Research on Safety Decision-Making Behavior in Megaprojects

Abstract

This research takes the construction companies and supervision units of megaprojects as the research objects and studies safety issues in construction decision-making for megaprojects. Using evolutionary game theory, we construct an evolutionary game model of safety decision-making behavior for construction companies and supervision units based on the bounded rationality assumption. The interaction and dynamic patterns of safety behaviors between the two construction entities are analyzed. Additionally, system dynamics Vensim PLE 10.2.1 software is employed to simulate and analyze the behavior of single entities as well as the impact of exogenous variables on the safety decision-making choices of both units. The research results indicate that positive choices in safety behavior decision-making contribute to enhancing the stability of megaproject construction. Exogenous variables significantly influence the safety behavior decisions of both the construction companies and the supervision units in megaprojects. An increase in cooperation benefits between the two parties fosters their active collaboration in completing mega engineering projects. This research promotes cooperation between construction companies and supervision units during a construction process and provides a reference for the safe and orderly implementation and development of megaprojects.

1. Introduction

Major infrastructure projects (referred to as ‘megaprojects’) are the kinds of national strategic projects that have a profound impact on the development of political, economic, social, scientific, and technological fields. Compared with general projects, they are characterized by large investments, long construction periods, high risk, and complex technology [1]. There are many engineering megaprojects in the world, such as the Hong Kong–Zhuhai–Macao Bridge, the Three Gorges Dam project, the Qinghai–Tibet Railway, the South-to-North Water Diversion Project in China, the Hoover Dam and the Denver International Airport in the U.S., the Aswan Dam in Egypt, the Panama Canal in Panama, and the Anglo–French Cross Harbor Tunnel [2]. These megaprojects have had a significant impact on the geography of the country as well as on the lives of the people [3]. According to the McKinsey Global Institute’s 2013 and 2016 reports, the estimated global spending on infrastructure is expected to reach USD 3.4 trillion per year from 2013 to 2030, accounting for roughly 4% of the total global gross domestic product, with the majority of investments going toward large-scale projects [4]. In the case of China, the country has constructed many megaprojects in recent years in order to accelerate the process of urbanization, which have strongly contributed to rapid economic development [5].

In the construction and engineering industry, safety has always been the focus of attention. In 2020, all kinds of production and safety accidents in China killed 27,412 people, compared with 29,519 people in 2019, which is a decrease of 2107 people or a decrease of 7.14%; in 2021, all kinds of production and safety accidents killed 26,307 people, compared with 27,412 people in 2020, which is a decrease of 1105 people or a decrease of 4.03%; in 2022, all kinds of production safety accidents killed a total of 20,963 people, compared with 26,307 people in 2021, which is a decrease of 5344 people or a decrease of 20.31%. From 2019 to 2022, the number of deaths in all kinds of production safety accidents in the country decreased year by year, but if it had not been effectively controlled, it would have a serious impact on the stability of society. In building construction management, in order to control project safety, it is necessary to enhance the coordination of the construction process, the visualization of the construction process, and the simulation of construction methods. This has led to the creation of construction safety management centered on the application of Big Data, artificial intelligence, and BIM technology [6,7,8].

In the construction process of mega engineering projects, there are many participants involved, including the construction companies, the supervision units, the material and equipment supply units, the audit units, the government, banks, and other financial institutions. These participants are intertwined to complete common mega engineering projects, forming an intricate organizational relationship. However, in the process of mega engineering construction, the interests of many participants are different, especially those of the construction companies and the supervision units. Due to asymmetric information, potential safety risks may occur, and the complexity of large-scale projects seriously hinders decision-making, management/governance, and execution within the project organization, which may lead to problems such as cost overruns or delivery delays during the implementation of these large-scale projects [9,10]. In mega engineering projects, the construction companies and the supervision units often play an important role. The different choices of behavior strategies of the parties may have a significant impact on the quality, safety, and other aspects of the project.

Based on the above analysis, this research focuses on two key participants in the construction of mega engineering projects: the construction companies and the supervisory units. It presents a dynamic evolution display and organizational behavior analysis of the behavior choices made by both parties during the project construction process. The significance and purposes of this research are as follows: (1) What exogenous variables influence the behavioral decisions of construction companies and supervisory units in mega engineering projects, and how do these variables affect their strategic choices? (2) How can we encourage construction companies and supervisory units to adopt safer behavior strategies in mega engineering projects by adjusting the cooperation benefits between them and their respective incentive mechanisms? (3) To enhance the execution efficiency and quality of mega engineering projects, what specific measures should construction companies and supervisory units take to optimize internal management, human resource allocation, and work processes?

2. Literature Review

This thesis analyzes the current state of the literature from two perspectives: studies related to construction megaprojects and studies related to safety management.

2.1. Construction Megaprojects

At present, many scholars have conducted research on construction megaprojects from different perspectives, and the research on megaprojects mainly focuses on the following: (1) Factors and characteristic methods of megaprojects management success; (2) Research on organizational behavior of megaprojects; (3) Research on innovation of megaprojects; (4) Problems and solutions in megaprojects; (5) Research on mega engineering decision-making issues; (6) Experiences and lessons learned in the construction of mega engineering projects. In the research on factors and characterization methods of success in mega engineering project management, Locatelli et al. [11] identified key characteristics associated with megaproject management success that can lead to improved efficiency in the design and delivery of mega engineering projects by means of quantitative analysis and machine learning techniques. Cepeda et al. [12] examined and analyzed mega engineering projects by means of quantitative and qualitative data analysis methods to examine and study the critical success factors of mega engineering projects in Colombia and provide recommendations to reduce project risks. Among the studies on organizational behavior in megaprojects, Le et al. [13,14] examined the impact of changes in various behavioral attributes of the executive team of a megaproject and governmental support on project performance, as well as examined the classification and evolution of improvisation in a megaproject to better cope with uncertainty in the project. Through constructing a cooperative game model, Ma [15] and their team discovered that reasonable allocation of control rights can improve the relationship between the government and project owners, enhance project value, and provide significant insights for cooperation among stakeholders in megaprojects. Al-Subaie et al. [16] conducted surveys and empirical tests on the transformational leadership style and project governance of megaproject managers, concluding that there is a positive correlation between transformational leadership style and megaproject performance, providing a theoretical basis for the success of megaprojects. Huda [17] examined the impact of authoritarian politicization on the risks and positive mechanisms of cross-border energy megaprojects. In terms of project innovation in megaprojects, Liu et al. [18] investigated the role of non-mediated power (expert and reference power), shared mental models, and team innovation efficacy in enhancing collaborative innovation performance in megaprojects. Cantarelli [19] explored innovation in megaprojects, focusing on its relationship with project complexity and the impact of innovation on both project complexity and performance. Jin et al. [20] studied the mega engineering innovation ecosystem with the Hong Kong–Zhuhai–Macao Bridge as an actual case of a megaproject and deconstructed the composition of the main body of the mega engineering innovation ecosystem as well as the dynamic evolution law. In the study of problems and solutions in megaprojects, Flyvbjerg and Ansar [21,22] proposed measures and strategies to improve the problems of megaprojects such as cost and time overruns, sources and financing, inadequate supply, poor quality of services, environmental hazards, and social aspects. Desouza [23] presented the problems and tensions between stakeholders in megaprojects and gave appropriate measures to cope with them. In the research on the complexity of decision-making in megaprojects, Sheng et al. [24,25,26] studied the complexity elements of decision-making in mega engineering projects and illustrated the complexity of decision-making with the Hong Kong–Zhuhai–Macao Bridge project, which provides a reference for the management practice of megaprojects. In the research of experiences and lessons learned in the construction of mega engineering projects, Albert P. C. et al. [27] used the construction of a mega engineering project in the Shanghai World Expo Park as a case study, proposing the design and implementation of a multi-criteria incentive mechanism, giving experiences and lessons learned and providing insights for the construction of future large-scale projects.

2.2. Engineering Safety Management

In the research of construction safety management, many scholars focus on the following aspects: (1) Safety hazards and obstacles in the project; (2) Research on safety risk management; (3) Management of project quality and safety; (4) Views on measures for safety management in civil engineering construction; (5) Research on safety management based on relevant theories and methods. In the study of safety hazards and barriers in engineering, Deng et al. [28] constructed a safety management module for construction hazards, combined it with Navisworks to simulate the emergency rescue of safety accidents, and verified its validity through engineering examples. Yang [29] and their colleagues conducted research on deep-rooted issues related to engineering safety and applied the latest fractal theory to engineering safety management. Zhang [30] introduced artificial intelligence machine vision technology for safety management in civil engineering, thereby improving the quality and safety of construction. Yap et al. [31] explored the application of emerging technologies in improving construction safety through questionnaire surveys and analysis, focusing on engineering safety issues and accident rates. Liu [32] researched on safety barriers, categorized the applications of barrier theory in engineering and management, and pointed out the research prospects and challenges in this field. For safety risk management, Qian and Lin [33] studied the progress and challenges of safety risk management in underground engineering in China in the past ten years and proposed improvement measures. Xiong et al. [34] studied the main progress of risk management in geotechnical engineering in China from 2010 to 2017, including scientific and technological projects, risk analysis methods, monitoring and early warning systems, information technology platforms, and intelligent risk management. Regarding the research on the management aspect of engineering quality and safety, Feng et al. [35] conducted research, based on game theory, on the actors of highway engineering quality and safety and provided methods and new ideas for the management of highway engineering quality and safety behaviors. In the research on safety management measures for civil engineering construction, He and Jia [36] analyzed the importance of safety management specific to civil engineering projects and proposed safety management measures, providing valuable references for civil engineering construction. In the research on construction engineering safety management based on game theory, Jiantao and Hong [37] analyzed the game process between the government and enterprises, as well as between enterprises and employees, from a game theory perspective. They pointed out the deficiencies and flaws in engineering safety management and provided recommendations. In the research on construction engineering safety management based on an improved neural network, Li and Suo [38] proposed an improved algorithm for assessing construction safety management based on the characteristics of safety management risks.

The research on construction engineering safety management mentioned above has achieved many results and provided many insights and methods for engineering safety management, including the following key points: (1) Construction safety management research includes potential safety hazards, obstacles, risk management, quality and safety management, and safety measures taken in civil engineering; (2) The prominent application of modern emerging technologies and safety management models in the field of construction safety management; (3) Research on safety risk management in specific engineering contexts, including assessments of construction safety management. This research progress has provided valuable experience for the construction and management of construction projects, and can improve the standards of engineering safety quality and risk control, which has certain theoretical significance and engineering practice value. However, there are still some shortcomings in the existing research on construction safety management: (1) Most studies only analyze safety management issues from the perspective of engineering construction, lacking analysis from the perspective of all participants in the construction project; (2) There is a lack of research on issues related to construction safety management from the perspective of organizational behavior and game theory between engineering participants.

2.3. Decision-Making Behavior in Megaprojects

In mega engineering projects, research on the game theory of executive behaviors has made significant progress, but there are still deficiencies: a lack of analysis of the causal relationship between their behaviors and system perspectives and limited research on construction safety behaviors. From the perspective of the organizational behaviors of construction companies and supervision units involved in mega engineering projects, this research constructs an evolutionary game model for their safety decision-making behaviors. It analyzes the causal relationships between the influencing factors of safety decisions through system dynamics and explores the paths of behavior selection strategies in different scenarios with numerical simulations. The optimal safety behavior decision-making strategy for cooperation between the two parties is derived, aiming to provide theory and guidance for the safe and orderly progress of large-scale project construction.

The prospects, significance, and contributions of this research are primarily manifested in three aspects: (1) Utilizing novel theoretical frameworks like evolutionary game theory and system dynamics, the research examines the influencing factors of behavior choices and the dynamic evolution of behaviors in construction companies and supervisory units, aiming to provide precise practical guidance for safety decision-making in real engineering projects; (2) It addresses the gaps in executive behavior game theory research in mega engineering projects from system perspectives and construction safety behaviors, thus enriching the research content in this field and offering a fresh perspective for understanding safety behaviors during the construction process; (3) The research introduces the optimal safety behavior decision-making strategy for cooperation between construction companies and supervisory units, fostering collaboration and aiding in the development of safety response capabilities in complex environments, the enhancement of safety awareness, and the reduction of engineering risks, as well as enhancing the prevention of potential safety hazards in construction, improving construction quality, and ultimately, improving overall safety management levels.

3. Evolutionary Game Model Construction

3.1. Basic Assumptions

Assumption 1.

In megaprojects, construction companies and supervisory units, as finite rational subjects, pursue the maximization of interests, and their safety decisions affect each other. Based on the assumption of limited rationality, both parties will not find the optimal strategy immediately but through the dynamic process of continuous learning and imitation, eventually reaching a stable state.

Assumption 2.

The participants in the game model are two parties: the construction companies and the supervisory units. The strategy set for the construction companies is to have proactive completion or speculative behavior, while the strategy set for the supervisory units is to have strict supervision or lax supervision. The probability of the construction companies choosing proactive completion to finish the project is x, and the probability of choosing speculative behavior is 1−-x, because the construction companies can only choose one of the strategies. Similarly, the probability of the supervisory units choosing a strict supervision strategy is y, and the probability of choosing a lax supervision strategy is 1 − y.

Assumption 3.

Let the set of pure strategies of the construction companies be (active completion, speculative behavior) when the project proceeds normally. If the construction companies adopt positive completion, they pay additional cost C₁ and gain good image and reputation benefits R₃; when they adopt speculative behavior, they suffer the corresponding punishment P₁ and loss of image and reputation C₂. When construction companies complete a megaproject, their normal benefits are R₁.

Assumption 4.

Let the set of pure strategies of the supervisory units when the project is carried out normally be (strict supervision, lax supervision). If the supervisory units adopt strict supervision, the additional costs they pay are C₃. When they adopt lax supervision, the costs they pay are C₄, and the penalties they receive due to the safety and quality issues of the project are P₂. The benefits to the supervisory units when they complete the project normally are R₂.

Assumption 5.

When the construction companies take a proactive completion strategy, the supervisory units take strict supervision, bringing benefits of good cooperation amounting to R₄. When the construction companies engage in speculative behavior, the supervisory units take loose supervision, obtaining additional benefits of R₅.

The explanations of some professional terms in the above content are as follows:

Supervisory units: These refer to the unit entrusted by the construction company or the owner to control the quality, progress, and cost of the construction project during the construction stage, manage contracts and information, coordinate the relationship between parties related to the construction project, and fulfill the statutory duties of safety production management for construction projects in accordance with relevant national laws and regulations, engineering construction standards, survey and design documents, and contracts, in order to achieve the goal of project construction.

Behavioral game of executives: In the process of enterprise management, senior executives, as decision-makers, engage in strategic choices and action adjustments with other stakeholders based on their respective goals of maximizing their interests under certain rules and information conditions.

Speculative behavior of construction companies: Construction companies use market fluctuations, policy changes, or information asymmetry to obtain additional benefits in the project or construction process through improper means, such as cutting corners, falsifying quantities, and subcontracting in violation of regulations, in order to obtain high profits in the short term. Such behavior often has a negative impact on the quality, safety, and long-term benefits of the project and also undermines the fair competitive environment of the market.

Loose supervision by the supervisory units: When performing the duties of engineering supervision, the supervision unit adopts a relatively loose and non-strict supervision and management attitude toward the behavior, project quality, safety, and other aspects of the construction unit, which may lead to problems in project quality and safety.

Proceeds to the construction companies on normal completion of megaprojects: The remaining amount, after deducting the relevant costs from the income obtained by construction companies upon normal completion of megaprojects, is an important indicator for measuring the economic benefits of the construction projects.

The relevant parameter settings for the evolutionary game model are detailed in

Table 1. Parameter Settings.

Subject of the Decision	Parameters	Explanation
Parameters of the construction companies	R1	Proceeds to the construction companies on normal completion of megaprojects
	R3	Good image and reputational benefits gained by the construction companies when completed positively
	C1	Additional costs incurred by the construction companies when actively completed
	P1	Penalties in case of speculative behavior of construction companies
	C2	Loss of image and reputation in case of speculative behavior of construction companies
Parameters of the supervisory units	R2	Proceeds to the supervisory units upon normal completion of the project
	P2	Penalties in case of lax supervision by the supervisory units
	C3	Additional costs incurred when supervisory units are strictly supervised
	C4	Costs incurred when supervisory units are lax in supervision
Other parameters	R4	Benefits of cooperation between the two parties from strict management by the supervisory units when the construction companies are actively completed
	R5	Other additional benefits from lax supervision by the supervisory units in the event of speculative behavior by the construction companies

.

3.2. Establishment of Benefit Matrix

Based on the above model assumptions, the benefit matrix for safety decision-making behaviors involving construction companies and supervisory units in megaprojects has been established, as presented in

Table 2. Benefits matrix of the evolutionary game between megaprojects construction companies and supervisory units.

Subjects of Decision		Supervisory Units
		Strict Supervision (y)	Lax Supervision (1 − y)
Construction companies	Proactive completion (x)	(R1 − C1 + R3 + R4, R2 − C3 + R4)	(R1 − C1, R2 − P2 − C4)
	Speculative behavior (1 − x)	(R1 − P1 − C2, R2 − C3)	(R1 − P1 − C2 + R5, R2 − P2 − C4 + R5)

.

4. Evolutionary Game Analysis

4.1. Expected Return Function

(1) Assuming that the expected return when the construction companies opt for a proactive completion strategy is U₁, the expected return when they engage in speculative behavior is U₂, and the average expected return is U_s, the expected return when the construction companies choose proactive completion strategy is shown in Equation (1):

U₁ = y × (R₁ − C₁ + R₃ + R₄) + (1 − y) × (R₁ − C₁)

(1)

The constructor’s expected return when choosing speculative behavior is shown in Equation (2):

U₂ = y × (R₁ − P₁ − C₂) + (1 − y) × (R₁ − P₁ − C₂ + R₅)

(2)

The average expected return for the construction companies can be derived as Equation (3):

U_s = x × U₁ + (1 − x) × U₂

(3)

(2) Assuming that the expected return of supervisory units in megaprojects is W₁ when they choose strict supervision, W₂ when they choose lax supervision, and the average expected return is W_s, the expected return of supervisory units when they choose strict supervision is shown in Equation (4):

W₁ = x × (R₂ − C₃ + R₄) + (1 − x) × (R₂ − C₃)

(4)

The expected benefit to the supervisory units when they choose lax regulation is shown in Equation (5):

W₂ = x × (R₂ − P₂ − C₄) + (1 − x) × (R₂ − P₂ − C₄ + R₅)

(5)

The average expected return of the supervisory units can be derived as Equation (6):

W_s = y × W₁ + (1 − y) × W₂

(6)

4.2. Replication Dynamic Equations

Combining Equations (1)–(3), the replication dynamic equation for the construction companies can be obtained as shown in Equation (7):

$$\begin{array}{l}F(x)={\displaystyle \frac{dx}{dt}}=x\times \left(U_1-U_s\right)=x\times (1-x)\times \left(U_1-U_2\right)\hfill \\ =x\times (1-x)\times \left[\left(R_3+R_4+R_5\right)\times y+C_2-C_1+P_1-R_5\right]\hfill \end{array}$$

(7)

Combining Equations (4)–(6), the replication dynamic equation for the supervisory units can be obtained as shown in Equation (8):

$$\begin{array}{l}F(y)={\displaystyle \frac{dy}{dt}}=y\times \left(W_1-W_s\right)=y\times (1-y)\times \left(W_1-W_2\right)\hfill \\ =y\times (1-y)\times \left[\left(R_4+R_5\right)\times x+C_4-C_3+P_2-R_5\right]\hfill \end{array}$$

(8)

By deriving the replication dynamic equations in Equations (7) and (8), respectively, we can obtain the following Equations (9) and (10):

F′(x) = (1 − 2x) × (R₃ × y + R₄ × y + R₅ × y + C₂ − C₁ + P₁ − R₅)

(9)

F′(y) = (1 − 2y) × (R₄ × x + R₅ × x + C₄ − C₃ + P₂ − R₅)

(10)

To find the equilibrium point of the evolutionary game between the major engineering construction unit and the supervision unit, we simultaneously establish two replicator dynamic equations and set F(x) = 0 and F(y) = 0. It can be seen that there are four equilibrium points: β₁(0,0), β₂(0,1), β₃(1,0), and β₄(1,1).

4.3. Evolutionary Game Stability Analysis

(1)

Stability analysis of pure strategies for construction companies in megaprojects.

Based on the above analysis, the replicator dynamic equation for construction units in megaprojects and its derivative result are shown in Equation (11):

$$\left\{\begin{array}{c}F\left(x\right)=x\times (1-x)\times \left[\right(R_3+R_4+R_5)\times y+C_2-C_1+P_1-R_5]\\ F\prime \left(x\right)=(1-2x)\times \left[\right(R_3+R_4+R_5)\times y+C_2-C_1+P_1-R_5] \end{array}\right.$$

(11)

When x = 0, x = 1, and (R₃ + R₄ + R₅) × y + C₂ − C₁ + P₁ − R₅ = 0, F(x) = 0 and F’(x) = 0 always hold true. Among the three stable points, x = 0 and x = 1 are the two pure strategy choices for the construction unit, while (R₃ + R₄ + R₅) × y + C₂ − C₁ + P₁ − R₅ = 0 represents the dividing line of the stable state.

If (R₃ + R₄ + R₅) × y + C₂ − C₁ + P₁ − R₅ > 0, at this point, the construction company will choose opportunistic behavior, i.e., F(x = 0) = 0, F’(x = 0) > 0 always holds true. When the construction company chooses to actively complete the project, i.e., x = 1, it is a stable gaming strategy for the construction company, indicating that choosing to actively complete the project is a stable state for the construction company at this time, while choosing opportunistic behavior is an unstable state.

On the other hand, if (R₃ + R₄ + R₅) × y + C₂ − C₁ + P₁ − R₅ < 0, at this point, when the construction unit chooses opportunistic behavior, i.e., x = 0, F(x = 0) = 0 and F’(x = 0) < 0 always hold true. When the construction unit chooses to actively complete the project, i.e., x = 1, F(x = 1) = 0, and F’(x = 1) > 0 always hold true. This indicates that x = 0 is a stable gaming strategy for the construction unit, meaning that opportunistic behavior is a stable state for the construction unit at this time, while actively completing the project is an unstable state.

(2)

Stability analysis of pure strategies for supervision units in megaprojects.

Based on the above analysis, the replicator dynamic equation for supervision units in megaprojects and its derivative result are shown in Equation (12):

$$\left\{\begin{array}{c}F\left(y\right)=y\times (1-y)\times \left[\right(R_4+R_5)\times x+C_4-C_3+P_2-R_5]\\ F\prime \left(y\right)=(1-2y)\times \left[\right(R_4+R_5)\times x+C_4-C_3+P_2-R_5] \end{array}\right.$$

(12)

When x = 0, x = 1, and (R₄ + R₅) × x + C₄ − C₃ + P₂ − R₅ = 0, F(x) = 0 and F’(x) = 0 always hold true. Among the three stable points, y=0 and y=1 are the two pure strategy choices for the supervisory units. The equation (R₄ + R₅) × x + C₄ − C₃ + P₂ − R₅ = 0 represents the boundary line of stability. If (R₄ + R₅) × x + C₄ − C₃ + P₂ − R₅ > 0, when the supervisory units adopt lax supervision, i.e., x = 0, F(x = 0) = 0 and F’(x = 0) > 0 always hold true. When the supervisory units choose strict supervision, i.e., x = 1, F(x = 1) = 0 and F’(x = 1) < 0 always hold true, indicating that x = 1 is the stable gaming strategy for the supervisory units. This suggests that the current stable state for the supervisory units is to choose strict supervision, while the unstable state is to choose lax supervision. Conversely, if (R₄ + R₅) × x + C₄ − C₃ + P₂ − R₅ < 0, when the supervision unit chooses lax supervision, i.e., x = 0, F(x = 0) = 0 and F’(x = 0) < 0 always hold true. When the supervisory units choose strict supervision, i.e., x = 1, F(x = 1) = 0, and F’(x = 1) > 0 always hold true, this indicates that x = 0 is the stable gaming state for the supervisory units. This suggests that in a current stable state, the supervisory units should choose lax supervision, while in an unstable state, they should choose strict supervision.

(3)

Analysis of the asymptotic stability of behavioral strategies for construction companies and supervisory units in megaprojects.

According to Friedman’s theory, to judge the strategy of evolutionary stability of the replicated dynamic system, it is necessary to construct the Jacobi matrix to assess its local stability [39,40]. By examining the sign of determinant (det) and trace (tr), the state of evolutionary stability of the system can be determined, which in turn can determine the evolutionary stability strategy of the construction companies and the supervisory units in megaprojects. The Jacobi matrix is constructed as Equation (13):

$$J=\left[\begin{array}{cc}{\displaystyle \frac{\partial F(x)}{\partial x}}& {\displaystyle \frac{\partial F(x)}{\partial y}}\\ {\displaystyle \frac{\partial F(y)}{\partial x}}& {\displaystyle \frac{\partial F(y)}{\partial y}}\end{array}\right]$$

(13)

The Jacobi matrix determinant (detJ) is shown in Equation (14):

$$detJ={\displaystyle \frac{\partial F(x)}{\partial x}}\times {\displaystyle \frac{\partial F(y)}{\partial y}}-{\displaystyle \frac{\partial F(x)}{\partial y}}\times {\displaystyle \frac{\partial F(y)}{\partial x}}$$

(14)

The trace (trJ) of the Jacobi matrix is shown in Equation (15):

$$trJ={\displaystyle \frac{\partial F(x)}{\partial x}}+{\displaystyle \frac{\partial F(y)}{\partial y}}$$

(15)

When the game equilibrium is in a steady state, it satisfies det(J) > 0 and tr(J) < 0. The values of det(J) and tr(J) for the four special equilibria are given in

Table 3. Game equilibrium points with det(J) and tr(J) values.

Equilibrium Point	det(J)	tr(J)
E1(0,0)	(C2 − C1 + P1 − R5)(C4 − C3 + P2 − R5)	C2 − C1 + P1 − R5+ C4 − C3 + P2 − R5
E2(0,1)	(C2 − C1 + P1 + R3 + R4)(C3 − C4 − P2 + R5)	C2 − C1 + P1 + R3 + R4+C3 − C4 − P2 + R5
E3(1,0)	(C1 − C2 − P1 + R5)(C4 − C3 + P2 + R4)	C1− C2 − P1 + R5+ C4 − C3 + P2 + R4
E4(1,1)	(C1 − C2 − P1 − R3 − R4)(C3 − C4 − P2 − R4)	C1 − C2 − P1 − R3 − R4+ C3 − C4 − P2 − R4

.

Based on the above table, it can be seen that there are numerous factors that affect the equilibrium stability of both the construction companies and supervision units in megaprojects. As the game of construction safety decision-making behavior between these two parties in megaprojects continues to evolve, the correlation between the involved variables will also increase accordingly. Conducting stability analysis using the Jacobi matrix alone can be cumbersome. Therefore, the system dynamics method will be employed to simulate and analyze the construction safety decision-making behavior of the construction companies and supervision units in megaprojects. This aims to provide a reference and theoretical support for the management of significant engineering projects.

Inference 1: The equilibrium point E₄(1,1) in Table 3 has practical significance. In megaprojects, when the additional cost incurred by the construction companies when actively completing the project is less than the loss of image and reputation caused by opportunistic behavior, that is, under the conditions C₁ − C₂ − P₁ − R₃ − R₄ < 0 and C₃ − C₄ − P₂ − R₄ < 0, the following holds: C₁ < C₂ + P₁ + R₃ + R₄.

5. Evolutionary Game Simulation Analysis

By utilizing the system dynamics method, a model integrating quantitative and conceptual models can be established, which helps analyze complex system problems. Specifically, Vensim PLE is an excellent system dynamics simulation software that supports graphical modeling. It allows users to build models by connecting various variables and arrows, creating models that include causal loops in a simple yet flexible manner, and visually displaying the causal relationships and dynamic changes between variables. This can help managers and decision-makers clarify the relationships between various factors in complex systems, thereby enabling them to make scientific and effective decisions. To better study the game process between the construction companies and the supervisory units in megaprojects under different states, a simulation with the help of system dynamics has been conducted. A causality diagram of safety decision-making behavior parameters for the construction companies and supervisory units has been constructed in megaprojects, as shown in Figure 1.

In this model, variables in the box, such as x and y, are state variables representing the probabilities of various safety decision-making behaviors of the construction companies and supervisory units, respectively. The rate variables in the middle represent the rates of behavioral change for the construction and supervisory units, which are determined by the functions F(x) and F(y) of the replicated dynamic Equations (7) and (8). The blue arrows in the diagram indicate causal relationships, reflecting the causal connections between various decision-making behaviors.

Figure 2 depicts all the representations of the behavior choices of the construction companies and the supervision units under various experimental conditions, and ultimately, both parties’ various behavior choices will tend toward a stable state of (1,1). The horizontal axis represents the probability of the construction companies’ behavior strategy, and the vertical axis represents the probability of the supervisory units’ behavior strategy. Different colored lines represent experiments with different initial values of behavior strategies for the construction companies and the supervisory units. For example, the initial probability composition of the construction companies and the supervisory units may be (0.1,0.2) or (0.2,0.3), etc., but all initial probability compositions will eventually evolve to (1,1).

The model shown in Figure 1 is simulated using numerical simulation. According to the constraints as well as the operation of the project, different variables are reasonably assigned values. Assuming that the initial time is 0, the simulation period is 40 months, the step size is 0.5, and the rest of the variables take the values of R₁, R₃, C₁, P₁, C₂, R₂, P₂, C₃, C₄, R₄, and R₅ as 1.2, 0.5, 0.3, 0.4, 0.3, 1.0, 0.4, 0.5, 0.3, 0.6, and 0.4, respectively.

5.1. Evolution of the Game Dynamics of a Single Subject’s Independent Behavior on the Behavioral Choices of Both Parties

(1) The choice of construction companies to actively fulfill their obligations has an impact on both sides of the game. When the initial behavioral strategy set of the two parties is (0.7,0.02), the evolution path diagram for the construction companies’ choice to actively fulfill their obligations is shown in Figure 3a. When construction companies choose to actively fulfill their obligations, supervisory units subsequently choose to strictly supervise, ultimately reaching a stable state of (1,1). This indicates that the active fulfillment by construction companies contributes to improving the stability of construction.

(2) When the initial behavioral strategy set for the construction companies and supervisory units in a megaproject is (0.02,0.7), the evolution path of the supervisory units’ strict supervision is depicted in Figure 3b. Initially, the supervisory units’ willingness to strictly supervise decreases, but as time passes, the construction companies choose to actively complete the project. Eventually, both parties reach a stable state of (1,1). This indicates that strict supervision by the supervisory units contributes to enhancing the stability of the project.

5.2. The Influence of Exogenous Variables on the Dynamic Evolution of the Game of Behavioral Strategies of a Single Subject

(1)

The influence of exogenous variables on the behavioral strategies of mega engineering construction companies.

The system dynamics Vensim PLE 10.2.1 software is used to study the influence of exogenous variables on the behavioral strategies of mega construction companies. Assuming that other parameters remain unchanged, simulations were conducted by varying certain variables. Specifically, the additional cost C₁ paid by the construction companies for active completion was adjusted to take the values of 0.3, 0.4, and 0.6 in sequence. Similarly, the penalty P1 incurred by the companies due to speculative behavior was modified to be 0.4, 0.6, and 0.8, respectively. Furthermore, the loss of the construction companies’ image and reputation, denoted as C₂, resulting from speculative behavior, was altered to values of 0.3, 0.5, and 0.7, respectively. The simulation results of the behavioral strategy of the construction companies are shown in Figure 4.

As shown in Figure 4a, construction companies are strongly influenced by completion costs when formulating their initial speculative strategies. Low additional costs prompt them to quickly adopt an aggressive completion approach, while high additional costs lead to prolonged decision-making processes and slow down the stabilization trend for construction companies. If the additional costs are excessively high, construction companies are more likely to choose speculative behavior for economic benefits. Figure 4b reveals that severe penalties for speculative behavior can rapidly motivate construction companies to adopt an aggressive completion strategy and quickly reach a stable state. Looking at Figure 4c, it is not difficult to find that the greater the reputational loss caused by speculative behavior, the faster the construction companies will adopt an aggressive completion strategy; conversely, the smaller the loss, the longer it takes to stabilize.

(2)

The effect of exogenous variables on the safety behavioral strategies of supervisory units in megaprojects.

With the help of Vensim PLE software, this research once again analyzed the impact of exogenous variables on the behavior strategies of the supervision unit of the megaproject. Under the premise of ensuring the stability of other parameters, the following scenarios were set for simulation: when the additional cost C₂ that the supervision unit needs to bear during strict supervision is 0.3, 0.5, and 0.7, respectively; when the punishment P₂ suffered by the supervision unit due to lax management is 0.4, 0.6, and 0.8, respectively; when the benefits R₄ obtained by the supervision unit and the partner are 0.6, 0.8, and 1.0, respectively; and when the additional benefits R₅ obtained by the supervision unit due to loose management are 0.4, 0.6, and 0.8, respectively. Under these settings, a simulation of the behavioral strategies of the supervision unit was conducted, and the results are shown in Figure 5.

In megaprojects, when the initial behavioral strategy of the supervisory units is set to lax regulation, the simulation analysis regarding its exogenous variables, as illustrated in Figure 5a–c, shows that the factor that has the greatest influence on the behavior of the supervisory units is the punishment P₂ received by them. As shown in Figure 5b, the supervisory units switch to strict supervision more quickly under a lax supervision strategy as the penalty for lax supervision increases to maintain a good image. Figure 5c shows that the supervisory units will tend to switch to strict supervision more rapidly when the cooperation gain increases and the construction companies choose to complete it positively. This has a positive impact on the completion of megaprojects, improving both quality and safety. Figure 5d shows that the supervisory units may abandon strict supervision and choose a lax strategy if they receive high additional benefits from lax management, thereby increasing project risks and construction safety hazards in megaprojects.

6. Conclusions

Based on the above analysis, the conclusions drawn in this research are as follows: (1) The behavioral decisions of the construction companies are influenced by other exogenous variables such as cost, punishment, and loss of image and reputation. When the required costs increase and potential losses decrease, the construction companies are more likely to choose opportunistic behavior rather than proactive completion. (2) The behavioral decisions of the supervision units are affected by exogenous variables such as punishment and cooperation benefits. Increased punishment and cooperation benefits will prompt the supervisory units to choose strict supervision strategies more quickly. (3) As the benefits from the cooperation between the two parties gradually increase, they will gravitate toward a safety-oriented behavioral strategy, wherein the supervisory units opt for strict supervision and the construction companies for proactive completion. This cooperation between the two parties has positive implications for the completion of the entire mega engineering project, providing greater guarantees for the quality and safety of the entire project.

Based on the above conclusions, the following prospects are proposed: (1) Construction companies can establish more reasonable compensation and incentive mechanisms to meet the actual needs of employees and enhance their work enthusiasm and satisfaction. This will enable employees of construction companies to better complete the construction of mega engineering projects, promote the selection of proactive completion strategies by construction companies, and ensure safer and more secure mega engineering projects. (2) Construction companies can refine goals and improve departmental execution capabilities. By clarifying the responsibilities and goals of each department and employee, construction companies can ensure project progress and quality, reducing delays and quality issues caused by poor execution. (3) Construction companies should allocate human resources more reasonably. Employees should be assigned to the most suitable positions based on factors such as their skills, experience, and personality, thereby enhancing overall work efficiency and team cohesion. (4) Supervisory units should strengthen communication and collaboration within the team. By clarifying the roles and responsibilities of team members and establishing effective communication mechanisms, the smooth progress of supervision work can be ensured. This also facilitates the selection of strict supervision strategies and enhances the safety of mega engineering projects. (5) Supervisory units should continuously improve the professional quality of supervision personnel. By providing systematic training and education to supervision personnel, they can acquire more professional knowledge and skills, enhancing their judgment and execution capabilities in supervision work, which contributes to enhancing the stability of mega engineering projects. (6) Supervisory units can optimize work processes and improve work efficiency. For example, by arranging work plans reasonably, clarifying work priorities, strengthening on-site inspections, and other measures, the comprehensiveness and effectiveness of supervision work can be ensured, thereby safeguarding the safe progress of mega engineering projects.

From the perspective of cooperation between construction companies and supervisory units in mega engineering projects, this research applies evolutionary game theory and system dynamics to analyze the safety behaviors of the two parties in a systematic and dynamic manner. However, there are still the following deficiencies and limitations: (1) This research mainly studies the safety behaviors of construction companies and supervisory units in mega engineering projects. However, in actual projects, there may be other factors—such as progress, cost, and duration—that can also affect the decision-making behaviors of the two parties. (2) In mega engineering projects, there are many participants, including design units, survey units, audit units, material and equipment suppliers, governments, banks, etc. These different participants form a complex network that also affects the behavior and decision-making of construction companies and supervision units. In our subsequent research, we will consider adopting a multi-stakeholder model when analyzing and managing mega engineering projects. This model can more accurately reflect the actual situation of mega engineering projects, help identify and manage the interests and needs of various stakeholders, and promote the achievement of mega engineering project goals. (3) For mega engineering projects, there may be many units within the research subject. For example, a mega engineering project may involve hundreds or even thousands of construction units during actual construction, and the internal game between them is also worth considering. The game between internal units within the research subject is not analyzed in this research, which is a limitation of the study.