Research on the Game Strategy of Mutual Safety Risk Prevention and Control of Industrial Park Enterprises under Blockchain Technology

Abstract

Systematic management of corporate safety risks in industrial parks has become a hot topic. And risk prevention and control mutual aid is a brand-new model in the risk and emergency management of the park. In the context of blockchain, how to incentivize enterprises to actively invest in safety risk prevention and control mutual aid has become a series of key issues facing government regulators. This paper innovatively combines Prospect Theory, Mental Accounting, and Evolutionary Game Theory to create a hypothetical model of limited rationality for the behavior of key stakeholders (core enterprises, supporting enterprises, and government regulatory departments) in mutual aid for safety risk prevention and control. Under the static prize punishment mechanism and dynamic punishment mechanism, the evolutionary stabilization strategy of stakeholders was analyzed, and numerical simulation analysis was performed through examples. The results show: (1) Mutual aid for risk prevention and control among park enterprises is influenced by various factors, including external and subjective elements, and evolves through complex evolutionary paths (e.g., reference points, value perception). (2) Government departments are increasingly implementing dynamic reward and punishment measures to address the shortcomings of static mechanisms. Government departments should dynamically adjust reward and punishment strategies, determine clearly the highest standards for rewards and punishments, and the combination of various incentives and penalties can significantly improve the effectiveness of investment decisions in mutual aid for safety risk prevention and control. (3) Continuously optimizing the design of reward and punishment mechanisms, integrating blockchain technology with management strategies to motivate enterprise participation, and leveraging participant feedback are strategies and recommendations that provide new insights for promoting active enterprise investment in mutual aid for safety risk prevention and control. The marginal contribution of this paper is to reveal the evolutionary pattern of mutual safety risk prevention and control behaviors of enterprises in chemical parks in the context of blockchain.

1. Introduction

Industrial parks play a crucial role in industrial development, relying on the formation of numerous enterprise clusters to drive economic growth, industrial upgrading, and agglomeration, thus enhancing industrial competitiveness. The park should have an advanced and standardized risk management foundation, but safety accidents occur frequently and the losses are huge. For example, in 2019, the “3.21” explosion in Xiangshui, Jiangsu, China caused 78 deaths and a direct economic loss of 1986.3507 million yuan [1]. Due to the large number of enterprises and hazards in the park, which are relatively densely arranged, it is highly likely to cause a “domino effect” of accidents [2], affecting adjacent hazards and causing greater catastrophic consequences. The park’s enterprises form a network of risk sharing interests [3,4]. The park’s enterprises, particularly supporting ones, are weak in preventing and controlling safety risks due to uneven safety production resources. Supporting enterprises are mostly small and micro enterprises, with limited investment in safety production [5,6,7]. Investment in safety includes investment in safety prevention, safety training and emergency drills. The use of systems thinking is a necessary method for effective safety management [8], and The park’s systematic risk management work is of utmost importance.

Safety is a fundamental element of industrial park construction and operation [9]. However, in these parks, the safety responsibilities of multiple companies often remain unclear [10], leading to vulnerabilities in risk prevention and control. The concept of mutual aid in risk management has emerged as a new paradigm, with initiatives like the establishment of safety production alliances in Suzhou Industrial Park in 2020 and the “Industrial Enterprise Safety Mutual Aid Alliance” platform in Chongqing Liangjiang New Area in 2023, emphasizing a collaborative approach to safety management. In the context of Security 4.0, the new generation of information technology has been widely applied in the field of security management [11]. Digital intelligence technology enhances risk perception and safety risk prevention and control by providing more accurate and effective solutions [12]. Based on this, Wang et al. proposed the theory and method of precise security management [13]. Empowering risk management with new generation information technology is a new method for park security management. Blockchain is a typical new information technology with features such as decentralization, immutability, transparency, and traceability [14]. Can enhance the effectiveness of risk monitoring and early warning for emergencies [15]. In 2022, the first batch of government blockchain application scenarios in Suzhou Industrial Park were officially launched, among which the safety production prediction and early warning monitoring platform was included. The platform utilizes blockchain technology to comprehensively enhance the safety production accident prevention and emergency management capabilities of park enterprises, and enhance their safety risk prevention and control capabilities. Because blockchain technology has the characteristics of decentralization, non-tampering and traceability, blockchain technology can enhance the penetration of safety production supervision, realize the supervision and management of the whole process of safety operation, reduce the risk of accidents and enhance the ability to cope with risks through digital work tickets, in-service deposit supervision and intelligent division of labor management.

In literature, managing park safety risks systematically has become a hot topic. Research primarily focuses on two aspects: (1) Influencing factors of park risk control, including various risk sources, infrastructure resilience [16], safety investment [17], and external environment [18], alongside the relationships among enterprises within the park [19]. (2) Main strategies for risk prevention and control in parks, such as purchasing third-party safety services [20] and promoting the safety & security integration in parks [13] are common strategies for risk prevention and control in parks. It is also an important strategy to form a safety production alliance led by the core enterprises to give full play to the spillover effect of the safety investment of the core enterprises [20], and at the same time to prevent the supporting enterprises from “hitching a ride” [21] and realize mutual assistance in safety risk prevention and control. The use of new-generation information technology like big data [22], IoT [23], and blockchain [24] is a growing trend in park risk management, enabling intelligent early warning and rapid emergency response. The game process of mutual safety risk prevention and control of enterprises in the park involves a number of players including core enterprises, supporting enterprises and government regulators. Different subjects form a game relationship with each other from the perspective of maximizing their own profits. Core enterprises are ahead of supporting enterprises in safety investment, and to a certain extent, they hope to help SMEs reduce safety costs. Supporting enterprises are mostly small and medium-sized enterprises, and due to resource constraints, there is a “free-rider phenomenon” in security investment. Although blockchain technology can enable the formation of penetrating production safety supervision and improve the effectiveness of supervision, the increase in cost will also affect the government’s decision-making. Game theory can portray the behavioral laws of multiple subjects in the park. The current research on preventing and controlling park safety risks using blockchain is insufficient, necessitating in-depth study and exploration of behavioral decision-making laws of multiple subjects under limited rationality.

Lewontin [25] introduced the evolutionary game concept, a method used in multi-agent decision-making. Reniers and co-authors [26] explored safety investment in chemical industrial parks using game theory. Kahneman and Tversky [27] proposed a prospect theory closer to real human decision-making than the utility theory from cognitive psychology. And Thaler [28] introduced the concept of psychological accounts, aiming to explain the real decision-making process, which was further refined by Alexander K. Koch [29]. The evolutionary game model constructed based on PT-MA takes into account the influence of psychological factors and risk preferences on decision-making subjects. Compared with the classic evolutionary game, it is closer to the reality and makes the model more reliable. In the field of safety production, most of the existing game models ignore the individual psychological factors and influence of decision makers. Scholars have introduced prospect theory and mental accounts to different fields, Chen et al. constructed a multilevel game model for public crisis governance [30], and Deng et al. constructed a three-party game model for emergency management investment in chemical enterprises [31]. A better portrayal of the behavioral patterns of safety management decision makers. Although game theory, based on prospect theory and mental accounts, is widely utilized in risk and emergency management, so far, no attention has been paid to the introduction of prospect theory and mental accounts into risk mutual aid prevention and control of enterprises in parks, and we have not yet realized the important role of blockchain technology in risk mutual aid prevention and control.

The purpose of this paper is to establish a hypothetical model of limited rationality of safety risk mutual aid actors (core enterprises, supporting enterprises and government regulators) in the zone, which means that the hypothetical conditions of this paper are between complete rationality and incomplete rationality. The following questions are addressed: What is the law of safety risk mutual aid behavior of enterprises in the park under block technology? What is the impact of the government dynamic reward and punishment mechanism on the safety risk mutual aid behavior of zones? This model can more reasonably and truly explain the behaviors of core enterprises, supporting enterprises and government regulators, which can provide decision-making reference for safety risk management in the park and promote the mutual assistance and prevention of safety risks in the park, and has practical and theoretical significance. This article consists of six sections: Section 2 is the construction of a game model; The Section 3 is the model analysis in the static reward and punishment mechanism; the Section 4 simulates the model with assumptions; The Section 5 is simulation with the assumption; and Section 6 outlines the study’s conclusions, limitations, and future outlook. A graphical summary of this paper is shown in Figure 1.

The marginal contributions of this paper mainly lie in the following three points:

(1) This paper aims to address the issue of safety risk mutual aid among park enterprises in the context of blockchain by combining the real situation, filling the gap of related research and helping to promote mutual aid in preventing and controlling the risk of active investment among enterprises. (2) Taking into account the psychological factors of the decision-making subject, this paper constructs an evolutionary game model under the blockchain technology based on PT-Ma, which is more in line with the reality and promotes the development of the relevant fields compared with the existing research. (3) Combining different reward and punishment mechanisms, this paper reveals the behavioral laws of core enterprises, supporting enterprises and the government under blockchain technology, which requires the adoption of reasonable reward and punishment mechanisms to promote mutual prevention and control of safety risks.

2. Game Modeling

2.1. Problem Description and Mechanism Analysis

The game process of mutual safety risk prevention and control of enterprises in the park involves players including core enterprises, supporting enterprises and government regulators. In this paper we look at the government as a whole, with the existence of core and supporting firms, rather than considering the game from the perspective of a specific regulator. In order to meet the government’s requirements, enterprises will invest in safety risk prevention and control, the core enterprise as the lead unit of the production safety alliance, in the risk prevention and control of investment, safety management experience and other aspects of the leading supporting enterprises, the core enterprise risk prevention and control measures have a certain degree of spillover, to a certain extent, to help support the enterprise to reduce the cost of safety. Most of the supporting enterprises are minor enterprises, the primary goal is to develop the enterprise, the pursuit of profit maximization, there is the phenomenon of “free-riding”, which may easily lead to the lack of strength of their own safety resources. The “free-rider effect” in parks means that the core security investment behavior of the group will benefit all the firms in the park, but the supporting firms in the park will not bear this cost.

Supporting enterprises on the one hand do not want to redundant safety investment, and hope to avoid supporting enterprises “free-riding”, will be negative input. On the other hand, they need to prevent safety accidents from happening and avoid causing property losses, and they are also worried about the shortcomings of safety risk prevention and control in the park, so they will actively invest in it. On the one hand, supporting enterprises would like to “free ride” and will invest negatively. On the other hand, they do not want accidents to happen in the park, and hope to gain more trust from the core enterprises, so they will actively invest in the park. The government can regulate through traditional methods like rule of law, dishonest constraints, and incentive measures. Incentives mainly include taxes, subsidies and other measures. On this basis, it can also improve the level of science and technology and informationization of regulation, and use blockchain technology to empower the regulatory work, but the application of blockchain will also increase the cost. The article presents a game model utilizing prospect theory and psychological account theory, involving core enterprises, supporting enterprises, and government regulatory departments, illustrated in Figure 2.

2.2. Basic Assumptions

Hypothesis 1. 

Assumptions about game subjects and their strategies. The three-way game focuses on core enterprises, supporting enterprises, and government regulators. Each subject in the game process are limited rationality, and in line with the value perception function $V$; three-party game subjects of the decision-making goal is to maximize their own revenue. Each game subject selects behavioral strategies based on their own perceived value. According to the strength and enthusiasm of safety risk prevention and control input, the strategy choice of core enterprises and supporting enterprises can be divided into (positive input, negative input); the government’s strategy choice can be categorized into (positive supervision, negative supervision), based on various supervision methods.

Hypothesis 2. 

Conditional assumptions that the park’s safety risk prevention and control inputs are at an optimum. The behavioral strategies of core and supporting enterprises are complementary to each other. Only when both parties choose positive behavior at the same time, i.e., (positive input, positive input), can ensure that the park’s safety risk prevention and control inputs are in an optimal state, otherwise there will be a risk loophole. The principle of risk sharing states that when one party takes positive action and the other takes negative action, the accident risk is transferred based on the risk transmission coefficient $\varphi$. According to the principle of risk spillover ($\alpha$ represents the externality coefficient), the risk of security accidents is represented by $L$, and the probability of security accidents is represented by $q$.

Hypothesis 3. 

Assumptions of the main parameters. Core enterprises need to pay a certain cost to actively invest $C_{ph}$, supporting enterprises need to pay a certain cost $C_{gh}$, and government regulators need to pay a certain cost to actively supervise $C_{gh}$. For the sake of modeling, this paper assumes that negative investment by core enterprises, negative investment by supporting enterprises, and negative supervision by the government will not incur costs. When enterprises make various investment choices, their safety level will also change accordingly. The enterprise’s initial safety level is denoted by $H_0$, while the safety level after active investment by core enterprises is denoted by $H_1$, and the degree of safety level after active investment by supporting enterprises is denoted by $H_2$. According to safety economics, core firms actively invest with a positive externality of $H_a$. Ancillary firms free-riding gains are $K$, government regulators regulate gains are $H_b$, park safety positive externality is $H_{\mathrm{c}}$, and park safety negative externality is $H_d$. The intensity of regulation by the government department leads to reputational changes, with reputational loss recorded as $M$ and reputational gain recorded as $N$. The government will reward or penalize firms based on their strategic choices to incentivize them to invest in safety, rewarding positive inputs and penalizing negative inputs, with fixed values for rewards ($F$) and penalties ($R$).

2.3. Model Construction

Table 1. Parameter symbols and meanings.

Parameters	Sense
$p$	Probability of active input from core firms
$g$	Probability of negative inputs from supporting firms
$e$	Probability of strict regulation by government regulators
$C_{ph}$	Perceived cost of active engagement by core businesses
$C_{gh}$	Perceived cost of positive inputs from supporting companies
$C_{eh}$	Perceived costs of active regulation by government regulators
$H_1$	The extent to which the core business actively invests in contributing to its own level of security
$H_2$	The extent to which positive inputs from supporting companies contribute to their own level of safety
$H_0$	Gain in units with improved safety levels
$H_a$	Positive externalities of safety investments in core firms
$K$	Accompanying Business Benefits
$H_b$	Government regulators regulate earnings
$H_c$	Positive park security externalities
$H_{\mathrm{d}}$	Negative park security externalities
$R$	Incentive levels (active engagement)
$F$	Penalty amount (negative inputs)
$W$	Probability of positive inputs/negative inputs being detected (probability in case of negative regulation; 1 in case of positive regulation)
$M$	Reputational damage to government regulators
$N$	Value added to the reputation of government regulators
$\varphi$	Risk transfer coefficient
$\alpha$	Risk spillover factor
$\psi$	risk factor
$L$	Risk of security incidents
$q$	Probability of a security incident
$C_0$	Blockchain technology application costs

displays the specific parameter settings in the revenue perception matrix.

The revenue perception matrix, as depicted in

Table 2. Earnings Perception Matrix.

	Government Regulator
		Active supervision	Negative regulation
Active engagement by core businesses $p$	Supporting Companies active participation $g$	$P(H_0{H}_1+R)-C(C_{ph})$	$P(H_0{H}_1+WR)-C(C_{ph})$
		$P(H_0{H}_2+H_a+R)-C(C_{gh})$	$P(H_0{H}_2+H_a+WR)-C(C_{gh})$
		$P(H_b+\alpha H_c+N)-C(C_0+C_{eh}+2R)$	$P(\alpha H_c+N)-C(2WR)$
	Supporting Companies Negative inputs $1-g$	$P(H_0{H}_1+R)+C(C_{ph}+\varphi \psi Lw(q))$	$P(H_0{H}_1+WR)+C(C_{ph}+\varphi \psi Lw(q))$
		$P(H_a+K)+C(F+\psi Lw(q))$	$P(H_a+K)+C(WF+\psi Lw(q))$
		$P(H_b+F)-C(C_0+C_{eh}+\alpha H_d+R+M)$	$P(WF)-C(\alpha H_d+WR+M)$
Negative inputs by core businesses $1-p$	Supporting Companies active participation $g$	$-C(F+\psi Lw(q))$	$-C(WF+\psi Lw(q))$
		$P(H_0{H}_2+R)-C(C_{gh}+\varphi \psi Lw(q))$	$P(H_0{H}_2+WR)-C(C_{gh}+\varphi \psi Lw(q))$
		$P(H_b+F)-C(C_0+C_{eh}+\alpha H_d+R+M)$	$P(WF)-C(\alpha H_d+WR+M)$
	Supporting Companies Negative inputs $1-g$	$-C(F+Lw(q))$	$-C(WF+Lw(q))$
		$-C(F+Lw(q))$	$-C(WF+Lw(q))$
		$P(2F)-C(C_0+C_{eh}+H_d+M)$	$P(2WF)-C(H_d+M)$

, is derived from the assumptions made above.

3. Analysis of the Model under Static Incentives and Disincentives

3.1. Stability Analysis of Core Business Strategies

The value perceptions and average value perceptions of core firms for “active inputs” and “passive inputs” are:

$$\begin{array}{l}{T}_{1p}=w(g)[w(e)(P(H_0{H}_1+R)-C(C_{ph}))+w(1-e)(P(H_0{H}_1+WR)-C(C_{ph}))]\\ +w(1-g)[w(e)(P(H_0{H}_1+R)+C(C_{ph}+\varphi \psi Lw(q)))+w(1-e)(P(H_0{H}_1+WR)+C(C_{ph}+\varphi \psi Lw(q)))]\end{array}$$

$$\begin{array}{l}{T}_{2p}=w(g)[w(e)(-C(F+\psi Lw(q)))+w(1-e)(-C(WF+\psi Lw(q)))]\\ +w(1-g)[w(e)(-C(F+Lw(q)))+w(1-e)(-C(WF+Lw(q)))]\\ \end{array}$$

$$\overline{Tp}=p{T}_{1p}+(1-p)T_{2p}$$

(1)

The core business replica dynamic equation is:

$$\begin{array}{l}F(p)=dp/dt=p(T_{1p}-\overline{T_p})=p(1-p)(T_{1p}-T_{2p})=p(1-p)\\ \left\{\begin{array}{l}w(g)w(e)[P(H_0{H}_1+R)+C(F+\psi Lw(q))-C(C_{ph})]+\\ w(g)w(1-e)[P(H_0{H}_1+WR)+C(WF+\psi Lw(q))-C(C_{ph})]+\\ w(1-g)w(e)[P(H_0{H}_1+R)+C(C_{ph}+\varphi \psi Lw(q))+C(F+Lw(q))]+\\ w(1-g)w(1-e)[P(H_0{H}_1+WR)+C(WF+Lw(q))+C(C_{ph}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

For computational convenience, let:

$$F\left(p\right)=p(1-p)[w(g)w(e)A_1+w(g)w(1-e)A_2+w(1-g)w(e)A_3+w(1-g)w(1-e)A_4]$$

(2)

$A_1$ denotes the value function when complementary firms are actively engaged and government regulators are actively supervising. $A_2$ denotes the value function when complementary firms are actively engaged and government regulators are negatively supervising. $A_3$ denotes the value function when complementary firms are negatively engaged and government regulators are positively supervising. And $A_4$ denotes the value function when complementary firms are negatively engaged and government regulators are negatively supervising.

Proposition 1: There is the following relationship to the core company’s duplicate equation:

$${\displaystyle \frac{\partial F\left(p\right)}{\partial H_a}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial H_{\mathrm{b}}}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial R}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial F}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial L_a}}>0$$

Proposition 1 denotes that the probability that a core firm is actively invested is positively correlated with the gain from the impairment of units actively invested in by the core firm, the gain from the increase in units actively invested in by the core firm, the perceived value of rewards by the core firm, the perceived value of penalties by the core firm, and the perceived loss of the core firm as a result of active regulation. It has a positive correlation with the perpetence of the penalty for punishment and the detection loss of the core company’s active coach. Therefore, in the decision-making of core chemical industry safety risks and controlled investment decisions, the decrease in units of aggressive investment in the core company, the increase in units of the core companies, and the value of the encouragement of the core companies. It can help core companies to choose more aggressive investments, increasing the value of the core company’s punishment and the loss of the core company’s leading supervision management.

3.2. Strategic Stability Analysis of Supporting Companies

The value perceptions of “active inputs” and “passive inputs” as well as the average value perceptions of the supporting firms are:

$$\begin{array}{l}{T}_{1g}=w(p)[w(e)(P(H_0{H}_2+H_a+R)-C(C_{gh}))+w(1-e)(P(H_0{H}_2+H_a+WR)-C(C_{gh}))]\\ +w(1-p)[w(e)(P(H_0{H}_2+R)-C(C_{gh}+\varphi \psi Lw(q)))+w(1-e)(P(H_0{H}_2+WR)-C(C_{gh}+\varphi \psi Lw(q)))]\end{array}$$

$$\begin{array}{l}{T}_{2g}=w(p)[w(e)(P(H_a+K)+C(F+\psi Lw(q)))+w(1-e)(P(H_a+K)+C(WF+\psi Lw(q)))]\\ +w(1-p)[w(e)(-C(F+Lw(q)))+w(1-e)(-C(WF+Lw(q)))]\end{array}$$

$$\overline{T_g}=g{T}_{1g}+(1-g)T_{2g}$$

(3)

Supporting firms replicate the dynamic equations as:

$$\begin{array}{l}F(g)=dg/dt=g(T_{1g}-\overline{T_g})=g(1-g)(T_{1g}-T_{2g})=g(1-g)\\ \left\{\begin{array}{l}w(p)w(e)[P(H_0{H}_2+H_a+R)-C(C_{gh}))-P(H_a+K)-C(F+\psi Lw(q))]+\\ w(p)w(1-e)[P(H_0{H}_2+H_a+WR)-C(C_{gh}))-P(H_a+K)-C(WF+\psi Lw(q)]+\\ w(1-p)w(e)[P(H_0{H}_2+R)+C(F+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]+\\ w(1-p)w(1-e)[P(H_0{H}_2+WR)+C(WF+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

For computational convenience, let:

$$F\left(g\right)=g(1-g)[w(p)w(e)B_1+w(p)w(1-e)B_2+w(1-p)w(e)B_3+w(1-p)w(1-e)B_4]$$

(4)

$B_1$ denotes the value function when core firms are actively engaged and government regulators are actively supervising. $B_2$ denotes the value function when core firms are actively engaged and government regulators are negatively supervising. $B_3$ denotes the value function when core firms are negatively engaged and government regulators are positively supervising. And $B_4$ denotes the value function when core firms are negatively engaged and government regulators are negatively supervising.

Proposition 2: The following relationships have the following relationships in the demonstration of dynamic equations that support firms:

$${\displaystyle \frac{\partial F\left(g\right)}{\partial H_c}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial w}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial C_{gh}}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial L_b}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial F}}>0$$

Proposition 2 denotes that the probability of supporting the aggressive investment of companies supports the declining profits obtained by the aggressive investment department of the company, supporting the increased profits of the company’s aggressive investment divisions, and supporting corporate encouragement. It has a positive correlation with perceptional value, support for corporate punishment, and perceptional value that supports the company’s aggressive supervision management. Therefore, in the decision-making of safety risk prevention and control inputs of chemical supporting enterprises, enhancing the gain from the reduction of the unit of positive inputs by supporting enterprises, the gain from the increase of the unit of positive inputs by supporting enterprises, the perceived value of incentives by supporting enterprises, the perceived value of penalties by supporting enterprises, and the perceived loss of supporting enterprises due to the active supervision will help the supporting enterprises to choose the active inputs more often. Increasing the perception value and the value of a company’s punishment, and the loss of corporate support by the management of the main operating supervision can support more aggressive investments by companies.

3.3. Analysis of the Stability of Government Strategies

The value perceptions and the average value perceptions of “active regulation” and “passive regulation” by the government are:

$$\begin{array}{l}{T}_{1e}=w(p)[w(g)(P(H_b+\alpha H_c+N)-C(C_0+C_{eh}+2R))+w(1-g)(P(H_b+F)-C(C_0+C_{eh}+\alpha H_d+R+M))]\\ +w(1-p)[w(g)(P(H_b+F)-C(C_0+C_{eh}+\alpha H_d+R+M))+w(1-g)(P(2F)-C(C_0+C_{eh}+H_d+M))]\end{array}$$

$$\begin{array}{l}{T}_{2e}=w(p)[w(g)(P(\alpha H_c+N)-C(2WR))+w(1-g)(P(WF)-C(\alpha H_d+WR+M))]\\ +w(1-p)[w(g)(P(WF)-C(\alpha H_d+WR+M))+w(1-g)(P(2WF)-C(H_d+M))]\end{array}$$

$$\overline{T_e}=e{T}_{1e}+(1-e)T_{2e}$$

(5)

The government replicates the dynamic equations as:

$$\begin{array}{l}F(\mathrm{e})=de/dt=e(T_{1\mathrm{e}}-\overline{T_e})=e(1-e)(T_{1e}-T_{2e})=e(1-\mathrm{e})\\ \left\{\begin{array}{l}w(p)w(g)[(P(H_b+\alpha H_c+N)+C(2WR)-C(C_0+C_{eh}+2R)-P(\alpha H_c+N)]+\\ w(p)w(1-g)[P(H_b+F)-P(WF)-C(C_0+C_{eh}+\alpha H_d+R+M)+C(\alpha H_d+WR+M)]+\\ w(1-p)w(g)[P(H_b+F)+C(\alpha H_d+WR+M)-C(C_0+C_{eh}+a{H}_d+R+M)-P(WF)]+\\ w(1-p)w(1-g)[P(2F)+C(H_d+M)-C(C_0+C_{eh}+H_d+M)-P(2WF)]\end{array}\right\}\end{array}$$

For computational convenience, let:

$$F\left(e\right)=e(1-e)[w(p)w(g)C_1+w(p)w(1-g)C_2+w(1-p)w(g)C_3+w(1-p)w(1-g)C_4]$$

(6)

$C_1$ represents the value function when the core firm is actively invested and the input sector of the supporting firm is actively invested. $C_2$ represents the value function when the core firm is actively invested and the input sector of the supporting firm is negatively invested. $C_3$ represents the value function when the core firm is negatively invested and the input sector of the supporting firm is positively invested. And $C_4$ represents the value function when the core firm is negatively invested and the input sector of the supporting firm is negatively invested.

Proposition 3: The following relationships have the following relationships in acquiring government copy-dynamic equations:

$${\displaystyle \frac{\partial F\left(e\right)}{\partial C_{eh}}}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial K}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial \alpha }}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial H_d}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial L}}<0$$

Proposition 3 reveals the government’s self-regulation probability, its sense of loss, positive correlation with disciplinary perpetration of core and support companies, and negative correlation with self-regulation labor costs. Therefore, in the practice of emergency response management of the government, the interests of the government’s leading supervision management, the sense of loss of the government, the value of the core and corporate punishment, and reduces the labor costs of government leading supervision management. The government can help choosing more leading supervision management.

3.4. Strategy Portfolio Stability Analysis

The replica dynamics equations are obtained from (2), (4), and (6). Lyapunov’s first law states that the Jacobian matrix of a replica dynamical system is:

$$J=\left[\begin{array}{l}\partial F\left(p\right)/\partial p\hspace{1em}\partial F\left(p\right)/\partial e\hspace{1em}\partial F\left(p\right)/\partial g\\ \partial F\left(g\right)/\partial p\hspace{1em}\partial F\left(g\right)/\partial e\hspace{1em}\partial F\left(g\right)/\partial g\\ \partial F\left(e\right)/\partial p\hspace{1em}\partial F\left(e\right)/\partial e\hspace{1em}\partial F\left(e\right)/\partial g\end{array}\right]=\left[\begin{array}{ccc}{F}_{11}& F_{12}& F_{13}\\ F_{21}& F_{22}& F_{23}\\ F_{31}& F_{32}& F_{33}\end{array}\right]$$

(7)

If the matrix satisfies the conditions det > 0 and trJ < 0, the proportion is an advanced stable strategy (ESS). In the replicated dynamic equation make ${\displaystyle \frac{dp}{dt}}=0,{\displaystyle \frac{dg}{dt}}=0,{\displaystyle \frac{de}{dt}}=0$. The optimal solution of Eq: $p=0$, $p=1$, $g=0$, $g=1$, $e=0$, $e=1$.

The eight local equilibrium points for the system’s evolution are $E_1(0,0,0)$, $E_2(1,0,0)$, $E_3(0,1,0)$, $E_4(0,0,1)$, $E_5(1,1,0)$, $E_6(1,0,1)$, $E_7(0,1,1)$, and $E_8(1,1,1)$.

Table 3. Strategy portfolio stability analysis.

Balance Point	$\mathbf{Eigenvalue}{\mathit{\lambda }}_1,{\mathit{\lambda }}_2,{\mathit{\lambda }}_3$	Positive and Negative Symbols	Stability
(0, 0, 0)	$A_{14},B_{14},C_{14}$	(×, ×, ×)	saddle point
(1, 0, 0)	$-A_{13},B_{13},C_{14}$	(×, ×, ×)	saddle point
(0, 1, 0)	$A_{12},B_{14},C_{13}$	(×, ×, ×)	saddle point
(0, 0, 1)	$A_{13},-B_{13},C_{14}$	(×, ×, ×)	saddle point
(1, 1, 0)	$-A_{12},B_{12},-C_{11}$	(×, ×, ×)	saddle point
(1, 0, 1)	$-A_{13},-B_{11},C_{12}$	(×, ×, ×)	saddle point
(0, 1, 1)	$A_{11},-B_{13},-C_{13}$	(×, ×, ×)	saddle point
(1, 1, 1)	$-A_{11},-B_{11},-C_{11}$	(×, ×, ×)	saddle point

shows the stability analysis of the policy combination. Saddle points are points that require specific conditions to be met in order to be a stable point in the evolution of the system.

Scenario 1: Conditions ① is satisfied, that is, when $A_{14}<0,B_{14}<0,C_{14}<0$, the stable point of the duplicated system is (0, 0, 0). In this case, the value-sensing revenue of the passive investment of the core company is greater than the value-sensitive income of active investment. The value recognition effect that supports the passive investment of companies is greater than the value recognition effect of active investment. The government’s voluntary regulation value recognition effect is greater than the recipient system value recognition effect. The evolutionary stabilisation strategy is (negative input, negative input, negative regulation).

Scenario 2: Conditions ② is satisfied, that is, when $A_{13}>0,B_{13}<0,C_{14}<0$, the stable point of the duplicated system is (1, 0, 0). At this point, the perception of the core company’s active investment is greater than the perception of passive investment, which can motivate the core enterprises to make positive inputs, the government chooses to regulate negatively, and the supporting enterprises will also choose negative input strategies. The final strategy that is considered evolutionary stable is (positive input, negative input, negative regulation).

Scenario 3: The stable point of the duplicated system is determined by the condition ③, where $A_{12}<0,B_{14}<0,C_{13}>0$. In this case, the value-perceived return on passive investment of the core enterprise is greater than the value-perceived return on active investment. Supporting active investment in enterprises has a greater value-perceived effect than passive investment. The value-perceived effect of passive government supervision and management is found to be more significant than that of active supervision and management. Therefore, the final evolutionary stabilisation strategy is (negative inputs, positive inputs, negative regulation).

Scenario 4: If condition ④ is met and $A_{13}<0,B_{13}>0,C_{14}<0$, point (0, 0, 1) is considered a stable point in the replica dynamic system. At this point, the value-perceived benefits of negative inputs of core enterprises dominate, and the benefits of “negative inputs” of supporting enterprises are greater than the benefits of their “positive inputs”, which will result in the situation of negative inputs of core enterprises and negative inputs of supporting enterprises, and after a long period of evolution, The government is set to adopt a “positive regulation” strategy. Therefore, the final strategy for evolutionary stabilization is (negative inputs, negative inputs, positive regulation).

Scenario 5: If condition ⑤ is met and $A_{12}>0,B_{12}<0,C_{11}>0$, point (1, 1, 0) is considered a stable point in the replica dynamic system. At this point, the perceived value of the core enterprise’s positive inputs is higher than the perceived value of its negative inputs, and the benefit of the government’s “positive inputs” is higher than that of its “negative inputs”, in which case the government’s “negative regulation” has a higher benefit than its “positive regulation”. In this situation, the effectiveness of government ‘passive control’ is higher than that of ‘active control’. And the final evolutionary stability strategy is (positive inputs, positive inputs, negative regulation).

Scenario 6: If condition ⑥ is met and $A_{13}>0,B_{11}>0,C_{12}<0$, then point (1, 0, 1) is considered a stable point in the replica dynamic system. If the value recognition revenue of the core company’s active investment is greater than the value recognition revenue due to passive investment. The value-sensing profit of supporting company passive investment is greater than the value-sensing profit of supervising the passive investment of companies. The government’s self-regulation value recognition effect is greater than the government’s reception regulations. The entire system reached the equilibrium. The final evolutionary stability strategy is (positive inputs, passive inputs, positive regulation).

Scenario 7: If condition ⑦ is met, i.e., $A_{11}<0,-B_{13}>0,-C_{13}>0$, then point (0, 1, 1) is considered a stable point in the replica dynamic system. The value-perceived profit of passive investment in core enterprises is higher than active investment, while active investment in related enterprises is higher than passive investment. Furthermore, the value-perceived profit of government active supervision and management is higher than passive supervision and management. Therefore, A strategy set was developed to stabilize the three-way game at a rate of (negative input, positive input, and positive regulation).

Scenario 8: If condition ⑧ is met and $A_{11}>0,B_{11}>0,C_{11}>0$, point (1, 1, 1) is considered a stable point in the replica dynamic system. At this point, The level of the core enterprise on active input, supporting enterprises on active input and the perceived value of active government control are high, the replica dynamic system eventually stabilised at (active input, active input, active supervision).

4. Analysis of the Model under the Dynamic Reward and Punishment Mechanism

The choice of static reward and punishment strategies by decision-makers may not always be optimal, and the system may not reach its expected optimal state. On the other hand, the reality of incentives and penalties also tends to change. Therefore, assuming an optimized dynamic punishment strategy, changing the prize-punishment strategy, and assuming government support for the company are associated with successful strategy selection. In other words, it is associated with the probability and linearness of the establishment of government prize punishment and the voluntary introduction of companies. The number of encouragement and punishment is optimized for the initial fixed constant $R$, $F$ (assuming this is the maximum number of encouragement and punishment) to the linear coefficient dynamic linear function $R(p)=kpR$, $F(p)=k(1-p)F$, and $k$ for the linear coefficients. And the reward and punishment strategy for two two combinations, respectively, to study (static rewards, dynamic punishment), (dynamic rewards, static punishment), (dynamic rewards, dynamic punishment) three different rewards and punishments strategy scenarios under the main body of the game’s behavioural decision-making laws.

4.1. Static Rewards and Dynamic Penalties

Assume that the penalties for government companies are believed to be linked to corporate strategic decisions, i.e., the government’s punishment for core and supporting enterprises is $F(p)=k(1-p)F$ and $F(g)=k(1-g)F$ respectively, and the reward remains a fixed constant of. The three-dimensional evolutionary game analysis of core companies, support companies, and governments is conducted under the government’s static prize punishment strategy. The core business replica dynamic equation is:

$$\begin{array}{l}F(p)=dp/dt=p(T_{1p}-\overline{T_p})=p(1-p)(T_{1p}-T_{2p})=p(1-p)\\ \left\{\begin{array}{l}w(g)w(e)[P(H_0{H}_1+R)+C(k(1-p)F+\psi Lw(q))-C(C_{ph})]+\\ w(g)w(1-e)[P(H_0{H}_1+WR)+C(Wk(1-p)F+\psi Lw(q))-C(C_{ph})]+\\ w(1-g)w(e)[P(H_0{H}_1+R)+C(C_{ph}+\varphi \psi Lw(q))+C(k(1-p)F+Lw(q))]+\\ w(1-g)w(1-e)[P(H_0{H}_1+WR)+C(Wk(1-p)F+Lw(q))+C(C_{ph}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

(8)

Supporting firms replicate the dynamic equations as:

$$\begin{array}{l}F(g)=dg/dt=g(T_{1g}-\overline{T_g})=g(1-g)(T_{1g}-T_{2g})=g(1-g)\\ \left\{\begin{array}{l}w(p)w(e)[P(H_0{H}_2+H_a+R)-C(C_{gh}))-P(H_a+K)-C(k(1-g)F+\psi Lw(q))]+\\ w(p)w(1-e)[P(H_0{H}_2+H_a+WR)-C(C_{gh}))-P(H_a+K)-C(Wk(1-g)F+\psi Lw(q)]+\\ w(1-p)w(e)[P(H_0{H}_2+R)+C(k(1-g)F+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]+\\ w(1-p)w(1-e)[P(H_0{H}_2+WR)+C(Wk(1-g)F+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

(9)

The government replicates the dynamic equations as:

$$\begin{array}{l}F(\mathrm{e})=de/dt=e(T_{1\mathrm{e}}-\overline{T_e})=e(1-e)(T_{1e}-T_{2e})=e(1-\mathrm{e})\\ \left\{\begin{array}{l}w(p)w(g)[(P(H_b+\alpha H_c+N)+C(2WR)-C(C_0+C_{eh}+2R)-P(\alpha H_c+N)]+\\ w(p)w(1-g)[P(H_b+k(1-g)F)-P(Wk(1-g)F)-C(C_0+C_{eh}+\alpha H_d+R+M)+C(\alpha H_d+WR+M)]+\\ w(1-p)w(g)[P(H_b+k(1-p)F)+C(\alpha H_d+WR+M)-C(C_0+C_{eh}+a{H}_d+R+M)-P(Wk(1-p)F)]+\\ w(1-p)w(1-g)[P(k(2-p-g)F+k(1-p)F)+C(H_d+M)-C(C_0+C_{eh}+H_d+M)-P(Wk(2-p-g)F)]\end{array}\right\}\end{array}$$

(10)

Proposition 4: There is the following relationship to the core company’s duplicate equation:

$${\displaystyle \frac{\partial F\left(p\right)}{\partial H_a}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial H_{\mathrm{b}}}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial R}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial F}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial L_a}}>0$$

Proposition 4 includes the probability of aggressive investment of core companies, impairment of aggressive investment per core company, increased profits of aggressive investment per core company, perception value of core companies, and core companies. Punishment and aggressive supervision of core companies have shown positive correlation. Therefore, in the investment decision of the core company, the investment decision of the core company unit, the increase in profits due to the introduction of the core company unit, the perception value caused by the encouragement of the core company, the perception of the core company, and the supervision of the core company. It helps the core company to be more likely to be sensed by the loss.

Proposition 5: The following relationships have the following relationships in the demonstration of dynamic equations that support companies:

$${\displaystyle \frac{\partial F\left(g\right)}{\partial H_c}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial w}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial C_{gh}}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial L_b}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial F}}>0$$

Proposition 5 suggests that supporting firms’ active investment is positively correlated with their gains, perceived losses, and perceived penalty value, while negatively correlated with their labor costs. Therefore, in the investment decision of supporting enterprises, enhancing the supporting enterprises’ returns to positive inputs, the supporting enterprises’ perceived losses due to positive inputs, the supporting enterprises’ perceived value of penalties, and decreasing the supporting enterprises’ labour costs of positive inputs will help the supporting enterprises to choose more positive inputs.

Proposition 6: The following relationships have the following relationships in acquiring government copy-dynamic equations:

$${\displaystyle \frac{\partial F\left(e\right)}{\partial C_{eh}}}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial K}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial \alpha }}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial H_d}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial L}}<0$$

Proposition 6 asserts that the likelihood of the government self-regulating depends on the effectiveness and interests of voluntary regulation, labor costs, risk overflow coefficients, safety accident risks, and negative correlations. As a result, the government’s voluntary regulation, risk overflow coefficient, and safety risks are reduced, and the effectiveness of the government’s voluntary regulation is enhanced.

4.2. Dynamic Rewards and Static Penalties

The government’s incentive policy for companies is believed to be linked to the selection of suppliers. In other words, the government’s incentives for core companies and incentives for support companies are $R(p)=kpR$ and $R(g)=kgR$, respectively. And the punishment is still a fixed constant $F$. The analysis of the three-dimensional evolution game among core enterprises, supporting enterprises, and the government is presented under dynamic rewards and static punishments strategies.

The core enterprise replicates the dynamic equation as:

$$\begin{array}{l}F(p)=dp/dt=p(T_{1p}-\overline{T_p})=p(1-p)(T_{1p}-T_{2p})=p(1-p)\\ \left\{\begin{array}{l}w(g)w(e)[P(H_0{H}_1+kpR)+C(F+\psi Lw(q))-C(C_{ph})]+\\ w(g)w(1-e)[P(H_0{H}_1+WkpR)+C(WF+\psi Lw(q))-C(C_{ph})]+\\ w(1-g)w(e)[P(H_0{H}_1+kpR)+C(C_{ph}+\varphi \psi Lw(q))+C(F+Lw(q))]+\\ w(1-g)w(1-e)[P(H_0{H}_1+WkpR)+C(WF+Lw(q))+C(C_{ph}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

(11)

Supporting firms replicate the dynamic equations as:

$$\begin{array}{l}F(g)=dg/dt=g(T_{1g}-\overline{T_g})=g(1-g)(T_{1g}-T_{2g})=g(1-g)\\ \left\{\begin{array}{l}w(p)w(e)[P(H_0{H}_2+H_a+kgR)-C(C_{gh}))-P(H_a+K)-C(F+\psi Lw(q))]+\\ w(p)w(1-e)[P(H_0{H}_2+H_a+WkgR)-C(C_{gh}))-P(H_a+K)-C(WF+\psi Lw(q)]+\\ w(1-p)w(e)[P(H_0{H}_2+kgR)+C(F+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]+\\ w(1-p)w(1-e)[P(H_0{H}_2+WkgR)+C(WF+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

(12)

The government replicates the dynamic equations as:

$$\begin{array}{l}F(\mathrm{e})=de/dt=e(T_{1\mathrm{e}}-\overline{T_e})=e(1-e)(T_{1e}-T_{2e})=e(1-\mathrm{e})\\ \left\{\begin{array}{l}w(p)w(g)[(P(H_b+\alpha H_c+N)+C(Wk(p+g)R)-C(C_0+C_{eh}+k(p+g)R)-P(\alpha H_c+N)]+\\ w(p)w(1-g)[P(H_b+F)-P(WF)-C(C_0+C_{eh}+\alpha H_d+kpR+M)+C(\alpha H_d+WkpR+M)]+\\ w(1-p)w(g)[P(H_b+F)+C(\alpha H_d+WkgR+M)-C(C_0+C_{eh}+a{H}_d+kgR+M)-P(WF)]+\\ w(1-p)w(1-g)[P(2F)+C(H_d+M)-C(C_0+C_{eh}+H_d+M)-P(W2F)]\end{array}\right\}\end{array}$$

(13)

Proposition 7: There is the following relationship to the core company’s duplicate equation:

$${\displaystyle \frac{\partial F\left(p\right)}{\partial H_a}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial H_{\mathrm{b}}}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial R}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial F}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial L_a}}>0$$

Proposition 7 states that the probability of investing in a core company is determined by the profit-and-expense gain per core company, the profit increase in investment per core company, the core company’s value, and the value of discipline. There is a positive correlation with the loss of the coaching of the core company. Therefore, in the investment decision of the core company, the investment decision of the core company unit, the increase in profits due to the introduction of the core company unit, the perception value caused by the encouragement of the core company, the perception of the core company, and the supervision of the core company. It helps the core company to be more likely to be sensed by the loss.

Proposition 8: The relationship for determining partial derivatives of dynamic equations supporting an enterprise exists:

$${\displaystyle \frac{\partial F\left(g\right)}{\partial H_c}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial w}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial C_{gh}}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial L_b}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial F}}>0$$

Proposition 8 is the probability of supporting the aggressive investment of companies, in return, supporting the aggressive investment of the company, the loss of the government’s aggressive supervision management, and the perpetratal correlation with the perpendicular value of the core company’s punishment. He pointed out that there is a negative correlation with the labor costs that support the aggressive investment of companies. Therefore, in the support of corporate investment decisions, returning the investment of companies, increasing the sense of detection of government supervision and imprisonment of core companies, and the labor costs and companies for government supervision management. It reduces labor costs for investment and helps the government choose more investment.

Proposition 9: The partial derivatives of the government replica dynamic equation have a specific relationship:

$${\displaystyle \frac{\partial F\left(e\right)}{\partial C_{eh}}}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial K}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial \alpha }}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial H_d}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial L}}<0$$

Proposition 9 asserts that the likelihood of the government self-regulating depends on the effectiveness and interests of voluntary regulation, labor costs, risk overflow coefficients, safety accident risks, and negative correlations. Therefore, it is important in government management to reduce the labor costs, risk overflow coefficient, and safety risks that the government voluntarily manages, increasing the effectiveness of active government regulation, and active government regulation make better protection of their own interests.

4.3. Dynamic Rewards and Penalties

Assuming that the penalty strategy for government companies is related to corporate strategic choices, it is assumed that the government’s encouragement to the government company is $R(p)=kpR;R(g)=kgR$ and the punishment is $F(p)=k(1-p)F;F(g)=k(1-g)F$. The three-dimensional evolutionary game analysis reveals the dynamic prize punishment strategy of the government against core companies, support companies, and governments.

The core enterprise replica dynamic equation is:

$$\begin{array}{l}F(p)=dp/dt=p(T_{1p}-\overline{T_p})=p(1-p)(T_{1p}-T_{2p})=p(1-p)\\ \left\{\begin{array}{l}w(g)w(e)[P(H_0{H}_1+kpR)+C(k(1-p)F+\psi Lw(q))-C(C_{ph})]+\\ w(g)w(1-e)[P(H_0{H}_1+WkpR)+C(Wk(1-p)F+\psi Lw(q))-C(C_{ph})]+\\ w(1-g)w(e)[P(H_0{H}_1+kpR)+C(C_{ph}+\varphi \psi Lw(q))+C(k(1-p)F+Lw(q))]+\\ w(1-g)w(1-e)[P(H_0{H}_1+WkpR)+C(Wk(1-p)F+Lw(q))+C(C_{ph}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

(14)

Supporting firms replicate the dynamic equations as:

$$\begin{array}{l}F(g)=dg/dt=g(T_{1g}-\overline{T_g})=g(1-g)(T_{1g}-T_{2g})=g(1-g)\\ \left\{\begin{array}{l}w(p)w(e)[P(H_0{H}_2+H_a+kgR)-C(C_{gh}))-P(H_a+K)-C(k(1-g)F+\psi Lw(q))]+\\ w(p)w(1-e)[P(H_0{H}_2+H_a+WkgR)-C(C_{gh}))-P(H_a+K)-C(Wk(1-g)F+\psi Lw(q)]+\\ w(1-p)w(e)[P(H_0{H}_2+kgR)+C(k(1-g)F+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]+\\ w(1-p)w(1-e)[P(H_0{H}_2+WkgR)+C(Wk(1-g)F+Lw(q))-C(C_{gh}+\varphi \psi Lw(q))]\end{array}\right\}\end{array}$$

(15)

The government replicates the dynamic equations as:

$$\begin{array}{l}F(\mathrm{e})=de/dt=e(T_{1\mathrm{e}}-\overline{T_e})=e(1-e)(T_{1e}-T_{2e})=e(1-\mathrm{e})\\ \left\{\begin{array}{l}w(p)w(g)[(P(H_b+\alpha H_c+N)+C(k(p+g)WR)-C(C_0+C_{eh}+k(p+g)R)-P(\alpha H_c+N)]+\\ w(p)w(1-g)[P(H_b+k(1-g)F)-P(Wk(1-g)F)-C(C_0+C_{eh}+\alpha H_d+kpR+M)+C(\alpha H_d+WkpR+M)]+\\ w(1-p)w(g)[P(H_b+k(1-p)F)+C(\alpha H_d+WkgR+M)-C(C_0+C_{eh}+a{H}_d+kgR+M)-P(Wk(1-p)F)]+\\ w(1-p)w(1-g)[P(k(2-p-g)F)+C(H_d+M)-C(C_0+C_{eh}+H_d+M)-P(k(2-p-g)WF)]\end{array}\right\}\end{array}$$

(16)

Proposition 10 outlines a relationship for determining the partial derivatives of the dynamic equation of enterprise replication:

$${\displaystyle \frac{\partial F\left(p\right)}{\partial H_a}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial H_{\mathrm{b}}}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial R}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial F}}>0,{\displaystyle \frac{\partial F\left(p\right)}{\partial L_a}}>0$$

Proposition 10 denotes that the probability of active investment of core enterprises is positively correlated with the profit gained by core enterprises from decreasing units of active investment, the profit gained by core enterprises from increasing units of active investment, the perceived value of encouragement of core enterprises, the perceived value of punishment of core enterprises and the perceived loss of active supervision of core enterprises. Therefore, in the investment decision-making of core enterprises, the perceived value of decreased returns on units of active investment in core enterprises, the perceived value of increased returns on units of active investment in core enterprises, the perceived value of encouragement in core enterprises, the perceived value of punishment in core enterprises and the perceived value of losses due to active government supervision and management can be increased, and core enterprises’ more active investment choices support.

Proposition 11: There is the following relationship as the disadvantages of government duplicate equations:

$${\displaystyle \frac{\partial F\left(g\right)}{\partial H_c}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial w}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial C_{gh}}}<0,{\displaystyle \frac{\partial F\left(g\right)}{\partial L_b}}>0,{\displaystyle \frac{\partial F\left(g\right)}{\partial F}}>0$$

The proposition 11 has a positive value of the positive introduction of assistant companies, the proceeds obtained from the active introduction of assistance companies, the detection loss of government aggressive supervision, and the aggressive imports of core companies. He pointed out that the workforce costs that the auxiliary companies are investing are negative correlation. As a result, the government leads to the government’s leading labor cost, risk overflow coefficient, and safety risks that the government leads, the government has increased the effectiveness of the government leading supervision, and supports corporate launch decisions. The profits of supervision and management support the choice of more led by companies, which helps maintain their own profits if the interests of the company are lost.

Proposition 12 outlines a relationship for obtaining partial derivatives of the government copy dynamic equation:

$${\displaystyle \frac{\partial F\left(e\right)}{\partial C_{eh}}}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial K}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial \alpha }}<0,{\displaystyle \frac{\partial F\left(e\right)}{\partial H_d}}>0,{\displaystyle \frac{\partial F\left(e\right)}{\partial L}}<0$$

Proposition 12 suggests that government self-regulation’s probability is positively correlated with its effectiveness and benefits, while negatively correlated with labor costs, risk overflow coefficient, and safety accident risk. Therefore, it is very important to increase the perceived value in favour of gains in favour of active input of enterprises, loss perception of active government supervision and management, and perceived value in favour of punishment of core enterprises and enterprises in government emergency management practices, and lowering the labour costs of positive inputs from core and supporting firms can help the government choose positive inputs more often.

5. Simulation Analysis

In order to further investigate the effect of each key element on the behavioural evolution and the actual operation of dynamic rewards and punishments, MATLAB R2021a was used to simulate the system. Referring to the randomised experimental data from scholars such as Gurevich [32], Tversky [33], et al. According to the literature of Deng et.al. [31], some parameters are assumed in the context of the actual situation. The parameter settings in this paper are shown in

Table 4. Initial parameter settings.

Parametric	$\mathit{p}$	$\mathit{g}$	$\mathit{e}$	${\mathit{C}}_{\mathit{p}\mathit{h}}$	${\mathit{C}}_{\mathit{g}\mathit{h}}$	${\mathit{C}}_{\mathit{e}\mathit{h}}$	${\mathit{C}}_{\mathit{p}\mathit{w}}$	${\mathit{H}}_0$	${\mathit{H}}_1$	${\mathit{H}}_2$	${\mathit{H}}_{\mathit{a}}$	${\mathit{H}}_{\mathit{b}}$	${\mathit{H}}_{\mathit{c}}$	${\mathit{H}}_{\mathit{d}}$	$\mathit{K}$
initial value	0.2	0.3	0.4	5	3	3	1	1	3	3	2.1	3	5	5	0.5
parametric	$R$	$F$	$\varphi$	$\alpha$	$\psi$	$L$	$K$	$q$	$U_0$	$C_0$	$U_1$	$\beta$	$\theta$	$\nu$	$\sigma$
initial value	8	8	0.2	0.5	0.5	10	0.5	0.03	1	1	1	0.88	0.88	0.98	0.98

.

5.1. Impact of Incentives and Disincentives

As can be seen from Figure 3a, under the static incentive and static penalty mechanism, system evolution is stable, and eventually converges to equilibrium (6, 1). At this time, the three-game-based strategy selection is stable for aggressive strategies. Figure 3b demonstrates that system evolution is stable under dynamic incentive and static penalty mechanisms, eventually convergent to equilibrium (2, 1). At this time, the three-game-based strategy selection is stable for aggressive strategies. Figure 3c demonstrates that the system’s evolution remains stable under both static encouragement and dynamic punishment mechanisms, that is, the company and the government have a negative strategic development tendency, and then equilibrium. Support for converging to (6, 1). At this time, the three-game-based strategy selection is stable for aggressive strategies. This may be due to unfamiliarity with the mechanism and caution about risk. However, over time, they gradually learn and adapt, recognising that there are additional benefits to be gained from active participation in security prevention and control, including increased market competitiveness and the establishment of trust relationships. This evolution reflects the gradual understanding and acceptance of reward and punishment mechanisms, which contributes to a healthier and sustainable safety prevention and control system. Figure 3d demonstrates that the system’s evolution is stable under dynamic incentives and punishments, eventually convergent to equilibrium (1, 1, 1), indicating stable strategy selection for aggressive tactics.

Through the comparison of Figure 3a–d, in terms of the speed of reaching the convergence point, the dynamic punishment mechanism > dynamic encouragement and static punishment mechanism > Static encouragement and dynamic punishment mechanism > Static encouragement and static punishment mechanism. That is, under the dynamic punishment mechanism, the speed of the system evolution convergence probability stabilises faster at 1. At this point, the park system is now relatively stable. In terms of the speed of reaching the convergence point, the dynamic prize mechanism is more advantageous compared to other prize-punishment mechanisms for a number of reasons. Firstly, the dynamic mechanism provides real-time rewards and penalties, enabling participants to understand the consequences of their behaviour immediately and thus make adjustments more quickly. This real-time feedback mechanism helps enterprises to adapt to new threats and challenges in a timely manner and accelerates the convergence process of security prevention and control.

Secondly, dynamic reward and punishment mechanisms are more flexible and sensitive. Compared to static mechanisms, dynamic mechanisms can respond more flexibly to changes in safety risks. Enterprises can instantly adjust their reward and punishment strategies to quickly adapt to new threats, thereby more effectively driving the entire ecosystem toward the security convergence point.

In addition, dynamic mechanisms incentivise innovation and initiative. The presence of real-time rewards drives enterprises to be more willing to invest resources and effort in finding new security solutions for additional rewards. This further promotes proactive behaviour in security prevention and control and helps achieve faster convergence.

Comparatively, other reward and punishment mechanisms, such as dynamic rewards and static punishments, static rewards and dynamic punishments, and static rewards and static punishments, may perform relatively slower in achieving the convergence point due to the lack of immediate feedback and flexible response capabilities. This highlights the unique advantages of dynamic reward and dynamic punishment mechanisms in facilitating the security and control process.

5.2. Influence of Reference Points

Figure 4 illustrates the strategy evolution process and results when $\left\{U_0=0,U_0=0.5,U_0=1\right\}$.

Figure 4 demonstrates that under the dynamic reward-punishment mechanism, the system’s evolution is steady and will eventually converge to the equilibrium point (1, 1), where the core enterprise and related enterprises will occur. The government has chosen to actively invest, and the government’s supervisory and management institutions have actively supervised and managed it. The study reveals that as power price reference points decrease, the convergence speed of system evolution accelerates.

The strategy evolution process and results are depicted in Figure 5, taking $\left\{U_1=0,U_1=0.5,U_1=1\right\}$.

Figure 5 demonstrates that the system evolution under the dynamic prize punishment mechanism is steady, and the evolutionary trajectory is ultimately converged to the equilibrium (1, 1), when the core firms and ancillary active investment, and the government regulator chooses to actively regulate. The convergence rate of system evolution is accelerated as the price reference point decreases.

Thus, the reference point significantly impacts the steady state of system evolution. And the impact of price standard points and cost standards on the system’s evolution and stabilization varies. In comparison, the stability of system evolution is stronger and the equilibrium solution is better under the low utility reference point and high cost reference point. This is consistent between the future theory and the discovery of psychological account theory. It is not an objective thing itself, but a subjective sense of objective things that affect the decision-making decision. If impactful elements like income and cost remain unchanged, the change in the reference point of the decision determined by the determination to determine the determinant differs from the external impact factor and the decision-determined person. It affects action decisions. Therefore, adjusting reference points based on the current situation is a crucial method for correcting systematic bias in decision-making processes.

5.3. The Impact of the Return on Active Investment by the Firms

Taking $\left\{H_a=3,H_b=2.1\right\}$, $\left\{H_a=6,H_b=4.1\right\}$ and $\left\{H_a=9,H_b=6.1\right\}$, Figure 6 illustrates the process and outcomes of strategy evolution.

Figure 6 demonstrates that core companies’ positive investment rate can significantly impact system evolution stability, as aggressive increase in investment revenue accelerates convergence speed and stabilizes the system under the dynamic punishment mechanism. By investing in advanced security technologies, implementing innovative prevention and control strategies, and promoting the development of new security solutions, core firms not only achieve a leading position in technology, but also are at the forefront of compliance and trust building. Such proactive investments not only inspire other supporting enterprises to pursue higher security standards and improve the compliance level of the entire ecosystem, but also build a close co-operation mechanism that pushes the entire system towards a common security goal in a more rapid and co-ordinated manner. Through demonstration effects, technological innovation and trust building, the positive investment of core enterprises becomes a key driver for the whole system to converge to a more stable state. It can be seen that the positive investment revenue can accelerate strategy evolution, and enhancing the return on investment in mutual safety risk prevention and control can encourage enterprises to invest more frequently in such measures.

6. Conclusions and Management Implications

6.1. Conclusions

The study investigates the dynamic punishment mechanism for mutual safety risk prevention control within a garden company using blockchain technology. Special attention is paid to the participation of core enterprises and supporting enterprises, and a three-party game model is established, and the system evolution stability is thoroughly discussed. Numerical simulation is also carried out to explore effective guiding measures to promote mutual assistance in the prevention and control of safety risks in the park and to coordinate development and safety.

(1)

Park enterprises’ risk prevention and control are influenced by various elements, including external factors and decision-makers’ supervisory factors. Enhancing the benefits of active regulation, enhancing the perceived value of punishment, and reducing the cost of blockchain technology help enterprises choose active inputs, thereby enhancing the overall risk management process. In terms of the decision-makers’ own factor values, adjusting the reference point, value perception and other factor values will help the park enterprise risk mutual aid prevention and control system to evolve in the direction of theoretical optimisation.

(2)

There is a significant difference in the effect of different reward and punishment reward and punishment policies on corporate behavior. Currently, the government’s static award policy is uncertain and ineffective, as it increases the financial burden on the government and hinders the ability of companies to restrain enterprises. Only the case of dynamic punishment has a relatively small role in promoting the system. Therefore, the government in the process of emergency management supervision work should be actively adjusted for the enterprise’s choice of reward and punishment policy, to mobilise enterprises to invest in mutual aid in preventing and controlling safety risks.

(3)

The government division has implemented a dynamic punishment mechanism to address the shortcomings of static reward and punishment mechanisms, combining multiple incentives and penalties to enhance investment decision-making, safety risk prevention, and enterprise control in the park. The dynamic reward and punishment mechanism provides a more flexible and positive response to the safety risk mutual aid prevention and control of enterprises in the park. In future research and practice, further attention should be paid to the implementation details of the dynamic incentive and dynamic penalty mechanism, the improvement of the regulatory framework, and the deepening of the cooperation between different types of enterprises, so as to further enhance the effectiveness and sustainability of mutual aid in the prevention and control of safety risks in park enterprises.

6.2. Recommendations and Management Insights

Based on the above conclusion, we can obtain the following management recommendations:

(1)

Blockchain technology promotes the level of safety risk prevention and control by creating a stricter regulatory environment. The cost of blockchain technology application for enterprises should be reduced. The formulation and implementation of the regulatory framework under blockchain technology should be strengthened so that it is more in line with the actual needs of enterprise safety risk prevention and control. In order to reduce the cost of enterprises’ investment in safety risk mutual aid and the use of blockchain technology, and promote more enterprises to participate in safety risk mutual aid prevention and control.

(2)

Government regulators can fully exploit the role of blockchain technology through incentive policies or reward mechanisms, and improve the enthusiasm of core enterprises and supporting enterprises in security prevention and control through “technological means + management strategy”, so as to drive the security level of the entire park system to improve. Core enterprises are encouraged to play a pivotal role in the co-creation of safety technology innovation, sharing of safety management experience, co-construction of emergency response teams, and joint investigation and management of risks and hidden dangers. Supporting enterprises are encouraged to actively invest and participate actively in the operation of the blockchain safety risk monitoring and early warning platform, so as to enhance the security trust among enterprises and reasonably control the cost of security input. Award and punishment mechanisms must be flexible. When a good atmosphere is formed in the park for mutual assistance in safety risk prevention and control, and the concept of integrating development and safety is deeply rooted in people’s hearts, enterprises will invest in safety risk prevention and control more actively, and the government should weaken the penalty policy at this time, and appropriately reduce the upper limit of prize punishment, and fulfill the prize punishment system.

(3)

Encourage enterprises in the park to provide continuous feedback on their experiences in practice so that the dynamic reward and dynamic penalty mechanism can be continuously improved. Flexibly adjust the mechanism to make it more in line with actual needs and ensure that the security control system can adapt to changing threats. Promote closer interaction and communication between regulators and enterprises. Understanding the actual problems faced by enterprises aids in adjusting regulatory policies to better align with the actual situation and enhance operability.

The article presents a comprehensive model of a core firm, which includes support for enterprises and government regulators. This paper puts forward countermeasures and suggestions such as continuously optimising the design of reward and punishment mechanisms, integrating blockchain technology + management strategies to motivate enterprise participation, and playing the role of participant feedback, which provide new ideas for promoting enterprises to actively invest in mutual assistance in the prevention and control of safety risks and help to promote the coordinated development and safety of parks and enhance the level of safety in the parks. The government should comprehensively operate means such as subsidies, tax revenues, blacklists, and white lists to improve the modernization level of emergency management in the park. The text still has a certain limit and can simplify the real scenes, which does not affect the whole framework of logical research. First, the decision on mutual safety risk prevention control of the garden company is not only affected by the government’s prize-punishment mechanism, and this paper does not take into account the influence of different policy tools such as tax, public expenditure and the management mode of the park. Secondly, only three games are considered, and local government policies are actually influenced by the central government, nearby residents, and the media. This paper does not take into account the influence of central government, individual risk perception levels [34], the media, and companies’ own knowledge accumulation [35] on mutual safety risk prevention and control in park companies; lastly, the relationship between the enterprises in the park is multiple, in addition to core-supporting this kind of complementary relationship, there are also competitive relationships, division of labour, this paper does not consider the impact of other market structures, suggesting that future research could benefit from these perspectives.