Evolutionary Game Analysis of Construction Worker Safety Supervision Based on Complex Network

Abstract

To further enhance the management of infrastructure construction projects and safeguard the lives and property of the public, effectively motivating and guiding construction workers’ behaviors has become a critical issue in workplace safety. This study constructs a dynamic game model among construction workers using the Newman–Watts small-world network as a framework, based on the evolutionary game theory of complex networks. It systematically analyzes the effects of reward and punishment mechanisms on workers’ safe behavior decisions. The results show that reasonable rewards and penalties, dynamic incentive-based compensation systems, and strict supervisory mechanisms can significantly enhance the diffusion of safe behavior. Compared with existing solutions, the proposed model more accurately simulates the evolution of construction workers’ safe behavior within complex social networks, providing deeper insights into how reward and punishment mechanisms influence safe behavior decisions. The findings offer theoretical support for construction worker safety supervision and provide practical guidance for formulating more targeted safety management policies and reducing safety risks.

1. Introduction

As of the end of June 2024, the number of construction enterprises engaged in construction activities in China had reached nearly 152,000, representing a year-on-year growth of 8.7%. The construction industry workforce has grown to 38.2 million people [1]. As the cornerstone of urban development, the construction workforce continues to expand, further highlighting the industry’s contribution to the national economy. However, due to its inherent characteristics—such as unstable work locations, high labor mobility, complex and ever-changing work environments, irregular work patterns, and dynamically evolving safety risks—the construction industry has long been one of the sectors with the highest incidence of occupational safety accidents [2].

Despite the government’s continuous efforts to strengthen construction safety supervision in recent years, with relevant laws, regulations, and safety standards gradually improving and the construction safety management system becoming increasingly refined, the overall safety production situation remains severe. Statistics show that while the construction industry accounts for only 7.5% of the global workforce, it contributes to 16.4% of all occupational fatalities [3], highlighting the significant safety management challenges within this industry. Among the primary causes of construction accidents, workers’ behavior plays a critical role [4], with unsafe behaviors being recognized as a core trigger of such incidents [5,6]. Research indicates that constraining unsafe behaviors can significantly reduce accident risks on construction sites [7]. Therefore, developing scientific and effective safety supervision strategies to regulate workers’ unsafe behaviors has become a pressing issue in construction safety management.

Given that workers’ unsafe behavior is the root cause of construction accidents, proposing appropriate management strategies to address this issue in practice is crucial, which has driven extensive exploration of construction workers’ safe behavior [8]. Studies indicate that workers’ safe behavior is influenced by multiple factors, including personal safety awareness, construction site safety culture, management systems, and supervisory mechanisms [9]. In the safety supervision system, the reward and punishment mechanism serves as an important incentive tool, directly impacting workers’ behavioral choices [10]. Specifically, reward measures can strengthen workers’ safety behavior [11], while punitive measures can effectively curb unsafe behavior [12,13]. Additionally, Shin et al. [14] pointed out that reward and punishment measures influence construction workers’ safety behavior by shaping their behavioral attitudes and intentions. However, existing research mainly focuses on the static incentive effects of reward and punishment mechanisms, with relatively insufficient analyses of the complex social interactions among construction workers and the dynamic behavioral decision making occurring under different reward and punishment combinations. This research limitation may lead to challenges in comprehensively evaluating the long-term effectiveness and dynamic impacts of these mechanisms in practical applications.

To address the aforementioned research gap, this study innovatively integrates complex network theory and evolutionary game theory to construct a diffusion game model of construction workers’ safe behavior based on the Newman–Watts (NW) small-world network. The complex network simulates the social relationships and information dissemination paths among construction workers on construction sites, while the evolutionary game theory reveals the dynamic evolution of workers’ behavior under different reward and punishment mechanisms. The main innovations of this study are as follows. Firstly, the complex network framework highlights the influence of social relationships on construction workers’ decision making, addressing the limitation of traditional safety management research that often overlooks worker interactions. Secondly, by conducting simulation analyses of dynamic adjustments in incentive and penalty mechanisms through evolutionary game theory, this study comprehensively considers the impact of dynamic reward measures and spillover penalties on workers’ behavioral decisions.

This study aims to explore the impacts of different reward and punishment mechanisms on construction workers’ safe behavior by constructing a complex network game model based on the NW small-world network. Accordingly, targeted suggestions are proposed. This study contributes to the theoretical framework of construction safety management and offers a potential tool for analyzing on-site safety practices. It is hoped that this study can provide theoretical support for reducing construction safety accidents and direct the industry towards sustainable development.

The remainder of this paper is structured as follows. Section 2 presents a literature review of related research. Section 3, based on the introduction and literature review, constructs a safe behavior diffusion model for construction workers using the NW small-world network and the Fermi strategy update rule according to the research hypotheses. Section 4 analyzes the impacts of reward and punishment mechanisms on the diffusion depth of construction workers’ safe behavior through simulation analysis and conducts a sensitivity analysis. Finally, the paper concludes with a summary of the findings, proposes targeted suggestions, and discusses the study’s limitations and future research directions.

2. Literature Review

2.1. Study on Unsafe Behavior of Workers

The unsafe behavior of construction workers is a significant cause of accidents. Haslam et al. [15] found that approximately 88% of safety accidents in the construction industry result from violations, improper use of equipment, and both conscious and unconscious unsafe behaviors. Existing studies on unsafe behavior primarily focus on the following three perspectives: behavior propagation, behavior causation, and behavior evolution.

From the perspective of behavior propagation, Wang et al. [3] established a propagation network model of coal mine group unsafe behavior based on social network theory. They explored the distribution characteristics, propagation rules, and internal attributes of group unsafe behavior and identified the key unsafe behaviors that affect network propagation. Liu et al. [16] constructed a Cellular Auto infection model on a small-world network, proposing that small-group patterns significantly enhance the spread and influence of unsafe behavior. Ma et al. [17] considered the impact of spatial proximity and suggested that strengthening worker interactions, increasing penalties, and emphasizing the role of opinion leaders can effectively suppress the spread of unsafe behavior. From the behavior causation perspective, Zhang et al. [18], through a novel method of causal inference, uncovered the specific impacts of eight management measures on 13 workers’ safe behavior, indicating that objectives and assessments, safety organization, and hazard and emergency management should be emphasized in the practice of safety management. Wang et al. [19] employed the stimuli–organism–response theory and 24 model to develop a comprehensive model that explains miners’ psychological and physiological influences generated by diverse environmental factors and the mechanisms leading to unsafe behavior. Yang et al. [20] pointed out that workers’ conscious unsafe behaviors are influenced not only by their factors, but also by the decisions of corporate executives and the level of investment in safety supervision. Zhou et al. [21] argued that improving the safety climate can significantly reduce accident rates in the construction industry. From the behavior evolution perspective, Yin et al. [22], based on the Moran process, analyzed the effects of selection intensity and conformity psychology on the evolution of construction workers’ behavior strategies. Li et al. [23] found that, under different conditions, the probability of coal miners choosing unsafe behaviors fluctuates with the leadership behavior of key figures and may reach an evolutionary equilibrium state. Fu et al. [24] confirmed that safety risk factors emanating from the owner or the social environment are instrumental in initiating and controlling the propagation of safe behavior risks.

2.2. Study on the Impact of Incentives and Disincentives on Workers

The aforementioned studies have thoroughly considered the impacts of both workers’ individual characteristics and external environments on their safe behavior choices, while also analyzing the decision-making interaction process. Among external environmental factors, safety regulation has been a key research focus for scholars. Cao et al. [25] proposed that providing appropriate material incentives can enhance workers’ overall productivity, willingness to participate, and work quality. Jiang et al. [26] suggested that an enterprise’s reward and punishment mechanism has a significant impact on employees’ strategic choices. Jiao et al. [27] found that the stricter the government’s reward and punishment measures for road transport enterprises, the more likely these enterprises are to adopt safe production strategies, though the effectiveness of such mechanisms can be indirectly influenced by third-party regulatory agencies. Ye et al. [28] argued that both rewards and punishments positively influence the evolution of workers’ safe behavior, with rewards having a more significant impact than punishments.

Construction workers, as a highly social group, are very susceptible to the influence of surrounding workers and influential worker members when making production decisions. To reflect the influence of this interactive relationship between groups, this paper innovatively introduces complex network game theory to research the safety production decisions of construction workers. This paper simulates worker groups and their social relations in a construction project as a small-world network, describes the decision-making interaction mechanism between individuals in the network with the tool of complex network evolution game theory, combines the spillover effect and dynamic reward and punishment theory, and explores the diffusion extent of the construction workers’ safe behavior under the influence of different parameters through simulation, in order to provide a reference for the design of a worker safety supervisory mechanism.

3. Model Building

The complex network evolution game model primarily consists of the following three elements: the evolution game model, the network structure, and the strategy updating rules, as illustrated in Figure 1. First of all, workers choose strategies based on their own needs and external influences, and obtain corresponding payoffs. Following the specific network structure and strategy updating rules, they learn the strategies and benefits of their neighbors, iteratively updating their strategies until an evolutionarily stable state is achieved.

3.1. Model Assumptions

In this study, the extent of the diffusion of safe behavior is defined as the proportion of workers who choose to work safely as a percentage of all workers, and the following assumptions are made for the study:

Assumption 1.

The game participants are any two construction workers, worker $i$ and worker j, and both workers have a strategy set of {safe behavior, unsafe behavior}. Safe behavior refers to strictly adhering to safety management regulations during the work process, while unsafe behavior refers to violating these regulations and standards, thereby posing risks to both project safety and personal safety. Workers are bounded rationality participants, and their behavioral decisions follow the principle of maximizing benefits.

Assumption 2.

When construction workers choose safe behavior, their net wage income is $R_1$; when they choose unsafe behavior, their net wage income is $R_2$. Due to workers’ lower sensitivity to construction accident risks, they tend to have an overly optimistic assessment of the benefits, effort savings, and time savings brought about by unsafe behavior, resulting in $R_2>R_1$.

Assumption 3.

For the management measures implemented on workers’ behaviors, the reward value for safe behavior is set as $s$ and the penalty value for unsafe behavior is set as $m$. Among them, unsafe behavior has a probability of $\mu$ of being detected by the safety manager, and once detected, the worker will face corresponding penalties. In addition, unsafe behavior also has a probability of $\epsilon$ of causing accidents. The safety risk cost borne by the worker due to an accident caused by unsafe behavior is $L$. Furthermore, there is a free-riding benefit associated with unsafe work, as follows: a worker choosing unsafe behavior might receive a free-riding benefit equal to $\left(1-\mu \right)s$, as they might avoid penalties by not being detected.

Based on the above three assumptions, the safety behavior decisions in the game will lead to four different payoff scenarios for player $i$, as follows:

Scenario 1: Both players choose the safe behavior strategy. In this case, both players can receive a safety reward s, so their payoff is $R_1+s$.

Scenario 2: Player $i$ chooses the safe behavior strategy and the other player $j$ chooses the unsafe behavior strategy. Worker $i$ will receive the behavior reward s, so the payoff is $R_1+s$. For player $j$, there is a probability of $\mu$ of paying the penalty $m$, a probability of $1-\mu$ of receiving the free-riding reward $s$, and a probability of $\epsilon$ of incurring the loss $L$. Therefore, their payoff is $R_2 + \left(1-\mu \right)s-\mu m-\epsilon L$.

Scenario 3: Player $i$ chooses the unsafe behavior strategy and the other player j chooses the safe behavior strategy. This scenario is similar to scenario 2.

Scenario 4: Both players choose the unsafe behavior strategy. In this case, the unsafe behavior will be detected by the safety manager, so both players’ payoff will be $R_2-m-\epsilon L$.

Based on the above four scenarios, the corresponding game payoff matrix is shown in

Table 1. Payoff matrix of construction workers’ game.

		$\mathbf{Worker} \mathit{j}$
		Safe Behavior	Unsafe Behavior
$\mathrm{Worker} i$	Safe behavior	$R_1+s$ $R_1+s$	$R_1+s$ $R_2+\left(1-\mu \right)s-\mu m-\epsilon L$
	Unsafe behavior	$R_2+\left(1-\mu \right)s-\mu m-\epsilon L$ $R_1+s$	$R_2-m-\epsilon L$ $R_2-m-\epsilon L$

.

3.2. Setting of the Network Structure

China’s construction industry is a labor-intensive sector, and complex relationships often exist within construction teams. On the one hand, workers may have social ties such as being from the same hometown, master–apprentice relationships, or kinship and friendships. On the other hand, the working process often involves collaborative cross-operations, which give rise to social relations such as “cooperation” and “help” [29]. These individual workers can be regarded as nodes in a complex network, while the intricate relationships between them represent the edges connecting these nodes. Within this tightly linked network system, the behavior of individual construction workers is highly susceptible to the influence of other members. This leads to continuous interactions, imitation, and learning, and prompts them to adjust their behavioral strategies. As a result, the network forms a complex system that is in a state of constant evolution.

Complex networks primarily include structures such as random networks, regular networks, small-world networks, and scale-free networks [30]. In the complex network structure where construction workers serve as nodes, key figures such as team leaders and technical experts often play leadership and management roles. These key figures form leadership–management critical paths through their connections with other workers. Since workers tend to interact and communicate more frequently with members on these critical paths, the overall network exhibits the characteristics of a small-world network [31]. This means that, although there are localized close connections within the team (i.e., high clustering coefficients), information and influence can still spread rapidly through the critical paths, resulting in a relatively short average path length.

In 1998, Watts and Strogatz [32] proposed the small-world network model (WS model), which effectively captures the characteristics of a real-world complex network, such as a relatively short average path length and a high clustering coefficient. In 1999, Newman and Watts proposed the NW (Newman–Watts) small-world network model based on the WS model, which replaces “the random edge reconnection mechanism” of the WS small-world model with “the random edge addition mechanism”, thus avoiding the possibility of isolated nodes in the network. This feature is particularly important in the network of construction workers. During construction, workers not only maintain stable cooperative or social relationships within their teams, but also interact with a broader range of workers as they move across different tasks and work areas. This mobility and dynamic connectivity allow the network to retain local stability while ensuring global connectivity through the random edge addition mechanism. Therefore, adopting the NW small-world network model is more suited to the actual characteristics of construction workers’ social networks, enabling a more accurate simulation of the spread and impact of safety behaviors within worker communities.

In this study, the NW small-world network is used to simulate the social connections among construction workers, such as cooperation, communication, and information dissemination. To facilitate the research, the following hypotheses are made:

Assumption 4.

Construction workers are positioned at network nodes and only engage in games with their adjacent nodes. Workers without network connections do not participate in games with each other.

Assumption 5.

All individuals in the network follow the same strategy update rule.

Based on these two assumptions, a complex network $G=(V,E)$ is constructed to depict the interaction relationships among individuals, where $V=(v_1,v_2,\cdots ,v_n)$ represents the set of all nodes in the network, with each node corresponding to a worker. $E$ represents the set of relationships between all nodes, expressed as Equation (1), as follows:

$$E=\left|\begin{array}{cc}\begin{array}{cc}{e}_{11}& e_{11}\\ e_{21}& e_{22}\end{array}& \begin{array}{cc}\cdots & e_{1N}\\ \dots & e_{2N}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ e_{N1}& e_{N2}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \dots & e_{NN}\end{array}\end{array}\right|$$

(1)

In this expression, $e_{ij} \left(i,j = \mathrm{1,2},3,\dots ,N\right)$ takes a value of one if there is a direct social relationship between nodes $v_i$ and $v_j$, and zero if no such relationship exists. Each worker is not connected to themselves, so $e_{ii }$ = 0.

The topology structures of the NW small-world network are constructed based on the following steps [33]. Step 1: Constructing the initial regular ring lattice. A standard nearest-neighbor coupling network with N nodes is constructed, with each node connected to its $w$/2 nearest neighbors on both sides, where $w$ is an even number and satisfies N > $w$ > ln(N) > 1. Step 2: Adding network connecting edges. A probability $p$ is set, and edges are added by randomly selecting node pairs with this probability, specifying that, at most, one edge exists between any two nodes and each node cannot be connected to itself. To provide a more intuitive visualization of the NW small-world network structure, N = 20 and $w$ = 4 are set for illustrative purposes in Figure 2.

3.3. Selection of Strategy Update Rules

The core issue of evolutionary game theory lies in how players learn and adjust their strategies. During the game, players’ strategies are not static, but are constantly adjusted according to the environment and the behavior of other participants. The strategy update rule describes how players update their decisions based on their own and others’ behaviors, aiming to simulate the learning and adaptation process of players in a dynamic environment. Currently, the main dynamic rules for individual strategy adjustment in games include Optimal Imitation, Replicator Dynamics, Moran process, and Fermi rule [34].

Considering that individuals with bounded rationality may make irrational decisions when adjusting their strategies, this study chooses the Fermi rule to illustrate the strategy updating probability of an individual during the game. The core idea is that, when updating strategies, individuals not only consider the payoff differences between themselves and their neighbors, but are also influenced by random factors, making the decision-making process more reflective of real-world scenarios. Specifically, when an individual i needs to update their strategy, they randomly select a neighbor j for a payoff comparison and imitate the strategy of neighbor j with a probability P(i←j). This probability is jointly determined by the payoff difference and the noise parameter K, as shown in Equation (2). By introducing the noise parameter, the Fermi rule can effectively simulate situations where individuals may make mistakes or be influenced by external disturbances in actual decision making.

$$P\left(i\leftarrow j\right)={\displaystyle \frac{1}{1+exp\left[\left(U_i-U_j\right)/K\right]}}$$

(2)

In this equation, $U_i$ and $U_j$ represent the payoffs obtained by game participants $i$ and $j$ in the current round of the game. $K$ characterizes the degree of bounded rationality, with its value reflecting the rationality and uncertainty of the individual during the strategy learning process. The larger the value of $K$, the lower the individual’s rationality, meaning they refer to less payoff information and the rule approaches random selection. On the contrary, when K is small, individuals are easily influenced by the difference in returns and are more inclined to adjust their strategies according to this difference in returns. Based on existing research, this study sets the degree of bounded rationality $K$ to 0.1 [35,36].

4. Numerical Simulation

4.1. Initial Parameter Setting

The safety supervision of construction workers involves different types and natures of construction enterprises. These enterprises differ in their specific production processes and safety management measures. Under the premise of meeting the basic logical requirements of the model assumptions, the network parameters and payoff parameters are set based on existing research. Since the core of this study lies in exploring the impact of parameter variation on the diffusion of safe behavior, rather than achieving precise predictions in specific scenarios, the model parameters are set with a greater focus on relative changes and trend analysis. Absolute accuracy of the parameters is, therefore, not strictly required. This approach not only ensures the generalizability of the model, but also enhances the applicability of the conclusions.

For the NW small-world network, the random edge addition probability $p$ is set as 0.2, each node has a total of $w=$6 neighbors [37], and the proportion of workers choosing the safe behavior strategy at the initial moment $y$ is 0.3 [38].

According to the monitoring of the average income of frontline employees in the labor market in a certain city in 2023, the monthly average income of frontline construction workers is around CNY 5000–6000 (Chinese Yuan). Referring to the penalty standards for construction sites, there is a fine of CNY 100 per person per incident for entering a site without a safety helmet; a fine of CNY 50 per person per incident for bringing safety helmets with damaged components (such as missing inner linings, straps, or cracks) onto a site; and a fine of CNY 200 per person per incident for workers who have not received level-three safety education or passed the safety exam and still enter a site for construction. Considering that the punishment for unsafe behavior has a cumulative effect within a work cycle, the ratio of fines to daily average income is controlled between 1.5 and 7. It is assumed that the net income for safe behavior $R_1$= 1 and that the net income for unsafe behavior $R_2$= 3.

According to Heinrich’s statistics, every 300 violations will lead to 1 safety accident, so the probability of the occurrence of safety accident $\epsilon$ is set to be 1/300. Referring to the related literature [28], the results from the simulation program are fitted with the general patterns of unsafe behavior dissemination in the real world, selecting the parameters that best suit these real-world patterns, as follows: the number of workers $N=100$, the loss value caused by unsafe behavior $L$= 200, the reward for safe behavior $s$= 1, and the penalty for unsafe behavior $m$= 1.

Through the simulation of the above parameters, it is observed that, when the game cycle reaches 25, the evolutionary results stabilize. Therefore, the game step size $t$ is set to 25. To ensure the stability of the analysis, each value in the simulation results is the average of 50 experimental results obtained under the same parameter conditions.

4.2. Impact of Reward and Penalty Mechanism

This section focuses on studying the impacts of changes in the rewards and penalties imposed by safety managers under different scenarios on workers’ strategy choices.

4.2.1. Reward Value for Safe Behavior $s$

The penalty for workers’ unsafe behavior is set as $m=1.00$, and the supervisory intensity is set to 0.30 for the simulation. The reward value $s$ starts from 0.00 and increases by steps of 0.25 up to 1.25. The simulation results are shown in Figure 3.

As shown in Figure 3, when the reward given by safety managers is used as the control variable, the following can be observed: when $s=0.00$, meaning no reward mechanism is implemented, the proportion of workers choosing safe behavior gradually decreases and approaches 0% over time. As the reward value increases and reaches 0.75, the system stabilizes at approximately 30% of workers choosing safe behavior, showing a small declining trend compared to the initial proportion. Further increasing the reward to 1.00 results in over 70% of workers opting for safe behavior, while at a reward value of 1.25, the proportion of safe workers reaches 90%. Beyond a certain threshold, the effect of increasing rewards on the diffusion extent of safe behavior first rises and then declines at the same rate of increment, possibly due to the diminishing marginal effect of rewards. Therefore, to enhance workers’ awareness of safe behavior, providing appropriate incentives can be effective. However, excessively increasing the reward may lead to increased management costs without further improving the effectiveness of management.

4.2.2. Penalty Value for Unsafe Behavior $m$

Taking the reward value $s=1.00$, the penalty value for unsafe workers is increased from 0.00 to 1.25 in steps of 0.25 and simulation analysis is carried out to obtain Figure 4.

As shown in Figure 4, it can be observed that increasing the penalty for unsafe behavior significantly enhances the diffusion extent of safe behavior. When the penalty is relatively low, the final stable state shows that only a few workers choose safe behavior. Specifically, when the penalty value $m=0.50$, the diffusion extent of safe behavior remains below 10%. When $m=0.75$, the diffusion extent approaches the initial level, indicating minimal improvement. However, when the penalty and reward values are both set to 1.00, the diffusion extent of safe behavior significantly rises to 70%. Further increasing the penalty to 1.25 results in a diffusion extent exceeding 90%, demonstrating that higher penalties significantly promote safe behavior adoption among workers.

However, based on psychological theories, although the implementation of a penalty mechanism can effectively reduce or suppress undesirable behaviors, excessive reliance on punishment may negatively impact workers’ psychological states, such as increasing anxiety or causing behavioral resistance, which can significantly affect their overall job satisfaction. In conjunction with Figure 3, it is evident that when safety managers formulate safety supervision policies for workers, merely adjusting the number of rewards or penalties yields similar results in improving safety management levels.

4.2.3. Combination of Reward $s$ and Penalty $m$

Based on the previous analysis, it can be seen that individual changes in both reward and penalty values significantly affect the extent of the diffusion of safe behavior among construction workers. Specifically, the reward mechanism can motivate workers to actively choose safe behavior, while the penalty mechanism reduces the probability of unsafe behavior through a deterrent effect. However, in actual safety supervision, rewards and penalties are often not applied independently, but rather interact with each other and jointly influence workers’ decision-making processes. Therefore, examining only the separate roles of the two may not be comprehensive enough. To further explore the influence of reward and penalty mechanisms on the diffusion of safe behavior, it is necessary to analyze the dynamic evolution of workers’ behavioral decision making when the combination of reward and penalty values changes and to examine how this influences workers’ safe behavior choices and the stability of the overall system under various combinations of incentives and penalties. The relevant results are shown in Figure 5.

As shown in Figure 5, the higher the values of rewards and penalties applied to workers, the higher the expectation of workers adopting safe behavior, while the expectation of adopting unsafe behavior is significantly lower. When the value of rewards and penalties in the system is zero or lower, workers’ payoffs mainly come from fixed wages and other income sources, while unsafe behavior will not be subject to any negative consequences, but instead may bring higher payoffs. Therefore, workers tend to choose unsafe behavior. As these reward and penalty values increase, there exists a critical point in the interval [0.85, 0.90] that makes the diffusion of safe behavior exceed the initial proportion by 30%. Further analysis shows that the diffusion extent of safe behavior reaches 90% when the punishment value $m$ = 1 and the reward value $s$ = 1.25 (Figure 3); about 90% when the reward value $s$= 1 and the punishment value $m$ = 1.25 (Figure 4); and nearly 100% when $s$=$m$= 1.25 (Figure 5). These results suggest that, in the process of safety supervision, managers can effectively guide construction workers to choose safe behavior by applying mechanisms in the form of rewards and penalties simultaneously, thus achieving more efficient safety management.

4.2.4. Supervisory Intensity of Safety Managers $\mu$

With the penalty value set at $m=1.00$ and the reward value at $s=1.00$, the supervision intensity $\mu$ is set to 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5, respectively. Based on these parameters, a simulation experiment is conducted, and the results are shown in Figure 6.

Increasing the intensity of supervision can effectively inhibit workers’ unsafe behavior. Strict supervision can not only regulate workers’ behavior through institutional constraints and punitive mechanisms, but also, more importantly, influence workers’ behavioral decisions through psychological mechanisms. When the intensity of supervision is increased, workers will feel greater psychological pressure and responsibility, and this nervous and vigilant psychological state will prompt them to assess the safety of their behavior more cautiously, thus reducing attempts at and the implementation of unsafe behavior. As can be seen from Figure 6, when management does not supervise, the number of workers choosing safe behavior decreases by 10% compared to the initial state, and as the intensity of supervision increases, the depth of the diffusion of safe behavior strategies also shows a clear upward trend. When the intensity of supervision reaches 50%, the proportion of the final evolution of safe behavior reaches over 90%, which achieves a more desirable evolutionary state. This phenomenon not only reflects the significant positive influence of supervision intensity on workers’ behavioral choices, but also reveals the important role of safety supervision in shaping safety culture and changing group behavioral patterns.

4.2.5. Spillover Effect and Dynamic Reward Systems

In actual production and daily life, the commonly implemented system is an incentive-based compensation system, where individual production efforts are considered and compensation is linked to employees’ safe production efficiency and the occurrence of unsafe behavior, thereby ensuring safe production. Based on existing research, the incentive given to workers is represented as a function of the frequency of safe behavior, $s^{\prime }=s(1+y)$. This reward mechanism is regarded as a dynamic reward.

When managing non-compliant behavior among employees, the spillover effect refers to the additional impacts that organizational management measures can have on other individuals or matters within and outside the organization, beyond their expected outcomes. In the context of safe behavior, the spillover effect manifests as follows: even if some workers strictly adhere to safety regulations, they may still experience indirect negative consequences (such as punishment or increased risk) due to the unsafe behavior of other workers. The extent of this negative impact can be represented as $\theta F$, and $\theta$ indicates the strength of the spillover effect.

Considering the above practical application scenarios, a simulation was conducted to analyze the probability of construction workers choosing safe behavior under spillover effects and dynamic reward systems.

Table 2. Payoff matrix of construction workers’ game under spillover effects and dynamic reward system.

		$\mathbf{Worker} \mathit{j}$
		Safe Behavior	Unsafe Behavior
$\mathrm{Worker} i$	Safe behavior	R1 + s(1 + y) R1 + s(1 + y)	R1 + s(1 + y) − μθF R2 + s(1 − μ)(1 + y) − μm − εL
	Unsafe behavior	R2 + s(1 − μ)(1 + y) − μm − εL R1 + s(1 + y) − μθF	R2 − m − εL R2 − m − εL

presents the payoff matrix of the game.

As shown in the above table, the safety behavior decisions in the game will lead to four different payoff scenarios for worker i, as follows:

Scenario 1: Both players choose the safe behavior strategy. In this case, both players can receive a safety reward, so their payoff is R₁ + s(1 + y), where y is the proportion of workers choosing the safe behavior strategy.

Scenario 2: Player $i$ chooses the safe behavior strategy and the other player j chooses the unsafe behavior strategy. Worker $i$ will receive the behavior reward s(1 + y), but if the unsafe behavior is detected, they will also face a spillover penalty θF. Therefore, their payoff is R₁ + s(1 + y) − μθF. For player j, there is a probability of μ of paying the penalty m, a probability of 1 − μ of receiving the free-riding reward s(1 + y), and a probability of $\epsilon$ of incurring the loss L. Therefore, their payoff is R₂ + s(1 − μ)(1 + y) − μm − εL.

Scenario 3: Player $i$ chooses the unsafe behavior strategy and the other player j chooses the safe behavior strategy. This scenario is similar to scenario 2.

Scenario 4: Both players choose the unsafe behavior strategy. In this case, the unsafe behavior will be detected by the safety manager, so both players’ payoff will be R₂ − m εL.

Setting $F = 4$, the evolution of safe behavior under the spillover effect and dynamic reward system is simulated and analyzed under the same parameter settings, and the results are shown in Figure 7.

According to the simulation results in Figure 7, the introduction of dynamic rewards significantly increases the diffusion extent of workers’ safe behavior, with an improvement of approximately 30%. This indicates that the dynamic reward mechanism effectively enhances workers’ awareness of safe behavior, encouraging them to adopt sustained safe behavior. This process forms a positive feedback loop. As more workers choose safe behavior, they receive greater rewards, which, in turn, reinforces their commitment to safety. This mechanism not only raises safety awareness, but also shifts workers from passive compliance with safety rules to an active pursuit of safe behavior. Through the cumulative effect of rewards, safety culture becomes more deeply internalized, fostering a sustainable pattern of safe behavior.

Considering the spillover effect of unsafe behavior, when the implemented penalty system extends its influence to other team members (i.e., $\theta \ne 0$), it exerts a negative impact on the diffusion extent of safe behavior. This suggests that punitive measures not only constrain the directly penalized individuals, but may also impose a deterrent effect on their colleagues, potentially reducing overall motivation for safe behavior adoption. To further investigate this phenomenon, we analyze the impact of varying spillover effect intensities on safe behavior diffusion. The corresponding simulation results, illustrating the extent of this influence under different conditions, are presented in Figure 8.

When $\theta ＝0$, there is no negative spillover effect from fines on workers, meaning that penalties are only imposed on the responsible individuals or those directly causing the accident, without negatively affecting the entire team. In this case, the system evolves in the expected direction, with a diffusion extent reaching 70%. When θ = 0.4, construction managers have a certain probability of implementing broader penalties if a safety incident occurs, but the likelihood remains relatively low. This indicates that workers adhering to safety protocols have a lower chance of being implicated due to accidents. However, as the negative spillover effect becomes more pronounced, the diffusion extent of safe behavior decreases accordingly. This suggests that a “uniform punishment” policy applied to entire work teams can lead to unintended negative spillover effects among individuals. Workers who consistently follow safety protocols may be unfairly penalized, discouraging their commitment to safety practices. As a result, this approach could potentially drive the entire system toward a stable state of unsafe behavior.

4.3. Sensitivity Analysis

Based on the previous analysis, a sensitivity analysis of the model under the spillover effect and dynamic reward system is conducted, with the spillover effect coefficient $\theta$ set to 0.1 and the spillover penalty F set to 4. The parameter combinations are defined as follows: Q1:$s = 1.00,m = 1.00, \mu = 0.2;$ Q2: $s = 1.25, m = 1.25, \mu = 0.2;$ Q3:$s = 1.00, m = 1.00, \mu = 0.4$. Under different parameter combinations, the impacts of the initial proportion, network structure, and bounded rationality on the above conclusions are examined.

4.3.1. Initial Proportion

To assess the impact of the initial proportion on the above results, numerical simulations were conducted with $y$= 0.3 and $y$= 0.6, as shown in Figure 9. Under the same parameter conditions, different initial proportions had no significant effect on the diffusion of safe behavior. By comparing the stable states of Q1 and Q2, it can be concluded that increasing reward and penalty values promotes the diffusion of safe behavior. The comparison between Q2 and Q3 indicates that the supervisory intensity of safety managers influences workers’ behavioral decisions. Therefore, the previous conclusions remain valid.

4.3.2. Network Structure

To evaluate the impact of network structure on the conclusions, analyses were conducted considering the following three aspects: network size, random edge addition probability, and network degree. For network size, numerical simulations were performed with $N$= 50 and $N$ = 100 (Figure 10a). For random edge addition probability, simulations were carried out with $p$= 0.1 and $p$= 0.5 (Figure 10b). For network degree (i.e., the number of edges connected to each node in the network), simulations were conducted with $w$= 6 and $w$= 36 (Figure 10c).

The results in Figure 10 indicate that the network structure has a minor impact on the final stable state of the model. In the evolutionary game process, individual behavioral decisions are primarily driven by payoffs, which, in this study, are more strongly influenced by the reward and punishment mechanism than by network topology alone. As a result, the influence of the network structure is not significant, and the conclusions drawn earlier remain valid.

4.3.3. The Degree of Bounded Rationality

To determine whether the parameter settings of the Fermi rule affect the conclusions, the values of $K$ for the degree of bounded rationality are taken as 0.1 and 0.5 for the simulation analysis. The results are shown in Figure 11.

According to the simulation results, as the parameter $K$ increases, the time required for the game to converge to a stable state is significantly prolonged. This phenomenon can be attributed to the fact that $K$ reflects the degree of bounded rationality among the game participants. Specifically, a higher $K$ value indicates a lower level of rationality in the decision-making processes of participants. When $K$ is elevated, the participants become less sensitive to differences in payoffs when adjusting their strategies, and their decisions are increasingly influenced by random factors rather than systematic analysis. This heightened randomness introduces a greater variability and unpredictability in individual strategy choices, causing more frequent fluctuations in the system. As a result, the overall game dynamics become more complex and unstable, requiring a substantially longer time to reach a stable state.

5. Discussion

5.1. Research Findings

This study constructs a safe behavior diffusion model based on the NW small-world network model, focusing on the evolutionary process of construction workers’ safe behavior under different reward and punishment mechanisms. Through simulation, the study further investigates the impact of the initial proportion and parameters on workers’ behavior strategies. The main findings are as follows.

First, an increase in reward and penalty values effectively promotes the diffusion of workers’ safe behavior. When either the reward value or the penalty value increases, the overall proportion of workers engaging in safe behavior significantly rises, driving the system toward a state of safe operations. This finding aligns with the results of Zohar et al. [39] and Qi et al. [40], who noted that incentive mechanisms can significantly influence construction workers’ safety-related decision making. Specifically, this study highlights that a simultaneous increase in both reward and penalty values leads to a more effective encouragement of safe behavior.

Second, compared to static rewards, the dynamic reward mechanism, which directly links rewards to the safety performance of the worker group, significantly enhances the extent to which workers choose safe behavior. This study demonstrates that the dynamic reward mechanism substantially increases the diffusion depth of safe behavior. Meng et al. [41] also noted in their research that the implementation of dynamic reward mechanisms yields better outcomes than static reward mechanisms.

Third, in the context of penalty mechanisms, spillover effects may negatively impact workers’ job satisfaction and psychological expectations, potentially undermining team collaboration. Therefore, managers should avoid a “one-size-fits-all” penalty system and reduce collective punishment practices, ensuring that penalties target individual violators rather than indiscriminately affecting the entire group. Mei et al. [42] also pointed out in their study that spillover penalties can demotivate enterprises that consistently invest in safety production.

Additionally, this study explores the impact of safety managers’ supervisory intensity on workers’ safe behavior. The simulation results indicate that as the intensity of safety supervisory increases, the diffusion depth of workers’ safe behavior significantly improves, suggesting that strengthening supervision can be an effective means of enhancing safety levels. This finding is consistent with the perspective of Fang et al. [43], who argued that managerial oversight can effectively reduce workers’ unsafe behaviors.

5.2. Suggestions

Based on the findings of this study, the following policy implications are proposed to enhance safety management practices in construction and other high-risk industries:

• Establishing a reasonable reward and punishment mechanism is a crucial strategy for enhancing construction workers’ safe behavior. Specifically, rewarding safe behavior while penalizing unsafe behavior can effectively regulate workers’ actions. Appropriately increasing reward and penalty values can further boost workers’ motivation to choose safe behavior and improve the overall effectiveness of safety supervision.
• Regarding the implementation of this reward and punishment mechanism, a dynamic reward mechanism should be emphasized. This approach links rewards to the safe performance of the worker group, thereby enhancing the diffusion of safe behavior. Compared with static rewards, dynamic reward mechanisms can better encourage workers to maintain safe behavior over the long term and foster a positive reinforcement cycle. Regarding penalties, a blanket approach should be avoided, especially in scenarios with spillover effects. Efforts should be made to prevent situations where the entire team is penalized due to the unsafe behavior of individual workers. It is recommended to adopt a precise punishment strategy, ensuring that penalties are targeted at specific violators rather than innocent team members. This helps to maintain team stability while effectively restraining unsafe behavior.
• Regarding safety supervision, it is necessary to appropriately enhance the supervisory intensity of safety managers and increase the frequency of on-site inspections. The timely identification and penalization of unsafe behaviors can significantly improve the effectiveness of safety supervision. At the same time, considering the increasing adoption of information technology, modern supervision tools, such as IoT monitoring and smart safety helmets, should be actively integrated into safety management. This allows for the real-time monitoring of workers’ safety and a better understanding of the safety status of the worker group.

6. Conclusions and Prospect

In summary, this research constructs a game model of construction workers’ safety supervision evolution based on the NW small-world network and systematically investigates the impacts of static incentive and penalty mechanisms, safety supervision intensity, dynamic reward mechanisms, and spillover penalty systems on construction workers’ safe behavior choices. Meanwhile, for the specific network structure, a sensitivity analysis of the initial proportion of safe behavior workers, network topology characteristics, and strategy updating rules is carried out to explore the influences of these factors on the evolution of the system. Based on the simulation analysis results, this research further proposes countermeasures for construction worker safety supervision, providing both theoretical foundations and practical guidance for improving safety management on construction sites.

However, it should be noted that this paper also has some limitations that need to be further improved and strengthened, including the following three aspects. (1) The study assumes that construction workers are homogeneous in the initial state, meaning all workers share the same characteristics. While this assumption simplifies the model construction and analysis process, the lack of consideration for individual differences may lead to discrepancies between model predictions and real-world situations. To better align with actual working conditions, future research could incorporate worker heterogeneity, such as developing differentiated models for workers in different trades. (2) To ensure model operability, this study simplifies the behavioral decision-making processes of workers, without fully accounting for other factors influencing workers’ safety behavior. Since workers’ decision making is a result of multiple interacting factors, future studies should consider the impacts of dynamic changes on construction sites, including different construction stages, shifting external environments, and workers’ psychological states. (3) This research primarily relies on theoretical modeling and simulation analysis, with a relatively limited application of empirical data. Future studies could integrate real-world engineering projects, collect worker behavior data, and validate the model’s effectiveness. Additionally, case studies could be used to explore the practical effects of different incentive mechanisms, enhancing the practical relevance of the research findings.