The Influence of the Spillover Punishment Mechanism Under P-MA Theory on the Balance of Perceived Value in the Intelligent Construction of Coal Mines

Abstract

The objective of this paper is to examine the game-theoretic relationship between local governments and coal mining enterprises with regard to the issue of coal mine intelligent construction. Firstly, this paper employs prospect theory to construct the value perception function and the decision weight function, which are then used to optimize the parameters of the traditional income matrix. The equilibrium point is then analyzed for stability under different conditions. Subsequently, Vensim PLE and MATLAB simulation software are employed to substantiate the impact of spillover penalties and associated parameters on the value perception equilibrium of the two parties. The results of the simulation demonstrate that, in addition to the initial strategy selected, the spillover penalty exerts a considerable inhibitory effect on the process of enterprise intelligence construction. Secondly, from the perspective of value perception, the lower the costs to enterprises of carrying out intelligent construction in terms of labor and mental effort, the more enterprises are inclined to engage in this construction. The higher the costs to enterprises of complying with strict government regulation, and the lower the costs to enterprises of deregulation, the more the government can govern by non-interference. Finally, the behavioral trends of local government departments are also correlated with additional revenue they receive from firms and the factor of fines linked to government performance.

1. Introduction

Coal remains fundamental to China’s energy structure and economic sustainability, accounting for over 55% of primary energy consumption and 60% of electricity generation. It supports grid stability, energy-intensive industries, and approximately 3 million jobs, particularly in rural regions [1]. To effectively diminish the occurrence of mining accidents, China’s National Development and Reform Commission issued the Guiding Opinions on Accelerating the Intelligent Development of Coal Mines, establishing three-stage targets for intelligent transformation [2]. However, the implementation remains in the preliminary phase, with coal mines still exploring practical approaches to intelligence reforms [3].

A key governance challenge arises from divergent perspectives between stakeholders. The government envisions intelligent mines as enabling a transition from ‘scale production’ to ‘quality and efficiency’, fostering innovation in intelligent equipment and robotics gains. In contrast, enterprises primarily focus on safety benefits, with limited economic returns. This skepticism is exacerbated by the lack of objective evaluation methods to quantify intelligent investments and benefits, hindering broader acceptance [4]. Consequently, policy implementation varies: some local governments delay rollout due to fiscal constraints, while certain enterprises—particularly small private mines—resist reforms citing high costs and uncertain returns on investment [5].

Our analysis of 12 provincial policy documents (2018–2023) and 37 enterprise case studies reveals three coexisting governance models for intelligent coal mine implementation, as shown in Figure 1. These models operate regionally within a dual framework: provincial authorities mandate model selection based on regional production and safety priorities, while enterprises determine specific implementation pathways according to ownership structures and technological capacity [4,5]. Specifically, Model 1 (Government-led) is enforced uniformly in state-owned mines, such as Shanxi’s key production bases; Model 2 (Government–Enterprise Cooperation) emerges through negotiated adoption in mixed-ownership enterprises, like those in Shaanxi’s transitional regions; and Model 3 (Enterprise-led) develops organically in private mines, such as those in Inner Mongolia, albeit under national baseline standards. This tripartite system reflects institutional tensions between top-down policy objectives and bottom-up economic realities.

The essential reason for these three modes is the game relationship between government and enterprises. Current research analyzing the government–enterprise game primarily evaluates local enterprises’ total benefits through economic metrics while accounting for tangible capital expenditures, particularly heavy-mining-equipment costs. However, the psychological cost equivalent price factor—encompassing (1) productivity losses during technology adaptation [6], (2) workforce retraining expenses, and (3) elevated safety risks during transition periods—remains systematically overlooked. As independent production units, coal enterprises incur these quantifiable psychological costs through miners’ behavioral responses to technological changes, which are further moderated by organizational safety climate [7] and leadership approaches [8]. This omission leads to significant underestimation of transformation barriers, as demonstrated by Bachar’s [9] finding that neglecting such factors results in 34% cost miscalculations. In addition, when the reform is carried out by the peer enterprise, the enterprise, as an observer, will also have an educational and warning effect on itself. These aspects should have been considered in the existing studies.

Thus, this paper will re-calculate the cost variables in the government–enterprise game model based on the prospect and psychological account theories. First, according to Adam Smith’s scientific management theory, this paper regards coal mining enterprises as independent ‘economic men’, and quantifies their labor costs, mental costs, and psychological costs from social norms during the intelligent construction of coal mines. They are then included in the game model between government and enterprise in coal mining, based on value perception. Second, considering that the subsidiary or associated coal mines of the penalized enterprise will be subject to joint penalties.

2. Literature Review

In the context of the contemporary process of intelligent transformation of coal mines, the resolution of safety issues is contingent not only on technological progress but also on a consideration of the intricate interplay between technology, psychology, and behavior. A considerable body of research conducted on an international scale has demonstrated a strong correlation between coal mine safety performance and the psychological acceptance of intelligent construction. This correlation is primarily reflected in three dimensions.

In relation to safety climate and behavioral interactions, the research conducted by Gao and Abegaz revealed key mechanisms. Gao employed a SEM-SD model to demonstrate that enhancements in safety climate effectively mitigate unsafe behaviors caused by work fatigue [6]. This finding is consistent with the results of Abegaz’s research in Ethiopia, which demonstrated that an increase of one point in safety climate scores resulted in a 29.2% increase in safety participation behavior [7]. These conclusions are directly relevant to the context of intelligent coal mining, as the visualization characteristics of technologies such as digital twins have been shown to enhance the perception of safety climate, thereby reducing miners’ resistance to intelligent equipment (mental costs) by over 40%. This positive feedback loop of ‘technology-enhanced climate—climate-facilitated acceptance’ is a significant finding of this study.

Given the unique characteristics of small and medium-sized coal mines, the research by Kima and Bachar provides quantitative evidence for cost–benefit analysis. Kima’s fishbone diagram model demonstrates that, in circumstances where resources are limited, equipment and management factors contribute 63% to safety performance, a figure that is significantly higher than that observed in large enterprises [10]. Bachar further demonstrated through Monte Carlo simulations that, in order to achieve baseline safety levels, small- and medium-sized enterprises require a safety investment rate of 3.8% [9]. This explains the root cause of the psychological burden faced by enterprises during the initial stages of intelligent transformation. However, the study also found that when the coverage rate of intelligent monitoring systems exceeds 70%, post-accident handling costs can be reduced by 58%, and the investment payback period is shortened to 2.3 years. This data provides a framework for decision-making support in addressing ‘investment phobia’.

In the leadership and resource allocation dimension, Ren’s and Zeibak-Shini’s findings offer important insights. Ren’s multilevel structural equation modeling (MSEM) shows that ethical leadership indirectly improves safety compliance behavior by reducing alcohol consumption by 23% [8]. This imposes new requirements on intelligent management: traditional ‘command-and-control’ leadership must be transformed into ‘empowering’ leadership. Zeibak-Shini’s AHP analysis based on the 5M model shows that in the prioritization of intelligent equipment configuration, personnel positioning systems should be prioritized over environmental monitoring devices [11]. This differentiated configuration strategy can improve the efficiency of safety fund utilization by 41%. Kim used SEM to compare the factors influencing safety behavior and perceptions between general contractors and subcontractor workers at construction sites in South Korea [12]. The study revealed differences in the mechanisms influencing safety behavior among personnel at different levels, providing key evidence for the strategic decisions of government and enterprises in the intelligent construction of coal mines.

In the domain of cross-cultural research, the findings of Bader and Eric are of particular significance. Bader’s survey revealed that management safety commitment and the need for multilingual training are the core variables influencing OHS compliance [13]. Eric’s ‘adaptive-awareness’ dual-factor model developed in Ghana demonstrated that culturally adapted smart training can increase the acceptance of safety behaviors by 2.3 times [14]. These findings guide us: the advancement of intelligent coal mining must be accompanied by ‘technology–culture’ adaptation mechanisms, such as developing intelligent terminals with ethnic language interfaces, which can reduce operational error rates by 35%. The association between technological innovation and psychological costs is reinforced in Gong’s and Sakdirat’s research. Gong’s BP-ARIMA model (MAE = 1.02%) reduced miners’ water hazard anxiety indices by 62% through precise predictions, demonstrating that technological reliability directly impacts psychological costs [15]. Sakdirat’s digital twin system showed that visualizing the carbon footprint across the entire lifecycle increased management’s willingness to invest in intelligent upgrades by 28 percentage points, with this ‘visible benefit’ significantly alleviating transition anxiety [16].

The above literature establishes that intelligent coal mine transformation operates through two interdependent mechanisms: (1) techno-psychological feedback, where safety climate enhancements via intelligent systems (e.g., digital twin visualization [6,7]) reduce equipment resistance by 4.2–29.2%; (2) cultural-leadership mediation, where empowering leadership [8] and localized interfaces [13,14], respectively, improve compliance by 19.7–23% and reduce errors by 35%, albeit with 18% cost premiums. Crucially, these studies collectively identify—but do not quantify—the nonlinear value perception gap between enterprises (ROI-focused) and governments (safety-priority), a theoretical void our prospect-theoretic game model (Section 3) specifically addresses by integrating Gong’s anxiety reduction coefficients [15] and Sakdirat’s visualization elasticity [16] into bilateral utility functions. Specifically, when the safety-effectiveness perception of intelligent systems among enterprise miners increases by one unit, their technical acceptance increases by less than one unit, while the government’s investment willingness in intelligent construction is significantly positively correlated with accident cost avoidance expectations. This imbalance in bilateral value perceptions is the core of the current game-theoretic dilemma, where the government prioritizes immediate safety gains while enterprises focus on the long-term return on investment. Therefore, focusing on the critical point calculation of intelligent adoption, that is, finding the Pareto optimal solution between psychological acceptance costs and corporate investment pressures, is the current research priority. On this basis, this paper addresses the issue of intelligent construction in coal mines under China’s current reform policies from the perspectives of traditional game theory, prospect theory, and mental accounting theory.

2.1. Game Problems of Government and Enterprise in Coal Mining

The existing literature demonstrates systematic limitations in modeling coal mine governance interactions, which our study addresses through value perception integration. While Liu’s [17] dynamic penalty model achieves 18–22% fluctuation reduction in the strategy choice of the three stakeholders in state-owned mines, its reliance on rational choice assumptions leads to significant prediction errors in private SMEs. Similarly, You’s [18] system dynamics approach reveals critical differences in equilibrium convergence times across stakeholders (regulators: 2.1 periods; miners: 5.7 periods), yet fails to account for cultural moderators, while our cross-regional analysis embeds cultural moderating factors into psychological costs to explain differences in the effectiveness of interventions. Most fundamentally, evolutionary game models [19,20,21,22,23] excel at capturing population-level dynamics but overlook individual cognitive biases—a gap our mental accounting framework bridges through prospect-dependent utility functions. Our integrated framework resolves these limitations by (i) transforming Zhou’s [24] stability parameters into prospect-theoretic value functions and (ii) embedding Yu’s [20] multi-level governance structure within a mental accounting architecture.

In addition to this, China has made it clear that the coal industry should follow a sustainable development path; the construction of a green energy supply system and green, intelligent, and safe coal mining has been listed as an essential task in their energy reform. Sun analyzed the strategies of the government and coal enterprises to reduce carbon emission pollution in resource integration [25]. On this basis, Fan constructed a tripartite evolutionary game model of local government, the power industry, and coal enterprises [26]. The above studies reveal two tension points our study incorporates: (1) time inconsistency between short-term costs and long-term benefits; (2) cognitive discounting of environmental risks. Therefore, our study is based on the psychological costs over time to measure the cognitive discounting that occurs when environmental pollution is caused by not constructing intelligently. The proposed model is consistent with the idea of constructing an evolutionary game model of ecological compensation from four perspectives: social benefits, regulatory costs, government subsidies, and ecological compensation [27,28].

2.2. Spillover Effect Theory

The spillover effect is when an organization carries out a particular activity and produces the expected effect of the activity, impacting people or society outside of the organization. This means that an individual enterprise’s behavior will cause good or bad economic effects on other enterprises in the industry. The spillover effect can be divided into knowledge spillover effect, technology spillover effect and economic spillover effect. The spillover effect based on organizational punishment refers to the spillover effect caused by the observer passively accepting the deterrent behavior of punishment, which belongs to the category of ‘economic spillover effect’.

The spillover effect based on organizational punishment explored in this paper refers to the deterrent behavior of bystanders passively accepting punishment, which belongs to the category of ‘economic spillover effect’. Also known as the joint liability penalty mechanism, this is what Chinese coal mining enterprises generally experience at present [29]. Its intention is to urge everyone to participate in management together. Enterprises subject to joint and several liability may incur fines due to regulatory violations committed by other associated enterprises. This will not only enhance the supervision and management of other enterprises, but their own management will also become more vigilant and responsible for their work. Companies engaging in regulatory infractions that result in the sanctioning of innocent entities are more prone to experience a sense of remorse. This remorse can subsequently evolve into a heightened awareness of safety measures. Similar research is often related to the Dupont–Bradley Curve. Dickinson verified the rationality of the existence of this curve at an institutional level, pointing out that the spillover punishment system for group mutual management is better than the non-spillover punishment system for individual independent management [30]. However, this assertion has been met with skepticism by some scholars, who have called into question the efficacy of this mechanism. These scholars argue that the introduction of joint and several liability does not contribute to the preservation of stability within the gaming system and has no discernible effect on the regulatory efficiency of government regulators [31].

It has been observed that the liability punishment mechanism in coal mines incorporates the spillover effect, and the merits and demerits of this effect for the production and operation of the enterprise have not been subject to universal consensus. Consequently, this paper, following the construction of the game model based on value perception, incorporated the psychological load induced by the spillover effect into the psychological cost account. It then compared the impact on the game trend in two distinct policy scenarios, thereby substantiating the role of the spillover penalty effect.

2.3. Prospect Mental Accounts Theory

According to Prospect Theory, the human decision-making process is divided into two stages [32]. The first stage includes the collection and sorting behavior of random events, event results, and related information; the second stage includes the evaluation and decision-making behavior after preprocessing the first-stage events [33]. The first stage of preprocessing mainly includes data integration and simplification. Because different integration and simplification methods will yield different events and combinations, this can lead to irrational behavior in people and the frame dependence effect; this eventually leads to inconsistency in people’s final decisions regarding the same problem [34]. Mental accounts refer to the fact that people unconsciously assign wealth to different accounts, for management at a psychological level, and different mental accounts have different bookkeeping methods and mental calculation rules, thus leading to irrational decision-making behavior [35]. Psychological accounts are divided into valence accounts and cost accounts, and each account has its corresponding perceptual reference point and prospect value perception function [36]. Combining these two theories gives rise to the prospect mental accounts theory (P-MA theory), a combined framework.

Based on this theory, Amaral constructed an evolutionary game matrix of value perception based on valence and cost accounts. They demonstrated the influence of behavioral cost, valence, reference point and risk preference on behavioral decision-making [37]. Based on this research, Zhao and Fennema conducted an evolutionary game analysis of prefabricated building safety management and PPP project risk management behavior, based on the P-MA theory [38,39]. On the other hand, Kang confirmed that improving a salary level and miners’ risk perception ability was conducive to reducing the incidence probability of HBV in miners, based on an improved cumulative prospect theory (CPT) [40]. These conclusions all confirm the high applicability of the P-MA theory in the process of government control and management of enterprises.

In the process of coal mine intelligent construction, the government observed that the efficacy of peer supervision surpassed that of government mandates to cease operations. The underlying cause of this phenomenon is attributable to the errors in wealth decision-making that managers have committed at the psychological level. The regulation of intelligent construction of coal mines based on the P-MA theory, however, utilizes the ‘loss-sensitive’ property of prospect theory to shift the consequences of safety violations from the expression of ‘fine amount’ to ‘potential mental cost’ and utilizes the ‘segmental assessment’ property of psychological accounts to dynamically adjust the regulatory thresholds with the industry average level of intelligence as the reference point. It reconstructed the regulator’s value function to amend the linear assumption of traditional cost–benefit analysis, enabling precise intervention of behavior while realizing early warning of risk.

To sum up, the research presented in Section 2.1, Section 2.2 and Section 2.3 has laid a specific theoretical foundation for the evolutionary mechanism behind the implementation of intelligent construction in coal mining enterprises. However, the following aspects can still be improved. (i) The existing research is mainly based on the traditional performance income matrix. It does not consider the psychological cost equivalent price factor, so the experimental conclusions may be biased because of the actual production activities. (ii) Previous studies mainly explored the government’s regulatory punishment of coal mining enterprises, from the perspective of the punished coal mining enterprises themselves, without considering the spillover effect onto others.

Therefore, this study introduces the inter-group spillover effect and perspective-psychological theory to the study of intelligent construction of coal mines, constructing an evolutionary game model of relevant psychological accounts of local governments and coal mining enterprises. This study innovatively introduces psychological cost equivalence factors, breaking through the limitations of traditional performance–benefit matrices. The quantification of this factor will help small- and medium-sized enterprises (SMEs) more accurately assess the true return on investment (ROI) of their intelligent transformation efforts. Additionally, by quantifying the equivalent price of psychological costs, the study addresses the challenge of monetizing ‘management soft factors’ in the Ovad’s fishbone diagram model. The spillover effect model explains the phenomenon observed by Eric, where the diffusion radius of safety culture in SMEs is limited. The final evolutionary game model provides SMEs with a gradual implementation path for intelligent transformation that balances psychological acceptance and economic benefits.

3. Methods

3.1. Game Design and Description

The three elements of the game system are as follows: (1) Players: The model only includes two interested subjects. A₁ represents the coal mining enterprises and A₂ represents local governments. Both players in the game are limited rational players and they choose their respective strategies based on the maximization of their respective safety perception benefits. (2) Strategy: The strategy space that coal mining enterprises can choose is A₁ = {full implementation, no implementation}, with probabilities p and 1 − p, respectively. The strategy space that the local government can choose is A₂ = {strict regulation, deregulation}, with probabilities q and 1 − q, respectively. (3) Income: This is determined by local government departments and coal mining enterprises to meet the valence account function V(x) and cost account function C(x) constructed based on the psychological account theory, which is expressed as follows:

$$V\left(x\right)=\left\{\begin{array}{c}{\left(x-U_0\right)}^{\theta },x\ge U_0\\ -\lambda {(U_0-x)}^{\beta },x<U_0\end{array}\right.$$

(1)

$$C\left(x\right)=\left\{\begin{array}{c}\delta {\left(x-U_1\right)}^{\phi },x\ge U_1\\ -{(U_1-x)}^{\sigma },x<U_1\end{array}\right.$$

(2)

In the equations, U₀ and U₁ represent reference points of the value perception; λ represents valence loss avoidance sensitivity; and β and θ represent the risk preference index of valence. φ and σ represent the risk preference index of cost, and δ represents the sensitivity of cost loss avoidance. The greater the risk preference index, the more sensitive the risk perception. According to the random test results for the relevant parameters, it is found that the values of U₀ and U₁ are between 0.5 and 1.4. In order to ensure the accuracy of the calculations, we referred to the value of Tversky and used the median interval of 0.9 [41]. To calculate the mental account decision weight function ω(ε), we used the following equations:

$${\omega }^{+}\left(\epsilon \right)={\displaystyle \frac{{\epsilon }^r}{{[{\epsilon }^r+{(1-\epsilon )}^r]}^{\frac{1}{r}}}}$$

(3)

$${\omega }^{-}\left(\epsilon \right)={\displaystyle \frac{{\epsilon }^i}{{[{\epsilon }^i+{(1-\epsilon )}^i]}^{\frac{1}{i}}}}$$

(4)

In Equations (3) and (4), ω⁺(ε) represents the decision weight when there is a gain; ω⁻(ε) represents the decision weight when there is a loss; r and i represent the decision influence coefficients; and the function is a monotone increasing function. In order to facilitate the subsequent equation derivation and calculation, according to the research of Dijk, the unified ω(ε) was used instead; the parameter is denoted as r and we set its value at 0.75 [42].

The following model assumptions are proposed, based on the above three elements.

Hypothesis 1:

Since the coal mining enterprise and the government mechanism take the obtained value function as the income target, all parameters involved in the value function are more significant than zero and are fixed [43].

Hypothesis 2:

The two sides of the game are mainly local government departments and coal mining enterprise groups, which have only limited rationality in the game process and conform to the value perception function E constructed based on the combination of prospect theory and mental accounting theory, i.e., the form of E = T(∆x) ω(ε) [44].

In addition, it is worth noting that only when the coal mining enterprises fully implement the intelligent mine construction, and the local government strictly supervises it, can the overall safety state be ensured, i.e., the safety risk cost is 0. Otherwise, there will be a risk, which is linear and transfers from one party to the other, and the transfer coefficient will vary from subject to subject [45].

The specific parameters related to valence and costs are shown in

Table 1. Meanings of variables in the evolutionary game.

Variables	Meanings of Variables	Notes
p	Rate of intelligent construction in coal mining enterprises	0 ≤ p ≤ 1
q	Rate of strict regulation by local government departments	0 ≤ q ≤ 1
m0	The labor cost of enterprises of fully implementing intelligent construction	m0 > 0
m1	The mental cost of enterprises of fully implementing intelligent construction	m1 > 0
m2	The psychological cost of enterprises of not fully implementing intelligent construction (from social norms)	m2 > 0
g0	The labor cost of strict regulation by local government departments	g0 > 0
g1	The mental cost of strict regulation by local government departments	g1 > 0
g2	The psychological cost of deregulation by local government departments (from superiors and the public)	g2 > 0
R1	The net revenue of coal mining enterprises intelligent construction (whether or not they undertake intelligent construction)	R1 > 0
R2	Additional revenue and rewards for companies due to intelligent construction	R2 > 0
B1	Tax revenue and performance of local governments in managing day-to-day affairs	B1 > 0
B2	Environmental and social benefits of local governments due to intelligent construction	B2> 0
t	Safety accident risk transfer coefficient	0 ≤ t ≤ 1
L	Cost of safety accident risk to be borne by the responsible party after an accident	L> 0
p0	Accident risk probability of safety hazards due to not updating intelligent equipment	p0 > 0
α1	The safety hazard factor when enterprises fully implement intelligent construction and local governments deregulation	α1 > 0
α2	The safety hazard factor when enterprises do not implement intelligent construction and local governments strict supervision	α2 > 0
μ	The fines factor of local governments is linked to their own reward coefficients	μ > 0
F1	Local government fines levied on coal mining enterprises that do not implement intelligent construction	F1 > 0
F2	The penalties from higher authorities when local governments deregulate	F2 > 0
G	The benefits received from enterprises when local governments deregulate	G > 0
p1	Probability of receiving benefits from enterprises when local governments deregulate	p1 > 0

. Therefore, the perceived safety benefit matrix of local governments and coal mining enterprises under non-spillover punishment measures is obtained, as shown in

Table 2. The evolutionary game income matrix of coal mine intelligent construction under non-spillover effects.

Games Strategy		Local Government
		Strict Regulation q	Deregulation 1 − q
Coal mining enterprise	full implementation p	V(R1 + R2) − C(m0 + m1) V(B1 + B2) − C(g0 + g1)	V(R1 + R2) − C(m0 + m1 + tα1ω(p0)L) V(B1 + B2) − C(g2 + F2 + α1ω(p0)L)
	no implementation 1 − p	V(R1) − C(m2 + F1 + α2ω(p0)L) V(B1 + μF1) − C(g0 + g1 + tα2ω(p0)L)	V(R1) − C(m2 + ω(p0)L) V(B1 + ω(p1)G) − C(g2 + F2 + ω(p0)L)

.

Lopez-Luzuriaga and Scartascini corroborated the assertion that the ‘one-size-fits-all’ punishment strategy implemented by regulatory authorities is equivalent to spillover effects. Specifically, if a coal mining enterprise in a certain region fails to complete intelligent construction, then the subsidiary coal mines or affiliated coal mines in that region will also receive joint punishment. In addition, they believe that local governments’ implementation of punitive spillover strategies on coal mining enterprises is conducive to local governments promoting the intelligent construction of coal mines [46]. However, under the psychological cost equivalent price factor, does this penalty measure also accelerate the pace of intelligent construction? Based on this, the following hypothesis is proposed.

Hypothesis 3:

Under the value perception balance model, spillover penalty measures can accelerate the government and enterprises to quickly reach a game equilibrium regarding coal mine intelligent construction.

In Lopez-Luzuriaga and Scartascini’s work, the spillover penalty benefit is quantified as s, s = qF₁, where q is the probability that the local government will strictly supervise coal mines in the region. We analogize the concept to the value-based perceived benefit game model in this study, and we can obtain the security of the perceived benefit game matrix under spillover effect, as shown in

Table 3. The evolutionary game income matrix of coal mine intelligent construction under spillover effects.

Games Strategy		Local Government
		Strict Regulation q	Deregulation 1 − q
Coal mining enterprise	full implementation p	V(R1 + R2) − C(m0 + m1 + qF1) V(B1 + B2)-C(g0 + g1)	V(R1 + R2) − C(m0 + m1 + tα1ω(p0)L) V(B1 + B2) − C(g2 + F2 + α1ω(p0)L)
	no implementation 1 − p	V(R1) − C(m2 + F1 + α2ω(p0)L) V(B1 + μF1) − C(g0 + g1 + tα2ω(p0)L)	V(R1) − C(m2 + ω(p0)L) V(B1 + ω(p1)G) − C(g2 + F2 + ω(p0)L)

.

3.2. Game Solution

According to the replicated dynamic equation of the evolutionary game, the value perception T_p and T_1−p of coal mining enterprises on the intelligent construction of ‘fully implemented’ and ‘not implemented’ enterprises, and their average value perception ${\overline{T}}_p$ are obtained by the following:

$$T_p=\omega \left(q\right)\left[V\left(R_1+R_2\right)-C\left(m_0+m_1+q{F}_1\right)\right]+\omega \left(1-q\right)\left[V\left(R_1+R_2\right)-C\left(m_0+m_1+t{\alpha }_1\omega \left(p_0\right)L\right)\right]$$

(5)

$$T_{1-p}=\omega \left(q\right)\left[V\left(R_1\right)-C\left(m_2+F_1+{\alpha }_2\omega \left(p_0\right)L\right)\right]+\omega \left(1-q\right)\left[V\left(R_1\right)-C\left(m_2+\omega \left(p_0\right)L\right)\right]$$

(6)

$${\overline{T}}_p=p{T}_p+(1-p)T_{1-p}$$

(7)

Similarly, the value perception T_q and T_1−q of ‘strict regulation’ and ‘deregulation’ of local regulatory departments, and the average value perception ${\overline{T}}_q$ of the whole of local government, are obtained by the following:

$$T_q=\omega \left(p\right)\left[V\left(B_1+B_2\right)-C\left(g_0+g_1\right)\right]+\omega \left(1-p\right)\left[ V\left(B_1+\mu F_1\right)-C\left(g_0+g_1+t{\alpha }_2\omega \left(p_0\right)L\right)\right]$$

(8)

$$T_{1-q}=\omega \left(p\right)\left[V\left(B_1+B_2\right)-C\left(g_2+F_2+{\alpha }_1\omega \left(p_0\right)L\right)\right]+\omega \left(1-p\right)\left[ V\left(B_1+\omega \left(p_1\right)G\right)-C\left(g_2+F_2+\omega \left(p_0\right)L\right)\right]$$

(9)

$${\overline{T}}_q=q{T}_q+\left(1-q\right)T_{1-q}$$

(10)

Combined with Equations (7) and (10), the asymmetric replication dynamic evolution equation is used to obtain the replication dynamic equation of p and q:

$$\begin{array}{ll}F(p)& ={\displaystyle \frac{\mathrm{d}p}{\mathrm{d}t}}=p(T_p-\overline{T_p})=p(1-p)(T_p-T_{1-p})\\ & =p(1-p)\left\{\begin{array}{l}\omega (q)[V(R_1+R_2)-V(R_1)+C(m_2+F_1+{\alpha }_2\omega (p_0)L)-C(m_0+m_1+q{F}_1)]+\\ \omega (1-q)[V(R_1+R_2)-V(R_1)+C(m_2+\omega (p_0)L)-C(m_0+m_1+t{\alpha }_1\omega (p_0)L)]\end{array}\right\}\end{array}$$

$$F_1(p,q)=p\left(1-p\right)\left(\omega \left(q\right)H+\omega \left(1-q\right)I\right)$$

(11)

For ease of calculation, we replace complex expressions with H and I, and so

$$H=V\left(R_1+R_2\right)-V\left(R_1\right)+C\left(m_2+F_1+{\alpha }_2\omega \left(p_0\right)L\right)-C(m_0+m_1+q{F}_1)]$$

(12)

$$I=V\left(R_1+R_2\right)-V\left(R_1\right)+C\left(m_2+\omega \left(p_0\right)L\right)-C\left(m_0+m_1+t{\alpha }_1\omega \left(p_0\right)L\right)$$

(13)

H represents the value function of fully implementing or not fully implementing intelligent enterprise construction when the local government carries out strict regulation. I represents the value function of fully implementing or not fully implementing intelligent enterprise construction when the local government deregulates.

$$\begin{array}{ll}F(q)& ={\displaystyle \frac{\mathrm{d}q}{\mathrm{d}t}}=q(T_q-\overline{T_q})=q(1-q)(T_q-T_{1-q})\\ & =q(1-q)\left\{\begin{array}{l}\omega (p)[C(g_2+F_2+{\alpha }_1\omega (p_0)L)-C(g_0+g_1)]+\\ \omega (1-p)[V(B_1+\mu F1)-V(B_1+\omega (p_1)G)+C(g_2+F_2+\omega (p_0)L)\\ -C(g_0+g_1+t{\alpha }_2\omega (p_0)L)]\end{array}\right\}\end{array}$$

$$F_2\left(p,q\right)=q\left(1-q\right)\left(\omega \left(p\right)S+\omega \left(1-p\right)T\right)$$

(14)

Again, for ease of calculation,

$$S=C\left(g_2+F_2+{\alpha }_1\omega \left(p_0\right)L\right)-C\left(g_0+g_1\right)$$

(15)

$$T=V\left(B_1+\mu F_1\right)-V\left(B_1+\omega \left(p_1\right)G\right)+C\left(g_2+F_2+\omega \left(p_0\right)L\right)-C\left(g_0+g_1+t{\alpha }_2\omega \left(p_0\right)L\right)$$

(16)

S represents the value function of strict regulation/deregulation of local government when coal mining enterprises fully implement intelligent construction. T represents the value function of strict regulation/deregulation of local government when coal mining enterprises do not implement intelligent construction.

4. Result and Discussion

4.1. Stability Analysis

According to the stability theorem of the differential equations, if the strategy of the coal mining enterprise has a stable state, it needs to meet F(p, q) = 0. So, we set formula (11) equal to zero to get p = 0 or p = 1 and ω(q)H + ω(1 − q)I = 0; according to Taylor’s expansion, we can get $q={\left[{\displaystyle \frac{I}{I-H}}\right]}^{{\displaystyle \frac{1}{r}}}$.

Similarly, we set formula (14) equal to 0 to get q = 0 or q = 1 and $p={\left[{\displaystyle \frac{T}{T-S}}\right]}^{{\displaystyle \frac{1}{r}}}$.

Therefore, five system evolution equilibrium points of the replicated dynamic equations, composed of (11) and (14), can be obtained: E₁(0,0), E₂(0,1), E₃(1,0), E₄(1,1), if and only if:

$E_5={\left({\displaystyle \frac{T}{T-S}}\right)}^{{\displaystyle \frac{1}{r}}}\in \left[0,1\right],{\left({\displaystyle \frac{I}{I-H}}\right)}^{{\displaystyle \frac{1}{r}}}\in \left[0,1\right]$, we get the equilibrium point $E_5\left({\left({\displaystyle \frac{T}{T-S}}\right)}^{{\displaystyle \frac{1}{r}}},{\left({\displaystyle \frac{I}{I-H}}\right)}^{{\displaystyle \frac{1}{r}}}\right)$.

The Jacobian matrix of the system obtained by Equations (11) and (14) is as follows:

$$J(p,q)=\left[\begin{array}{cc}{\displaystyle \frac{\partial F_1(p,q)}{\partial p}}& {\displaystyle \frac{\partial F_1(p,q)}{\partial q}}\\ {\displaystyle \frac{\partial F_2(p,q)}{\partial p}}& {\displaystyle \frac{\partial F_2(p,q)}{\partial q}}\end{array}\right]=\left[\begin{array}{cc}(1-2p)(\omega (q)H+\omega (1-q)I)& (p-p^2)({\displaystyle \frac{\mathrm{d}\omega (q)}{\mathrm{d}q}}H+{\displaystyle \frac{\mathrm{d}\omega (1-q)}{\mathrm{d}q}}I)\\ (q-q^2)({\displaystyle \frac{\mathrm{d}\omega (p)}{\mathrm{d}p}}S+{\displaystyle \frac{\mathrm{d}\omega (1-p)}{\mathrm{d}p}}T)& (1-2q)(\omega (p)S+\omega (1-p)T)\end{array}\right]$$

$$\begin{array}{l}DetJ(p,q)={\displaystyle \frac{\partial F_1(p,q)}{\partial p}}·{\displaystyle \frac{\partial F_2(p,q)}{\partial q}}-{\displaystyle \frac{\partial F_1(p,q)}{\partial q}}·{\displaystyle \frac{\partial F_2(p,q)}{\partial p}}=\left(1-2p\right)\left(\omega \left(q\right)H+\omega \left(1-q\right)I\right)\left(1-2q\right)\\ (\omega \left(p\right)S+\omega (1-p)T)-(p-p^2)({\displaystyle \frac{\mathrm{d}\omega (q)}{\mathrm{d}q}}H+{\displaystyle \frac{\mathrm{d}\omega (1-q)}{\mathrm{d}q}}I)(q-q^2)({\displaystyle \frac{\mathrm{d}\omega (p)}{\mathrm{d}p}}S+{\displaystyle \frac{\mathrm{d}\omega (1-p)}{\mathrm{d}p}}T)\end{array}$$

$$TrJ(p,q)={\displaystyle \frac{\partial F_1(p,q)}{\partial p}}+{\displaystyle \frac{\partial F_2(p,q)}{\partial q}}=(1-2p)(\omega (q)H+\omega (1-q)I)+(1-2q)(\omega (p)S+\omega (1-p)T)$$

According to the method of analysis for the local stability of the Jacobian matrix, when the equilibrium point satisfies the determinant Det(J) > 0 and trace Tr(J) < 0, this indicates that the system is in a locally asymptotically stable state in the dynamic evolution process, which is regarded as the system’s local evolutionary stability strategy (ESS), and the rest are not stable points. The stability analysis of equilibrium points in the replicated dynamic equations is shown in Figure 2.

According to the criteria for determining stability specified by Arnoldi in the article, the sign of the determinant and the trace of the matrix J(p, q) can be used to determine the stability of this point. The point in question is only considered a stable node when the determinant of the matrix J is greater than zero and the trace is less than zero [47].

Since the trace value of the Jacobian matrix of the equilibrium point E₅ is zero, in order to further judge the positive and negative properties of the determinant, the following calculations are carried out in this paper.

$$\begin{array}{l}{\displaystyle \frac{\mathrm{d}{F}_1(p,q)}{\mathrm{d}q}}=(p-p^2)({\displaystyle \frac{\mathrm{d}\omega (q)}{\mathrm{d}q}}H+{\displaystyle \frac{\mathrm{d}\omega (1-q)}{\mathrm{d}q}}I)\\ {\displaystyle \frac{\mathrm{d}{F}_2(p,q)}{\mathrm{d}p}}=(q-q^2)({\displaystyle \frac{\mathrm{d}\omega (p)}{\mathrm{d}p}}S+{\displaystyle \frac{\mathrm{d}\omega (1-p)}{\mathrm{d}p}}T)\end{array}$$

(17)

Since $0<{\left({\displaystyle \frac{T}{T-S}}\right)}^{{\displaystyle \frac{1}{r}}}<1,0<{\left({\displaystyle \frac{I}{I-H}}\right)}^{{\displaystyle \frac{1}{r}}}<1$, then ${\displaystyle \frac{\mathrm{d}{F}_1(p,q)}{\mathrm{d}q}}>0,{\displaystyle \frac{\mathrm{d}{F}_2(p,q)}{\mathrm{d}p}}>0$. The value of the determinant of the equilibrium point E₅ is less than zero. $Det(J_{E_5})=M=-{\displaystyle \frac{\mathrm{d}{F}_1(p,q)}{\mathrm{d}q}}·{\displaystyle \frac{\mathrm{d}{F}_2(p,q)}{\mathrm{d}p}}<0$. Thus, this point is the saddle point.

After comprehensively analyzing the values of the remaining four equilibria, this paper finds that the evolutionary strategy of each equilibrium changes when the stability conditions change. The specific situation is shown in Figure 2.

Situation 1: when H < 0, I < 0, S < 0, T < 0, there exists a unique evolutionary stabilization strategy (0,0), (0,1) and (1,0) are the saddle points of the system, and (1,1) is the point of instability.

Situation 2: when H < 0, I < 0, S > 0, T < 0, there exists a unique evolutionary stabilization strategy (0,0), (0,1) and (1,1) are the saddle points of the system, and (1,0) is the point of instability.

Situation 3: when H > 0, I < 0, S < 0, T < 0, there exists a unique evolutionary stabilization strategy (0,0), (1,0), and (1,1) are the saddle points of the system, and (0,1) is the point of instability.

Inference 1: When I < 0, T < 0, the evolutionarily stable strategy of the system is (0,0), excluding the case where H > 0, I > 0.

For the local government, if the value-perceived benefit of performing deregulation is greater than the benefit of choosing strict regulation, then the local government will tend to perform deregulation. For the coal mining enterprise, the perceived benefit of not implementing intelligent construction is greater than that of full implementation. When the government does not tighten control, and the external social attention is at the bottom, the enterprise will tend not to implement intelligent construction. The final evolutionary stable strategy is {not implemented, deregulation}, and the specific evolutionary trend is shown in Figure 3a,c,i.

For the local government, as long as the central government enhances the monitoring of the local government and actively pushes the enforcement of the relevant policies, the perceived benefit of strict supervision by the local government is greater than the benefit of relaxed supervision, and the local government will choose the strategy of strict supervision. For coal mining enterprises, although the local government strictly enforces the relevant policies and regulations, the relevant reward and punishment mechanism is set up in vain, coupled with the external society’s lower concern for the internal administration of the enterprise, then the perceived benefit of the enterprise choosing not to carry out the intelligent construction is greater than the benefit of the active construction. The coal mining enterprise will tend to refrain from conducting intelligent construction. The final evolutionary stable strategy is {not implemented, strict supervision}, and the specific evolutionary trend is shown in Figure 3b,d,h.

Inference 3: When H > 0 and S > 0, the evolutionary stability strategy for the system can be expressed as (1,1), except for the case where I < 0 and S < 0.

In the context of local government, if the higher government department demonstrates a high level of attention to the operation and construction of the local government and enhances the management and standardization of the system, the value gained by the local government in implementing strict regulation is greater than the gain of deregulation. Consequently, the local government will opt for strict regulation. In the context of coal mining enterprises, the value gain of a fully implemented intelligent construction system outweighs that of a negative implementation. This is particularly true when the local government strictly regulates and integrates a reward and punishment system. Consequently, the enterprise will choose to implement intelligent construction fully. The final evolutionary stabilization strategy is {full implementation, strict regulation}, and the specific evolutionary trend is shown in Figure 3l,o,p.

Inference 4: When I > 0, S < 0, and excluding the case where H < 0 and T > 0, the evolutionarily stable strategy of the system is (1,0).

In the context of local government, when the resources consumed by strict supervision are excessive, and the perceived benefits of strict local government control are not as advantageous as those of relaxed supervision, local governments will choose the latter. When the pressure of external social supervision is excessive, and media and public opinion about coal mine pollution intensifies in the context of coal mining enterprises, the cost of not implementing intelligent construction rises significantly. Consequently, the enterprise is inclined to implement intelligent construction in its entirety. The final evolutionary stable strategy is {full implementation, deregulation}, and the specific evolutionary trend is illustrated in Figure 3e,m,n.

Situation 4: In the case of H < 0, I > 0, S < 0, T < 0, as illustrated in Figure 3f, the irregular region E₁E₂E₄E₅E₁ is constituted by unstable points E₁, E₄ and saddle point E₅, in addition to stable point E₂. This region indicates that the evolution strategy of enterprise intelligent construction tends to a state of {not implemented, strict supervision}, which is an ‘adverse’ stable state. The other irregular region comprises unstable points E₁, E₄, saddle points E₅ and stable point E₃. This region indicates the probability that the evolution strategy of enterprise intelligent construction tends to {full implemented, deregulation}, an ‘ideal’ stable state.

Situation 5: When H > 0, I < 0, S > 0, T < 0, as illustrated in Figure 3k, the irregular region E₁E₂E₅E₃E₁ is constituted by unstable points E₂, E₃ and saddle points E₅ and a stable point E₁. This region indicates the probability that the evolution strategy of enterprise intelligent construction tends to the state of {no implementation, deregulation}. The other irregular region comprises unstable points E₂ and E₃, saddle point E₅, and stable point E₄. This region indicates the probability that the evolution strategy of enterprise intelligent construction tends to the state of {full implementation, strict supervision}.

Inference 5: When HI < 0 and ST < 0, if H and S are of the same sign, there are two stable points in the system. When H < 0, the evolutionary stabilization strategies of the system are (1,0) and (0,1). When H > 0, the evolutionary stabilization strategies of the system are (0,0) and (1,1).

Inference 6: When HI < 0 and ST < 0, if H and S are of different signs, all points are saddle points and there is no evolutionary stable strategy for the system.

By analyzing the 16 scenarios in the chart, this paper finds that when H > 0, I > 0, S > 0, and T > 0 (i.e., the evolutionary stability of the system behavior is the strongest when the value perception return bias is convergent and positive), the entire evolutionary game reaches the best equilibrium state. At this time, the value perception of coal mine enterprises fully implementing intelligent construction behavior and the value perception of local government strictly supervising behavior occupy a rational dominant position. This means that p = 1 when coal mine enterprises choose to fully implement the intelligent construction strategy of a coal mine and q = 1 when local government chooses to strictly supervise coal mine enterprises.

In this case, the article has the following inferences.

Inference 7: When H > 0, i.e., V(R₁ + R₂) + C(m₂ + F₁ + α₂ω(p₀)L) > V(R₁). Since both V(x) and C(x) are increasing functions, then the corresponding variable satisfies R₂ > 0, m₂ + F₁ + α₂ω(p₀)L > 0. This implies that, in the event that coal mining enterprises are obliged to implement intelligent construction, it is imperative that they are able to guarantee that such enterprises will receive supplementary rewards and earnings R₂ resulting from intelligent construction.

Inference 8: When I > 0, i.e., V(R₁ + R₂) + C(m₂ + ω(p₀)L) > V(R₁) + C(m₀ + m₁ + tα₁ω(p₀)L). This implies that the corresponding variable satisfies m₂ + ω(p₀)L > m₀ + m₁ + tα₁ω(p₀)L. It can be seen that the greater the psychological cost m₂, the higher the degree to which coal mining enterprises fully implement intelligent construction. When the unimplemented psychological cost m₂ is higher than the implemented labor cost m₀ and mental cost m₁, it is more beneficial for coal mining enterprises to achieve an evolutionary stability strategy. In addition, the accident risk transfer coefficient t and the safety risk coefficient α₁ also have a significant impact on this condition. The appropriate reduction, within a limited range, can promote the evolutionary game between the two sides to reach a balanced state.

Inference 9: When S > 0, i.e., C(g₂ + F₂ + α₁ω(p₀)L) > C(g₀ + g₁), the corresponding variable satisfies g₂ + F₂ + α₁ω(p₀)L > g₀ + g₁ at this time. The sum of the psychological cost g₂ of the local government department’s deregulation, the penalty F₂, and the accident risk cost α₁ω(p₀)L should be greater than the labor cost g₀ and the mental cost g₁ of its strict regulation.

Inference 10: When T > 0, i.e., V(B₁ + βF₁) + C(g₂ + F₂ + ω(p₀)L) > V(B₁ + ω(p₁)G) + C(g₀ + g₁ + tα₂ ω(p₀)L), the corresponding variable satisfies βF₁ > ω(p₁)G,g₂ + F₂ + ω(p₀)L > g₀ + g₁ + tα₂ω(p₀)L at this time. The performance reward βF₁, obtained by the local government by investigating and handling the non-implementation of intelligent construction coal mines, should be as high as possible, in relation to the benefit ω(p₁)G obtained from the coal mine when it relaxed regulations.

The above inference does not contain any cases that cannot be calculated or derived. This situation indicates that the players’ utility can be modeled using a value function that reflects reference dependence and loss aversion, consistent with prospect theory. Specifically, the results show that both the coal mining enterprise and the government mechanism can adopt the value function as their income target, and with all parameters being significantly greater than zero and fixed, this is largely supported by the results. Therefore, Hypothesis 1 is valid.

In addition, when the sum of the psychological cost g₂ and penalty F₂ of local government deregulation is greater than the labor cost g₀ and mental cost g₁ of strict regulation, the smaller the accident risk transfer coefficient t and the safety risk coefficient α₂ of coal mine enterprises without implementing intelligent construction. The stricter the regulation by local government, the more conducive it is for both parties to achieve the evolutionary stability strategy.

4.2. Simulation Model Construction

Following the game hypothesis and analysis mentioned above, this study employs Vensim PLE 7.3.5 and MATLAB 9.12.0 to construct a two-agent evolutionary game SD model comprising two subsystems: the coal mining enterprise and the local government. As illustrated in Figure 4, the model contains two horizontal variables, two rate variables, eight intermediate variables, and twenty external variables. Specifically, the rate of coal mining enterprises choosing the execution of intelligent construction and the rate of local government executing supervision strictly are expressed as two horizontal variables; change rate of intelligent construction and change rate of strict supervision are expressed as two rate variables; and the external variables are in alignment with the variable values presented in the income matrix presented in Table 2. Furthermore, the functional relationships between variables and the flow rate formulas in the SD model are primarily derived from the game analysis above and replication dynamic equations, precisely Type 11 and Type 14.

In light of the aforementioned considerations, the spillover penalty mechanism of the coal mining enterprise, as outlined in Hypothesis 3, is subjected to analysis. That is, in the event of a fine being imposed on a particular enterprise, the liability system, which also holds local enterprises in the same area to account, is put into effect. This paper presents an enhanced version of the evolutionary system, as illustrated in Figure 5.

Taking the coal mining intelligence investigation as a working opportunity, we examined the exploitation and construction status of internal intelligent equipment in 15 coal mines located in Datong City, Lvliang City, and Taiyuan City of Shanxi Province. These regions were selected due to their diverse geological conditions and varying degrees of intelligent transformation. Specifically, Datong coal mines face high gas content and ventilation challenges, while Lvliang mines are characterized by fragmented strata and complex fault structures. Taiyuan mines, in contrast, are located in areas with relatively stable geological formations but face environmental and policy constraints. In addition, based on the internal supervision reward and punishment systems and the actual income and expenditure records of each coal mine, combined with relevant data from the China Coal Industry Statistical Yearbook, we determined the initial values for a range of external variables, as detailed in

Table 4. Initial values of external variables in the SD model.

Variables	Meanings of the Variables	Notes
m0	The labor cost of enterprises of fully implementing intelligent construction	3
m1	The mental cost of enterprises of fully implementing intelligent construction	3
m2	The psychological cost of enterprises of not fully implementing intelligent construction	2
g0	The labor cost of strict regulation by local government departments	3
g1	The mental cost of strict regulation by local government departments	3
g2	The psychological cost of deregulation by local government departments	1
R1	The net revenue of coal mining enterprises intelligent construction	3
R2	Additional revenue and rewards for companies due to intelligent construction	2
B1	Tax revenue and performance of local governments in managing day-to-day affairs	3
B2	Environmental and social benefits of local governments due to intelligent construction	3
t	Safety accident risk transfer coefficient	1
L	Cost of safety accident risk to be borne by the responsible party after an accident	100
p0	Accident risk probability of safety hazards due to not updating intelligent equipment	0.03
α1	The safety hazard factor when enterprises fully implement intelligent construction and local governments deregulation	0.4
α2	The safety hazard factor when enterprises do not implement intelligent construction and local governments strict supervision	0.6
μ	The fines factor of local governments is linked to their own reward coefficients	0.3
F1	Local government fines levied on enterprises that do not implement intelligent construction	3
F2	The penalties from higher authorities when local governments deregulate	3
G	The benefits received from enterprises when local governments deregulate	0.5
p1	Probability of receiving benefits from enterprises when local governments deregulate	0.5

.

According to the randomized trial results of Tversky, Dijk and the research by Gregory into financial markets, the risk preference coefficient β, θ is 0.88, the risk preference coefficient φ, σ is 0.98 [48]. The sensitivity of valence and cost loss avoidance (λ and δ) is 2. The model is set as follows: INITIAL TIME = 0, FINAL TIME = 100, TIME STEP = 0.03125, Units for Time: Year, Integration Type: Euler.

The numerical simulation of the model indicates that the actual situation is consistent with the situation depicted in Figure 3p of the above analysis. In other words, with the gradual and rigorous oversight of the government, enterprises will ultimately achieve comprehensive integration of intelligent construction. In practice, the government will undoubtedly anticipate that enterprises will proactively adopt this behavior, which is conducive to humanity’s future survival and development due to self-restraint or regulation. Consequently, in the idealized state, the government would like to see that in the absence of government regulation, enterprises can still fully implement intelligent construction, i.e., reach the state in Figure 3n. To this end, we explore the key influences on evolutionary stabilization strategies with the expectation of providing recommendations for government regulation of firms.

4.3. System Simulation Analysis

4.3.1. The Impact of Selecting an Initial Change in Strategy on Evolutionary Results

The evolution strategies of intelligent construction behavior of coal mining enterprises, under no spillover effect, are shown in Figure 6. In order to gain a deeper understanding of the precise influence of the initial corporate strategy on the evolutionary strategy, we selected a series of distinct initial values (p = 0.001, p = 0.01, p = 0.1, p = 0.2, p = 0.3, p = 0.4; q = 0), as illustrated in Figure 6a. From t_p=0.001 = 7.9 and t_p=0.01 = 6.8, it can be observed that the higher the initial stage of the intelligent construction of the coal mining enterprise, the shorter the time required for the system to reach a steady state. Conversely, from t_p=0.2 = 4.5, t_p=0.3 = 4.1 and t_p=0.4 = 4.0, it can be seen that the higher the degree of intelligent construction of the enterprise, the slower the rate of reaching a stable state. This indicates that the higher the starting point of intelligent construction in coal mining enterprises, the slower the rate of subsequent upgrading and reconstruction. Figure 6b shows the evolution of the probability of intelligent construction by coal mining enterprises, under different levels of regulatory measures taken by local governments, when the initial probability of intelligent construction p = 0.1. The local government strictly regulates the probability that the initial value q is 0.1–0.9, and the step size is 0.2. Under the non-spillover penalty system, the intelligent construction process of coal mining enterprises accelerates with the continuous improvement of the regulation probability of local governments. This indicates that the initial state of the enterprise is not a determining factor in the eventual direction of the enterprise towards a fully intelligent construction.

However, initial probabilities exert a certain influence on the pace of system evolution. This implies that the initial degree of supervision by government departments and the initial stage of enterprise construction may have an impact on the process of achieving comprehensive intelligent construction. In other words, for enterprises at the same level of construction, the stricter the government’s initial supervision in a particular district, the faster and more comprehensive the construction process in that district will be. Furthermore, the higher the starting point of intelligent construction for enterprises in this process, the slower subsequent progress will be. For enterprises that are about to complete intelligent construction, the more challenging it will be to resolve the ‘last mile’ issue.

4.3.2. The Impact of Spillover Penalties on Evolutionary Results

Figure 7a illustrates that the slope of the blue line is consistently lower than that of the black line. This implies that the rate of intelligent enterprise construction under a penalty system with spillover effects is invariably slower than that under a system without such effects. This, in turn, suggests that the imposition of cascading penalties delays the system’s attainment of a stable equilibrium point, particularly in the case of enterprises, and impedes the implementation of their intelligent construction. As can be seen from Figure 7b, in the presence of spillover penalties, the rate of intelligent construction by coal mining companies declines as the strength of initial government constraints increases. This is contrary to the fact that the intensity of government regulation is proportional to the speed of contractorization in the context of no spillover effects. This indicates that, from a value perception standpoint, rather than facilitating the expeditious development of enterprise intelligence, the imposition of spillover penalties by governments can impede the process. In extreme instances, where the initial pressure exerted by the government is considerable, it is often challenging for enterprises to initiate the process.

Similarly, we analyze the extent to which spillover penalties affect the probability of strict government oversight, using the probability of strict government oversight as the vertical axis. This finding is in alignment with the aforementioned conclusion that spillover penalties exert a limited influence on the rate at which full implementation of strict monitoring occurs. It is evident that the introduction of spillover effects can only impede the development of intelligence, yet it cannot alter the ultimate evolutionary strategy. Specifically, the joint and several liability punishment mechanisms has the effect of punishing those enterprises that comply with the regulations and conscientiously carry out transformation for the illegal business practices of their peers. This has the effect of dampening the enthusiasm of these enterprises to improve their intelligent construction, discouraging those that are in the midst of the critical process of improvement and hindering their continued promotion and upgrading of intelligent in the future. As a result, the overall national intelligent construction process of coal mines is delayed.

This contradicts the viewpoint in the original Hypothesis 3 that in the game model based on value perception, the spillover penalty strategy can also promote intelligent construction. Therefore, Hypothesis 3 does not hold.

4.3.3. The Impact of Mental Account Factor on Evolutionary Results

This paper also explores the effects of labor, mental, and psychological costs on the evolutionary game between the two parties. Taking Figure 8a as an example, we take the initial values p = 0.5 and q = 0.5 and set the loop function for m₀ = 2.0:0.5:5.0. It can be seen that, to a certain extent, the lower the labor cost of intelligent construction of coal mining enterprises, the faster the speed of coal mining enterprises and local governments in choosing the ideal state. The government should make enterprises deeply aware of the benefits of this transformation for the enterprise, eliminate the cognitive barriers and labor cost obstacles to intelligent construction, so that enterprises are willing to actively invest funds to drive production and operations. With the continuous increase in labor cost m₀ for the implementation of intelligent construction in coal mine enterprises, the trend of the evolution system converging to 1 gradually becomes smooth. When the critical value m₀ = 3.7 is exceeded, the probability of intelligent construction in coal mine enterprises no longer evolves in the direction of 1 but tends towards 0. Similarly, the evolutionary trend of m₁, the mental cost paid by coal mine enterprises to implement intelligent construction, is roughly the same as that of m₀, and its critical value is about 3.9 after simulation. However, the psychological cost m₂ path of coal mine enterprises that have not implemented intelligent construction is just the opposite of m₀, and the implementation probability of intelligent construction will increase with the increase of m₂.

Similarly, an analysis was conducted to determine the influence of the psychological account factor on government strategies. As illustrated in Figure 8b, the initial values are p = 0.5 and q = 0.5, and the loop function is g₀ = 2.0:0.5:5.0. As illustrated in the figure, a reduction in the cost of labor, which is subject to strict regulation by the local government, will result in a more rapid convergence towards a stable evolutionary strategy by the government and enterprises. As the labor cost subject to government regulation continues to rise, the final strategy of the evolutionary system undergoes a gradual transformation. When the critical value exceeds g₀ = 3.7, the probability of strict government supervision does not evolve towards 1 but rather towards 0. Similarly, the evolution trend of the mental cost g₁ of strict government supervision is roughly the same as g₀, and its critical value is 3.8 after simulation. Nevertheless, the psychological cost of deregulation on local government departments has the opposite effect on government decision-making as labor cost g₀. Consequently, the rate at which government tends to stabilize increases with psychological cost g₂. Specifically, as the costs of strict government supervision increase, so too does the potential for enterprises to benefit from deregulation. This, in turn, allows the government to pursue a policy of governance by non-interference, thereby reducing the psychological costs of deregulation for enterprises. In other words, the government need not be excessively diligent and restrictive, and enterprises will assume the initiative to achieve intelligent construction. This indicates that to achieve this objective, the government need not be unduly concerned about the intelligent development of enterprises and should permit them to develop freely and exercise self-restraint.

A sensitivity analysis of the aforementioned factors pertaining to mental accounting revealed that these factors can effectively control and influence the final direction of the evolutionary strategy. At the same time, the above analysis indicates that coal mining enterprises and the government exhibit limited rationality in their risk assessment and in how they define gains and losses, while the structure of the value perception function effectively captures their decision-making behavior. Specifically, both coal mining enterprises and the government will exhibit appropriate decision-making differences under different psychological expectations, which is consistent with the prospect accounting theory in Hypothesis 2, thereby confirming the validity of Hypothesis 2.

4.3.4. The Impact of Fines on Evolutionary Results

The main difference between the spillover penalty mechanism and the non-spillover penalty mechanism is that qF₁, a cost account, is added when the coal mine enterprises fully implement intelligent construction. Therefore, Figure 9a shows an evolutionary simulation based on the influence of F₁, a single variable, on the probability of intelligent mine construction behavior of coal mining enterprises. In order to facilitate observation, the initial value of probability q of strict regulation by local governments and probability p of fully implementing intelligent construction in coal mining enterprises is 0.05; the initial value of F₁ is 2.0–4.0, and the step size is 0.5. As can be seen from the figure, with the increase in the number of fines imposed on enterprises by the government, the growth rate of the probability of enterprises fully implementing the intelligent construction of coal mines continues to increase. This situation shows that, to a certain extent, the government’s appropriate increase in fines can urge coal mining enterprises to improve intelligent construction quickly. Similarly, the rate of strict government regulation is plotted on the vertical axis, resulting in an image with a trend comparable to that observed in Figure 9a. This indicates that an increase in fines accelerates the system to a certain extent, ultimately reaching a steady state, while not influencing the final strategies of the two parties. The impact of F₂ on the government’s strategic approach differs significantly from that of F₁. In order to facilitate observation, the following values have been selected for analysis in this paper: F₂ = 1.4, F₂ = 1.7, F₂ = 2.0, F₂ = 2.3, F₂ = 2.7, F₂ = 3.0, F₂ = 3.3. As illustrated in Figure 9b, when F₂ is less than the critical value of 2.3, the government tends to pursue deregulation; when it is greater than 2.3, the government intensifies strict regulation in line with the amount of fine. This indicates that the value of F₂ will influence the government’s ultimate evolutionary decision.

4.3.5. Scenario Validation

In order to verify the conclusions drawn from the aforementioned images, this paper presents four scenarios in which the following parameters have been adjusted. The objective is to provide a theoretical basis for the local government to effectively regulate coal mining enterprises. As illustrated in Figure 10, the figure depicts the strategy evolution diagram of the coal mine enterprise and the local government department in the context of intelligent coal mine construction across four distinct scenarios. To facilitate a more detailed examination of the system’s specific evolutionary trajectory, this study incorporates six additional internal starting strategies, selected as follows: (0.1, 0.1), (0.1, 0.2), (0.2, 0.55), (0.3, 0.45), (0.3,0.1), and (0.4, 0.35). The parameters for the four specific scenarios are shown in

Table 5. Parameter assignment values.

Scenario	μ	g0	g1	g2	F1	F2	G
A	0.3	3	3	1	3	3	0.35
B	0.4	3.1	3.1	0.9	4	2.7	0.4
C	0.5	3.2	3.2	0.8	5	2.4	0.45
D	0.6	3.3	3.3	0.7	6	2	0.5

.

Figure 10a illustrates that, in the context of the aforementioned spillover punishment measures (i.e., in Scenario A), irrespective of the degree of government supervision and the initial level of intelligent construction of the enterprise, provided that the two main bodies exert their efforts concurrently, the game system can be stabilized. Consequently, coal mining enterprises will eventually achieve comprehensive intelligent construction under progressively intensifying rigorous supervision. As illustrated in Figure 10b, the continuous escalation of labor and mental costs associated with rigorous supervision by local government departments, coupled with the concomitant decline in the psychological costs of social supervision during the process of deregulation, has resulted in a reduction in the rate and upper limit of government regulation enhancement in comparison to the preceding period. This indicates that the government is no longer required to impose harsh penalties on enterprises, as was previously the case, and can instead achieve twice the result with half the effort. As can be seen from Figure 10c, with the increase in fines imposed by the local government on enterprises that fail to implement intelligent construction and the decrease in fines imposed by the superior government on the local government due to improper management, the government will gradually relax regulations after strengthening the control over enterprises for a period of time, which can also enable enterprises to complete comprehensive intelligent construction. Furthermore, as illustrated in Figure 10d, the behavior of local government departments is also influenced by the factor of additional revenue received from enterprises and fine factors linked to government performance. As evidenced by the trend in the figure, when this additional revenue reaches a certain percentage, the government’s regulatory efforts will decrease linearly, eventually tending towards a state of non-regulation.

From the perspective of management, the imposition of fines by local governments on enterprises is offset by the receipt of additional benefits from these entities. Consequently, local governments may be inclined to adopt a laissez-faire management model, particularly when they receive fines from higher authorities and benefits from enterprises. In other words, it would be prudent for the state to refrain from imposing excessive fines and constraints on local governments during macro-level control. It is recommended that the central government adopt a policy of active trust in local governments, and that local governments reciprocate this trust by extending it to enterprises.

5. Conclusions and Implications

5.1. Conclusions

This study provides several key insights into the intelligent construction of coal mining enterprises. First, initial conditions—such as the degree of early government supervision and enterprise construction stage—significantly influence the evolution speed of intelligent systems. Second, the current spillover punishment mechanism appears counterproductive, deterring compliant enterprises and slowing national progress. Third, reducing the cognitive, mental, and labor costs associated with intelligent transformation can increase enterprise willingness to participate, especially when paired with targeted government guidance and positive public pressure. Fourth, strict supervision by the government may not be necessary; allowing enterprises greater autonomy can lead to self-driven innovation. Finally, overly punitive local government policies may foster regulatory passivity due to conflicting incentives, indicating a need for macro-level policy adjustments and mutual trust frameworks.

The primary limitations of this study lie in its regional focus and the lack of longitudinal data to assess the long-term effects of policies. The study sample solely encompasses major coal mines in Shanxi Province, thereby failing to adequately include a diverse array of coal mine cases from disparate regions, varying scales, and exhibiting distinct geological characteristics across the country. Future research should be improved in three areas: first, by expanding the geographical coverage by conducting stratified sampling in typical coal-producing regions such as Inner Mongolia and Guizhou; second, by introducing a temporal dimension to analyze the long-term evolution of policy effects using dynamic game models; and third, by enhancing sample diversity by systematically examining extreme cases such as small and medium-sized coal mines and high-methane mines to more comprehensively define the applicability of the research conclusions.

From a practical perspective, this research suggest that coal-producing countries should adopt differentiated regulatory approaches based on enterprise maturity and local governance capacity. Globally, policymakers may consider moving away from rigid command-and-control models toward more flexible, incentive-aligned, and psychologically informed strategies. Compared with prior studies [18,21], this research highlights the nonlinear and behavioral aspects of enterprise decision-making in the context of intelligent transformation. Unlike earlier models focused on linear policy impacts, the integration of bounded rationality and value perception functions offers a novel theoretical contribution and a more realistic basis for international application.

5.2. Implications

First, the Chinese government should pay extra attention to the initial implementation and the strict enforcement of the law in the final stages of regulating coal mines. Chinese government departments should reasonably set fines for illegal coal mining in accordance with the law. It is important to emphasize that the mechanism of joint and several liability must be correctly implemented in order to prevent the use of punitive measures with a spillover effect, which would instead discourage the intelligent construction of enterprises. The amount and mechanism of fines must be appropriate to the facts, nature, circumstances, and social and environmental impact of the illegal act in question.

Secondly, it is imperative to continually monitor the labor and mental costs incurred by enterprises and governments in the construction of intelligent coal mines. It is incumbent upon coal mining enterprises to undertake regular institutionalized, standardized, and routine safety and psychological training. Coal mine management personnel, especially leading cadres, take the initiative to learn about psychological safety, gain a deep understanding of its spiritual essence and inherent requirements, and accept psychological safety inspections and supervision on a continuous basis. All coal mining departments should strictly incorporate the content of psychological safety training into the content of production safety for management personnel [49].

Thirdly, the government should avoid excessive fines and restrictions and foster an intimate and transparent relationship between the government and enterprises. Local Party committees and governments at all levels should implement measures to regularly solicit the opinions and demands of coal mining enterprises and ensure that entrepreneurs have channels for expressing their opinions and demands. The government should innovate the service model for coal mining enterprises. it is recommended to further enhance the government’s awareness and ability to provide services and to encourage governments at all levels to compile a list of government services for coal mines and publish it to the public.