Evolutionary Game Analysis of Credit Supervision for Practitioners in the Water Conservancy Construction Market from the Perspective of Indirect Supervision

Abstract

Credit supervision of practitioners in the water conservancy construction market, a vital pillar of national infrastructure development, significantly impacts project safety and the maintenance of order in the industry. From the perspective of indirect supervision, this study constructs a tripartite evolutionary game model involving government departments, enterprises, and practitioners to analyze the dynamic evolution mechanism of credit supervision. By examining the strategic interactions among the three parties under different regulatory scenarios, we identify key factors influencing the stable equilibrium of evolution and verify the theoretical conclusions through numerical simulations. The study yields several key insights. First, while government regulation and social supervision can substantially increase the likelihood of practitioners’ integrity, relying solely on administrative regulation has an efficiency limit. Second, the effectiveness of the reward and punishment mechanism of the direct manager plays a crucial leveraging role in credit evolution. Lastly, under differentiated regulatory strategies, high-credit practitioners respond more strongly to long-term cost optimization, while low-credit practitioners are more effectively deterred by short-term, high-intensity disciplinary actions. Based on these findings, this study proposes a systematic governance framework of “regulatory model innovation–corporate responsibility enhancement–social supervision deepening.” Unlike previous studies, this framework adopts a comprehensive approach from three dimensions: regulatory model innovation, corporate responsibility enhancement, and social supervision deepening. It offers a more holistic and systematic solution for refining the credit system in the water conservancy construction market, providing both theoretical support and practical approaches.

1. Introduction

This study centers on the crucial area of credit supervision for practitioners in the water conservancy construction market. Water conservancy construction is a vital part of national infrastructure development, and the credit status of practitioners in this market directly impacts the quality, safety, and progress of projects, thereby influencing the healthy and stable development of the entire industry. However, existing research on credit supervision has significant shortcomings. Previous studies have predominantly focused on direct supervision models with the government as the sole subject, lacking in-depth discussions on the complex interactions among the government, enterprises, and practitioners in credit supervision, and failing to fully consider the dynamic nature of credit behavior, which changes over time and with the environment.

Given this, this study aims to break through the limitations of traditional research. From the perspective of indirect supervision, it constructs an evolutionary game model involving the government, enterprises, and practitioners. Through this model, it delves into the strategic choices and dynamic evolution processes of the three parties under different regulatory scenarios, exploring key factors that influence the stable equilibrium of credit supervision, such as the intensity of government regulation, the reward and punishment mechanisms of enterprises, and the credit awareness of practitioners. Ultimately, based on the research findings, a systematic governance framework is proposed to provide theoretical support and practical guidance for optimizing credit supervision of practitioners in the water conservancy construction market, contributing to improvement in the industry’s credit system and the regulation of order in the market.

In recent years, alongside the rapid growth of China’s economy, the water conservancy industry, as one of the basic industries of the national economy has also witnessed substantial development. China’s investment in water conservancy construction exceeded CNY 1 trillion in 2022, making an important contribution to stabilizing the general macroeconomic situation and driving the economy toward steady growth and upward momentum. However, a series of water conservancy construction market practitioners, such as illegal affiliation, fraud, bribery, and other malpractices, have frequently emerged as prominent issues in the current water conservancy construction sector. Moreover, the lack of credibility among practitioners in the water conservancy construction market has severely hindered the sustainable development of water conservancy. Therefore, exploring regulatory strategies for practitioners in the water conservancy construction market to promote their integrity has become an urgent problem to be solved. Strengthening the utility of government supervision represents a critical initiative at this stage to address the problem of bad faith among such practitioners. Government departments strive to solve the problem of bad behavior among credit practitioners. The main goal is to establish a comprehensive water conservancy construction market credit system as the core of the regulatory mechanism. Since the establishment of the water conservancy construction market service supervision platform and credit information platform, the two supervision platforms have been gradually improved, considerably optimizing the water conservancy construction market credit system and making it more practical, scientific, and effective. However, the construction of China’s credit system for the water conservancy construction market has undergone a relatively lengthy process, with the current level of development remaining low and still in its primary stage. In the short term, it does not effectively constrain the behavior of practitioners or compel them to uphold good faith. In this case, to curb the problem of practitioners’ lack of credibility, it is necessary to strengthen the utility of government supervision.

Since the reform and opening up of China, the form of government supervision is changing from the traditional direct supervision of “covering everything” to the indirect supervision of “streamlining administration and instituting decentralization.” In the early days of the water conservancy qualification system, the water administrative department assumed the responsibility for the qualification management of water conservancy practitioners, implementing a direct supervision model. As the Ministry of Water Resources underwent governmental function transformation, it transferred the supervision of cost estimators, quality inspectors, and other aspects of water conservancy practitioners’ qualification management to the Chinese Hydraulic Engineering Society. These water conservancy practice qualifications began to be monitored by industry self-regulation, according to the latest water conservancy cost engineers, supervision engineers, and other managing engineers. Practitioners in water administrative departments at all levels are responsible for supervision. Meanwhile, relevant self-regulatory organizations in the water conservancy industry also play an important role in strengthening the water conservancy practitioners’ self-discipline, while encouraging water conservancy practitioners to join relevant industry self-regulatory organizations. Therefore, at present, practitioners in China’s water conservancy construction market implement the dual regulatory model of direct supervision and indirect supervision based on industry self-regulatory management. However, inherent limitations in both government and industry self-regulation have hindered the effective implementation of direct and indirect supervision roles in the water conservancy construction market. Specifically, these dual regulatory approaches have failed to form effective constraints on practitioners, leaving the problem of credit deficiency among water conservancy construction market participants unresolved. Considering this paper’s indirect regulatory perspective, regulatory strategy research by practitioners in the water conservancy construction market is conducive to solving the problem of water conservancy construction market practitioners’ lack of credibility, thereby promoting the healthy development of the water conservancy industry and stabilizing the national economy and society.

The world’s earliest registration system for practitioners is the system of certified building engineers established in 1843 in the United Kingdom. This system has been developed for approximately 180 years and has formed a set of relatively mature practice qualification systems. It was subsequently adopted in countries such as the United States, France, and Japan. By comparison, China’s development in this field is relatively recent. Owing to the early initiation, completeness, and maturity of foreign practice qualification systems, foreign research literature related to this area is relatively limited and mainly involves the construction of practitioner qualification certification systems and qualification registration systems. Winch [1] and Turne [2] advocated integrating the two management concepts of “project management” and “personnel management” in the licensing system to give full expression to the role of collaboration between actual controllers and practitioners in the process of comprehensive management of engineering projects. George et al. [3] explored the connection or relationship between public policy and engineering construction reform. In addition, scholars have frequently attempted to apply the international practice qualification system to the study of the practice system in their countries. Hea et al. [4] looked for ways to improve the qualification requirements for interior architecture in Korea by analyzing the qualification systems at home and abroad. China’s practice qualification system represents a major initiative to reform the management of vocational and technical talents. Guided by the principle of balancing compulsoriness and flexibility, this system aims to improve the standardization of the state’s management and cultivation of relevant vocational and technical talents while aligning with the market economy’s principle of prioritizing the market mechanism’s regulatory role.

Many scholars in the field of regulatory theory have observed that traditional Western regulatory theory holds a monistic view, considering the government as the sole regulatory authority. However, with the development of the market economy, there has been a shift towards the pluralism of regulatory bodies, forming new types of regulation and applying them to various industries. Traditional Western regulatory theory advocates that the government is the only regulatory subject and can monopolize the right to regulate, equating regulation with government regulation. However, with the development of the market economy, scholars generally realize that the regulatory body is not limited to the government; instead, it should also include non-governmental organizations, individuals, and third-party regulatory bodies. Consequently, both in theoretical research and practical application, there has been a shift toward the two-way expansion of governmental and non-governmental regulation. Scholars have gradually come to a consensus on the pluralism of regulatory bodies, eventually formed a new type of regulation represented by collaborative, responsive, and voluntary regulation, and began to be apply it to the regulation of various industries.

Foreign scholars have conducted in-depth research on government regulation in the construction field, focusing on regulatory mechanisms, modes, and systems. The study of government regulation emerged first in the United States in the 1970s. The focus of this study is mainly concentrated in the fields of economics, politics, jurisprudence, and other disciplines. In the field of construction, foreign scholars have also carried out in-depth research, primarily focusing on regulatory mechanisms, modes, systems, etc. [5,6,7]. Hancger et al. [8] suggested that in order to build a high-quality supervision system, efforts should be made to evaluate supervision and develop a set of rigorous certification systems to regulate the market access of construction enterprises; Michael and Alexander [9] claimed that to improve government enthusiasm for supervising PPP projects, the performance of the project must be linked to the supervisors so as to strengthen the responsibility of the project supervisors. Robert [10] highlighted the necessity of increasing incentives for the construction team to minimize costs and improve project quality. Kaiser et al. [11] proposed and constructed an integrated supervision method and system for assessing construction project quality on the basis of analyzing the current development situation of the construction market. Concurrently, foreign scholars have researched government supervision, market regulation, public participation, and stakeholder supervision. They have also constructed a relatively sound water conservancy construction market supervision system based on credit, insurance, guarantee, etc., which is of great significance for the supervision of China’s water conservancy construction market main body. Meanwhile, at present, market supervision is predominantly adopted for practitioners, resulting in limited research literature on practitioner supervision.

Many domestic and foreign scholars have conducted research on social supervision in the construction field, mainly involving NGOs and the public. Foreign research in this area is relatively mature, while domestic research is still in the primary stage. In the water conservancy construction market, research on the social indirect supervision of practitioners is also in the initial stage. Social supervision refers to supervision and management by non-governmental organizations (NGO), social public enterprises, network media, etc. If it performs well, it can effectively inhibit the behavior of the regulated and improve the utility of government supervision. The concept of the NGO originated in the middle of the 19th century and was defined by the United Nations. Any organization not established under an intergovernmental agreement can be considered an NGO. The four main types of NGO in China are civic academic associations, private non-enterprise units, highly administrative organizations (e.g., the Communist Youth League, etc.) or relatively administrative organizations (such as trade associations).

At present, non-governmental supervision in China’s water conservancy construction market is mainly implemented through the purchase of social services and self-regulatory management by industry associations. Public supervision is also incorporated into this process through social service procurement. Public supervision mainly refers to the general public using letters, visits, networks, media, and other methods to communicate complaints, criticisms, suggestions, whistleblowing, accusations, etc. Generally, it focuses on post-incident supervision. At present, in terms of the theory of public social supervision, foreign research is relatively mature, not only involving various sectors of society but also rich in practical experience. However, domestic research in this field is still in the primary stage due to the influence of social systems and cultural backgrounds. Some domestic scholars have also explored the issue of the public supervision of society in the field of construction. In general, the research on social indirect supervision of practitioners in the water conservancy construction market at home and abroad is still in the initial stage. Sun et al. [12] constructed a media supervision mechanism for enterprise subjects by introducing a game model, verified the utility of media supervision in improving the supervision mechanism, and put forward an innovative idea for indirect supervision. Zhao and Sun [13] proposed a new type of credit supervision by analyzing the tripartite game among the government, the safety supervisory platform, and the practitioners. They verified that the credit feedback mechanism based on indirect supervision could operate effectively. They also considered the implementation of a reasonable reward and punishment mechanism by the government on the basis of the credit supervision mechanism to be an important measure to realize the ideal stable state. Wu et al. [14] constructed a networked game model of joint supervision by the government, enterprises, and third-party associations based on the problems of the cost of supervision in the construction market and the inefficiency of the supervision, etc. They verified the influence of government regulatory efficiency and social demand on the adoption of socially beneficial decisions by enterprises. Hu et al. [15] analyzed the behavior of stakeholders in high-risk production scenarios and pointed out that the level of government penalties does not affect the strategic choices of enterprises. However, they claimed that it does affect the system’s evolution towards the optimal state. They also noted that the government’s regulatory effectiveness is inhibited by the environment to a certain extent, highlighting the urgent need for a new and efficient regulatory mechanism. Chang [16] further examined firms’ green production strategies and pointed out that government incentives and public scrutiny affect the likelihood of firms adopting green production decisions, revealing the importance of socially beneficial decision-making for individuals or firms under the indirect regulatory model.

When delving into the credit behavior of practitioners, scholars are biased towards the motivations behind credit behavior decision-making, the meaning of bad faith behavior, influencing factors, and governance. In terms of the motivations behind credit behavior decision-making, Hegarty et al. [17] proposed that costs and benefits have an important influence on employee behavior, based on their study of malpractice motivation. May et al. [18] argued that factors such as the team, interpersonal relationships, organizational context, and individuals exert an impact on employee credit behavior. Branzei et al. [19] observed that the corporate culture affects the credit level of employees within the enterprise. Sheldon [20] verified the influence of psychological needs on credit behavior through a model. Based on the credit violation situation in South Africa’s construction market, Bowen et al. [21] proposed that credit violation includes two aspects: information leakage and conflict of interest. They also suggested that severe penalties or supervision, regular and irregular inspections, and strengthening corporate culture can effectively reduce misconduct in the construction market. Kim et al. [22,23] posited that an organization’s mistreatment of employees can induce normative behavioral responses from them. Many experts believe that professional codes can effectively reduce the bad behavior of employees. However, in practice, even with a professional code, employees’ lack of credibility is unavoidable [24]. In the research on regulation strategies for the water conservancy construction market, scholars usually adopt the methods of system dynamics or evolutionary game theory, which involves the regulation of environmental governance [25,26], internet finance [27,28,29], and construction safety [30,31,32].

To summarize, there are relatively few studies on the water conservancy practice qualification system at home and abroad, and the focus of the studies mainly involves the construction and implementation of the system. There are considerable studies on credit behavior, credit evaluation, and the credit system of construction market practitioners. However, they are mainly concentrated on the construction industry, with research regarding water conservancy construction market practitioners rarely reported. At present, some scholars employ evolutionary game theory to analyze regulatory strategies for construction market practitioners; however, their analyses of regulatory strategies remain incomplete. Moreover, the market targeted by this study is mostly the construction market, with minimal research addressing the specific context of the water conservancy construction market. In response to this gap, this paper, from the perspective of indirect regulation, adopts evolutionary game theory and system dynamics methods to systematically research a regulatory strategy got water conservancy construction market practitioners, thereby enriching the governance system of the water conservancy construction market.

2. Model Building

2.1. Problem Description and Model Construction

Currently, regulatory enforcement is confronted with numerous predicaments. The issues plaguing regulatory bodies, such as an imperfect regulatory system, inadequate regulatory capabilities, and insufficient regulatory independence, along with the problems in market incentives—including the conflict between enterprises’ profit, oriented goals and quality, and safety objectives, the irrational incentive mechanisms for practitioners, and the absence of incentive mechanisms for public supervision—collectively hinder the effective implementation of law enforcement. This paper primarily focuses on analyzing the game relationships among government departments, enterprises, and practitioners during government supervision of practitioners in the water conservancy construction market. It aims to innovate the regulatory governance framework with the hope of enhancing governance efficiency.

This study selects evolutionary game theory to construct the supervision model for practitioners in the water conservancy construction market, as it aligns well with the characteristics of this scenario. Water conservancy regulation involves multiple bounded–rational actors, including government departments, enterprises, and practitioners, who have limitations in information acquisition and cognition. Evolutionary game theory does not require complete rationality but focuses on the dynamic strategy adjustment process of actors based on limited information, which is consistent with the actual situation. Water conservancy regulation is complex and dynamic, with each actor’s strategy changing over time in response to the environment and based on the behaviors of other actors. For example, the government adjusts the intensity of regulation according to the violation situation, enterprises change their business strategies according to policies, and practitioners modify their professional behaviors according to regulatory requirements. This theory can simulate the dynamic evolution of strategies, analyze payoff changes to reveal strategy stability and trends, help us understand the interactions among actors and the long-term changes in the system, predict strategy choices and system directions under different policies, and provide theoretical support for formulating effective regulatory policies, making it an appropriate method for studying this complex problem.

The process of direct government supervision of practitioners in the water conservancy construction market involves three core subjects: water administrative authorities at all levels (hereinafter referred to as government departments), water conservancy teams where practitioners are registered (hereinafter referred to as enterprises), and practitioners. In the process of water conservancy project construction, the government departments, as the regulator, regulate the behavior of enterprises and practitioners. Enterprises are both regulated by the government departments and, as a supervisor, supervise and manage the behavior of practitioners. Practitioners are the regulated subjects, whose practices are under the dual supervision of government departments and enterprises. The game relationship among government departments, enterprises, and practitioners is illustrated in Figure 1, where the dashed arrows represent the information-disadvantaged parties.

In the process of government supervision of practitioners in the water conservancy construction market, the interests of government departments, enterprises, and practitioners are inconsistent. Specifically, government departments primarily aim to ensure project quality and safety implementation to maintain social stability and uphold government image; enterprises seek to achieve the goal of the contract and pursue profit maximization; and practitioners mainly focus on completing tasks assigned by enterprises and maximizing their personal interests. Therefore, under information asymmetry and lax government supervision, practitioners may engage in dishonest behaviors such as fraud or bribery to maximize personal interests. Meanwhile, enterprises, aiming to save costs, may relax the supervision and management of the practitioners or even collude in rent-seeking and conceal unethical conduct to pursue greater profits, exacerbating moral hazard under asymmetric information. In the process of water conservancy project construction, the enterprise will entrust the task of project construction to the practitioners. Relative to the enterprise, the practitioners, as the main executors of the project, have a natural information advantage. Practitioners’ personal interests and the enterprise’s goals are different. Therefore, when enterprises actively manage the behavior of the practitioners, the practitioners may still engage in credibility deficiencies—such as breaching contractual agreements with enterprises—to serve their own interests under information asymmetry, acts that are detrimental to corporate interests.

This paper studies the game relationship among government departments, enterprises, and practitioners in the water conservancy construction market. It also considers the effects of cost, overhead input, rewards and punishments, public supervision, and losses caused by problems in the project on the strategic choices of the government, enterprises, and practitioners. Moreover, the following hypotheses are put forward:

Assumption 1.

All parties involved in the game are bounded rational individuals, specifically including government departments, enterprises, and practitioners. The strategy space of the government department is (strict regulation, not strict regulation); the strategy space of the enterprise is (positive management, negative management); and the strategy space of the practitioners is (honesty, bad faith). No bribery or harboring occurs between government departments and practitioners and enterprises. However, there is rent-seeking behavior between enterprises and practitioners.

Assumption 2.

The government department strictly regulates the behavior of practitioners with probability $x$ and does not strictly regulate with probability $1-x$. The cost of strict regulation by a government department is $C_1$, the intensity of regulation when it is not strict is $r_1$, and there will not be a situation where the government department does not regulate at all, i.e., $r_1>0$. In the process of regulation, if the government department finds that the behavior of practitioners is honest, it rewards them $E$, and penalizes them for the opposite $F$; if the government department finds that firms actively manage practitioners, it rewards the firms $J$, and penalizes them for the opposite $Q$.

Assumption 3.

Firms manage practitioner behavior positively with probability  $y$ and negatively with probability $1-y$. Firms positively manage costs $C_2$, management efforts $r_2$, and firms’ rent-seeking probability $1-r_2$. Enterprises managing practitioners will be punished if they are found to be lacking credibility $I$. Conversely, when practitioners have been practicing with integrity, they will be rewarded by the enterprise $K$, including bonuses, promotions, honors, etc.

Assumption 4.

The practitioner adopts a good faith strategy during the construction of a water project with probability $z$ and a bad faith strategy with probability $1-z$. The practitioner receives a gain of $R_1$ for completing the project and an additional gain of $R_2$ for adopting the bad faith strategy. The practitioner, when adopting the bad faith strategy, gives the firm a certain amount of money to seek shelter, and the firm receives a gain $R_3$ if the rent-seeking is successful.

Assumption 5.

The public, too,  $w$ ($0\le w\le 1$) have the strength to monitor and report the behavior of practitioners. Successful public supervision and reporting of practitioners’ lack of credibility behavior, if investigated and dealt with by the enterprise, will be rewarded by the practitioner $R_4$; if at this time, the enterprise’s negative management is investigated and dealt with by the government departments, it will be rewarded by the enterprise; if government departments fail to strictly supervise the enterprise’s negative management, the credibility of the government departments will decline $G$, the enterprise will be subjected to additional penalties $Q_1$, and the credibility of the practitioner will also be affected $L$.

Assumption 6.

In general, the malpractice of the practitioners may lead to certain engineering hazards in the water conservancy project, which will bring direct or potential risks to the project. Moreover, the projects risk of loss is affected by the intensity of the supervision, duration, and the degree of harm. Enterprises and practitioners belong to a principal–agent relationship, and, to a certain extent, form a community of interest and bear joint and several liability. Assume that when the practitioner adopts a trust-breaking strategy, the practitioner expects a loss of $D$, and the proportion of this loss passed on to the firm is $\alpha$. If the firm chooses an active management strategy, it bears the loss discount factor $\beta$.

Assumption 7.

All parameters in this game model can be numerically expressed, with no consideration given to the influence of external factors outside the model. The specific meanings of the parameters are presented in

Table 1. Parameter description.

Parameters	Meaning and Description
$x$	$\mathrm{Government} \mathrm{departments} \mathrm{to} \mathrm{adopt} \mathrm{strict} \mathrm{regulatory} \mathrm{probabilities}; 0\le x\le 1$
$C_1$	Costs of adopting strict regulation incurred by government departments
$r_1$	$\mathrm{Intensity} \mathrm{of} \mathrm{regulation} \mathrm{by} \mathrm{government} \mathrm{departments}; 0<r_1<1$
$E$	Rewards from government departments when practitioners are honest
$F$	Penalties for government departments when practitioners lack credibility
$J$	Incentives from government departments when companies adopt proactive management strategies
$Q$	Penalties imposed by government departments when enterprises adopt negative management strategies
$y$	$\mathrm{Probability} \mathrm{of} \mathrm{a} \mathrm{firm} \mathrm{adopting} \mathrm{an} \mathrm{active} \mathrm{management} \mathrm{strategy} 0\le y\le 1$
$C_2$	Costs when firms adopt active management strategies
$r_2$	$\mathrm{Business} \mathrm{management} \mathrm{efforts} 0<r_2<1$
$I$	Penalties for firms when a practitioner lacks credibility
$K$	Rewards for businesses when practitioners are honest
$z$	$\mathrm{Probability} \mathrm{of} \mathrm{a} \mathrm{practitioner} \mathrm{using} \mathrm{an} \mathrm{honest} \mathrm{strategy}; 0\le z\le 1$
$R_1$	Normal earnings of practitioners on completion of projects
$R_2$	Additional benefits for practitioners adopting bad faith strategies
$R_3$	Benefits of successful rent-seeking by firms and practitioners
$w$	Efforts of the public to monitor and report the behavior of practitioners
$R_4$	Benefits of successful reporting by the public
$G$	Loss of credibility of government departments in adopting less stringent regulatory strategies when the public report successfully
$Q_1$	Additional penalties imposed by government departments on enterprises for negative management in the event of a successful report by the public
$L$	Loss of credibility of the practitioner in the event of successful public reporting
$D$	Anticipated losses, including honor and finances, incurred by a practitioner who adopts a bad faith strategy
$\alpha$	$\mathrm{Percentage} \mathrm{of} \mathrm{losses} \mathrm{passed} \mathrm{on} \mathrm{to} \mathrm{the} \mathrm{business} \mathrm{when} \mathrm{the} \mathrm{practitioner} \mathrm{causes} \mathrm{the} \mathrm{project} \mathrm{to} \mathrm{be} \mathrm{lost}; 0\le \alpha \le 1$
$\beta$	$\mathrm{Discount} \mathrm{factor} \mathrm{for} \mathrm{losses} \mathrm{incurred} \mathrm{by} \mathrm{the} \mathrm{firm} \mathrm{when} \mathrm{it} \mathrm{adopts} \mathrm{an} \mathrm{active} \mathrm{management} \mathrm{strategy}; 0<\beta <1$

.

According to the above assumptions, the mixed-strategy game payment matrix can be constructed for the government departments, enterprises, and practitioners in the water conservancy construction market, as shown in

Table 2. Game payment matrix.

Government Branch	Corporations	Practitioner
		Integrity ($\mathit{z}$)	Lack of Credibility ($1-\mathit{z}$)
Strict supervision ($x$)	Active management ($y$)	$-C_1-E-J$ $J-C_2-K$ $R_1+E+K$	$F-C_1-J$ $J+I-\alpha \beta D-C_2$ $R_1+R_2-F-I-D-w(R_4+L)$
	Negative management $(1-y$)	$Q-C_1-E$ $-r_2{C}_2-Q-r_{2}K$ $R_1+E+r_{2}K$	$F-C_1+Q+w{Q}_1$ $r_{2}I-r_2{C}_2-Q-\alpha D+(1-r_2)R_3-w(R_4+Q_1)$ $R_1+R_2-(1-r_2)R_3-F-D-r_{2}I-wL$
Not strictly regulated $(1-x$)	Active management ($y$)	$-r_{1}E-r_1{C}_1-r_{1}J$ $r_{1}J-C_2-K$ $R_1+K+{\mathrm{r}}_{1}E$	$r_{1}F-r_1{C}_1-r_{1}J$ $r_{1}J+I-\alpha \beta D-C_2$ $R_1+R_2-I-r_{1}F-D-w(R_4+L)$
	Negative management $(1-y$)	$r_{1}Q-r_1{C}_1-r_{1}E$ $-r_2{C}_2-r_{1}Q-r_{2}K$ $R_1+r_{1}E+r_{2}K$	$r_{1}F-r_1{C}_1+r_{1}Q-wG+r_{1}w{Q}_1$ $r_{2}I-r_2{C}_2-r_{1}Q-\alpha D+(1-r_2)R_3-r_{1}w(R_4+Q_1)$ $R_1+R_2-(1-r_2)R_3-r_{1}F-D-r_{2}I-wL$

.

2.2. Model Solving and Analysis

2.2.1. Analysis of Regulatory Strategies of Government Departments

The government department’s strict regulation strategy, non-strict regulation strategy, and the average expected return are $U_{11}$, and $U_{12}$, and $U_1$, respectively, which can be obtained according to the game payment matrix:

$$\begin{array}{cc}\hfill U_{11}& =yz(-C_1-E-J)+y(1-z)(F-C_1-J)\hfill \\ & +(1-y)z(Q-C_1-E)+(1-y)(1-z)(F-C_1+Q+w{Q}_1)\\ & =(1-z)F-C_1+(1-y)Q-yJ-zE+(1-y)(1-z)w{Q}_1\end{array}$$

(1)

$$\begin{array}{cc}\hfill U_{12}& =yz(-r_{1}E-r_1{C}_1-r_{1}J)+y(1-z)(r_{1}F-r_1{C}_1-r_{1}J)\hfill \\ \hfill & +(1-y)z(r_{1}Q-r_1{C}_1-r_{1}E)+(1-y)(1-z)(r_{1}F-r_1{C}_1+r_{1}Q-wG+r_{1}w{Q}_1)\hfill \\ \hfill & =r_1\left[(1-z)F-C_1+(1-y)Q-yJ-zE\right]+w(r_1{Q}_1-G)(1-y)(1-z)\hfill \end{array}$$

(2)

$$U_1=\mathrm{x}{U}_{11}+(1-x)U_{12}$$

(3)

According to Formulas (1)–(3), the replication dynamics equation of the government department $F(x)$ can be obtained as

$$\begin{array}{ll}F(x)& ={\displaystyle \frac{dx}{dt}}=x(U_{11}-U_1)=x(1-x)(U_{11}-U_{12})\\ & =x(1-x)\left\{\begin{array}{l}(1-r_1)\left[(1-z)F-C_1+(1-y)Q-yJ-zE\right]\\ +(1-y)(1-z)w\left[(1-r_1)Q_1+G\right]\end{array}\right\}\end{array}$$

(4)

2.2.2. Analysis of Firms’ Expected Return Game Strategies

Assuming that the firm’s positive management strategy, negative management strategy, and average expected return are $U_{21}$, $U_{22}$, and $U_2$, and based on the game payment matrix, the following formulas can be obtained:

$$\begin{array}{cc}\hfill U_{21}& =\mathrm{x}z(J-C_2-K)+x(1-z)(J+I-\alpha \beta D-C_2)\hfill \\ \hfill & +(1-x)z(r_{1}J-C_2-K)+(1-x)(1-z)(r_{1}J+I-\alpha \beta D-C_2)\hfill \\ \hfill & =(x-x{r}_1+r_1)J+(1-z)I-(1-z)\alpha \beta D-C_2-zK\hfill \end{array}$$

(5)

$$\begin{array}{ll}{U}_{22}& =\mathrm{x}z(-r_2{C}_2-Q-r_{2}K)+x(1-z)\left[r_{2}I-r_2{C}_2-Q-\alpha D+(1-r_2)R_3-w(R_4+Q_1)\right]\\ & +(1-x)z(-r_2{C}_2-r_{1}Q-r_{2}K)\\ & +(1-x)(1-z)\left[r_{2}I-r_2{C}_2-r_{1}Q-\alpha D+(1-r_2)R_3-r_{1}w(R_4+Q_1)\right]\\ & =-r_2{C}_2-(x+r_1-x{r}_1)Q-z{r}_{2}K\\ & +(1-z)\left[r_{2}I-\alpha D+(1-r_2)R_3-w(R_4+Q_1)(x+r_1-x{r}_1)\right]\end{array}$$

(6)

$$U_2=\mathrm{y}{U}_{21}+(1-y)U_{22}$$

(7)

According to Formulas (5)–(7), the replication dynamic equation of the enterprise strategy $F(y)$ can be obtained as

$$\begin{array}{ll}F(y)& ={\displaystyle \frac{dy}{dt}}=y(U_{21}-U_2)=y(1-y)(U_{21}-U_{22})\\ & =y(1-y)\left\{\begin{array}{l}(x-x{r}_1+r_1)(J+Q)-(1-r_2)C_2-(1-r_2)zK\\ -(1-z)\left[\begin{array}{l}(1-r_2)(R_3-I)-(1-\beta )\alpha D\\ -w(x+r_1-x{r}_1)(R_4+Q_1)\end{array}\right]\end{array}\right\}\end{array}$$

(8)

2.2.3. Analysis of Practitioners’ Expected Return Game Strategies

Assuming that the practitioner’s honesty strategy, default strategy, and average expected return are $U_{31}$, $U_{32}$, and $U_3$, and based on the game payment matrix, the following formulas can be obtained:

$$\begin{array}{ll}{U}_{31}& =\mathrm{xy}(R_1+E+K)+x(1-y)(R_1+E+r_{2}K)\\ & +(1-x)y(R_1+K{+\mathrm{r}}_{1}E)+(1-x)(1-y)(R_1+r_{1}E+r_{2}K)\\ & =R_1+(x+{\mathrm{r}}_1-x{\mathrm{r}}_1)E+(y+{\mathrm{r}}_2-y{\mathrm{r}}_2)K\end{array}$$

(9)

$$\begin{array}{ll}{U}_{32}& =\mathrm{xy}\left[R_1+R_2-F-I-D-w(R_4+L)\right]\\ & +x(1-y)\left[R_1+R_2-(1-r_2)R_3-F-D-r_{2}I-wL\right]\\ & +(1-x)y\left[R_1+R_2-I-r_{1}F-D-w(R_4+L)\right]\\ & +(1-x)(1-y)\left[R_1+R_2-(1-r_2)R_3-r_{1}F-D-r_{2}I-wL\right]\\ & =R_1+R_2-D-(1-y)(1-r_2)R_3-(x+r_1-x{r}_1)F-(y+r_2-y{r}_2)I-wL-yw{R}_4\end{array}$$

(10)

$$U_3=\mathrm{z}{U}_{31}+(1-z)U_{32}$$

(11)

According to Formulas (9)–(11), the replication dynamic equation of the practicing personnel $F(z)$ can be obtained as

$$\begin{array}{ll}F(z)& ={\displaystyle \frac{dz}{dt}}=z(U_{31}-U_3)=z(1-z)(U_{31}-U_{32})\\ & =z(1-z)\left[\begin{array}{l}(x+{\mathrm{r}}_1-x{\mathrm{r}}_1)(E+F)+(y+{\mathrm{r}}_2-y{\mathrm{r}}_2)(K+I)\\ -R_2+D+(1-y)(1-r_2)R_3+wL+yw{R}_4\end{array}\right]\end{array}$$

(12)

2.3. Evolutionary Stability Analysis

2.3.1. Evolutionary Game Analysis of Game Subjects

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Evolutionary Equilibrium Analysis of Government Sectors

Derivation of Equation (4) yields

$$F^{\prime }(x)=(1-2x)\left\{\begin{array}{l}(1-r_1)\left[(1-z)F-C_1+(1-y)Q-yJ-zE\right]\\ +(1-y)(1-z)w\left[(1-r_1)Q_1+G\right]\end{array}\right\}$$

(13)

The stability theorem of differential equations reveals that the strategy choice of the government sector $x$ has to satisfy $F(x)=0,F^{\prime }(x)<0$ to be stable. According to the theorem, the strategy choices of government departments will be analyzed for stability.

Let $\mathrm{X}={\displaystyle \frac{(1-r_1)\left[(1-z)F-C_1+Q-zE\right]+(1-z)w\left[(1-r_1)Q_1+G\right]}{(1-z)w\left[(1-r_1)Q_1+G\right]+(1-r_1)(Q+J)}}$, as shown in Figure 2. When $\mathrm{y}=\mathrm{X}$, then $F(x)\equiv 0$. At this time, all the values will be in a stable state; if $y\ne \mathrm{X}$, then let $F(x)=0$; two stable points, $x=0$ and $x=1$, can be obtained.

When $y>\mathrm{X}$, $F^{\prime }(0)<0, F^{\prime }(1)>0$, i.e., $x=0$ is a stable strategy, the government department chooses not to regulate strictly; when $y<\mathrm{X}$, $F^{\prime }(0)>0, F^{\prime }(1)<0$, i.e., $x=1$ is a stable strategy, the government department chooses to regulate strictly. Therefore, according to the evolutionary strategy of practitioners, it can be concluded that the probability of strict regulation by government departments decreases as the probability of active management by enterprises increases and decreases as the probability of practitioner integrity increases.

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Evolutionary Equilibrium Analysis of Firms

The derivation of Equation (8) yields

$$F^{\prime }(y)=(1-2y)\left[\begin{array}{l}(x-x{r}_1+r_1)(J+Q)-(1-r_2)C_2-(1-r_2)zK\\ -(1-z)\left[(r_2-1)I-(1-\beta )\alpha D+(1-r_2)R_3-w(x+r_1-x{r}_1)(R_4+Q_1)\right]\end{array}\right]$$

(14)

The stability theorem of differential equations indicates that the firm’s strategy choice $y$ has to satisfy $F(y)=0,F^{\prime }(y)<0$ to be stable. According to the theorem, the strategy choice of the firm will be analyzed for stability.

Let $\mathrm{Y}={\displaystyle \frac{(1-r_2)(R_3+C_2-I)-(1-\beta )\alpha D-(x-x{r}_1+r_1)(J+Q+w(R_4+Q_1))}{(1-r_2)(R_3-K-I)-(1-\beta )\alpha D-w(x+r_1-x{r}_1)(R_4+Q_1)}}$, as shown in Figure 3. When $\mathrm{z}=\mathrm{Y}$, then $F(y)\equiv 0$. At this time, all the values will be in a stable state; if $z\ne Y$, then let $F(y)=0$; two stable points, $y=0$ and $y=1$, can be obtained.

When $z>Y$, at time $F^{\prime }(0)>0, F^{\prime }(1)<0$, i.e., $y=1$ is a stable strategy, the enterprise chooses positive management; when $z<Y$, $F^{\prime }(0)<0, F^{\prime }(1)>0$, i.e., $y=0$ is a stable strategy, the enterprise chooses negative management. Therefore, according to the evolution strategy of enterprises, it can be concluded that the probability of positive management of enterprises increases with increasing probability of strict supervision by government departments. This underscores that the probability of strict supervision by government departments plays a promotional role in mobilizing the enthusiasm of enterprise management.

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Evolutionary Equilibrium Analysis of Practitioners

The derivation of Equation (12) yields

$$F(z)=(1-2z)\left[\begin{array}{l}(x+{\mathrm{r}}_1-x{\mathrm{r}}_1)(E+F)+(y+{\mathrm{r}}_2-y{\mathrm{r}}_2)(K+I)\\ -R_2+D+(1-y)(1-r_2)R_3+wL+yw{R}_4\end{array}\right]$$

(15)

According to the stability theorem of differential equations, it is known that for a practitioner’s strategy choice $z$ to be a stable strategy, it must satisfy $F(z)=0,F^{\prime }(z)<0$. Following this theorem, the strategy choice of the practitioner will be analyzed for stability.

Let $\mathrm{Z}={\displaystyle \frac{R_2-(y+{\mathrm{r}}_2-y{\mathrm{r}}_2)(K+I)-D-(1-y)(1-r_2)R_3-wL-yw{R}_4-{\mathrm{r}}_1(E+F)}{(1-{\mathrm{r}}_1)(E+F)}}$, as shown in Figure 4. When $\mathrm{x}=\mathrm{Z}$, then $F(z)\equiv 0$. At this time, all the values are in a stable state; if $x\ne Z$, then let $F(z)=0$; two stable points, $z=0$ and $z=1$, can be obtained.

When $x>Z$, $F^{\prime }(0)>0, F^{\prime }(1)<0$, i.e., $z=1$ is a stable strategy, the practitioners choose honest behavior; when $x<Z$, only $F^{\prime }(0)<0, F^{\prime }(1)>0$, i.e., $z=0$ is a stable strategy, the practitioners choose dishonest behavior. Therefore, the evolutionary stable strategy of practitioners reveals that the probability of practitioners’ integrity increases with increasing probability of strict regulation by government departments and that of active management by enterprises.

2.3.2. Evolutionary Equilibrium Analysis of the Three-Way Game

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Equilibrium Analysis

In order to determine the equilibrium state in which the model evolves and stabilizes, we combined Equations (4), (8) and (12) such that $F(x)=0$, $F(y)=0$, and $F(z)=0$. Nine Nash equilibria can be obtained for this equation, including eight pure-strategy equilibrium solutions (0, 1, 0), (1, 1, 0), (0, 1, 1), (0, 0, 0), (1, 0, 1), (1, 1, 1), (1, 0, 0), and one mixed-strategy equilibrium solution ($x*$,$y*$,$z*$) and $x*$,$y*$,$z*$ ∈ (0, 1).

According to Friedman’s theory, the stability of the equilibrium point of the evolutionary game system can be analyzed using the Jacobian matrix. If the characteristic roots of the Jacobian matrix are all less than 0, its corresponding equilibrium point is the evolutionary stable strategy (ESS) of the system; otherwise, it is the source or saddle point.

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

(16)

Among them,

$$\left\{\begin{array}{l}{a}_{11}=(1-2x)\left\{\begin{array}{l}(1-r_1)\left[(1-z)F-C_1+(1-y)Q-yJ-zE\right]\\ +(1-y)(1-z)w\left[(1-r_1)Q_1+G\right]\end{array}\right\}\\ a_{12}=x(1-x)\left\{(1-r_1)(-Q-J)-(1-z)w\left[(1-r_1)Q_1+G\right]\right\}\\ a_{13}=x(1-x)\left\{(1-r_1)(F+E)-(1-y)w\left[(1-r_1)Q_1+G\right]\right\}\\ a_{21}=y(1-y)\left[(1-r_1)(J+Q)-(1-z)w(1-r_1)(R_4+Q_1)\right]\\ a_{22}=(1-2y)\left\{\begin{array}{l}(x-x{r}_1+r_1)(J+Q)-(1-r_2)C_2-(1-r_2)zK\\ -(1-z)\left[(r_2-1)I-(1-\beta )\alpha D+(1-r_2)R_3-w(x+r_1-x{r}_1)(R_4+Q_1)\right]\end{array}\right\}\\ a_{23}=y(1-y)\left[-(1-r_2)K+(r_2-1)I-(1-\beta )\alpha D+(1-r_2)R_3-w(x+r_1-x{r}_1)(R_4+Q_1)\right]\\ a_{31}=z(1-z)(1-{\mathrm{r}}_1)(E+F)\\ a_{32}=z(1-z)\left[(1-{\mathrm{r}}_2)(K+I)-(1-r_2)R_3+w{R}_4\right]\\ a_{33}=(1-2z)\left[\begin{array}{l}(x+{\mathrm{r}}_1-x{\mathrm{r}}_1)(E+F)+(y+{\mathrm{r}}_2-y{\mathrm{r}}_2)(K+I)\\ -R_2+D+(1-y)(1-r_2)R_3+wL+yw{R}_4\end{array}\right]\end{array}\right\}$$

(17)

According to Equations (16) and (17), the eigenvalues of each equilibrium point can be calculated, as shown in

Table 3. Eigenvalues of each equilibrium point.

Balance Point	Eigenvalue 1	Eigenvalue 2	Eigenvalue 3
(0, 0, 0)	$\begin{array}{l}(1-r_1)(w{Q}_1+F\\ +Q-C_1)+wG\end{array}$	$\begin{array}{l}{r}_1(J+Q+w{R}_4+w{Q}_1)\\ +(1-r_2)(I-C_2-R_3)\\ +(1-\beta )\alpha D\end{array}$	$\begin{array}{l}{r}_2(K+I)+r_1(E+F)\\ -R_2+(1-r_2)R_3+D+wL\end{array}$
(0, 1, 0)	$(1-r_1)(F-C_1-J)$	$\begin{array}{l}-(1-\beta )\alpha D\\ -(1-r_2)(I-C_2-R_3)\\ -r_1(J+Q+w{R}_4+w{Q}_1)\end{array}$	$\begin{array}{l}{r}_1(E+F)+w(L+R_4)\\ -R_2+K+I+D\end{array}$
(1, 1, 0)	$(1-r_1)(J-F+C_1)$	$\begin{array}{l}-(1-\beta )\alpha D-J-Q-w{R}_4\\ -(1-r_2)(I-C_2-R_3)-w{Q}_1\end{array}$	$\begin{array}{l}K+I+D+E+F\\ +w(L+R_4)-R_2\end{array}$
(0, 1, 1)	$-(1-r_1)(E+C_1+J)$	$(1-r_2)(C_2+K)-r_1(J+Q)$	$\begin{array}{l}{R}_2-K-r_1(E+F)\\ -w(L+R_4)-I-D\end{array}$
(0, 0, 1)	$(1-r_1)(Q-E-C_1)$	$r_1(J+Q)-(1-r_2)(C_2+K)$	$\begin{array}{l}{R}_2-(1-r_2)R_3-D-wL\\ -r_2(K+I)-r_1(E+F)\end{array}$
(1, 0, 1)	$(1-r_1)(E+C_1-Q)$	$J+Q-(1-r_2)(C_2+K)$	$\begin{array}{l}{R}_2-r_2(K+I)-E-F\\ -wL-D-(1-r_2)R_3\end{array}$
(1, 0, 0)	$\begin{array}{l}(1-r_1)(C_1-F-Q\\ -w{Q}_1)-wG\end{array}$	$\begin{array}{l}(1-r_2)(I-C_2-R_3)+w{Q}_1\\ +(1-\beta )\alpha D+J+Q+w{R}_4\end{array}$	$\begin{array}{l}{r}_2(K+I)+E+F+wL\\ +D+(1-r_2)R_3-R_2\end{array}$
(1, 1, 1)	$(1-r_1)(E+C_1+J)$	$(1-r_2)(C_2+K)-J-Q$	$\begin{array}{l}{R}_2-K-I-D-E\\ -F-w(L+R_4)\end{array}$

.

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Analysis of Stability Conditions and Discussion of Results

In Table 3, except for the sign of eigenvalue 1 of the equilibrium points (1, 1, 1) and (0, 1, 1), which can be determined as positive and negative, respectively, the sign of the other eigenvalues cannot be determined. Thus, the equilibrium point (1, 1, 1) is not an evolutionary stable strategy. Consistently, the characteristic root of the equilibrium point ($x*$,$y*$,$z*$) is a pure imaginary root, and it can be observed from the conclusion of Taylor that despite being a stable equilibrium point of the game system, this point does not have asymptotic stability; the strategy evolution trajectory of each game subject is a closed-loop curve formed around this point, and the system will not be automatically stabilized to this point; therefore, it is not an evolutionary stable strategy (ESS). Therefore, the stability of the equilibrium points (0, 0, 0), (0, 1, 0), (1, 1, 0), (0, 1, 1), (0, 0, 1), (1, 0, 1), and (1, 0, 0) and their stabilization conditions are delved into.

Case 1: When $\left\{\begin{array}{l}(1-r_1)(w{Q}_1+F+Q-C_1)+wG<0\\ r_1(J+Q+w{R}_4+w{Q}_1)+(1-r_2)I+(1-\beta )\alpha D<(1-r_2)(C_2+R_3)\\ r_2(K+I)+r_1(E+F)+(1-r_2)R_3+D+wL<R_2\end{array}\right.$, the system has a stabilizing strategy (0, 0, 0), i.e., government departments do not regulate strictly, enterprises are negatively managed, and practitioners lose credibility. At this time, the cost of regulation by government departments is overly large, exceeding the sum of the penalties obtained from enterprises and practitioners and the loss of credibility after reporting by the public. Specifically, the relative net benefit of adopting a strict regulation strategy is less than 0, which makes the regulation decline. For enterprises, this involves balancing penalties imposed on practitioners, government-administered rewards and penalties, enterprise-required rewards following public reports, and additional government penalties. If the sum of the expected loss relief from undertaking the project is less than that of its management costs and rent-seeking gains, i.e., the enterprise’s relative net gain from active management is less than 0, and the government does not strictly regulate, then the negative management strategy is optimal; if the practitioners’ additional gain from dishonest behavior exceeds the sum of enterprise-imposed rewards and penalties, the government’s rewards and penalties, the rent-seeking costs, the expected project-failure losses, and reputational damages upon public discovery, the relative net gain from lack of credibility is greater than 0, and the bad faith strategy is preferred. In this case, government departments do not strictly supervise, enterprises are negatively managed, and practitioners choose bad faith behavior to maximize their own interests, which is a manifestation of government and market failure.

Case 2: When $\left\{\begin{array}{l}F<C_1+J\\ (1-r_2)I+r_1(J+Q+w{R}_4+w{Q}_1)+(1-\beta )\alpha D>(1-r_2)(C_2+R_3)\\ r_1(E+F)+w(L+R_4)+K+I+D<R_2\end{array}\right.$, the system has a stabilizing strategy (0, 1, 0), i.e., government departments do not regulate strictly, firms actively manage, and practitioners lose their credibility. Compared with Case 1, the enterprise manages to choose active management with a relative net benefit greater than 0. At this time, the government department does not have to consider the reduction in credibility and the enterprise’s punishment, mainly considering the rewards of the enterprise’s active management. When the rewards are substantial, the penalties imposed on the defaulting practitioners may fail to cover the regulatory costs incurred by government departments and the expenditure for rewarding enterprises’ active management. In this case, the relative net benefit of strict regulation is less than 0, making the non-strict regulation strategy optimal. In this scenario, firms adopt active management strategies, increasing rewards and penalties but reducing the cost of rent-seeking by practitioners, and the government department does not regulate strictly. The overall relative net gain from practitioners’ dishonest behavior remains greater than 0, so they continue to adopt the dishonest strategy.

Case 3: When $\left\{\begin{array}{l}{C}_1+J<F\\ J+Q+w(R_4+Q_1)+(1-r_2)I+(1-\beta )\alpha D>(1-r_2)(C_2+R_3)\\ K+I+D+E+F+w(L+R_4)<R_2\end{array}\right.$, the system has a stable strategy (1, 1, 0), featuring strict regulation by government departments, active management by firms, and loss of trust by practitioners. Compared with Case 2, the gain of government department regulation is greater than 0, leading to the choice of strict regulation. Although strict regulation by the government department increases the rewards and penalties for practitioners, it still does not make the relative net gain of practitioners’ dishonest behavior less than 0, failing to incentivize the integrity strategy. In addition, the higher the reward for successful public reporting, the lower the practitioners’ willingness to breach trust, indicating an inverse proportional relationship between the probability of practitioners breaching trust and the reward for successful public reporting.

Case 4: When $\left\{\begin{array}{l}E+C_1+J>0\\ (1-r_2)(C_2+K)-r_1(J+Q)<0\\ R_2<K+r_1(E+F)+w(L+R_4)+I+D\end{array}\right.$, the system has stable strategies (0, 1, 1), featuring no strict regulation by government departments, active management by firms, and honesty by practitioners. Compared with Case 2, the relative net benefit of the practitioner integrity strategy is greater than 0 when choosing integrity. In this case, the firm does not have to consider the loss caused by public reporting. The firm’s active management increases the penalties for practitioner misconduct and the rewards for honest behavior. The government department is negatively managed due to the lack of gains from penalties as a result of positive management by firms and honest practice by practitioners. In terms of long-term evolution, practitioners begin to choose dishonest behavior, government departments regulate actively, and firms manage negatively. However, as firms’ strategic choices gradually converge towards the positive direction, practitioners face higher penalties for dishonest behavior and greater rewards for honest conduct. Consequently, practitioners ultimately choose honesty, and the government department gradually reduces the intensity of its regulation due to the lack of revenue, shifting toward passive regulation—a scenario consistent with the resolution of practitioners’ dishonesty. This scenario is the ideal state of government regulation of practitioners. However, this scenario is based on the condition of $0<r_1<1$. If $r_1=0$, then $(1-r_2)(C_2+K)-r_1(J+Q)>0$, and the value of the characteristic root 2 of the equilibrium point (0, 1, 1) is greater than 0. Thus, it is not an evolutionary stable strategy. It demonstrates that when government departments entirely cease regulation, relying on the power of only one side of the enterprise to regulate the practitioners cannot achieve the purpose of promoting the integrity of the practitioners in legal practice.

Case 5: When $\left\{\begin{array}{l}Q<E+C_1\\ r_1(J+Q)<(1-r_2)(C_2+K)\\ R_2<D+wL+r_2(K+I)+r_1(E+F)+(1-r_2)R_3\end{array}\right.$, the system has a stabilization strategy (0, 0, 1) featuring no strict regulation by government agencies, negative management by firms, and honesty of practitioners. Compared to Case 4, the relative net benefit of positive management by firms is less than 0, and management is reduced. Negative management by firms reduces penalties and rewards for practitioners, but the relative net benefit of practitioner integrity remains greater than 0, and the integrity strategy is chosen. Concurrently, from the stabilization conditions of practitioners’ integrity strategy, it can be seen that stronger supervision by government departments, increased rewards and penalties from both the government and enterprises, and greater reporting efforts by the social audience are associated with higher willingness among practitioners to choose the integrity strategy.

Case 6: When $\left\{\begin{array}{l}E+C_1<Q\\ J+Q<(1-r_2)(C_2+K)\\ r_1(E+F)+w(L+R_4)+K+I+D>R_2\end{array}\right.$, the system has a stabilizing strategy (1, 0, 1), featuring strict regulation by the government sector, negative management by the firms, and honesty by the practitioners. Compared to Case 5, the relative net benefit of strict regulation by the government sector is greater than 0 in favor of strict regulation. In this case, the government increases the penalties and rewards for firms and practitioners. However, the costs and bonuses when firms manage positively are overly high, exceeding the sum of the penalties and rewards given by the government, which leads to a relative net benefit of less than 0, prompting firms to reduce regulatory intensity.

Case 7: When $\left\{\begin{array}{l}(1-r_1)(C_1-F-Q-w{Q}_1)-wG<0\\ (1-r_2)(I-C_2-R_3)+w{Q}_1+J+Q+w{R}_4+(1-\beta )\alpha D<0\\ r_2(K+I)+E+F+wL+D+(1-r_2)R_3<R_2\end{array}\right.$, the system has a stabilizing strategy (1, 0, 0), featuring strict regulation by government departments, negative management by firms, and loss of trust by practitioners. Compared with Case 1, the government department strictly regulates, with a relative net benefit greater than 0. The strictness of government departments’ regulations enhances the rewards and punishments for enterprises and practitioners. However, the relative net gain of enterprises’ positive management and practitioners’ integrity remains less than 0, leading them to respectively choose passive management and trust-breaking strategies. This scenario bears resemblance to the current situation in China’s water conservancy construction market. At present, in China’s water conservancy construction market, while the government supervision of practitioners remains relatively strict, with the implementation of punitive measures and credit information regulatory mechanisms, the primary entity playing a supervisory role over practitioners in actual regulatory processes is enterprises, while the role of government supervision remains relatively limited. The government departments have not intervened too much in the behavior of the enterprise management practitioners, resulting in most of the enterprises, especially small- and medium-sized ones, not having high enthusiasm for the management of the practitioners. In the absence of direct and effective supervision by the government, enterprises often opt for faith-breaking behaviors when confronted with significant interests, despite the need for active management.

Case 8: The evolutionary game model of direct government regulation of practitioners in the water conservancy construction market is that there will be no stable strategy (1, 1, 1), namely, strict regulation by the government sector, active management by the firms, and honesty of the practitioners, as the condition of $\left\{\begin{array}{l}(1-r_1)(E+C_1+J)<0\\ (1-r_2)(C_2+K)-J-Q<0\\ R_2-K-I-D-E-F-w(L+R_4)<0\end{array}\right.$ is not achievable. This is the reason for the lack of stable internal constraints (invisible contract) in the government sector. When enterprises and practitioners adopt active management and honesty strategies, if the government sector implements a strict regulation strategy, it not only fails to obtain benefits from the external (firms and practitioners) but also incurs certain costs (regulatory costs, incentives for firms and practitioners, etc.). Moreover, under the premise of the economic man hypothesis, the government department will gradually reduce the intensity of regulation out of self-interest and ultimately adopt the strategy of non-strict regulation.

3. Simulation Analysis of Evolutionary Game Models

3.1. Model Parameterization

John Stedman proposed that when constructing a simulation model, its focus should be on the more practical aspects, such as depicting intrinsic patterns of change. There is no need to probe too much into the assignment of initial values. It is challenging to obtain the data regarding exogenous variables in this model, and the system dynamics are mainly adopted to describe the trend of the influence of each variable on the subject’s strategy selection. It is assumed that the temporal parameters of the system are set as follows: INITIAL TIME = 0, FINAL TIME = 20, TIME STEP = 1, and Units for Time: Years.

In order to verify the match between the model and the actual situation while ensuring the accuracy of the simulation’s numerical settings, this paper takes the regulation of water conservancy practitioners in Province SC as an example for research. As a large water conservancy province in the west, Province SC has invested considerably in water conservancy in recent years and launched multiple water conservancy engineering projects. This has been accompanied by frequent trust-breaking behaviors among water conservancy practitioners, posing significant risks to project quality. Therefore, in order to address the problem of lack of credibility among water conservancy practitioners, Province A has invested greatly into the supervision of practitioners. It has not only established relevant mechanisms to strengthen the effectiveness of government supervision, but also vigorously promoted credit supervision, industry self-regulation, and other methods, yielding certain outcomes. Therefore, choosing this province as a case study, its research results are not only typical and persuasive, but also align with the needs of this thesis to study the regulation of practitioners under the indirect regulation model. For the indirect regulation system model of practitioners in the water conservancy construction market, a total of five different levels of water administrative authorities and five water conservancy construction enterprises in Province SC were selected for the research, and the initial values of five exogenous variables were determined. These include the proportion of the practitioners who cause project losses passed to the enterprises $\beta =0.8$, the penalties of the enterprises when the practitioners lose their trust $I=1$, the penalties of the governmental departments when the practitioners lose their trust $F=1.5$, the intensity of the supervision of the governmental departments $r_1=0.5$, and the costs when the enterprises adopt an active management strategy $C_2=1.5$.

At the same time, in the context of the policy of “management and service,” the optimal strategy for government departments, enterprises, and practitioners is (no strict regulation, active management, and integrity), i.e., (0, 1, 1). This indicates that enterprises and practitioners can spontaneously carry out active management and practice with integrity in the absence of strict regulation by the government. This also reveals that the system achieves the ideal stable state of regulation of practitioners in the water conservancy construction market. Moreover, according to the results of Case 4, it can be observed that when $E+C_1+J>0$, $(1-r_2)(C_2+K)<r_1(J+Q)$, and $R_2<K+r_1(E+F)+w(L+R_4)+I+D$, the water conservancy construction market practitioners’ government regulation evolution game has the optimal strategy (0, 1, 1). Through legal channels, we obtained project data for SC’s water engineering construction from 2018 to 2023 (covering all 21 prefecture-level cities), qualification and performance records of certified professionals (exceeding 100,000 entries), and approximately 2000 penalty cases issued by regulatory authorities. These cases were systematically reviewed and summarized to determine variable assignments for the analysis., This paper integrates the conditions of satisfying the case (0, 1, 1) with the initial assignment of the remaining exogenous variables of the governmental regulation system of water conservancy construction market practitioners, which are as follows: $E=0.5$, $C_1=1.2$, $J=1$, $Q=1.5$, $r_2=0.5$, $K=0.7$, $R_2=3.5$, $R_3=1$, $w=0.4$, $R_4=0.5$, $G=2$, $Q_1=0.5$, $L=0.8$, $D=1$, and $\alpha =0.3$.

3.2. Simulation Experiment Analysis

3.2.1. Analysis of Pure Simulation Strategies

When the initial strategies of all three parties, namely, government departments, corporations, and practitioners, are pure strategies, there are a total of eight strategy combinations, i.e., (0, 1, 0), (1, 1, 0), (0, 1, 1), (0, 0, 1), (0, 0, 0), (1, 0, 1), (1, 1, 1), and (1, 0, 0). However, with these eight pure strategy combinations, no side will actively try to adjust their strategy choices to disrupt the existing equilibrium. Nevertheless, once one or more of the participating subjects make minor adjustments, this equilibrium will be disrupted. The decision-making behaviors of each participating subject then begin to evolve through mutual interaction, eventually forming a new equilibrium.

For the sake of image interpretation, this paper takes the initial strategy combination (0, 0, 0) as an example. Firstly, the pure strategy combination (0, 0, 0) is substituted into the system dynamics model of the tripartite game involving the government department, corporation, and practitioner. Subsequently, the Vensim 10.2.0 software is utilized for simulation to obtain the evolution of the pure strategy combination (0, 0, 0), as detailed in Figure 5. Meanwhile, each pure strategy among the eight kinds of pure strategy combinations is mutated with the probability of 0.01, e.g., (0, 0, 0), with the initial value of simulation being (0.01, 0.01, 0.01), which is then substituted into the system dynamics model of the tripartite game involving the government department, corporation, and practitioner for simulation, respectively. We set the probability of strict supervision by government departments as x, the probability of active management by enterprises as y, and the probability of integrity among practitioners as z. Finally, the evolution process of the eight initial pure strategy combinations is obtained after mutation, as shown in Figure 5a–h.

As indicated by the simulation results in Figure 6, none of the parties, whether government departments, businesses, or practitioners, are willing to take the initiative to adjust their strategies to upset the equilibrium, thus leading to the system remaining in a state of relative equilibrium. Furthermore, once the strategy of each participant mutates, the system starts to evolve and the equilibrium is broken. Each participant adjusts its current strategy to seek higher self-benefit until a new equilibrium is achieved. As evidenced by the simulation results in Figure 5a, when the initial pure strategy (0, 0, 0) of the governmental departments, enterprises, and practitioners mutates to (0.01, 0.01, 0.01), the three parties’ strategies all start to undergo adjustments and eventually evolve from (0, 0, 0) to the state of (0, 1, 1).

According to the simulation results in Figure 5, no matter what the initial strategy of the three parties—government department, enterprise, or practitioner—is, it will eventually evolve to (0, 1, 1). As indicated by the simulation results in Figure 5a,g, when the government department initially chooses the strict regulation strategy, compared with the initial choice of the non-strict regulation strategy, the probability of active management of enterprises and the probability of integrity of practitioners increase relatively quickly. This indicates that strict regulation by the government department has a positive impact on the enterprise’s choice to pursue active management and the practitioner’s choice to pursue an integrity strategy. According to the simulation results in Figure 5a,b, when the initial strategy of the enterprise is positive management, compared with the initial selection of the negative management strategy, the time for the government department to choose less strict regulation and the practitioners to choose the integrity strategy are both shorter. This reveals that the enterprise’s positive management exerts an inhibitory effect on the government department’s strict regulation and has a promotional effect on the practitioners’ integrity. This is due to the fact that when enterprises engage in active management, government departments lose the benefits from penalizing enterprises, thereby reducing their incentive for strict regulation. According to the simulation results in Figure 5a,c, when practitioners adopt an initial honest strategy as opposed to a dishonest one, government departments evolve toward less strict regulation at a faster rate, while enterprises evolve toward active management at a slower rate. This indicates that practitioners’ honesty exerts an inverse effect on both strict regulation by government departments and active management by enterprises.

3.2.2. Sensitivity Analysis

Through research and literature review, it can be found that in the current water conservancy construction market, the strategies of government departments, enterprises, and certified professionals are in states of being relatively strict, unenthusiastic, and semi-dishonest, respectively. The main objective of this study is to help these three parties reach the (0, 1, 1) equilibrium state as soon as possible, namely (non-strict supervision, proactive management, and integrity). Therefore, (0.9, 0.1, 0.5) is selected as the initial strategy for simulation analysis under varying changes in different variables.

(1)

Analysis of the Impact of Strategic Choices of Government Departments

In order to explore the influence of the main variables on the strategy selection of government departments, it is assumed that the initial strategy of government departments is strict, i.e., $x=0.9$. By changing the values of the variables, eight variables, such as $G$, $w$, $E$, $C_1$, $J$, $Q_1$, $Q$, etc., are respectively analyzed, and the specific simulation results are shown in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14.

According to the simulation results in Figure 7 and Figure 8, with the loss of credibility of government departments $G$ or the increase in public supervision and reporting $w$, the probability of government departments adopting strict regulation declines more slowly. This suggests that both government credibility loss and enhanced public supervision play a contributing role in the selection of government departments to implement strict regulatory strategies. When the public pay close attention to water conservancy project construction, endeavors will be made to strengthen the supervision and reporting efforts of practitioners. When practitioners’ misconduct is exposed, the likelihood of such exposure increases. Once bad behavior is detected and the government departments fail to enforce strict regulations, it will damage the government’s image and erode public credibility. As the supervisor and coordinator of the water conservancy construction market, government departments attach great importance to their own image and credibility. Therefore, government departments will strengthen the supervision to reduce the practitioners’ dishonest behavior so as to maintain their own image and credibility.

According to the simulation results from Figure 9, Figure 10 and Figure 11, the probability of strict regulation by government departments decreases faster with the increase in the incentives given by government departments to practitioners $E$, the cost of strict regulation by government departments $C_1$, or the incentives received by enterprises from government departments $J$. Specifically, the incentives given by government departments to practitioners and enterprises, as well as the cost of strict regulation, have an inhibitory effect on the selection of strict regulation strategies by government departments. As the cost of regulating practitioners in the government sector increases, its financial expenditure will be higher, and thus the benefits gained by the government sector when strictly regulating will be reduced. Under the homo economicus hypothesis, government departments will choose not to regulate strictly to control the cost of regulation, aiming to reduce their fiscal expenditures.

According to the simulation results from Figure 12, Figure 13 and Figure 14, the rate at which government departments choose not to strictly regulate slows down with the increase in additional penalties $Q_1$ imposed on the enterprise by the government department, the penalties $Q$ imposed on the enterprise by the government department, and the penalties $F$ given to the practitioners by the government department. That is to say, both the penalties imposed by government departments on both practitioners and enterprises have a positive effect on the government department’s decision to adopt a strict regulation strategy. When the penalties given by government departments to enterprises for negative management and practitioners for lack of credibility are strengthened, the benefits gained from their strict regulation will increase accordingly. Thus, under the economic man assumption, the enthusiasm of government departments to regulate will be mobilized, ultimately leading to a slower rate of government departments choosing not to strictly regulate.

(2)

Impact Analysis of Practitioner Strategy Selection

In order to analyze the influence of the main variables on the strategy choice of the practitioners, it is assumed that the initial strategy of the practitioners is not negative, i.e., $y=0.1$. By adjusting the values of the variables, the twelve variables, such as $E$, $K$, $R_2$, $I$, $F$, $R_3$, $D$, $w$, $R_4$, $L$, $r_2$, $r_1$, etc., are respectively analyzed, and the specific simulation results are shown in Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24.

As illustrated in Figure 15 and Figure 16, with the continuous increase in rewards given to practitioners by government departments $E$ or rewards received by practitioners from enterprises $K$, the probability of practitioners choosing honesty accelerates, indicating that the rewards given to practitioners by government departments or enterprises facilitate practitioners’ honest conduct in practice. When government departments or enterprises increase rewards for practitioners, the benefits of adopting an integrity strategy rise, thereby prompting practitioners to choose the integrity strategy.

As shown in Figure 17, with the increase in the extra benefit $R_2$ when the practitioners lose their trust, the probability of the practitioners choosing honesty slows down or decreases. This indicates that the extra benefit when the practitioners lose their trust has an inhibitory effect on the practitioners’ honesty in practice. In the process of water conservancy project construction, the main goal of the practitioners is to complete the business tasks given by enterprises and to maximize their personal interests. Therefore, when the additional gains from practitioners’ dishonesty increase, they tend to choose the dishonesty strategy driven by interests.

According to the simulation results from Figure 18 and Figure 19, the probability of practitioners choosing honesty gradually accelerates with the increasing of the penalties imposed on them by enterprises $I$, the penalties imposed on them by government departments $F$, the successful gains from rent-seeking by enterprises and practitioners $R_3$, and the expected losses from payouts for the loss of trust by practitioners $D$. This indicates that penalties imposed by enterprises, penalties imposed by government departments, the rent-seeking gains of enterprises and practitioners, and practitioners’ expected losses from trust-breaking compensation all have a promotional effect on practitioners’ honest conduct. When government departments or enterprises increase penalties against practitioners, or when the rent-seeking gains of enterprises and practitioners rise, the expected losses for practitioners’ dishonest behavior increase. This raises the cost of adopting a dishonest strategy, reducing the benefits of dishonesty and thus inhibiting the practitioner’s bad faith behavior.

According to the simulation results from Figure 20, Figure 21 and Figure 22, with the increase in the strength of public supervision and reporting $w$, higher rewards for public reporting $R_4$, and the loss of reputation of practitioners reported by the public $L$, the probability of practitioners choosing honesty is gradually accelerated. This indicates that the strength of public supervision and reporting, higher rewards for public reporting, as well as the loss of reputation of practitioners reported by the public all promote practitioners’ honest conduct. When the strength of public supervision and reporting increases, the probability of practitioners choosing integrity increases accordingly. When the strength of public supervision and reporting increases, the probability of practitioners’ dishonesty being detected by government departments rises, leading to harsher penalties. This elevates the cost or risk of choosing dishonesty, prompting practitioners to prefer an integrity strategy. Meanwhile, the practitioner’s credibility loss intensifies when the lack of credibility is successfully reported or exposed by the practitioner. For most practitioners, credibility is of paramount importance, being closely related to salary, status, promotion, and benefits. Therefore, to maintain their credibility, practitioners also tend to choose integrity.

According to Figure 23 and Figure 24, with the increasing strength of enterprise management $r_2$ or government supervision $r_1$, the probability of practitioners’ integrity gradually increases, indicating that the strength of enterprise management or government supervision has a facilitating effect on practitioners’ choice of integrity. When the management intensity of enterprises or the supervision intensity of government departments increases, the penalties or incentives imposed by government departments or enterprises on practitioners will be strengthened. As a result, practitioners will face heavier punishment for dishonesty or greater rewards for integrity, prompting them to choose the integrity strategy. Meanwhile, it can also be found through simulations that when the initial probability of strict government regulation or proactive enterprise management is lower, the promoting effect of government regulatory intensity or enterprise management intensity on practitioners’ integrity becomes more pronounced.

4. Policies and Recommendations

The standardized operation of the water conservancy construction market cannot be separated from the effective supervision of practitioners, and the current problem of lack of credibility should be solved through systematic reform. Based on evolutionary game and simulation analysis, this paper proposes countermeasures at three levels: optimizing government supervision, strengthening corporate responsibility, and deepening social supervision, with an aim to establish a multi-party synergistic and efficiently operated supervision system.

(1)

We recommend innovating the mode of government supervision and enhancing the effectiveness of supervision. Currently, there are problems such as high cost and low efficiency in single government supervision, and it is necessary to promote the transformation of the supervision mode to “multi-dimensional common governance.” On the one hand, based on the simulation results, it is evident that the involvement of non-governmental actors in supervision can enhance overall supervision effectiveness. However, delegating regulatory authority to non-governmental entities is a complex and high-stakes process that requires careful planning and execution. To achieve this, we should first conduct a comprehensive assessment of the capabilities and reliability of industry associations, enterprises, and the public in terms of regulatory functions. Then, we can gradually and selectively delegate appropriate regulatory tasks to them, starting with areas where they have demonstrated expertise and a high level of responsibility. At the same time, a well-defined and transparent regulatory framework should be established to clearly outline the roles, responsibilities, and rights of both the government and non-governmental actors in the supervision process. This framework should also include mechanisms for accountability and oversight to ensure that non-governmental actors perform their regulatory duties effectively and in compliance with the law. By doing so, we can gradually form a synergistic governance pattern of “government-led + industry self-regulation + social supervision,” which not only aims to improve supervision effectiveness but also helps to reduce the administrative burden on the government in a more secure and sustainable manner. On the other hand, the simulation shows that when the accuracy of credit information supervision increases by 30%, the probability of practitioners choosing integrity rises by about 10%. It is necessary to improve the construction of the credit information supervision platform, realize the dynamic sharing of national credit data, unify evaluation standards, and incorporate the function of public reporting to improve supervision accuracy. Concurrently, the division of powers and responsibilities within the government should be optimized, the regulatory responsibilities of each department should be clarified, the interface between the upper and lower levels should be strengthened, and the motivation of regulation should be enhanced through the mechanism of rewards and punishments so as to avoid the loss efficiency caused by the intersection of functions. Additionally, it is also imperative to strengthen supervision during and after the incident, formulate supporting regulations, and establish joint industry associations with the media, etc., to carry out dynamic sampling, to change the status quo of “heavy on approval but light on supervision,” and to ensure full coverage of whole-process supervision.

(2)

We recommend strengthening the primary responsibility of enterprises and building a joint credit constraint mechanism. The simulation shows that enterprises’ management enthusiasm and reward policies have a significant impact on practitioners’ integrity behavior. For this reason, the credit linkage mechanism of “enterprise–individual” should be established, and the credit of the practitioners should be incorporated into the credit rating system of the enterprise to encourage the enterprise to strengthen its internal management. At the same time, efforts should be dedicated to improving the reward and punishment policy. Capital subsidies, tax incentives, and other incentives should be provided to enterprises with good credit, while penalties for enterprises that tolerate or conceal dishonest behavior should be increased to raise the cost of their violations. Additionally, it is important to optimize the market access mechanism. This involves gradually reducing the rigid linkage between enterprise and practice qualifications, increasing the weight of credit evaluation in bidding and reducing “dependence” and other rent—seeking behaviors. Through policy guidance, enterprises will shift from passive compliance to active management, thereby forming a market self-regulatory mechanism.

(3)

We recommend the improvement of social supervision and the credit system to establish long-term constraints. The simulation results show that social public supervision and reporting intensity, reporting success benefits, and reputation loss due to being reported all have a promoting effect on practitioners’ integrity. Social supervision is an important supplement to government supervision, and public participation should be stimulated through system optimization. On the one hand, the reporting incentive mechanism should be improved, the bonus standard should be raised, the monitoring channels should be broadened, and publicity and guidance should be strengthened to enhance public awareness of monitoring. On the other hand, it is imperative to strengthen credit information disclosure and expose typical cases through credit platforms and the media to magnify the reputational loss of non-compliant behaviors and prompt practitioners to pay attention to long-term credibility. In addition, it is necessary to accelerate the construction of the credit system, establish a credit scoring system for practitioners, implement differentiated supervision, tilt policies towards those with high scores, and subject those with low scores to joint disciplinary measures. At the same time, market-based restraints such as professional liability insurance can be explored to make credit the core competitive metric of practitioners in the industry. This will ultimately form an all-round governance pattern featuring “government regulation+ enterprise self-discipline + social supervision + credit restraint.”

Compared with the existing regulatory frameworks in other infrastructure sectors such as transportation and energy, the framework proposed in this study is more targeted and comprehensive. In the transportation sector, supervision mainly focuses on safety standards and operational norms, while the framework in this study emphasizes the core role of credit in supervision. In the energy sector, the regulatory focus is on resource utilization efficiency and environmental protection, whereas the framework in this study constructs a more comprehensive credit supervision system from the perspective of multi-party collaboration. This indicates that the proposed framework has unique applicability and value in the water conservancy construction market.

5. Conclusions

With the rapid development of the water conservancy construction market, building a scientific and efficient credit supervision system has become the key to guaranteeing the healthy operation of the industry. As an important part of national infrastructure, the credit behavior of water conservancy project practitioners directly affects project quality and public safety. From the perspective of indirect regulation, this paper systematically analyzes the dynamic game process among government departments, enterprises, and practitioners in credit regulation by integrating evolutionary game theory. It reveals the evolutionary laws of strategic choices by each stakeholder under different regulatory situations. By constructing a three-party evolutionary game model, this paper explores the credit supervision mechanism for water conservancy engineering practitioners under the indirect supervision mode. The results indicate that: ① The enhancement of government supervision and the strengthening of social supervision significantly promote the integrity behavior of practitioners, yet the sole reliance on government supervision may lead to inefficiency; ② As the direct manager of practitioners, the enterprise’s management enthusiasm and the effectiveness of its reward–punishment mechanism play a key role in the credit evolution; ③ In the long run, reducing the cost of trustworthiness and optimizing the credit evaluation system are essential for guiding the behavior of the high-credit groups. For low-credit groups, however, a short-term high-intensity disciplinary mechanism should be implemented in conjunction.

Based on the conclusions of the study, this paper puts forward policy recommendations for the optimization of government functions, the implementation of corporate responsibility, and the deepening of social supervision, aiming at building a multi-dimensional synergistic regulatory system of “government-led–corporate self-regulation–social participation.” Overall, this study not only enriches the theoretical framework of credit governance in the water conservancy construction market but also provides practical references for regulators to formulate differentiated policies. This is of positive significance for standardizing the market and enhancing project quality.

This study exhibits notable novelty and innovation. Theoretically, it pioneers the application of a three-party evolutionary game model involving government departments, enterprises, and practitioners to analyze credit supervision in the water conservancy construction market, offering a fresh perspective on credit governance in this field. Practically, it proposes a multi-dimensional synergistic regulatory system of “government-led–corporate self-regulation–social participation” for credit supervision, differentiating policy recommendations for high-credit and low-credit groups. This provides targeted and effective guidance for regulators, which is a significant contribution to both theoretical understanding and practical policy-making in the water conservancy construction market.

However, the broader applicability of the study’s results and suggestions still needs further exploration. Although the credit supervision dynamics and policy recommendations in the water conservancy construction market may offer some insights for other infrastructure sectors, there are differences in market environments and regulatory focuses among different industries. Future research could conduct policy piloting in selected regions or projects within the water conservancy construction market to validate the effectiveness of the policy suggestions in this study and optimize the framework based on the pilot results. Meanwhile, cross-sectoral comparative studies can be carried out to understand the similarities and differences between the credit supervision mechanisms in the water conservancy construction market and those in other infrastructure sectors, providing a basis for cross-industry experience sharing.