needs to be discussed in different situations. As can be seen from Table 2, there are four evolutionary stable states of the system.

(1)

A combination of conditions containing two stable solutions. When $\alpha pU-(1-\theta )fQ>-F$ and $(1-\alpha )pU+pd+B-C-\theta QM>Pd-Nd$ and $L-B>S$ achieved, the point O₁ (1,1,1) is evolutionarily stable; further, if the condition $F<fQ$ and $pd+pU+B-C-\theta QM-\theta QV<Pd-Nd$ is also fulfilled, the O₇ (0,0,1) is another evolutionary stable point. In this case, the evolutionary game system has two evolutionarily stable strategy combinations: {compliance disposal, investment participation, incentives, and constraints} and {illegal dumping, traditional production, incentives, and constraints}. At this point, regardless of the strategic choices made by construction waste producers and recyclers, the government will firmly carry out strict supervision and intervention with the goal of recycling construction waste. The reason is that compared to the total amount of savings in regulatory costs and subsidies from relaxed supervision, government departments are more reluctant to bear the negative consequences of relaxed supervision, such as loss of government credibility and decreased resident satisfaction. Furthermore, a comprehensive comparison between O₁ and O₇ and the strategic combinations they represent reveals that the former implies the achievement of construction waste reduction and recycling goals and successful policy implementation, while the latter indicates significant inefficiencies and failures in government policies and their implementation. This inspires us that under the macro background of the government advocating for construction waste reduction and recycling, efforts should be made to optimize policy tools and implementation means so that the benefits of active cooperation between construction waste producers and recyclers are significantly higher than those of passively avoiding, promoting the evolutionary stability of the system away from O₇ and towards O₁. The above analysis not only explains the reasons for the past failures of the policy but also verifies the space and possibilities for the government to optimize policy and implementation, which is of great significance to the conclusions of this study.

(2)

When $pd-C-\theta QV-\theta QM<PD-ND$ and $L-S<-F$ achieved, the point is the only stable point, {illegal dumping, traditional production, negative regulation} is the ESS. At this point, the government deems the loss of image and credibility due to inaction on the issue of construction waste management to be entirely acceptable. In comparison, they are more reluctant to bear the relatively high regulatory costs, even if fines can be imposed on enterprises. It is precisely because of the government’s withdrawal that construction enterprises and construction waste recyclers have lost government support, resulting in a serious imbalance between benefits and costs, ultimately refusing to participate in construction waste reduction and recycling efforts. Point O₈ (0,0,0) is not an ideal evolutionarily stable strategy, and it is even the worst one.

(3)

When $pd-C-\theta QV-\theta QM>PD-ND$ and $L-S<B-F$ achieved, point O₆ (0,1,0) is the only stable point, {illegal dumping, investment recovery, negative regulation} is the ESS. At this time, even without government support and cooperation from construction companies, it is still an advantageous strategy for construction waste recyclers to rely on their own efforts and market share to manufacture and sell recycled building materials compared to the traditional market, as it offers greater profit margins. The reason for the government’s passive governance at this time is that adopting an active strategy would require paying “expensive” subsidies to construction waste recyclers, which are so costly that the government prefers to bear the loss of reputation, especially since they can also collect fines from enterprises. Although it may sound incredible, the situation represented by this point is actually happening in some economically backward areas. In these areas, the government’s priority is to address economic development and food and clothing issues for the people rather than social issues related to higher-level needs such as environmental protection and green sustainability.

(4)

When $F<(1-\theta )fQ-\alpha pU$ and $L-S>B-F$ achieved, point O₄ (0,1,1) is the only stable point, {illegal dumping, investment recovery, regulatory constraints} is the ESS.

(5)

When $F>fQ$ and $pU-\alpha pU+pd+B-C-\theta QM>Pd-Nd$ and $L-S>0$ achieved, Point O₃ (1,0,1) is the only stable point, {compliance disposal, conventional production, regulatory constraints} is the ESS.

Both (4) and (5) reflect situations where the government achieves dual cooperation with either construction companies or construction waste recyclers. Such conditional combinations imply that only one of the two parties, either construction companies or construction waste recyclers, finds it more beneficial to cooperate with the government in construction waste management than not to cooperate. The reason the other party chooses not to cooperate is that under the given conditions, non-cooperation represents a strategically more profitable combination in terms of overall benefits.

When situation (4) or situation (5) occurs, it means that the government’s policies and implementation processes for construction waste management have begun to take effect, but there may be directionality and bias. This suggests that the government has overlooked the role of either construction companies or construction waste recyclers in construction waste management due to omissions in macro planning. These inefficiencies can be addressed through the optimization of government policies and implementation processes, but the key lies in the government establishing the concept of collaborative governance among multiple stakeholders.

3. Evolutionary Simulations

To verify the tripartite collaborative evolutionary game model for the reduction and recycling of construction waste and to explore the impact of human-controllable factors on the stability of system evolution in order to gain richer insights and conclusions, the study used MATLAB R2018b to conduct system simulation analysis.

3.1. Parameter Setting

This study emphasizes the use of authentic data and case study data as the basis for assigning values to numerical simulation parameters. The aim is to ensure that the process and results of the numerical simulation analysis truthfully reflect the interactive relationship between the interests of construction waste producers, recyclers, and the government. This approach serves to validate the mathematical model constructed by the research and ensures the validity of its findings. Given its past efforts in the recycling of construction waste, Qingdao, China, was selected as the sample city for this study. Qingdao has issued regulations such as the “Regulations on the Resource Utilization of Construction Waste”, which explicitly stipulate the management of construction waste: ① For the disposal fee of construction waste if the transportation distance is within 10 km, the transportation cost is 23.03 yuan per cubic meter. For distances exceeding 10 km, the transportation cost increases by 0.95 yuan per cubic meter for each additional kilometer. Based on this, the study assigns a value of 25 yuan per cubic meter to f. ② Under the same rationale, if the producer of construction waste fails to cooperate, building material manufacturers must collect scattered construction waste themselves and transport it back to the processing center, doubling the transportation costs and significantly exceeding f. Therefore, the study assigns a value of 50 yuan per cubic meter to V. ③ For violations of regulations involving the disposal of construction waste without resource utilization; the municipal and county-level urban and rural construction administrative departments will order corrections within a specified period and impose fines ranging from 30,000 to 200,000 yuan. Based on market research, the study assigns a value of 50,000 yuan to F. ④ For technological transformation projects and equipment renewal projects related to the resource utilization of construction waste, a 10% subsidy is provided based on the actual investment in equipment. Considering local equipment import prices, the study assigns a value of 100,000 yuan to B. ⑤ According to the refund ratio of construction waste disposal fees, subsidies for the promotion of recycled products, and the quantity of construction waste determined by market research, the increase in market share is estimated to be 5000 cubic meters, which serves as the basis for assigning a value to U. Additionally, for parameters such as the unit price and manufacturing cost of raw materials, the unit price and manufacturing cost of recycled building materials, and market demand for both materials, the study refers to the “Basic Information List of Enterprises Engaged in the Resource Utilization of Construction Waste” published on relevant websites. Through contact with enterprises for field visits and investigations, a comprehensive comparison of survey data was conducted to determine the final values of relevant parameters. (Data source: http://sjw.qingdao.gov.cn/, (accessed on 19 September 2023)).

The initial parameter assignments are shown in

Table 3. Parameter initial assignment table.

Parameter	Value	Unit	Assignment Basis	Parameter	Value	Unit	Assignment Basis
α	0.1	Null	Expert interview	P	40	¥100,000/10,000 m3	Market research
p	20	¥100,000/10,000 m3	Market research data	d	10	10,000 m3	Market research
U	0.5	10,000 m3	Local government portal	D	15	10,000 m3	Market research
f	2.5	¥100,000/10,000 m3	Local laws and regulations	N	20	¥100,000/10,000 m3	Market research
θ	0.5	Null	Expert interview	C	6	¥100,000	Government department research
Q	4	10,000 m3	Market research	M	5	¥100,000/10,000 m3	Market research
F	0.5	¥100,000	Local laws and regulations	L	3	Null	Expert interview
V	5	¥100,000/10,000 m3	Local government portal	S	0.5	¥100,000	Government department research
B	1	¥100,000	Local laws and regulations

.

3.2. Evolutionary Equilibrium Based on Initial Assignment

Figure 2 shows the results of the evolutionary game system evolving over time from different initial strategy combinations based on the initial assignments. It can be seen that as time progresses, the system stabilizes towards the direction of {illegal dumping, no investment, incentive, and constraint}. Unfortunately, the ideal outcome of {compliant disposal, investment participation, incentive, and constraint} has not been achieved. This indicates that the current management and resource utilization of construction waste is facing a dilemma of government efforts alone and the reluctance of relevant enterprises to cooperate, resulting in the failure to achieve governance goals. Furthermore, this also confirms that the government’s approach or choice in implementing policies for the management and resource utilization of construction waste is not satisfactory, and optimization and adjustment are still needed to achieve the goals of construction waste reduction and resource utilization.

3.3. Model Parameter Analysis under Multiple Equilibrium

Given the system evolution results based on the initial assignments, how the government should adjust its policies and plans has become a necessary question to answer in order to achieve the governance goals. To address this issue, this study conducts a sensitivity analysis of key parameters involved, aiming to clarify the direction and form of the impact of parameter changes on the system evolution process and outcomes.

3.3.1. The Effect of Protected Market Share (U) Change on System Evolution

With all other parameters remaining unchanged, we assign values of 0.5, 1, 1.5, and 3 to U, respectively, to observe the impact of changes in the protected market share of resource utilization products such as government purchases and franchising on the evolution and evolutionary path of the system. As can be seen from Figure 3a, with the increase of U, the equilibrium result of system evolution changes from {illegal dumping, no investment, incentive and constraint} to the ideal state of {compliant disposal, investment participation, incentive and constraint}. Meanwhile, according to Figure 3b, the increase of U not only changes the stable strategies of construction enterprises and construction waste recyclers but also accelerates the speed of convergence of their strategic choices to stable solutions. It is worth mentioning that construction waste recyclers are more sensitive to the increase of U, and they make strategic adjustments before construction enterprises.

Analysis reveals that increasing the consumption of construction waste resource utilization products by the government as a buyer can significantly enhance the likelihood of construction enterprises and construction waste recyclers choosing cooperation strategies. When U is low, the sales channels for recycled products from construction waste recyclers are limited, facing higher market risks, which makes their economic returns less robust. However, if the government intervenes to guarantee a portion of the sales of recycled products, it effectively raises and secures the lower limit of additional revenue for construction enterprises and construction waste recyclers participating in resource utilization projects. This can significantly enhance their willingness to participate and achieve governance goals.

3.3.2. The Effect of Price (p) Change of Construction Waste Recycling Products on System Evolution

With all other parameters remaining unchanged, we assign values of 30, 40, 50, and 60 to p, respectively, and observe the impact of changes in the price of recycled products on the evolution and evolutionary path of the system. As can be seen from Figure 4a, with the increase in the price of recycled construction waste products, the system evolution changes from the stable strategy combination of {illegal dumping, no investment, incentive, and constraint} to {compliant disposal, investment participation, incentive, and constraint}. Furthermore, Figure 4b also illustrates that with the increase of p, both construction waste recyclers and construction enterprises change their strategies successively. And the higher the value of p, the faster their strategies converge to a stable solution.

This indicates that the price of recycled products with environmental protection attributes is a factor that construction enterprises and construction waste recyclers need to consider in their behavioral decisions under established policies. When p is low, the economic benefits obtained from selling recycled products are inferior to those of traditional products, so businesses tend to choose a non-cooperative strategy to ensure their operating profits. However, as p increases, participating in the construction waste resource utilization project becomes more profitable, and both parties subsequently change their strategies in pursuit of higher economic returns.

3.3.3. The Effect of the Change of Construction Waste Recycling Ratio (θ) on the System Evolution

With all other parameters remaining unchanged, we assigned values of 0.25, 0.5, 0.75, and 1 to θ to observe the impact of changes in the proportion of construction waste recycling on system evolution and evolutionary paths. As can be seen from Figure 5a, when θ is small, the system evolution initially moves towards (0,0,1) and (0,1,1) but ultimately stabilizes at the ideal state of (1,1,1), achieving the stable strategy combination of {compliant disposal, investment participation, incentive, and constraint}. When θ is large, the system stabilizes at the non-ideal strategy combination of {illegal dumping, no investment, incentive, and constraint}. In other words, an increase in θ is not conducive to the achievement of tripartite cooperation. Figure 5b further illustrates that, in response to an increase in θ, construction waste recyclers react more quickly and adjust their strategies before construction enterprises.

The above analysis results indicate that the proportion of construction waste recycling plays a decisive role in whether recyclers participate. Although achieving complete recycling of construction waste is the ultimate environmental goal, based on the current recycling capabilities of recyclers, an excessively high recycling proportion will only result in them bearing costs that exceed their revenues. At that time, both they and construction enterprises will withdraw from the cooperation.

3.3.4. The Effect of Penalty Amount (F) Change on System Evolution

Keeping all other parameters constant, we assigned values of 0.5, 1, 2, 3, and 4 to F, respectively, to observe the impact of changes in fines on the evolution and evolutionary path of the system. As Figure 6a illustrates, when F is at a lower level, the system evolves steadily towards the direction of (0,0,1). However, as F increases, the system’s evolution shifts towards (1,1,1) via (1,0,1) and ultimately stabilizes at (1,1,1). In other words, increasing the fines for enterprises can facilitate the evolution of the game system towards an ideal state. Figure 6b demonstrates that as F increases, the cost of violating regulations due to illegal dumping also rises, forcing construction enterprises to adopt compliant disposal strategies. Moreover, the larger the F is, the faster their strategies converge to a stable solution. Since construction enterprises adopt a cooperative strategy, this reduces the cost of construction waste recycling for recyclers, increases the profits from investing in resource utilization projects, and reduces risks, ultimately prompting recyclers to follow the strategy changes of construction enterprises.

The above analysis suggests that the cost of illegality serves as a basis for construction enterprises’ strategic choices. The punishment mechanism within policies on construction waste management and resource utilization is reasonable and effective. When the government establishes construction enterprises as the core of the construction waste management system and increases the intensity of supervision and fines for their behavior, it can not only force enterprises to reduce waste emissions but also incentivize construction waste recyclers to adopt cooperative strategies, ultimately achieving tripartite cooperation.

3.3.5. The Effect of Changes in the Amount of Funding Subsidies (B) on the Evolution of the System

While keeping all other parameters constant, we assigned values of 2, 4, 8, and 16 to B, respectively, to observe the impact and extent of the government’s direct economic subsidies for construction waste recycling enterprises on the evolution and evolutionary path of the system. As Figure 7a illustrates, when B is relatively low, the system evolves stably towards the direction of (0,0,1). However, as B increases, the system’s evolution becomes unstable, lacking a stable solution. The content presented in Figure 7b also confirms that as B increases, the strategic choices of construction waste recycling enterprises shift from stabilizing at y = 0 to fluctuating between [0, 1]. Simultaneously, the government’s strategic choices also become unstable, oscillating around z = 1. Notably, changes in B have no impact on the strategic choices and probabilities of construction enterprises.

This suggests that the government’s incentive policy of providing direct economic subsidies only to construction waste recycling enterprises is ineffective in promoting the achievement of construction waste management and resource utilization goals. It cannot guarantee that construction enterprises and recyclers adopt long-term cooperative strategies and behaviors. The reason lies in the fact that direct subsidies can only alleviate the cost-benefit contradiction faced by construction waste recyclers during their participation in resource utilization projects, but they do not effectively incentivize or intervene with construction waste generators. The absence of construction enterprises leads to instability in the relationship of cooperation between the government and construction waste recycling enterprises. In addition, direct economic subsidies are provided beforehand, which creates the possibility for construction waste recyclers to engage in speculative behaviors to fraudulently obtain subsidies. This could also be a contributing factor to the ineffectiveness of the policy.

3.3.6. The Effect of Fixed Investment of Construction Waste Recyclers on System Evolution

While keeping all other parameters constant, we assigned values of 3, 2, 1, and 0 to C, respectively, to observe the impact of changes in the fixed costs of construction waste recycling utilization projects on the evolution and evolutionary path of the system. Notably, C = 0 represents an ideal scenario where the transition cost for traditional building material producers to become manufacturers of construction waste recycling products is zero. As Figure 8a illustrates, when C is relatively high, the system evolves stably towards the direction of (0,0,1). However, as C decreases, the system evolves towards a stable strategic combination of (1,1,1) through (0,1,1). The content presented in Figure 8b also confirms that when C decreases beyond a certain threshold, the larger C is, the faster x and y converge to a stable solution. Furthermore, construction waste recycling enterprises are more sensitive to changes in C, and their strategic adjustments precede those of construction enterprises.

This illustrates that excessively high upfront investment often serves as a barrier for construction waste recyclers to participate in resource recovery and utilization projects. By providing quality services and technological innovations and simplifying qualification review procedures, the government can lower the barriers to entry for the construction waste recycling industry, thereby facilitating the achievement of tripartite cooperation. Compared to direct economic subsidies, providing technical support and talent guarantees can better incentivize construction waste recyclers to participate in recycling utilization projects. Moreover, incentivizing construction waste recyclers through the reduction of barriers to entry represents a form of post hoc incentive, which helps to avoid fraudulent subsidy claims by business entities and eliminate the negative phenomenon of misappropriation of special funds.

To this point, this study has completed a sensitivity analysis of the parameters U, p, α, θ, F, B, and C included in the replication dynamic equations, establishing an interpretive framework that explains how changes in these parameters affect the process and outcome of strategic choices made by construction enterprises, construction waste recyclers, and the government. The results of the sensitivity analysis will serve as the primary source for the conclusions of this study and provide the basis and guidance for policy recommendations. Additionally, this study did not conduct a sensitivity analysis on parameters such as f, Q, V, P, d, D, N, and M. One reason is that some of these parameters are determined by the market and are endogenous, hardly affected by policy changes or the behavior of stakeholders, thus analyzing them lack practical significance. For example, the total demand for building materials in the market (d and D) and the amount of construction waste generated (Q) fall into this category. Another reason is that changes in some parameters do not affect the evolution and path of the system. Due to space limitations, the author did not choose to report on them, such as the price of traditional products (P) and the unit production cost of traditional products (N). If readers require information on the parameters not covered in this study and their sensitivity analysis results, they can contact the email address provided in this article for further inquiry.

3.4. Discussion

3.4.1. Evolutionary Equilibrium Based on Adjusted Assignment

In practice, to achieve policy effectiveness, few policy implementers adopt a single policy tool, and the combined use of multiple policy tools is considered a more effective implementation strategy. Based on this perspective, research needs to analyze the equilibrium state of the evolutionary game system when multiple parameters change simultaneously. Therefore, based on the research results from Section 3.3.1 and Section 3.3.2, the study adjusts the parameter values in a favorable direction simultaneously to observe the equilibrium outcomes of the evolutionary game system, thereby clarifying the effectiveness of policy tool combinations. The specific parameter adjustment process and simulation results are shown in

Table 4. Parameter adjustments and new arrays.

Parameter	α	p	U	f	θ	Q	F	V	B	P	d	D	N	C	M	L	S
Initial Value	0.1	20	0.5	2.5	0.5	4	0.5	5	1	40	10	15	20	6	5	3	0.5
Adjustment	+	+	+	0	0	0	+	0	0	0	0	0	0	−	0	0	0
The Adjusted Value	0.3	30	2	2.5	0.5	4	1	5	1	40	10	15	20	5	5	3	0.5

In this context, “+” represents increasing the value, “−” represents decreasing the value, and “0” represents no adjustment.

.

According to Figure 9, under the new set of conditions, the evolutionary game system ultimately stabilizes at the point (1,1,1), with the evolutionarily stable strategy combination being {compliant disposal, investment participation, incentive, and constraint}. At this point, construction enterprises, construction waste recyclers, and the government have reached a collaborative relationship on the issue of construction waste resource utilization, working together to achieve this goal. This also confirms that the research results in Section 3.3 of this study are valid.

Firstly, as the main producer of construction waste, construction enterprises are committed to taking reduction measures at the source, such as optimizing architectural design, improving construction techniques, and enhancing material utilization efficiency to reduce the generation of construction waste. At the same time, construction enterprises also adopt scientific and standardized methods to collect, classify, and store the generated construction waste, aiming to minimize the operational costs for recyclers.

Secondly, construction waste recyclers are responsible for the collection, screening, and processing of construction waste. They possess professional technology and equipment, enabling them to effectively separate and recycle renewable materials from construction waste. Additionally, recyclers also serve as building material manufacturers, converting recovered construction waste into recycled building materials, transforming waste into resources, and achieving circular utilization of resources. To facilitate collaboration, construction waste recyclers may cede some economic benefits to construction enterprises as an incentive and expression of gratitude for their cooperation.

Lastly, the government plays a pivotal role in this entire process. Its primary responsibility is to regulate the conflicting relationship between costs and benefits faced by construction enterprises and construction waste recyclers when participating in construction waste management through policy optimization and process design. It is through the government’s incentive measures such as rewards, fines, subsidies, and technical support that construction enterprises and construction waste recyclers obtain significant positive utility when engaging in environmental issues like construction waste management, effectively addressing the practical challenges of inefficient policy implementation and the absence of commercial entities.

3.4.2. The Availability of Sufficient Economic Income through the Sale of Recycled Building Waste Products Serves as a Crucial Influencing Factor in the Strategic Decisions Made by Construction Enterprises and Building Waste Recyclers

The findings of the system simulation analysis reveal that augmenting the collaborative profits of construction enterprises and building waste recyclers can be achieved by elevating the pricing and sales volume of recycled products or by intensifying penalties for illegal disposal of construction waste. This strategy facilitates the establishment of a tripartite collaboration and realizes the overarching goal of construction waste management. However, in contemporary construction industry practices, stakeholders such as developers, contractors, and consumers harbor biases against recycled building waste products and structures utilizing them. This results in their rejection in the end-consumer market, leading to price declines and the inability of recycled products to generate sufficient cash flow. Consequently, recyclers are unable to recoup their initial investments promptly, necessitating their withdrawal from collaboration and a return to traditional production methods. This disrupts the chain for the recycling and utilization of construction waste.

Therefore, in optimizing policies for construction waste management, the government must prioritize enhancing the economic incentives for commercial entities to engage in collaboration. This necessitates a shift away from a sole reliance on administrative intervention and instead an analysis of the profit models of construction enterprises and waste recyclers. Such an analysis should aim to provide guarantees, support, and services to expand the market share and sales of recycled products. Once the chain for construction waste management and resource utilization is completed, the market will become more receptive to recycled products, thereby augmenting the economic benefits for commercial entities.

3.4.3. Significant Participation Costs and Uncertainty Risks Are the Main Obstacles Hindering Construction Enterprises and Building Waste Recyclers from Choosing Cooperation Strategies

The outcomes of the system simulation analysis suggest that minimizing the costs incurred by recyclers in participating in construction waste management and resource utilization projects or augmenting the financial penalties for illegal practices by construction enterprises are both instrumental in attaining governance objectives. Unlike the protracted and indirect nature of economic benefits, costs exert a more profound influence on the short-term economic returns of commercial entities. Consequently, in numerous instances, the reluctance of construction enterprises and building waste recyclers to adopt cooperative strategies is often attributed to budgetary constraints or insufficient attention rather than disagreement with potential economic gains.

Accordingly, in the subsequent policy refinement process, the government must also deliberate on means to mitigate the entry barriers and transformation costs for commercial entities. This approach aims to ensure that their initial willingness to engage can seamlessly transition into long-term collaborative behavior, thereby enhancing the sustainability and effectiveness of construction waste management initiatives.

4. Conclusions

The minimization and resource utilization of construction waste represents a multifaceted societal challenge encompassing environmental protection, resource conservation, and economic development. Despite government efforts and academic research, long-standing issues like policy inconsistencies, ambiguous accountability, and insufficient incentives persist, impeding the enhancement of public value and societal welfare. The sustained engagement of construction enterprises and building material manufacturers, as both producers and recyclers of construction waste, is pivotal to attaining policy objectives. Thus, a paramount task for governments is to devise institutional frameworks and optimize execution processes to foster multi-stakeholder collaboration and unleash policy synergies. This study, adhering to the principle of mathematically modeling objective realities, constructs an evolutionary game model encompassing construction enterprises, recyclers, and the government, utilizing empirical data for systematic simulation analysis. The aim is to contribute towards resolving the aforementioned challenges.

The conclusions of this article are: Firstly, the implementation of China’s construction waste recycling and resource utilization policies is facing the issue of low willingness to participate among construction waste producers and recyclers, necessitating the optimization of government policies and the updating of processes. Secondly, increasing the benefits of participation for all parties, raising the prices of recycled products, reducing the cost of participation, implementing stricter regulatory and punitive measures, and so on are effective and feasible optimization contents and directions.

In light of the analysis, the following policy recommendations are proffered:

The current low-efficiency mode of construction waste recycling and resource utilization, reliant solely on government initiatives, necessitates urgent policy innovation and execution process optimization. Government departments, at all levels, must maintain resolute governance determination and provide sustained support for construction waste management until the governance goals are attained.

The specific operational steps include:

Establish a Dedicated Working Group: Form a specialized working group involving multiple departments, such as environmental protection, housing, urban-rural development, finance, etc., to be responsible for policy research and formulation.

Conduct Research and Evaluation: Carry out a comprehensive survey of the existing construction waste recycling and resource utilization models, assessing their efficiency and identifying areas of concern.

Develop a Policy Draft: Based on the research findings, formulate a policy draft that incorporates innovative policies and process optimizations.

Seek Public Opinions: Broadly solicit opinions from industries, enterprises, and the public through government websites, symposiums, and other channels.

Refine and Release the Policy: Modify and improve the policy based on the feedback received, officially release it, and clarify the implementation timeline and responsible departments.

Training and Promotion: Organize policy interpretation training sessions, strengthen publicity efforts towards enterprises and the public, and ensure a high level of policy awareness.

As the architect and navigator of the construction waste recycling and resource utilization system, government departments should lead by example, purchasing and utilizing recycled construction waste products. This not only ensures commercial entities reap economic benefits from their participation but also spurs societal and public consumption of related recycled products.

The implementation steps are as follows:

Government Procurement Preference: Establish a government procurement catalog, specifying the scope and standards for giving priority to purchasing products made from recycled construction waste.

Demonstration Project Construction: Select typical projects as demonstrations to showcase the application effects of recycled products, thereby attracting more enterprises and projects to participate.

Establish Incentive Mechanisms: Provide tax reductions, subsidies, and other incentive measures to enterprises and projects that use recycled products.

As the watchdog of construction waste management and reduction policies, the government must rigorously regulate and impose hefty fines on construction enterprises for waste discharge, internalizing the costs of environmental degradation and resource waste they inflict.

The necessary steps include:

Improving the Regulatory Framework: Revise or enact relevant laws and regulations to clarify the standards for construction waste discharge and the corresponding penalties.

Strengthening Enforcement: Increase the frequency of inspections and utilize modern technological means (such as drones and remote sensing monitoring) to enhance regulatory efficiency.

Public Exposure and Punishment: Publicly expose enterprises that illegally discharge waste and impose legal penalties such as heavy fines or suspension of operations.

Establishing a Whistleblower Reward System: Encourage public and media participation in oversight by offering rewards to those who report genuine violations.

Rather than direct subsidies, government departments should prioritize technical or talent support for recyclers, encouraging R&D innovation and other forms of assistance, thereby reducing the participation threshold in resource utilization projects. This also aims to mitigate fraudulent subsidy claims and ensure the effective utilization of government funds.

The following steps can be taken to achieve this:

Establish Research and Development Funds: The government can invest in setting up special research and development funds to support the research and innovation of technologies for construction waste recycling and resource utilization.

Establish a Platform for Industry-University-Research Cooperation: Promote collaboration between universities, research institutions, and enterprises to accelerate the transformation and application of scientific and technological achievements.

Talent Cultivation Plan: Develop a talent cultivation plan to strengthen the training and recruitment of professionals in related fields.

Technical Support and Consultation Services: Provide enterprises with technical consultation, project design, and other support services to lower the barriers to their participation.

Moreover, the government should minimize stringent administrative interventions and embrace flexible governance mechanisms. Studies indicate that recyclers are only willing to engage in construction waste resource utilization projects within their capabilities and under favorable policy environments. Therefore, fostering a favorable environment and ensuring recyclers’ autonomy is paramount.

Ultimately, the study establishes a tripartite cooperation governance model for construction waste and conducts numerical simulation validation to assess its effectiveness and sensitivity. The results indicate that factors such as the amount of construction waste generated (Q) and the disposal fee (f) have an impact on the probability of behavioral choices made by each participant, which in turn affects the equilibrium and stability of the tripartite cooperation system. These findings not only validate previous research suggesting the benefits of increasing disposal fees for construction waste generators but also further elaborate on how to enhance these fees and the subsequent effects of such changes on the behaviors of other participants.

Therefore, the advantage of this paper over existing research lies in its more thorough revelation of the inherent mechanisms of cooperative governance of construction waste, shedding light on numerous perplexing issues faced by governments and enterprises in reality and enhancing the depth of the research. Given that the mathematical model constructed in this paper profoundly reflects objective realities, governments can obtain detailed operational measures rather than general policy recommendations, which is also one of the innovative aspects of this paper.

Additionally, it must be acknowledged that this study still has some limitations, which are difficult to address in the short term due to current practical conditions and the author’s capabilities, among other factors, and will need to be resolved in future research. For instance, while the author has established a three-way cooperation mechanism involving the government, construction waste producers, and construction waste recyclers, it is also recognized that buyers of recycled materials, private investors, loan banks, and other stakeholders have influences on the recycling and utilization of construction waste. However, under current conditions, we are temporarily unable to clarify their mechanisms of action, and thus, these issues will need to be addressed when future conditions permit. Furthermore, as the research on carbon emissions and carbon footprints from construction waste is still ongoing, this paper believes that integrating the resource utilization of construction waste with macro-topics such as carbon neutrality and carbon targets will be a major research direction in the future and also a way to deepen the research.