Promoting Multi-Agent Collaborative Governance of Construction Safety Risks: Considering Strategic Heterogeneities of Projects with Different Costs

Abstract

Numerous safety hazards in construction projects can readily cause safety accidents. While collaborative governance among stakeholders is vital for construction safety, it is hampered by interest-related factors. Evolutionary game theory is an excellent tool for analyzing participants’ behavioral decisions based on interest factors, and it is employed in this study to explore strategies for promoting collaborative governance. However, existing studies rarely mention the concept of collaborative governance of construction safety risks, seldom focus on construction payment disputes between owners and contractors, and barely take into account the differences in interests and decisions faced by stakeholders under projects of varying costs. Based on this, an evolutionary game model among the government, owner and contractor is established by taking China’s construction industry as an example, and MATLAB numerical simulation is conducted. First, the heterogeneity of the laws of strategy evolution under different cost levels was verified. Subsequently, cost levels were divided into two major categories and four subcategories based on strategy evolution results, and sensitivity analysis was conducted for each corresponding scenario. It was found that rewards for owners and contractors are barely effective, while cutting government regulatory costs and boosting positive governmental incentives generally play a positive role. The effects of penalties for inadequate safety investment and safety accidents on collaboration differ across project costs. Nevertheless, collaborative governance can be achieved via reasonable parameter optimization. This study addresses the critical issue of interest factors hindering collaborative governance, and provides a critical perspective for promoting construction safety and the sustainability of the construction industry. Cost-stratified analysis reduces overly definitive suggestions, offering valuable insights for both theory and practice.

1. Introduction

Construction projects are labor-intensive, operate in dynamic environments, and involve complex processes, creating numerous safety risks and uncertainties that can easily lead to accidents [1,2]. Frequent construction safety accidents occur worldwide, resulting in numerous casualties and a series of losses, making the construction industry a widely recognized high-risk industry [3]. Enhancing safety management and promoting safe production play an important role in the sustainable development of the construction industry [4,5]. Work safety in the construction industry has received extensive attention from many countries, and the work safety governance system is constantly being improved. However, construction safety accidents still occur frequently. The key reasons lie in management dominated by “post-event response” and insufficient consideration of the real-time and dynamic nature of the construction process; therefore, proactive governance of safety risk factors during the construction process is crucial [6,7].

The main stakeholders in safety-risk governance are typically the government, the contractor and the owner. The government is responsible for formulating construction-safety policies and regulations, supervising on-site safety conditions, and rewarding or penalizing enterprises [8,9]. The contractor must manage site safety, maintain order, and prevent casualties [10,11]. In addition to construction management, the owner is also obliged to pay the contract sum, which usually covers construction-safety-related costs [12,13,14]. Organizational factors, managerial factors, legal factors, environmental factors, and other categories of factors are generally identified as influencing factors of construction safety, and these factors are interrelated with one another [15]. Given the complexity, relying on a single actor to manage the continuously changing safety risks is challenging; effective solutions require collaborative governance among the stakeholders [16,17,18].

Collaboration in construction-safety-risk governance faces resistance, and conflicts over benefits and interests need to be taken into account. Specifically, stakeholders may be unwilling to invest in safety-risk governance because of cost–benefit considerations [19,20]; disputes over payments may also arise between the owner and the contractor [13], while the government’s priority—public security and social stability—differs from the cost–benefit calculus of construction enterprises [21]. Existing evidence indicates that factors such as the costs incurred by strengthened regulation and the punitive mechanisms implemented can influence the behavioral decision-making of governments and construction enterprises [22,23]. Evidently, the actions of each stakeholder bear on the extent to which collaborative governance can be realized. These intricate interest interdependencies constitute a structural barrier to stakeholder collaborative governance, rendering their resolution an issue of paramount urgency. However, existing studies rarely address the owner as a key stakeholder at the safety management level, and the interests associated with this stakeholder require further consideration. Against the backdrop of continuous technological advancement, safety accidents still occur frequently [24], and exploring the collaborative governance of safety risks from the perspective of benefits may provide a good explanation. Evolutionary game theory coupled with numerical simulation has proven useful for disentangling multi-stakeholder interest configurations and behavioral patterns and has begun to appear in construction-management studies; accordingly, it will inform the methodological design of this study.

Among projects with different cost scales, the relevant interests in safety risk governance may differ. For instance, analyses of projects in multiple regions, including Singapore, Spain, and Turkey, show that safety-management costs customarily fall within a certain band of total project cost [25,26,27,28]; In China, it is explicitly stipulated that safety production expenses should be extracted at a certain percentage of the total construction cost [14]. Furthermore, project costs have an extremely wide distribution range, and conducting single-factor sensitivity analysis directly makes it difficult to cover various practical scenarios in safety risk governance. Based on the above reasons, it is necessary to conduct a classified exploration according to the project cost situation. While cost is not the sole factor, a systematic investigation is still required into the strategy evolution mechanisms and collaborative governance effects under different cost scales, given the varying benefit scenarios associated with different cost levels as well as the flexible and widely ranging magnitude of costs. In addition, a brief illustration will be provided regarding how to refer to the findings of this study when other factors—such as changes in project complexity—are taken into consideration.

The rest of this study is organized as follows: Section 2 summarizes the relevant studies on collaborative governance and the game of safety behavior, and further clarifies the work and innovations of this paper. In Section 3, an evolutionary game model for collaborative governance of construction safety risks is constructed. By analyzing the evolutionarily stable strategy (ESS), the feasibility of joint governance is preliminarily explored. In Section 4, this study verifies the heterogeneity of behavioral decisions under different project costs through numerical simulations, classifies them based on evolutionary paths, and conducts single-factor sensitivity analysis in each category, respectively. In Section 5, strategies for enhancing collaborative risk governance under varying cost scales are compared and analyzed.

2. Literature Review

2.1. Collaborative Governance in Constuction and Safety

The term “collaborative governance” can be traced back to at least the end of the 20th century. Scholars have attempted to define it from specific fields or contexts; yet, collaborative governance generally refers to a governance arrangement centered on public affairs. It involves public institutions in collaboration with non-state stakeholders, and adopts formal, consensus-oriented, and deliberative collective decision-making processes for joint participation and decision-making [29]. In recent years, the concept of collaborative governance has been applied to construction management. Shen et al. (2023) [30] explored the resource utilization rate of construction demolition waste from the perspective of interest balance, and determined collaborative goals and reward or punishment mechanisms. Tang et al. (2025) [31] investigated the collaborative governance mechanism and optimization strategies for construction waste resource utilization based on actor-network theory, structural equation models, and system dynamics. Liu et al. (2021) [32] studied the mechanisms for effective collaborative governance in urban renewal projects. These studies have confirmed the significant role of collaborative governance in construction management.

In the field of safety management, existing research on collaborative governance has also explored this topic from various perspectives. Guo and Li (2022) [33] empirically examined the institutional system of collaborative governance for community public safety during the COVID-19 outbreak. Using network analysis, Ma et al. (2024) [34] validated the pivotal role of the Arctic Council in facilitating collaborative governance for Arctic shipping safety. Yang et al. (2022) [35] leveraged social network analysis to explore the synergistic mechanisms of tower crane safety governance. It can be observed that collaborative governance also plays a pivotal role in safety management. The implementation of safety collaborative governance hinges on the behavioral decisions of stakeholders. Based on an evolutionary game model comprising local governments, social organizations and the public, Nan et al. (2024) [36] explored the behavioral strategies and influencing factors in the management of Public Health and Health Engineering (MPHE), providing a reference for the improvement of collaborative governance, Li et al. (2025) [18] adopted evolutionary game theory to explore the collaborative governance mechanisms and promotional strategies among stakeholders in China’s occupational safety sector. Relatively little research has addressed the collaborative governance of safety risks in construction processes. Furthermore, few studies have examined this issue through the lens of stakeholders’ payoffs and behavioral strategies. Accordingly, there is a clear need to analyze safety collaborative governance within the construction engineering sector from a game-theoretic perspective.

Existing game-theoretic research on occupational safety centers its analysis on governments, enterprises, and employees as core stakeholders [18]. Nevertheless, construction safety entails greater complexity, with its key stakeholders potentially diverging from those in standard occupational safety settings. First and foremost, although construction workers often appear to be the direct cause of accidents in many cases, they generally possess relatively limited professional skills and can hardly exert a decisive role during the construction process. By contrast, construction enterprises play a fundamental role in construction safety [10,37,38]. Second, the construction process is rarely undertaken by a single independent enterprise; it requires close collaboration between at least the owner and the contractor. The conflicts of interest between these two parties, though seldom examined from a safety perspective, are critically important. In its regulatory oversight, the government must naturally take into account the respective responsibilities of both the owner and the contractor. Given the distinctive characteristics of stakeholders and interest linkages in construction safety governance, an independent game-theoretic analysis is required.

2.2. Evolutionary Game in Construction Safety Management

Remarkable progress has been made in the field of construction safety risk management, encompassing risk factor identification, safety culture, safety assessment, intelligent safety management, and other related domains [39,40,41]. Luo et al. (2022) [42] integrated the structure entropy weight method, matter-element theory, and evidence theory to investigate the construction safety risk assessment of prefabricated subway stations. Kou et al. (2025) [43] adopted methods including AHP, DEMATEL, and the extension cloud model to investigate the safety resilience assessment of civil engineering construction projects. Mostofi and Toğan (2023) [44] focused on improving the performance of construction safety prediction, in which a multi-head graph attention network (GAT) and a novel sparse construction safety network were applied. These findings undoubtedly contribute to the control of construction safety risks. Nevertheless, their implementation still depends on the behaviors of stakeholders. From the perspective of industrial sustainability, the joint and active participation of stakeholders is highly desirable. Existing research has validated that human behavior constitutes the primary contributor to safety incidents, with interest factors standing as a key lens for examining stakeholders’ behavioral decisions [10,22]. Classical systems engineering, decision-making modeling methods, and artificial intelligence algorithms employed in existing studies have played a significant role in the quantification and assessment of safety risks. However, these methods can hardly address the behavioral and collaborative issues of stakeholders under the influence of interest factors. A game-theoretic perspective is therefore more appropriate.

The evolutionary game approach, based on traditional game theory, takes into account the bounded rationality of players and allows for the dynamic adjustment of their strategies. It was initially applied in the biological field and later adopted by more other disciplines, including the field of construction management [9,45]. For example, Ding et al. (2023) [46] used evolutionary game theory to explore the complex relationships among stakeholders in the construction industry during the adoption of blockchain technology. Huang et al. (2024) [47] applied evolutionary game theory to investigate the decision-making problems of contractors facing project claims. These successful examples demonstrate that the stakeholders in construction projects are boundedly rational and that there are interactive interests among them. A number of scholars have already applied evolutionary game theory to the behavioral research of construction safety management.

Scholars have explored the government’s supervision of corporate management behaviors from various perspectives. Gong et al. (2021) [48] constructed a dynamic safety investment supervision mechanism and used evolutionary game theory to explore the decision-making interactions among stakeholders under both the current static supervision mechanism and the proposed dynamic supervision mechanism. Ning et al. (2022) [22] utilized evolutionary game theory to explore the decision-making of government and enterprises in the supervision of safety behaviors under both the entity responsibility mechanism and the third-party participation mechanism. Jiang et al. (2023) [9] established a tripartite evolutionary game model among government regulatory agencies, supervisory engineers, and general contractors to study the construction safety supervision mechanism in China. Zhang et al. (2023) [23] constructed an evolutionary game model between government regulatory agencies and construction parties regarding the dynamic supervision of construction safety, aiming to explore the issues of safety supervision in prefabricated building construction. Zhang et al. (2025) [49] constructed an evolutionary game model among leasing enterprises, engineering contractors, and government departments to address the issue of insufficient safety investment in tower cranes.

The strategic interactions between enterprises and construction workers, as well as among the government, enterprises, and workers, have also garnered significant attention. For instance, Guo et al. (2021) [11] established a tripartite evolutionary game model among the government, construction units, and workers to explore strategies for promoting construction safety education. Wu et al. (2022) [10] posited that general contractors and construction workers are key stakeholders in construction safety management, and constructed an evolutionary game model between these two parties to explore their safety behavior strategies. Huang et al. (2022) [50] constructed a bilateral evolutionary game model consisting of workers and managers to explore the evolutionary mechanism of workers’ unsafe behaviors and their control strategies. Yue et al. (2025) [20] identified the key factors influencing the decision-making behaviors of employers, contractors, supervisors, and construction workers through questionnaires and interviews, and then employed evolutionary game theory to simulate the behaviors of these stakeholders and proposed recommendations to enhance safety supervision.

The aforementioned studies each have their own focus in the selection of stakeholders and the setting of variables. For example, Gong et al. (2021) [48] considered the competitive relationships among different contractors. Jiang et al. (2023) [9] elaborated on the role of supervising engineers and related rent-seeking issues. Yue et al. (2025) [20] meticulously examined the hidden costs associated with construction safety. Nevertheless, some common interests in previous studies can still be summarized, which mainly include (1) The costs of safety supervision incurred by the government and construction enterprises; (2) The positive incentives received by the government and contractors when their safety performance is good; (3) The general penalties imposed on contractors for inadequate supervision during the construction process; (4) The losses caused by safety accidents and the penalties imposed on the responsible parties.

2.3. Knowledge Gap and Research Design

Existing studies have made significant contributions to areas such as construction safety management behaviors and collaborative governance of construction projects, but there are still some issues to be further discussed. First, existing research on collaborative governance in construction has paid less attention to construction safety risk governance. Due to the unique nature of construction projects and the complex interactions among stakeholders, it differs from safety studies in other fields, making it necessary to explore this as a specialized research topic. Second, existing studies lack a precise definition of the interest conflicts among stakeholders: the application premise of game theory is that there exist interest conflicts among participants, and such conflicts serve as an important basis for model assumptions, which should be clarified before model construction. Thirdly, existing studies pay insufficient attention to the guarantee role of owners’ safety investment: owners and contractors may have disputes over project funds, and safety investment is usually included in project funds, which is a key factor to be prioritized in interest relationships. Finally, existing research tends to propose deterministic strategies and suggestions, with insufficient stratified discussions for specific scenarios. For example, in projects of different cost scales, the evolutionary mechanisms of stakeholders’ behavioral strategies may vary. In terms of methodological application in simulation analysis, when there exist variables with an extremely wide range of variation whose fluctuation magnitude is notably higher than that of other variables, the results derived from single-factor sensitivity analysis can hardly cover all potential scenarios.

To sum up, this study uses evolutionary game theory to explore strategies for promoting the collaborative governance of construction safety risks. In addition to the respective costs and benefits of each stakeholder, it also focuses on the interest conflicts regarding safety investment between owners and contractors, and takes into account the differences in interest goals between government departments and enterprises. The novelty of this study lies in: (1) It proposes the research objective of collaborative governance of safety risks in construction projects, rather than merely focusing on the evolution of behavioral strategies of a single stakeholder, as the former is more crucial for risk control and sustainable construction. (2) This study considers the constraints of project owners’ safety investment behaviors on safety risk governance and accounts for the interest conflicts between project owners and contractors regarding project payments. (3) This study identifies the significant correlation between construction project cost and safety investment, as well as the wide variability of cost ranges. Such factors may lead to divergent collaborative governance mechanisms across different cost levels. Accordingly, we conduct scenario-based sensitivity analysis and attempt parameter optimization.

3. Evolutionary Game Analysis

3.1. Model Description and Basic Assumptions

This study constructs a tripartite evolutionary game model among the government, the owner, and the contractor, aiming to explore the strategic interaction relationships among the three parties and further explore strategies to promote collaborative governance. The assumptions and parameter settings of the model take the Chinese context as an example. In this model, the owner is required to provide sufficient safety investment for the contractor, who must reasonably utilize these funds for construction safety management, and the government has the obligation to supervise them [14]. The assumptions were as follows:

(1)

The participants in the evolutionary game model include the government, the owner, and the contractor. All three parties possess bounded rationality. They can independently select their own behavioral strategies and dynamically adjust them based on the pay-off situation.

(2)

Each participant has only two evolutionary strategies to choose from. Specifically, the government’s strategy set is (strict supervision, lenient supervision), the owner’s strategy set is (proactive investment, reactive investment), and the contractor’s strategy set is (active management, passive management). The probability that the government chooses strict supervision is x, and the probability of choosing lenient supervision is 1 − x. The probability that the owner chooses proactive investment is y, and the probability of choosing reactive investment is 1 − y. The probability that the contractor chooses active management is z, and the probability of choosing passive management is 1 − z. It is regarded as achieving collaborative governance when $x=y=z=1$. In view of the strict current regulation on construction qualifications, this study excludes capacity-level issues and defines the simultaneous active participation of the three parties as the achievement of collaboration.

(3)

The cost of safety investment is set according to the “Measures for the Extraction and Use of Enterprise Production Safety Expenses.” Assuming the construction cost of the project is $C$, the minimum extraction ratio of production safety expenses is ${\alpha }_1$ [14]. Due to the complexity of the construction site, the actual safety investment may be higher than the minimum standard. It is not unreasonable to assume that under proactive safety investment, the extraction ratio of production safety expenses can reach ${\alpha }_2({\alpha }_2\ge {\alpha }_1)$ [51,52].

3.2. Parameters and Pay-Off Calculation

Based on the basic assumptions, this model encompasses a total of eight strategy combinations. Next, we calculate the payoffs for the government, owner, and contractor for each combination. In this process, it is convenient to introduce the relevant parameters. Once a parameter is introduced, it will not be reintroduced in subsequent text to conserve space.

Strategy Combination {Strict Supervision, Proactive Investment, Active Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G1}$, $P_{O1}$, and $P_{N1}$, respectively. At this point, the cost of government supervision is $S_1$, the owner provides safety production expenses in accordance with the actual project as ${\alpha }_{2}C$, and the contractor fully utilizes the expenses for safety production. Assuming that safety accidents do not occur in this scenario [10,20]. Given the excellent synergistic effect achieved under this strategy, the owner and the contractor, respectively, receive government rewards $A_1$ and $A_2$, and the government’s credibility enhanced by $R$. Thus, $P_{G1}=R-S_1-A_1-A_2$, $P_{O1}=A_1-{\alpha }_{2}C$, $P_{N1}=A_2$.

Strategy Combination {Strict Supervision, Proactive Investment, Passive Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G2}$, $P_{O2}$, and $P_{N2}$, respectively. The owner provides safety production expenses amounting to ${\alpha }_{2}C$, but the contractor only invests according to the minimum standard of ${\alpha }_{1}C$. The contractor will face a penalty from the government, which is $k({\alpha }_{2}C-{\alpha }_{1}C)$$(1.2\le k\le 1.5)$ [23,48]. Additionally, let the probability of an accident be denoted as $\epsilon$, the loss due to an accident as $L$, and in the event of an accident, the contractor faces an administrative fine from the government, denoted as $F_2$ [53]. The cost of accident investigation is denoted as $S_C$. Thus, $P_{G2}=-S_1+k({\alpha }_{2}C-{\alpha }_{1}C)+\epsilon F_2-\epsilon S_C$, $P_{O2}=-{\alpha }_{2}C$, $P_{N2}=({\alpha }_2-{\alpha }_1)C-\epsilon (L+F_2)-k({\alpha }_{2}C-{\alpha }_{1}C)$.

Strategy Combination {Strict Supervision, Reactive Investment, Active Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G3}$, $P_{O3}$, and $P_{N3}$, respectively. The owner invests only according to the minimum standard, while the contractor increases investment on their own initiative to ensure safety. Upon discovery through strict government supervision, the owner will be required to provide compensation to the contractor at a multiple of $\lambda$. Under this hypothetical scenario, sufficient safety investment can barely ensure the minimum level of safety; however, given that construction safety requires collaboration among all stakeholders, safety performance in such cases fails to meet the reward criteria. Therefore, $P_{G3}=-S_1+k({\alpha }_{2}C-{\alpha }_{1}C)$, $P_{O3}=-{\alpha }_{1}C-k({\alpha }_{2}C-{\alpha }_{1}C)-\lambda ({\alpha }_{2}C-{\alpha }_{1}C)$, $P_{N3}={\alpha }_{1}C-{\alpha }_{2}C+\lambda ({\alpha }_{2}C-{\alpha }_{1}C)$.

Strategy Combination {Strict Supervision, Reactive Investment, Passive Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G4}$, $P_{O4}$, and $P_{N4}$, respectively. In the event of an accident, the owner shall bear a loss proportion of $\omega$, while the contractor shall bear a proportion of $1-\omega$. The additional administrative fine faced by the project owner is $F_1$ [53]. Thus, $P_{G4}=-S_1+2k({\alpha }_{2}C-{\alpha }_{1}C)+\epsilon (F_1+F_2)-\epsilon S_C$, $P_{O4}=-{\alpha }_{1}C-k({\alpha }_{2}C-{\alpha }_{1}C)-\epsilon (\omega L+F_1)$, $P_{N4}=-\epsilon [(1-\omega )L+F_2]-k({\alpha }_{2}C-{\alpha }_{1}C)$.

Strategy Combination {Lenient Supervision, Proactive Investment, Active Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G5}$, $P_{O5}$, and $P_{N5}$, respectively. At this point, the cost of government regulation is $\beta S_1(0<\beta <1)$. Safety investments can be guaranteed, so let us assume that no accidents occur [10,20]. Therefore, $P_{G5}=-\beta S_1$, $P_{O5}=-{\alpha }_{2}C$, $P_{N5}=0$.

Strategy Combination {Lenient Supervision, Proactive Investment, Passive Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G6}$, $P_{O6}$, and $P_{N6}$, respectively. In the event of an accident, the government assumes responsibility for the cost of losses, with the transfer coefficient being denoted as e [22,48]. So that $P_{G6}=-\beta S_1-\epsilon eL+\epsilon F_2-\epsilon S_C$, $P_{O6}=-{\alpha }_{2}C$, $P_{N6}=({\alpha }_2-{\alpha }_1)C-\epsilon (L+F_2)$.

Strategy Combination {Lenient Supervision, Reactive Investment, Active Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G7}$, $P_{O7}$, and $P_{N7}$, respectively. $P_{G7}=-\beta S_1$, $P_{O7}=-{\alpha }_{1}C$, $P_{N7}=({\alpha }_1-{\alpha }_2)C$.

Strategy Combination {Lenient Supervision, Reactive Investment, Passive Management}: It is assumed that the payoffs for the government, the owner, and the contractor are denoted as $P_{G8}$, $P_{O8}$, and $P_{N8}$, respectively. $P_{G8}=-\beta S_1-\epsilon eL+\epsilon (F_1+F_2)-\epsilon S_C$, $P_{O8}=-{\alpha }_{1}C-\epsilon (\omega L+F_1)$, $P_{N8}=-\epsilon [(1-\omega )L+F_2]$.

3.3. Model Establishment

Based on the payoff calculations described above, the evolutionary game model can be established, with the payoff matrix as shown in

Table 1. Payoff Matrix of the Evolutionary Game Model.

		Owner	Contractor
			Active Management z	Passive Management 1 − z
Government	Strict Supervision x	Proactive Investment y	$(P_{G1},P_{O1},P_{N1})$	$(P_{G2},P_{O2},P_{N2})$
		Reactive Investment 1 − y	$(P_{G3},P_{O3},P_{N3})$	$(P_{G4},P_{O4},P_{N4})$
	Lenient Supervision 1 − x	Proactive Investment y	$(P_{G5},P_{O5},P_{N5})$	$(P_{G6},P_{O6},P_{N6})$
		Reactive Investment 1 − y	$(P_{G7},P_{O7},P_{N7})$	$(P_{G8},P_{O8},P_{N8})$

. In evolutionary game theory, the replicator dynamics equation is a fundamental tool for describing how strategies evolve within a population. According to previous studies, the process of calculating the replicator dynamics equation is necessary before determining the ESS [9,23].

Firstly, let the expected payoffs for the government’s strict supervision and lenient supervision be $E_{11}$ and $E_{12}$, respectively, and assume that the average expected payoff is $E_1$. Then, let $E_{21}$, $E_{22}$, and $E_2$ represent the expected payoffs for the owner’s proactive investment, the owner’s reactive investment, and the owner’s average expected payoff, respectively. Finally, Let $E_{31}$, $E_{32}$, and $E_3$ represent the expected payoffs for the contractor’s active management, the contractor’s passive management, and the contractor’s average expected payoff, respectively. Furthermore, let $F(x)$, $F(y)$, and $F(z)$ be the replicator dynamics equations for the government, the owner, and the contractor, respectively.

The specific calculation process for the replicator dynamics equations is as follows: First, based on Formulas (1)–(3), the replicator dynamics equation for the government’s strategy selection is calculated, as shown in Formula (4).

$$E_{11}=yz{P}_{G1}+y(1-z)P_{G2}+(1-y)z{P}_{G3}+(1-y)(1-z)P_{G4}$$

(1)

$$E_{12}=yz{P}_{G5}+y(1-z)P_{G6}+(1-y)z{P}_{G7}+(1-y)(1-z)P_{G8}$$

(2)

$$E_1=x{E}_{11}+(1-x)E_{12}$$

(3)

$$\begin{array}{c}F(x)=x(E_{11}-E_1)=x(x-1)[S_1-\beta S_1+2C{\alpha }_{1}k-2C{\alpha }_{2}k-\epsilon eL+(A_1+A_2-R)yz\\ +(C{\alpha }_{2}k-C{\alpha }_{1}k)y+(C{\alpha }_{2}k+\epsilon eL-C{\alpha }_{1}k)z]\end{array}$$

(4)

Then, based on Formulas (5)–(7), the replicator dynamics equation for the owner’s strategy selection is calculated, as shown in Formula (8).

$$E_{21}=xz{P}_{O1}+x(1-z)P_{O2}+(1-x)z{P}_{O5}+(1-x)(1-z)P_{O6}$$

(5)

$$E_{22}=xz{P}_{O3}+x(1-z)P_{O4}+(1-x)z{P}_{O7}+(1-x)(1-z)P_{O8}$$

(6)

$$E_2=y{E}_{21}+(1-y)E_{22}$$

(7)

$$\begin{array}{r}F(y)=y(E_{21}-E_2)=y(1-y)[C{\alpha }_1-C{\alpha }_2+\epsilon F_1+\epsilon \omega L-(\epsilon F_1+\epsilon \omega L)z\\ +(A_1+C\lambda {\alpha }_2-C\lambda {\alpha }_1)xz+(C{\alpha }_{2}k-C{\alpha }_{1}k)x]\end{array}$$

(8)

Lastly, based on Formulas (9)–(11), the replicator dynamics equation for the contractor’s strategy selection is calculated, as shown in Formula (12).

$$E_{31}=xy{P}_{N1}+x(1-y)P_{N3}+(1-x)y{P}_{N5}+(1-x)(1-y)P_{N7}$$

(9)

$$E_{32}=xy{P}_{N2}+x(1-y)P_{N4}+(1-x)y{P}_{N6}+(1-x)(1-y)P_{N8}$$

(10)

$$E_{32}=xy{P}_{N2}+x(1-y)P_{N4}+(1-x)y{P}_{N6}+(1-x)(1-y)P_{N8}$$

(11)

$$\begin{array}{r}F(z)=z(E_{31}-E_3)=z(1-z)[C{\alpha }_1-C{\alpha }_2+\epsilon F_2+(1-\omega )\epsilon L+\epsilon \omega Ly\\ +(A_2-C\lambda {\alpha }_2+C\lambda {\alpha }_1)xy+(C{\alpha }_{2}k-C{\alpha }_{1}k+C\lambda {\alpha }_2-C\lambda {\alpha }_1)x]\end{array}$$

(12)

3.4. Stable Strategy Analysis

From $F(x)=0$, $F(y)=0$, and $F(z)=0$, we can obtain the equilibrium points of the system: $E_1(0,0,0)$, $E_2(1,0,0)$, $E_3(0,1,0)$, $E_4(0,0,1)$, $E_5(1,1,0)$, $E_6(1,0,1)$, $E_7(0,1,1)$ and $E_8(1,1,1)$. To determine whether these equilibrium points can become ESS, further calculations are required. According to previous research, the Jacobian matrix is composed of the first-order partial derivatives of the system. By calculating the eigenvalues of the Jacobian matrix, the local stability of the system at the equilibrium points can be determined. If all the real parts of the eigenvalues are less than zero, the corresponding equilibrium point is locally asymptotically stable [10,54,55]. The Jacobian matrix for this tripartite evolutionary game is as follows:

$$J=\left[\begin{array}{ccc}\partial F(x)/\partial x& \partial F(x)/\partial y& \partial F(x)/\partial z\\ \partial F(y)/\partial x& \partial F(y)/\partial y& \partial F(y)/\partial z\\ \partial F(z)/\partial x& \partial F(z)/\partial y& \partial F(z)/\partial z\end{array}\right]$$

(13)

Next, substitute each of the 8 equilibrium points into the Jacobian matrix and calculate the eigenvalues of the resulting matrices. The calculation results are shown in

Table 2. Eigenvalues of the Jacobian matrix.

Equilibrium Point	Eigenvalues
	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$
(0, 0, 0)	$C{\alpha }_1-C{\alpha }_2+\epsilon F_1+\epsilon L\omega$	$C{\alpha }_1-C{\alpha }_2+\epsilon F_2+\epsilon L-\epsilon \omega L$	$\begin{array}{l}\beta S_1-S_1-2C{\alpha }_{1}k\\ +2C{\alpha }_{2}k+\epsilon eL\end{array}$
(1, 0, 0)	$\begin{array}{l}{S}_1-\beta S_1+2C{\alpha }_{1}k\\ -2C{\alpha }_{2}k-\epsilon eL\end{array}$	$\begin{array}{l}C{\alpha }_1-C{\alpha }_2+\epsilon F_1-kC{\alpha }_1\\ +kC{\alpha }_2+\epsilon \omega L\end{array}$	$\begin{array}{l}C{\alpha }_1-C{\alpha }_2+\epsilon F_2+\epsilon L-\lambda C{\alpha }_1\\ +\lambda C{\alpha }_2-kC{\alpha }_1+kC{\alpha }_2-\epsilon \omega L\end{array}$
(0, 1, 0)	$C{\alpha }_2-C{\alpha }_1-\epsilon F_1-\epsilon \omega L$	$C{\alpha }_1-C{\alpha }_2+\epsilon F_2+\epsilon L$	$\beta S_1-S_1-C{\alpha }_{1}k+C{\alpha }_{2}k+\epsilon eL$
(0, 0, 1)	$C{\alpha }_1-C{\alpha }_2$	$\beta S_1-S_1-kC{\alpha }_1+kC{\alpha }_2$	$C{\alpha }_2-C{\alpha }_1-\epsilon F_2-\epsilon L+\epsilon \omega L$
(1, 1, 0)	$\begin{array}{l}{S}_1-\beta S_1+C{\alpha }_{1}k\\ -C{\alpha }_{2}k-\epsilon eL\end{array}$	$\begin{array}{l}C{\alpha }_2-C{\alpha }_1-\epsilon F_1+kC{\alpha }_1\\ -kC{\alpha }_2-\epsilon \omega L\end{array}$	$\begin{array}{l}{A}_2+C{\alpha }_1-C{\alpha }_2+\epsilon F_2\\ +\epsilon L-kC{\alpha }_1+kC{\alpha }_2\end{array}$
(1, 0, 1)	$S_1-\beta S_1+kC{\alpha }_1-kC{\alpha }_2$	$\begin{array}{l}{A}_1+C{\alpha }_1-C{\alpha }_2-\lambda C{\alpha }_1\\ +\lambda C{\alpha }_2-kC{\alpha }_1+kC{\alpha }_2\end{array}$	$\begin{array}{l}C{\alpha }_2-C{\alpha }_1-\epsilon F_2-\epsilon L+\lambda C{\alpha }_1\\ -\lambda C{\alpha }_2+kC{\alpha }_1-kC{\alpha }_2+\epsilon \omega L\end{array}$
(0, 1, 1)	$C{\alpha }_2-C{\alpha }_1$	$C{\alpha }_2-C{\alpha }_1-\epsilon F_2-\epsilon L$	$R-A_2-A_1-S_1+\beta S_1$
(1, 1, 1)	$A_1+A_2-R+S_1-\beta S_1$	$\begin{array}{l}C{\alpha }_2-C{\alpha }_1-A_2-\epsilon F_2\\ -\epsilon L+kC{\alpha }_1-kC{\alpha }_2\end{array}$	$\begin{array}{l}C{\alpha }_2-C{\alpha }_1-A_1+\lambda C{\alpha }_1\\ -\lambda C{\alpha }_2+kC{\alpha }_1-kC{\alpha }_2\end{array}$

.

Based on the eigenvalues corresponding to each equilibrium point, we can preliminarily exclude some equilibrium points that cannot become ESS. Given that $C{\alpha }_2-C{\alpha }_1\ge 0$, $1.2\le k\le 1.5$, $\lambda >0$, and $\epsilon L>\epsilon \omega L$, the strategies (0, 1, 1), (1, 0, 1), (1, 1, 0), and (1, 0, 0) are unable to constitute evolutionary stable strategies. The remaining equilibrium points all have the potential to become ESS. Specifically, if $R+\beta S_1>A_1+A_2+S_1$ is satisfied, (1, 1, 1) can become ESS. This indicates that collaborative governance of safety risks is achievable at any cost level. However, the equilibrium point that ultimately becomes ESS depends on parameter values under realistic conditions and the level of construction cost. In the next section, numerical simulations will explore the level of coordination between stakeholders and investigate how collaborative governance can be achieved.

4. Numerical Simulation

4.1. Data and Parameters

Before conducting simulation analysis, initial values are assigned to the variables. Data can be obtained from policy and legal documents, government website data, or previous studies. Parameter values vary across different studies. To avoid discrepancies caused by non-uniform units of variable values, we have made adjustments in light of the actual situation. The final assignment results are as follows. Firstly, let $S_1=17$, $A_1=11.9$, $A_2=11.9$, $k=1.35$, $L=50$, $\epsilon =0.03$, $\beta =0.5$, $e=1$, $R=10.2$ and $\omega =0.5$ [9,10,20,22,23,48,56,57]. Then, according to the “Measures for the Extraction and Use of Enterprise Production Safety Expenses,” we set ${\alpha }_1=3\%$. The actual safety expense extraction ratio varies depending on the project situation, and we temporarily set ${\alpha }_2=3.1\%$ [14]. According to the data from the “National Engineering Quality and Safety Supervision Information Platform” and the provisions of the “People’s Republic of China Law on Safety in Production,” the fines for general accidents in construction safety accidents are typically between 300,000 and 1,000,000 CNY [53,58]. In order to maintain consistency with the numerical relationships among other parameters, we set $F_1=65$ and $F_2=65$. Finally, based on practical considerations and the complexity of calculations, we set $\lambda =1$. The following simulation analyses are all based on the above assignments.

4.2. The Impact of Construction Cost on System Evolution

Due to the broad distribution of engineering construction costs, there are no fixed criteria for evaluating the high or low cost. For the sake of illustration, let us assume $C$ = 200, 1100, 2000, 5000, 10,000, respectively. The simulation results are shown in Figure 1. It can be observed that the cost of engineering construction exerts a significant influence on the evolutionary path of the participants’ behaviors. $\exists \xi \in (2000,5000)$, when $C<\xi$, (0, 0, 1) constitutes the ESS of the system. Conversely, when $C>\xi$, the evolutionary path of the system becomes exceptionally complex, prone to falling into a cycle of strategy switching.

Specifically, when C is less than $\xi$, the paths generally exhibit two states: one is that the government and contractors adopt lenient supervision strategies and active management strategies, respectively, at an early stage, followed by the owner’s gradual transition to a reactive investment strategy; the other is that the government implements lenient supervision early on, and subsequently, the owner and contractors evolve into a reactive investment strategy and an active management strategy, respectively. Of these, the corresponding cost of the latter is relatively higher. Otherwise, when C is greater than $\xi$, the paths are also generally divided into two states: one where, under relatively lower costs, the evolution path shows a smaller range of cycles, and the owner’s safety investment behavior remains relatively passive throughout the process; the other where, under relatively higher costs, the system falls into a large-scale cyclic state, with significant changes in the strategies of the participants, making it impossible to provide targeted strategies. Based on this, it is necessary to conduct a classified study on the aforementioned four paths. Considering the complexity of the system’s evolutionary mechanism, it is challenging to carry out simulation of the evolutionary paths under all construction cost values within the limited space available. Setting $C$ to 500, 2000, 5000, and 8000, respectively, to represent these four evolutionary paths for simulation analysis is an efficient approach. For the sake of discussion, we tentatively define costs below $\xi$ as low, and those above $\xi$ as high. Among them, a cost of 500 represents a very low cost, while a cost of 8000 represents a very high cost.

4.3. Parameter Sensitivity Analysis and Optimization Under Different Cost Scenarios

4.3.1. Scenario 1: Low Cost

Firstly, the value ranges of the main variables during simulation are stipulated. As there is currently no unified regulation on the values of the enterprise reward amount and government credibility, we moderately expand the range of values. $A_1$ and $A_2$ take values within the range of 0.9–22.9, and $R$ takes values within the range of 5.2–25.2. The efficiency of government regulation has garnered attention from scholars, and it is necessary to focus more on enhancing efficiency and controlling costs [22,48]. Therefore, the value of $S_1$ is set within the range of 8–20. Additionally, the values of $F_1$ and $F_2$ are set within the range of 30 to 100, and the value of $k$ is set within the range of 1.2 to 1.5. Next, we will conduct a sensitivity analysis of the key variables by taking $C=500$ and 2000, respectively.

The impact of reward and punishment amounts on evolution is shown in Figure 2. It can be concluded that regardless of the value of C, changing a single factor alone cannot alter the final ESS of (0, 0, 1). The results obtained when C is set to 500 and 2000 share many commonalities. Regarding the reward amounts, a substantial increase in the reward for the owner only has a very minimal positive effect on the owner’s behavior during the evolutionary process; a significant increase in the reward for the contractor has almost no impact on the evolutionary trajectory. Therefore, controlling the reward amounts is conducive to conserving resources. From the perspective of penalty amounts, the punishment for insufficient safety investment has little effect on the evolution of the system. Increasing the penalty for accidents involving owners is conducive to enhancing the initiative of owners in management during the evolutionary process. The difference under the two cost scenarios lies in the fact that when $C=500$, appropriately reducing the severity of penalties for contractors’ accidents can ensure the proactive engagement of the owner’s investment while maintaining the contractor’s enthusiasm for management. However, when $C=2000$, reducing the penalties for contractors’ accidents will diminish the deterrent effect, decrease the contractor’s motivation for management, and simultaneously lead the system into a state of dynamic cycle, which is not conducive to the formulation of targeted strategies.

The impact of government regulatory costs and credibility on evolution is shown in Figure 3. The alteration of a single factor likewise cannot change the overall direction of system evolution. In terms of regulatory costs, a reduction in costs is beneficial for improving the behavior of the three participating parties, and this improvement is more pronounced when $C=2000$. In terms of credibility, when the cost is very low (e.g., C = 500), credibility has almost no impact on the system’s evolution. However, when the cost is a little higher (e.g., C = 2000), it has a slight effect on improving the behavior of the owner and plays a role in promoting the proactive management behavior of the contractor.

Based on the results of the sensitivity analysis, we attempt to adjust the parameters to enable all stakeholders to efficiently achieve collaborative governance. When $C=500$, increasing or decreasing the reward amount hardly exerts any positive influence on the evolution. In consideration of the conservation of social resources, efforts should be made to minimize the reward amount. Additionally, appropriately increase the penalty amount imposed on the owners, while suitably reducing the penalty amount imposed on the contractors; and control the cost of government oversight. Let $S_1=9$, $A_1=1$, $A_2=0.8$, $F_1=82$, $F_2=47.5$, while keeping the values of the other parameters unchanged. After optimization, the system evolves to (1, 1, 1) with higher efficiency, as shown in Figure 4a. When C = 2000, efforts should be made to minimize the reward amounts. Within the bounds permitted by law, the penalty amounts for owners and contractors should be increased. The cost of government regulation should be controlled, and the government’s credibility should be enhanced under good safety performance conditions. Let $S_1=9$, $A_1=2$, $A_2=2$, $F_1=82$, $F_2=82$, $R=15$, while keeping the values of the other parameters unchanged. The optimized evolutionary path is shown in Figure 4b, which also evolves to (1, 1, 1) with higher efficiency. It should be emphasized here that the purpose of optimizing parameter values is to provide a reference for the direction of efforts of stakeholders, rather than to offer a set of absolutely definitive numerical values for direct use.

4.3.2. Scenario 2: High Cost

Sensitivity analysis of the main variables is conducted by taking C = 5000 and 8000, respectively. In this subsection, the positive impact of a parameter on evolution is mainly measured in two aspects: first, it can reduce the amplitude of strategy changes; second, it has an improving effect on the behavior of participants.

The impact of the reward amount on evolution is shown in Figure 5. Although changes in a single factor cannot efficiently drive the system to an ESS at (1, 1, 1), most factors can play a certain role in either reducing the oscillation range of the evolutionary path or enhancing the enthusiasm of the participants for management. Regarding the reward amount for owners, controlling the reward amount is conducive to narrowing the range of strategy changes among all parties and facilitating targeted management. When C = 8000, reducing the amount can also play a good role in constraining the behavior of contractors. As for the reward for contractors, when C = 5000, controlling the reward amount can reduce the range of strategy changes for the government and contractors, while it will increase the range of strategy changes for property owners. Despite this, it still has a positive effect on the improvement of the owners’ behavior. When C = 8000, reducing the reward amount can not only effectively control the range of strategy changes but also significantly increase the probability of property owners actively investing.

The impact of penalty amounts on evolution is shown in Figure 6. Overall, changes in the penalty for contractors’ accidents have the most significant effect on system evolution, while changes in the penalty for owners’ accidents have almost no effect on the system. Increasing the penalty intensity for contractors’ accidents is conducive to controlling the range of changes in the evolutionary path and enhancing the probability of contractors’ active management, with the latter being particularly significant when $C=8000$. Additionally, increasing the penalty for insufficient safety investment is conducive to improving the behavior of both property owners and contractors. The impact of government regulatory costs and credibility on evolution is shown in Figure 7. The reduction in government regulatory costs can significantly increase the probability of active management by owners and contractors. In particular, when $C=5000$, reducing regulatory costs can enable contractors to maintain an active management strategy in the long term. Changes in credibility values do not make the evolutionary path of the system more convergent. However, during the evolution process, they have a certain positive effect on the behavior of property owners and contractors.

Based on the results of the sensitivity analysis, we attempt to adjust the parameters to evolve the model more efficiently towards (1, 1, 1). When $C=5000$, we control the reward amounts for owners and contractors. Within the bounds permitted by reality, we increase the penalties for insufficient safety investment and for contractors’ safety accidents. Additionally, we reduce the government’s regulatory costs and enhance the positive incentives for credibility under good performance conditions. The new values obtained are: $S_1=9$, $A_1=5$, $A_2=2$, $k=1.5$, $F_2=85$, $R=17$, and the remaining parameters remain unchanged. Although the optimization mechanisms behind C = 5000 and C = 8000 are different, the results are similar. Therefore, similarly, let $S_1=9$, $A_1=6$, $A_2=4$, $k=1.5$, $F_2=85$, $R=19$. The other parameters remain unchanged. As shown in Figure 8, collaborative governance has been achieved in both scenarios, which is conducive to construction safety and sustainable construction.

5. Discussion

5.1. Results Overview

By constructing an evolutionary game model among the government, owners, and contractors and conducting numerical simulation analysis, this paper finds that, based on the existing parameters, it is difficult to achieve the collaborative governance of stakeholders for projects of any cost. When the project cost is relatively low, (0, 0, 1) will become the ESS of the system; on the contrary, the system will enter a cyclic evolution state. This differs from previous studies, where the system possesses a clear ESS or the proportion of a certain strategy can achieve stability [9,22,23]. However, the lack of ESS under the current regulatory model has also been identified [48]. Differences in project costs may account for this discrepancy. The sensitivity analysis yields a series of insightful findings, including that positive incentives exert virtually no effect or even produce counterproductive outcomes, the effectiveness of penalties for insufficient safety investment varies with construction costs, and the mechanisms through which penalties for safety accidents operate exhibit considerable complexity across different stakeholders and cost levels. However, although collaborative governance is difficult to achieve by modifying a single parameter, it can still be realized through the joint optimization of multiple parameters.

5.2. Collaborative Governance Realization Mechanism

Through sensitivity analysis of the reward amount, this study reveals that for construction projects of any scale, increasing reward intensity fails to produce a fundamental improvement effect on the behaviors of owners and contractors. In the case of low project costs, increasing rewards for owners has an extremely weak incentive effect on their behaviors, while raising rewards for contractors has almost no impact on the system; in the scenario of high project costs, increasing the reward amount exerts a significant adverse effect. This contradicts the common sense that more rewards may help promote enterprises to adopt positive strategies [11]. The reason for this discrepancy may be that after considering the restrictive effect of owners’ safety investments, the system becomes more complex, and simple rewards are insufficient to improve enterprises’ behaviors. Therefore, it is suggested that for projects of various costs, the reward amount should be reasonably controlled on the whole. For low-cost projects, an appropriate amount of positive incentives may be provided to owners during the process; for high-cost construction projects, stricter control should be exercised over the incentive amounts allocated to the owner and the contractor.

The research findings regarding the intensity of punishment are not entirely consistent with the existing knowledge system. From the perspective of penalties in routine supervision, it is generally believed that strengthening penalties can promote the system to evolve towards an ideal strategy [23,59]. However, this paper finds that for projects with low costs, increasing the penalty intensity within the bounds permitted by reality does not serve as a constraint. This constraining effect only gradually becomes apparent as the project cost increases. Second, from the perspective of penalties for safety accidents, increasing the punishment intensity for owners has a positive effect on low-cost projects but almost no effect on high-cost projects. Regarding the increase in punishment intensity for contractors, for very low-cost projects, such an increase to a certain extent reduces owners’ enthusiasm, thereby being detrimental to collaborative governance; for general low-cost projects, it exerts a positive effect; while for high-cost projects, increasing the punishment always plays a positive role, which is reflected in narrowing the strategy fluctuation range or improving enterprises’ behaviors. In previous studies, high fines for safety accidents are to a certain extent conducive to stimulating enterprises’ positive management behaviors [11]. However, when considering project costs and disputes over project payments, this conclusion does not hold under all conditions. Therefore, for low-cost projects, it is recommended that resources allocated to supervising the sufficiency of safety investment should be rationally conserved, and penalties for accidents should be taken as the primary control measure. Specifically, this includes appropriately increasing the penalty intensity for the owner, and adopting the following strategy for contractors: appropriately reducing penalties for very low-cost projects while increasing penalties for general low-cost projects. For high-cost projects, a two-pronged strategy combining the supervision of safety investment compliance and accident penalties should be implemented. The penalty severity for both owners and contractors arising from insufficient safety investment shall be intensified, with a particular focus on raising the penalties imposed on contractors for safety accidents.

We also found that reducing the government’s regulatory costs can stimulate the government’s regulatory behavior, which is basically consistent with the existing knowledge system [60]. This, in turn, can have a certain positive effect on the behavior of owners and contractors. However, the improvement of government credibility under good performance has no significant effect on very low-cost projects, while it exerts a positive effect on all other types of projects: In low-cost projects, this is mainly reflected in the improvement of contractors’ behaviors; in high-cost projects, it exerts a certain degree of improvement effect on the behaviors of all three parties. Previous research has suggested that if the government does not receive sufficient returns under strict regulation, it may reduce its enthusiasm for strong oversight [23]. According to the findings of this paper, this effect is more pronounced when the cost is high. Therefore, it is recommended to promote a digital and intelligent supervision system, improve the organizational structure to reduce supervision costs, clarify the assessment methods for the construction safety management of government departments, and strengthen information perceptible to the public.

5.3. Research Contributions and Limitations

The main contributions of this study are as follows: Firstly, this study identified the importance of collaborative governance in the field of construction safety, placing full emphasis on stakeholder collaboration rather than being limited solely to the behaviors of specific stakeholders. This provides a more systematic research perspective for safe production in the construction industry. Secondly, this study incorporates the constraining effect of owners’ safety investment, as well as the interest game between owners and contractors in safety management, which helps bring the research results closer to actual construction practices. Thirdly, this study verifies that the mechanisms for achieving collaborative governance differ across projects with varying cost levels. By flexibly employing game theory and simulation techniques to conduct categorical discussions, this research avoids the one-size-fits-all problem in strategic recommendations to a certain extent, thereby constituting an extension of the existing theoretical and methodological frameworks. Finally, the research outcomes enable stakeholders to better perceive the interest factors confronting them and inform decision-making for projects with varying costs, offering actionable insights for relevant actors. The strategic recommendations proposed from a collaborative perspective incorporate the evolutionary mechanisms of stakeholders’ strategies, which helps systematically promote safe production and thereby contributes to the sustainability of the construction industry.

Nevertheless, this study is inevitably subject to limitations. This paper mainly takes project cost as the classification basis. For complex projects, reference can be made to higher-cost categories (according to “Stable Strategy Analysis”, the difference between the actual safety investment $C{\alpha }_2$ and the statutory minimum safety investment $C{\alpha }_1$ determines whether a set of strategies can become an ESS, and ${\alpha }_2$ will increase in complex projects). However, its practicality and convenience are still subject to certain limitations. In addition, due to the complexity of construction scenarios, it is difficult to provide a highly precise cut-off value between low-cost and high-cost projects. Future research will collect a sufficient number of cases, incorporate factors such as project complexity and changes in construction technology into consideration, and conduct a more precise analysis of the collaborative governance mechanism through machine learning.

6. Conclusions

This paper explores the realization mechanism of collaborative governance of construction safety risks by constructing an evolutionary game model between the government, owners, and contractors. The strategies of the participants are numerically simulated with the aid of MATLAB 2016b. Firstly, the heterogeneity of strategy evolution under different cost levels has been confirmed. Subsequently, the paper categorically explores the role of key parameters in system evolution under different project costs, leading to the following conclusions: (1) Rewards for owners and contractors have almost no effect on promoting collaborative governance. (2) Punishment for insufficient safety investment exerts a promotional effect on collaborative governance, which is mainly reflected in high-cost projects. (3) Regarding the role of increasing the punishment intensity for parties liable for safety accidents in collaborative governance, strengthening the punishment for owners has a promotional effect on low-cost projects, while enhancing the punishment for contractors exerts a positive effect except for very low-cost projects. (4) The reduction in government regulatory costs has a positive effect on collaborative governance. Except for projects with very small costs, positive incentives for the government also play a favorable role. This study provides a more fundamental and systematic perspective for construction safety governance, and makes a certain contribution to the sustainability of the construction industry.