Exploring the Cross-Sectoral Joint Fire Management Mode Driven by Fire Information in China: From the Perspective of Organizational Interaction

Abstract

With the increase in types of fire risk and the expansion of fire management coverage, it is urgent to involve multiple subjects in fire management. Cross-sectoral joint fire management is a new fire management mode based on collaboration between the fire management sector and the industry management sector in China. Additionally, fire information from multiple sources plays a significant role in the formation of the cross-sectoral joint fire management mode. To explore the operating characteristics and influencing factors of the cross-sectoral joint fire management mode, this paper constructed a cross-sectoral joint fire management game model by focusing on the interactions and game relationships between multiple organizations. Through numerical simulation analysis, the mechanisms by which the sharing level, coverage range, and disclosure degree of fire information influence the evolution of the game system are investigated. The results show that with the improvement in the sharing level, the coverage range, and the disclosure degree of fire information, although the evolutionary paths of the game system and game subjects’ strategies are different, the cross-sectoral joint fire management game system can form a stable strategy combination of (1,1,1). This indicates that the sharing level, coverage range, and disclosure degree of fire information play positive driving roles in the formation of the cross-sectoral joint fire management mode. Furthermore, it is found that the fire management sector has a greater influence on the cross-sectoral joint fire management mode. Finally, the implications of improving the effectiveness of cross-sectoral joint fire management are proposed: enhancing institutional support, promoting information sharing, and expanding channels for information disclosure.

1. Introduction

With the rapid development of urban industrialization and information technology, high-rise buildings, underground spaces, large commercial complexes, and underground rail transit have developed rapidly [1,2,3]. New technologies, new materials, and new forms of business continue to accumulate new risks, and new situations, as well as problems of fire safety management, are gradually increasing [4,5,6]. Compound disasters and cascade disasters are more diversified and prominent [7]. At present, urban fire risks and the difficulty of fire management are rising [8,9]. It is necessary to further improve the effectiveness of fire management and strengthen the support of fire management for social stability [10]. As an important component of government management, fire management refers to the supervision of fire risks and fire management measures by government departments, which is an important law enforcement behavior used to improve urban safety level and ensure social stability [11]. Existing studies have fully affirmed that fire management involves all aspects and the whole process of social management [12,13]. In order to improve urban fire management capacities, some scholars have conducted explorations on fire safety situation prediction [14,15], fire probability measurement [16], fire risk assessment [17,18], and fire management personnel layout [19]. Meanwhile, the relevant research also fully considers the new problems and new characteristics of fire safety and analyzes the fire management of new places, the identification of new fire risks, and the fire management of weak links [20,21,22]. Discussing the new mode of fire management under the background of emerging technology is also an important aspect of fire management research [23]. In addition, the existing studies are combined with fire management practice to put forward countermeasures to improve fire management measures. On the whole, theoretical exploration and practical experience in fire management research are closely combined and mutually supportive.

At this stage, from the perspective of fire management practice in China, a single government sector can no longer effectively prevent all kinds of fire risks [24]. Similarly, in studies on the fire management organizational mode, it has been fully recognized that it is difficult for the fire management sector to complete fire management operations independently [25]. Meanwhile, the social fire co-management mode, joined by the public, has also been discussed and explored. Exploring fire management modes with the participation of different types of subjects is an important urban management measure actively promoted by the Chinese government [26].

In order to comprehensively clarify the provisions and distribution of responsibilities of multiple subjects in fire management and improve the fire safety responsibility system, the central government of China has issued the Measures for the Implementation of the Fire Safety Responsibility System [27]. In addition to stipulating the management scope of the fire management sector and the responsibilities for coping with fire risks, the policy has detailed the fire management responsibilities of 38 industry management sectors, including education, water resources, public health, transportation, agriculture, banking, electricity, commerce, and other fields. Furthermore, the provincial and municipal governments of China have formulated implementation measures of the fire safety responsibility system in light of actual fire management in their own regions. It can be seen that the fire management system of multisubject collaboration is constantly enriched and expanded in practice [28]. The cross-sectoral joint fire management mode is a new organizational structure based on the implementation and performance of fire safety management responsibilities by the fire management sector and the industry management sector. Further summarizing the experience of the cross-sectoral joint fire management mode and improving the cross-sectoral joint fire management system are of great value to improving urban fire prevention capabilities and reducing fire losses.

As an innovative fire management mode, the cross-sectoral joint fire management mode is significantly different from the traditional mode in terms of subjects, mechanisms, and features. At present, there is little research on cross-sectoral joint fire management. It is difficult to provide practical guidance for the construction of a cross-sectoral joint fire management system with multiple subjects’ participation due to the lack of analysis of how to improve the fire management effect from the perspective of organizational interaction. The cross-sectoral joint fire management mode is similar to that in other safety management fields in that there are interaction relationships between managers and those who are managed. Meanwhile, there is mutual influence and mutual restriction between the two, which directly affects the efficiency of fire management [29]. Meanwhile, in the process of implementing the cross-sectoral joint fire management mode, the fire management sector and the industry management sector continuously improve the efficiency of cross-sectoral joint management through modern information technology [30], such as the establishment of a cross-sectoral fire information sharing mechanism, the use of Internet of Things technology to monitor fire risks [31,32], and improvements in the cross-sectoral joint punishment mechanism. Fire information comes from multiple sources [33], which also promotes interaction and game relationships between multiple subjects. The above practice of a cross-sectoral joint fire management mode provides a research opportunity for us to explore and optimize the fire management cooperation mechanism and to reveal the interactive relationships of subjects’ strategy choices. Therefore, based on fire management practice in China, this study explores the main features of the cross-sectoral joint fire management mode by considering the driving effect of fire information.

Specifically, it focuses on an organizational game perspective and introduces evolutionary game theory to construct this study. Evolutionary game theory is an important research method used to analyze the interaction and dynamic characteristics of the relationships between game subjects [34,35]. The conclusions of the existing studies have positive reference values with which to interpret the ideal safety management mode and safety development trends and provide a practical decision scheme that can be followed. The relevant research results are shown in

Table 1. The combination of evolutionary game theory and safety management research.

Authors and References	Safety Management Scenario	Subjects Involved	Game System Involved
Liu Q, et al. [36]	Coal mining safety	(1) State Administration of Coal Mine Safety (2) Local regulation departments of coal mine safety (3) Coal enterprises	Coal mining safety inspection game model.
Luo E, et al. [37]	Food safety	(1) Government regulatory authorities (2) Production enterprises (3) Third-party testing agencies	Food safety management stochastic evolutionary game model.
Wang X, et al. [38]	Chemical safety	(1) Chemical enterprises (2) Government regulators	Chemical safety supervision game model.
Teng Y, et al. [39]	Agriculture safety	(1) The government (2) Farmers’ professional cooperatives (3) Farmers	Agriculture products’ quality and a safety game model.
Feng F, et al. [40]	Railway transportation safety	(1) State Railway Administration (2) China Railway Corporation (3) The public	Railway transportation safety management game model.

.

Therefore, evolutionary game theory can clearly show the dynamic evolution process of organizational relationships in safety management. It can provide methodological support and observation perspectives for exploring the cross-sectoral joint fire management mode driven by fire information. In conclusion, based on the existing research design, a cross-sectoral joint fire management game model can be constructed in this study. Meanwhile, based on a numerical simulation analysis, the main factors driving and influencing the cross-sectoral joint fire management mode are clarified. On this basis, countermeasures and suggestions to optimize the cross-sectoral joint fire management system are proposed to improve fire management efficiency.

The research framework of this paper is as follows: Section 2 puts forward the research design of this study. Based on the description of the parameters of the cross-sectoral joint fire management game relationships, the replication dynamic equations of the game subjects are obtained. Then, a cross-sectoral joint fire management game model is constructed. Section 3 discusses the effects of the fire information’s sharing level, coverage range, and disclosure degree on the cross-sectoral joint fire management game system and strategy choices of the game subjects. Section 4 further explains the driving mechanism of fire information for the cross-sectoral joint fire management mode and discusses the effectiveness of the cross-sectoral joint fire management mode. Section 5 summarizes the research conclusions and puts forward the implications of improving the cross-sectoral joint fire management mode.

2. Research Problem and Model Construction

2.1. Research Problem Description

In a traditional urban fire management system, the fire management sector is the only responsible subject; however, due to the increasingly extensive scope and field of urban fire management, it is urgent for the industry management sector to participate in fire management. The industry management sector comprises departments in different industries, such as the public health management sector, education management sector, transportation management sector, commercial management sector, and cultural management sector.

At this stage, in order to better manage the industry operator in different fields, the fire management sector and the industry management sector seek to establish a cross-sectoral joint fire management mode. In the cross-sectoral joint fire management mode, the divisions and functions of the fire management sector and the industry management sector are not the same as each other. On the one hand, the fire management sector needs the support of the industry management sector in order to expand management coverage; on the other hand, the fire management of the industry management sector needs the service guidance of the fire management sector in order to improve management efficiency. Meanwhile, the joint management of the fire management sector and the industry management sector makes the penalty losses of the industry operator violating fire management regulations further increase; therefore, it can be found that there are mutual constraints and games among the fire management sector, industry management sector, and industry operator.

According to fire management practice, fire information plays a key role in the construction of a cross-sectoral joint fire management mode. Fire information refers to the information data and resources related to fire risks, fire prevention facilities, and fire management measures. Fire information can promote communication and cooperation between the fire management sector and the industry management sector. Moreover, it can strengthen the management sectors’ identification and response to an industry operator’s fire risks.

Therefore, in this study, the cross-sectoral joint fire management mode is abstracted as the behavioral interaction and strategic game process among the fire management sector, industry management sector, and industry operator. By establishing a payoff matrix, which can describe the behavior characteristics of game subjects, the corresponding game model is constructed. Considering the driving effect of fire information on the cross-sectoral joint fire management mode, the strategy choices of the fire management sector, industry management sector, and industry operator are discussed. We also clarify the influencing factors of the formation and operation of the cross-sectoral joint fire management mode in order to provide a reference for improving the efficiency of cross-sectoral joint fire management.

2.2. Assumptions of the Cross-Sectoral Joint Fire Management Game Model

This work constructed a cross-sectoral joint fire management game model composed of the fire management sector, the industry management sector, and industry operators from the perspective of fire information driving (see Figure 1). In order to better describe the game relationships between game subjects, the following specifications and parameter settings were proposed.

Specification 1. The game subjects in the cross-sectoral joint fire management game model all have bounded rationality. The strategy choices of the fire management sector, industry management sector, and industry operators in the cross-sectoral joint fire management game are independent and random. In the cross-sectoral joint fire management system, the fire management sector can choose a positive joint management strategy or a negative joint management strategy. The corresponding strategy choice probabilities are x (0 ≤ x ≤ 1) and 1 − x, respectively. Similarly, the industry management sector also has two strategy choices. The industry management sector can decide whether to form a cross-sectoral joint fire management with the fire management sector. The probabilities corresponding to the positive joint management strategy and negative joint management strategy are y (0 ≤ y ≤ 1) and 1 − y, respectively. In the daily operation process, the industry operator can choose a safe management strategy or unsafe management strategy; the corresponding strategy choice probabilities are z (0 ≤ z ≤ 1) and 1 − z, respectively.

Specification 2. The administrative costs of the fire management sector for the industry operator in the region are C₁. Correspondingly, the safety benefits obtained by the fire management sector due to the reduction in fires and the stability of the social situation are G1. The industry management sector also needs to perform fire management duties in corresponding fields, and the administrative costs are C₂. Similarly, the safety benefits obtained by the industry management sector due to the reduced probability of fires are G₂. In order to establish and carry out the cross-sectoral joint fire management mode, the additional fire management costs for both the fire management sector and the industry management sector are A. Meanwhile, the additional safety benefits of the fire management sector and the industry management sector due to the establishment of cross-sectoral joint fire management are M.

Specification 3. μ and λ are the fire management intensity of the fire management sector and the industry management sector for the industry operator, respectively. When μ and λ are larger, the management costs and safety management benefits of the fire management sector and the industry management sector are higher. Specifically, when the fire management sector and the industry management sector choose a positive joint management strategy, μ = 1 and λ = 1. Moreover, it should be pointed out that when either or both the fire management sector and the industry management sector choose a negative joint management strategy, the benefits from the implementation of joint fire management will be affected.

Specification 4. The input costs of fire management by the industry operator are C₃, which mainly includes responsibility implementation costs and purchase costs of firefighting equipment. η is the fire management input intensity of the industry operator; a larger η means higher fire management costs for the industry operator. When the industry operator chooses the safe management strategy, η = 1. Under an unsafe management strategy, the input costs of fire management for the industry operator are ηC₃. Correspondingly, if the industry operator is punished by the fire management sector and the industry management sector for fire risks, the corresponding punishment losses are F₁ and F₂, respectively. Under the cross-sectoral joint fire management mechanism, the industry operator will also suffer joint punishment losses, K, from the fire management sector and the industry management sector.

Specification 5. In the cross-sectoral joint fire management mode, the flow and sharing of fire information will play important roles; therefore, this study introduced the sharing level of fire information, β, the coverage range of fire information, α, and the disclosure degree of fire information, θ.

The sharing level of fire information, β, represents the fire information interaction level between the fire management sector and the industry management sector; a larger β means that the joint management level between the fire management sector and the industry management sector is higher, and the communication costs are lower. Therefore, the sharing level of fire information, β, is inversely proportional to the costs of fire management and the joint punishment costs of the fire management sector and industry management sector.

The coverage range of fire information, α, indicates the number of industry fields covered by the cross-sectoral joint fire management mode; therefore, a larger α means that the costs and benefits of implementing the cross-sectoral joint fire management of the fire management sector and the industry management sector are higher. Meanwhile, the coverage range of fire information, α, also describes the level of understanding of the fire management sector and the industry management sector of the safety fire information of the industry operators; therefore, the industry operators under an unsafe management strategy will suffer higher joint punishment losses.

The disclosure degree of fire information, θ, indicates the degree to which the fire management sector and the industry management sector disclose the safety information of the industry operators to the public. The fire management sector and the industry management sector can obtain social credibility benefits, R, due to information disclosure. The reputation losses and additional operating losses suffered by the industry operators due to the disclosure of unsafe information are L, and the additional input costs to repair the credit and reputation are W. Therefore, the disclosure degree of fire information, θ, is proportional to the social credibility benefits, R, for management sectors, reputation land operating losses of the industry operator, L, and the repair costs, W.

In summary, the parameters of the cross-sectoral joint fire management game model are detailed in

Table 2. Parameter settings of the cross-sectoral joint fire management game model.

Parameter	Parameter Meaning	Parameter Range
C1	The administrative costs to the industry operators of the fire management implemented by the fire management sector.	C1 > 0
C2	The administrative costs to the industry operators of the fire management implemented by the industry management sector.	C2 > 0
C3	The input costs of the industry operator to implement safe management and carry out the fire management of a place.	C3 > 0
G1	The safety benefits obtained by the fire management sector from the implementation of fire management.	G1 > 0
G2	The safety benefits obtained by the industry management sector from the implementation of fire management.	G2 > 0
A	The additional costs of undertaking joint fire management between the fire management sector and the industry management sector.	A > 0
M	The additional safety benefits of joint fire management between the fire management sector and the industry management sector.	M > 0
R	The public credibility benefits of the fire management sector and the industry management sector due to information disclosure.	R > 0
F1	The punishment losses suffered by the industry operators due to the unsafe management of the industry management sector.	C1 > 0
F2	The punishment losses suffered by the industry operators due to the unsafe management from the fire management sector.	C1 > 0
K	The joint punishment losses suffered by the industry operator due to the unsafe management from the fire management sector and the industry management sector.	C1 > 0
L	The reputation losses and additional operating losses of the industry operator due to the information disclosure of unsafe management behavior.	C1 > 0
W	The input costs suffered by the industry operator to repair credit and reputation.	C1 > 0
μ	The intensity of fire management of the fire management sector.	0 ≤ μ ≤ 1
λ	The intensity of fire management of the industry management sector.	0 ≤ λ ≤ 1
η	The intensity of fire management of the industry operator.	0 ≤ η ≤ 1
β	The sharing level of fire information.	0 ≤ β ≤ 1
α	The coverage range of fire information.	0 ≤ α ≤ 1
θ	The disclosure degree of fire information.	0 ≤ θ ≤ 1

.

2.3. Construction of the Cross-Sectoral Joint Fire Management Game Model

In order to obtain the cross-sectoral joint fire management game model, combined with the above parameter settings and analysis conditions, the following payoff matrix can be obtained based on the game relationships between the fire management sector, industry management sector, and industry operators in cross-sectoral joint fire management (see

Table 3. The payoff matrix of the cross-sectoral joint fire management game model.

Fire Management Sector	Industry Management Sector	Industry Operator
		Safe Management Strategy z	Unsafe Management Strategy 1 − z
Positive joint management strategy, x	Positive joint management strategy, y	$\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\alpha M$,	$\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\alpha M+\theta R$,
		$\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\alpha M$,	$\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\alpha M+\theta R$,
		$-C_3$	$-\eta C_3-F_1-F_2-\alpha K-\theta L-\theta W$
	Negative joint management strategy, 1 − y	$\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\lambda \alpha M$,	$\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\lambda \alpha M+\lambda \theta R$,
		$\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\lambda \alpha M$,	$\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\lambda \alpha M+\lambda \theta R$,
		$-C_3$	$-\eta C_3-F_1-\lambda F_2-\alpha K-\theta L-\theta W$
Negative joint management strategy, 1 − x	Positive joint management strategy, y	$\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \alpha M$,	$\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \alpha M+\mu \theta R$,
		$\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\mu \alpha M$,	$\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\mu \alpha M+\mu \theta R$,
		$-C_3$	$-\eta C_3-\mu F_1-F_2-\alpha K-\theta L-\theta W$
	Negative joint management strategy, 1 − y	$\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \lambda \alpha M$,	$\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \lambda \alpha M+\mu \lambda \theta R$,
		$\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\mu \lambda \alpha M$,	$\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\mu \lambda \alpha M+\mu \lambda \theta R$,
		$-C_3$	$-\eta C_3-\mu F_1-\lambda F_2-\alpha K-\theta L-\theta W$

). Specifically, the payoff matrix consists of eight game scenarios: (x, y, z), (x, 1 − y, z), (x, y, 1 − z), (x, 1 − y, 1 − z), (1 − x, y, z), (1 − x, 1 − y, z), (1 − x, y, 1 − z), and (1 − x, 1 − y, 1 − z).

2.3.1. Strategy Benefits and Replication Dynamic Equation of the Fire Management Sector

As can be seen from Table 3, the expected benefits of the fire management sector choosing a positive joint management strategy, $E_{11}$, are as follows:

$$\begin{array}{l}{E}_{11}=yz\left[\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\alpha M\right]+y\left(1-z\right)\left[\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\alpha M+\theta R\right]\\ +z\left(1-y\right)\left[\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\lambda \alpha M\right]+\left(1-y\right)\left(1-z\right)\left[\left(1-\beta \right)\left(-C_1-\alpha A\right)+G_1+\lambda \alpha M+\lambda \theta R\right]\end{array}$$

(1)

Correspondingly, when the fire management sector chooses a negative joint management strategy, the expected benefits, $E_{12}$, are as follows:

$$\begin{array}{l}{E}_{12}=yz\left[\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \alpha M\right]+y\left(1-z\right)\left[\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \alpha M+\mu \theta R\right]\\ +z\left(1-y\right)\left[\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \lambda \alpha M\right]+\left(1-y\right)\left(1-z\right)\left[\left(1-\beta \right)\left(-\mu C_1-\mu \alpha A\right)+\mu G_1+\mu \lambda \alpha M+\mu \lambda \theta R\right]\end{array}$$

(2)

Given that the average benefits of the joint management strategy of the fire management sector are $\overline{E_1}=x{E}_{11}+\left(1-x\right)E_{12}$, the replication dynamic equation of the joint management strategy of the fire management sector can be further obtained as follows:

$$H\left(x\right)=\frac{dx}{dt}=x\left(1-x\right)\left[\left(1-\beta \right)\left(1-\mu \right)\left(-C_1-\alpha A\right)+\left(1-\mu \right)\left(G_1+\lambda \alpha M\right)+y\alpha M\left(1-\mu \right)\left(1-\lambda \right)+\left(1-\mu \right)\left(1-\mathrm{z}\right)\theta R\left(y+\lambda -y\lambda \right)\right]$$

(3)

2.3.2. Strategy Benefits and Replication Dynamic Equation of the Industry Management Sector

In the cross-sectoral joint fire management game system, the expected benefits of the industry management sector when choosing a positive joint management strategy, $E_{21}$, are as follows:

$$\begin{array}{l}{E}_{21}=xz\left[\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\alpha M\right]+z\left(1-x\right)\left[\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\mu \alpha M\right]\\ +x\left(1-z\right)\left[\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\alpha M+\theta R\right]+\left(1-x\right)\left(1-z\right)\left[\left(1-\beta \right)\left(-C_2-\alpha A\right)+G_2+\mu \alpha M+\mu \theta R\right]\end{array}$$

(4)

Conversely, when the industry management sector chooses a negative joint management strategy, the expected benefits, $E_{22}$, are as follows:

$$\begin{array}{l}{E}_{22}=xz\left[\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\lambda \alpha M\right]+z\left(1-x\right)\left[\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\mu \lambda \alpha M\right]\\ +x\left(1-z\right)\left[\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\lambda \alpha M+\lambda \theta R\right]+\left(1-x\right)\left(1-z\right)\left[\left(1-\beta \right)\left(-\lambda C_2-\lambda \alpha A\right)+\lambda G_2+\mu \lambda \alpha M+\mu \lambda \theta R\right]\end{array}$$

(5)

Furthermore, given that the average benefits of the joint management strategy of the industry management sector are $\overline{E_2}=y{E}_{21}+\left(1-y\right)E_{22}$, the replication dynamic equation of the joint management strategy of the industry management sector can be obtained as follows:

$$P\left(y\right)=\frac{dy}{dt}=y\left(1-y\right)\left[\left(1-\beta \right)\left(1-\lambda \right)\left(-C_2-\alpha A\right)+\left(1-\lambda \right)\left(G_2+\mu \alpha M\right)+x\alpha M\left(1-\mu \right)\left(1-\lambda \right)+\left(1-\lambda \right)\left(1-\mathrm{z}\right)\theta R\left(x+\mu -x\mu \right)\right]$$

(6)

2.3.3. Strategy Benefits and Replication Dynamic Equation of the Industry Operator

Under the joint management of the fire management sector and the industry management sector, the expected benefits of the industry operator when choosing a safe management strategy, $E_{31}$, are as follows:

$$E_{31}=xy\left(-C_3\right)+x\left(1-y\right)\left(-C_3\right)+y\left(1-x\right)\left(-C_3\right)+\left(1-x\right)\left(1-y\right)\left(-C_3\right)$$

(7)

The expected benefits of the industry operator when choosing an unsafe management strategy, $E_{32}$, are as follows:

$$\begin{array}{l}{E}_{32}=xy\left(-\eta C_3-F_1-F_2-\alpha K-\theta L-\theta W\right)+x\left(1-y\right)\left(-\eta C_3-F_1-\lambda F_2-\alpha K-\theta L-\theta W\right)+\\ y\left(1-x\right)\left(-\eta C_3-\mu F_1-F_2-\alpha K-\theta L-\theta W\right)+\left(1-x\right)\left(1-y\right)\left(-\eta C_3-\mu F_1-\lambda F_2-\alpha K-\theta L-\theta W\right)\end{array}$$

(8)

Similarly, by analyzing the average benefits of the management strategy of the industry operator, $\overline{E_3}=z{E}_{31}+\left(1-z\right)E_{32}$, the replication dynamic equation of the management strategy of the industry operator can be obtained as follows:

$$Q\left(z\right)=\frac{dz}{dt}=z\left(1-z\right)\left[-\left(1-\eta \right)C_3+\alpha K+\theta L+\theta W+\mu F_1+\lambda F_2+x{F}_1\left(1-\mu \right)+y{F}_2\left(1-\lambda \right)\right]$$

(9)

By combining Formulas (3), (6), and (9), we can obtain the cross-sectoral joint fire management game system, as shown in Formula (10):

$$\{\begin{array}{l}H\left(x\right)=x\left(1-x\right)x\left(1-x\right)\left[\left(1-\beta \right)\left(1-\mu \right)\left(-C_1-\alpha A\right)+\left(1-\mu \right)\left(G_1+\lambda \alpha M\right)+y\alpha M\left(1-\mu \right)\left(1-\lambda \right)\right]\\ P\left(y\right)=y\left(1-y\right)\left(U_{21}-U_{22}\right)=y\left(1-y\right)\left[\left(1-\beta \right)\left(1-\lambda \right)\left(-C_2-\alpha A\right)+\left(1-\lambda \right)\left(G_2+\mu \alpha M\right)+x\alpha M\left(1-\mu \right)\left(1-\lambda \right)\right]\\ Q\left(z\right)=z\left(1-z\right)\left[-\left(1-\eta \right)C_3+\alpha K+\theta L+\theta W+\mu F_1+\lambda F_2+x{F}_1\left(1-\mu \right)+y{F}_2\left(1-\lambda \right)\right]\end{array}$$

(10)

3. Numerical Simulation Analysis of the Cross-Sectoral Joint Fire Management Game System

In the cross-sectoral joint fire management game system, the strategy choices of the fire management sector, industry management sector, and industry operators are interactive and dynamic. Moreover, the important topic of this study is to interpret how fire information drives the formation of the cross-sectoral joint fire management mode. Therefore, numerical simulation analysis is introduced to visually demonstrate the influence mechanism of the sharing level of fire information, β, the coverage range of fire information, α, and the disclosure degree of fire information, θ, on the game strategy combination. The efficient operation of the cross-sectoral joint fire management mechanism can also be explained.

As for the parameter setting in the cross-sectoral joint fire management game model, this study invited researchers in the field of fire management and government personnel to conduct questionnaire scores. Using the Delphi method, after three rounds of scoring and confirmation, the initial values of parameters in the game model are finally obtained, where C₁ = 34, C₂ = 31, C₃ = 41, G₁ = 15, G₂ = 13, A = 22, M = 18, R = 11, F₁ = 12, F₂ = 9, K = 8, L = 6, W = 3, μ = 0.6, λ = 0.6, and η = 0.4. In addition, the initial value of the game strategies of the fire management sector, industry management sector, and industry operators in the simulation analysis is 0.5.

3.1. Simulation Analysis of the Evolution of the Game System Driven by the Sharing Level of Fire Information

The sharing level of fire information, β, is the parameter that characterizes the efficiency of information transfer and interworking between the fire management sector and the industry management sector. A higher fire information sharing level, β, indicates that the fire management sector and the industry management sector have formed cooperative relationships of mutual trust in previous fire management. Additionally, it can further enhance information transmission and improve the efficiency of cross-sectoral joint fire management. Meanwhile, the sharing level of fire information, β, can reduce the cross-sectoral costs of the fire management sector and the industry management sector. This is not only reflected in daily fire management but also in the joint punishment between the fire management sector and the industry management sector.

Firstly, the evolution paths of the cross-sectoral joint fire management game system, corresponding to different sharing levels of fire information, are presented, as shown in Figure 2. It can be seen that (0,0,0) and (1,1,1) are both possible stable strategy combinations of the cross-sectoral joint fire management game system. When β = 0.1, β = 0.3, and β = 0.5, the information sharing degree between the fire management sector and the industry management sector is not high. The fire management sector and the industry management sector carry out fire management in organizations; manpower and capital costs are high, and they converge to x = 0 and y = 0, respectively. At this time, the industry operator lacks the management constraints of the fire management sector and the industry management sector and has a low perception of penalty losses, which will also form a stable strategy of unsafe management. When β = 0.7 and β = 0.9, information sharing between the fire management sector and the industry management sector will help reduce the costs of fire management. Correspondingly, the perception of punishment losses of the industry operator increases and converges to z = 1.

On this basis, this study will discuss the independence and characteristics of the game strategy evolution of the fire management sector, industry management sector, and industry operators under different sharing levels of fire information (see Figure 3). By comparing Figure 3a,b and combining with the evolution trajectory of Figure 2, it can be seen that the fire management sector and the industry management sector will stabilize at x = 0 and y = 0 with an increase in evolution time. Moreover, the evolution time of the industry management sector towards the negative joint management strategy, y = 0, is longer. Meanwhile, by comparing Figure 3a, Figure 3b, and Figure 3c, it can be seen that when β = 0.1 and β = 0.3, the fire management sector and the industry management sector converge to x = 0 and y = 0 faster than the industry operator to form a stable strategy. When β = 0.7 and β = 0.9, the fire management sector and the industry management sector also converge faster to x = 1 and y = 1 than the industry operator converges to z = 1. This also confirms that the influence of the sharing level of fire information, β, on the industry operator is indirect.

3.2. Simulation Analysis of Evolution of Game System Driven by Coverage Range of Fire Information

The coverage range of fire information, α, is the parameter that describes the management sector’s control of the industry operator’s fire information, which is related to the level of fire safety informatization. For example, when the firefighting equipment of the industry operator is connected to the fire Internet of Things, or the daily fire safety management records and measures of the industry operator are uploaded to the fire information system, the coverage range of fire information, α, is at a higher level. Meanwhile, a higher α indicates that the fire management sector has established cooperation mechanisms with the industry management sector in more fields. In other words, cross-sectoral joint fire management has been formed to manage industry operators in more fields.

When the coverage range of fire information, α, is set to 0.1, 0.3, 0.5, 0.7, and 0.9, the evolution trajectories of the cross-sectoral joint fire management game system are shown in Figure 4. When α = 0.1, the strategy choices of the fire management sector, industry management sector, and industry operator show an evolutionary trend of recurrent fluctuation. The cross-sectoral joint fire management game system fails to form a stable combination of strategies. When α = 0.3 or α = 0.9, (1,1,1) is the stable state of the cross-sectoral joint fire management game system. When α = 0.5, the stability strategies of the fire management sector and the industry management sector change. (0,0,0) becomes the stable state of the cross-sectoral joint fire management game system. When α = 0.7, the stability strategy of the industry operator changes. A negative joint management strategy (x = 0), a negative joint management strategy (y = 0), and safe management strategy (z = 0) are the evolutionarily stable strategies of the cross-sectoral joint fire management game system.

Furthermore, the simulation results of the coverage range of fire information, α, on the strategy choices of the fire management sector, industry management sector, and industry operator are given, as shown in Figure 5. It can be seen from Figure 5a,b that the impact of the coverage range of fire information, α, on the fire management sector and the industry management sector is similar. When the coverage range of fire information, α, is low (α = 0.1), the game strategies of the fire management sector and the industry management sector are unstable. As the coverage range of fire information, α, increases, the game strategies of the fire management sector and the industry management sector range from a positive joint management strategy (α = 0.3) to a negative joint management strategy (α = 0.5 or α = 0.7) to positive joint management (α = 0.9).

As can be seen from Figure 5c, when α = 0.3, the fire management sector and the industry management sector gradually evolve into a stable strategy of positive joint management. Therefore, although the industry operator converges to z = 0 at the initial stage of evolution, it eventually forms a stable state of z = 1 (safe management strategy) with the evolution time. When α = 0.5, the stable strategy of the fire management sector and the industry management sector is negative, so the perception of joint punishment losses received by the industry operator is lower. The industry operator increases the tendency to choose an unsafe management strategy. When α = 0.7 or α = 0.9, the difference of expected benefits between a safe management strategy and an unsafe management strategy chosen by the industry operator is always > 0; therefore, the industry operator forms a stable strategy of z = 1.

3.3. Simulation Analysis of the Evolution of the Game System Driven by the Disclosure Degree of Fire Information

The fire management sector and the industry management sector adopt social information disclosure to release the fire risks and illegal information of the industry operator to society and the public. On the one hand, it can strengthen the supervision of society and the public of the industry operator and increase the illegal costs of the industry operator. On the other hand, the fire management sector and the industry management sector will receive certain credibility benefits; therefore, information disclosure can be regarded as an important supplement to the cross-sectoral joint fire management mode, which is of positive significance for improving the overall level of fire management.

Figure 6 shows the influence of different disclosure degrees of fire information on the cross-sectoral joint fire management game system. As the disclosure degree of fire information, θ, increases, the cross-sectoral joint fire management game system evolves to a steady state of (0,0,0), (0,0,1), and (1,1,0). When θ = 0.1, the expected benefits of the fire management sector as well as the industry management sector, and the expected losses of the industry operator, are lower; therefore, game subjects will converge to x = 0, y = 0 and z = 0, respectively. When θ = 0.3, θ = 0.5, and θ = 0.7, the industry operator’s perception of reputation losses and operating losses is further increased. This can effectively inhibit the willingness of the industry operator to choose an unsafe management strategy. When θ = 0.9, the perception that the fire management sector and the industry management sector receive social reputation benefits further increases and drives the choosing of positive strategies. Therefore, positive joint management strategy, positive joint management strategy, and safe management strategy become a stable combination of strategies for the cross-sectoral joint fire management game system.

Furthermore, the simulation analysis results of the strategy evolution of the fire management sector, industry management sector, and industry operator can be obtained, as shown in Figure 7. By comparing Figure 7a,b, it can be seen that when the negative strategy is the stable strategy of the fire management sector and the industry management sector, the evolution of the industry management sector into a stable strategy is faster and shorter. When the positive strategy is the stable strategy of the fire management sector and the industry management sector, the fire management sector will converge to x = 1 more quickly. As can be seen from Figure 7c, the disclosure degree of fire information, θ, can affect the industry operator’s willingness to choose a safe management strategy. When θ = 0.1, the industry operator first evolves into a safe management strategy, but because of the low loss perception of the industry operator, a stable strategy of z = 0 is finally formed. With the increase in the disclosure degree of fire information, θ, the evolution speed of the industry operator to a safe management strategy is gradually accelerated.

4. Discussion

4.1. Discussion of Analysis Results

Fire management is a socialized systematic project that involves all fields and the whole process of society and needs the cooperation of, as well as the communication between, multiple sectors; therefore, this study presented the construction paths and characteristics of the cross-sectoral joint fire management mode by considering the main management responsibility of the fire management sector and the field management responsibility of the industry management sector. The cross-sectoral joint fire management mode is conducive to the formation of collaboration management and is of great significance for improving the overall efficiency of urban fire management. On this basis, by constructing a cross-sectoral joint fire management game model composed of the fire management sector, industry management sector, and industry operators, the factors affecting cross-sectoral joint fire management are discussed. In fire management practice, information and digital construction have become important supports with which to improve the efficiency of fire management. This study mainly discusses and reveals the influence mechanisms of the sharing level of fire information, the coverage range of fire information, and the disclosure degree of fire information on the cross-sectoral joint fire management game system.

According to the simulation analysis results, the sharing level of fire information, β, the coverage range of fire information, α, and the disclosure degree of fire information, θ, are all conducive to promoting the formation of the cross-sectoral joint fire management mode. This is because the improvement in the sharing level of fire information, the coverage range of fire information, and the disclosure degree of fire information can effectively strengthen the willingness and initiative of the fire management sector and industry management sector. This is not only reflected in the reduction in management costs but also the gain in fire management and credibility benefits. Meanwhile, improving the coverage range of fire information, α, and the disclosure degree of fire information, θ, can increase the industry operator’s perception of punishment losses, reputation losses, and additional business losses. In addition, the industry operator can send the device information and fire management information of the place to the fire management sector and industry management sector in the form of information that is conducive to the construction of the cross-sectoral joint fire management mode; therefore, it is necessary to adopt measures with which to require and stimulate the industry operator to increase the input costs of informatization.

As can be seen from Figure 5, Figure 6 and Figure 7, fire-information-related parameters have similar influence trends on the strategy choices of fire management sector and the industry management sector. The fire management sector is more sensitive to changes in fire information-related parameters, while the industry management sector is less sensitive, and its response to the change in strategy lags. Moreover, the fire management sector is also sensitive to the game strategy changes of the industry management sector and the industry operator; therefore, it can be seen that the fire management sector can quickly respond to changes in the external environment of the game system and the strategies of game subjects and dynamically adjust its strategies.

Meanwhile, by comparing Figure 7a,b, it can be seen that when x = 0 and y = 0 are stable states, the evolution speed of the industry management sector is faster. In contrast, when x = 1 and y = 1 are stable states, the fire management sector converges to the stable state more quickly. As indicated above, the fire management sector is in a core position in the cross-sectoral joint fire management mode, and the industry management sector is in a cooperation position. How to strengthen the management and supervision of the industry operator in the industry management sector and effectively identify the fire safety problems and types of risks in the field are important issues that need further research.

4.2. Limitations and Contributions

Based on the above analysis, it can be seen that exploring the cross-sectoral joint fire management mode driven by fire information is of great significance in improving urban fire management capacities; however, there are still some limitations to this study. On the one hand, this study takes into account the influence of the industry management sector and industry operators on fire management and enters them into the game model for analysis. Nevertheless, this study has not focused on specific industry fields. In the following stage, it should consider the characteristics of fire management in different industry fields to expand the game subject, enrich the parameters, and optimize the game model. For example, research on fire management mechanisms in the field of health can be carried out for the fire management sector, public health management sector, and hospitals. On the other hand, regarding the model parameters and initial value settings, optimization can be combined with actual cases of fire management. This can further enhance the applicability of the game model and the guiding value of the research conclusions for fire management practice.

To sum up, this study is an important attempt to describe organizational relationships in urban fire management. In general, the research contributions mainly include the following: In previous studies on fire management, not much of the literature has taken the industry management sector as the management subject into the research content. To some extent, this ignores the systematic nature of fire management and its coverage of social fields. This study proposes that the fire management sector and the industry management sector are both important in the cross-sectoral joint fire management model. On this basis, evolutionary game theory is used to describe the dynamic management behavior of the fire management sector and the industry management sector from a micro-perspective. In addition, this study provides a reference research scheme for exploring the interaction and game relationships between multiple management sectors in safety management research.

5. Conclusions and Implications

5.1. Research Conclusions

According to fire management practices, the fire management sector and the industry management sector jointly constitute the basic structure of the cross-sectoral joint fire management mode. Meanwhile, fire information is very important in driving the construction and operation of a cross-sectoral joint fire management mode. In order to accurately describe the organizational relationships in the cross-sectoral joint fire management mode, a cross-sectoral joint fire management game model was constructed by introducing evolutionary game theory. On this basis, considering the influence of the sharing level of fire information, the coverage range of fire information, and the disclosure degree of fire information on game subjects’ strategy choice, a numerical simulation analysis of the cross-sectoral joint fire management game system driven by fire information was carried out. The following conclusions can be drawn from the analysis results:

(1)

With the increase in the sharing level of fire information, the coverage range of fire information, and the disclosure degree of fire information, although the evolution path of the cross-sectoral joint fire management game system and the strategy evolution trajectory of the game subjects are not the same, each cross-sectoral joint fire management game system can form a stable strategy combination of (1,1,1). This indicates that the sharing level of fire information, β, the coverage range of fire information, α, and the disclosure degree of fire information, θ, all play a positive driving role in the formation of the cross-sectoral joint fire management mode.

(2)

The sharing level of fire information can effectively save management costs for the fire management sector and the industry management sector, as well as increase the probabilities of the fire management sector and the industry management sector choosing positive strategies. Although the sharing level of fire information, β, does not directly affect the industry operator, the industry operator’s perception of the punishment losses will also converge to z = 1 with an increase in the fire information sharing level.

(3)

Increasing the coverage range of fire information can promote and inhibit the enthusiasm of the fire management sector and the industry management sector to participate in joint fire management. The influence of the fire information coverage, α, on the strategy choice of the industry operator is smaller than the influence of the fire management sector, and the industry management sector on the strategy choice of the industry operator.

(4)

Information disclosure is an important supplement to the cross-sectoral joint fire management mode between the fire management sector and the industry management sector. It can improve the social credibility benefits of the management sectors. Meanwhile, information disclosure encourages the industry operator to choose a safe management strategy by increasing the industry operator’s perception of punishment losses.

(5)

The influence trends in the sharing level of fire information, β, the coverage range of fire information, α, and the disclosure degree of fire information, θ, on the fire management sector’s strategy choice and the industry management sector’s strategy choice are similar; however, the fire management sector is more sensitive to changes in the relevant parameters and game subjects’ strategies. Meanwhile, the fire management sector has a greater influence on the cross-sectoral joint fire management mode.

5.2. Implications of the Research Results

Combined with the above research conclusions and fire management practice, this research proposes that the implications of improving the effectiveness of cross-sectoral joint fire management arise from three aspects: enhancing institutional support, promoting information sharing, and expanding channels for information disclosure.

(1)

Enhancing institutional support for the cross-sectoral joint fire management mode. With the continuous development of new industry forms and new technologies, the fire management sector can no longer cope with the new risks and problems emerging in fire management alone. Cross-sectoral joint fire management is the organizational mode that integrates resources from the fire management sector and industry management sector to fill the blind area of fire management and improve the effectiveness of fire management. The complete institutional system is important support for the development of the cross-sectoral joint fire management mode. Therefore, it should further formulate and improve the policy system of the cross-sectoral joint fire management mode to promote the gradual institutionalization and standardization of the cross-sectoral joint fire management mode. Meanwhile, the construction, operation, and evaluation of the cross-sectoral joint fire management mode should be defined. It should further optimize the cooperation and interaction between organizations based on the cross-sectoral joint fire management mode by making clear the specific responsibilities of the fire management sector and the industry management sector in order to avoid and reduce the conflicts caused by cross-sectoral and overlapping functions.

(2)

Promoting the communication and sharing of cross-sectoral information. The construction of the cross-sectoral joint fire management mode should fully rely on the information sharing of the fire management sector, industry management sector and industry operator. The construction of the cross-sectoral joint fire management mode should fully rely on the information sharing of the fire management sector, industry management sector, and industry operator. It can realize the effective aggregation of multilevel, multidimensional, and multisource fire information. The fire management sector can comprehensively promote fire informatization construction according to the fire management platform, as well as connect the industry management sector in different fields to the port. Meanwhile, it can rely on the Internet of Things, big data, cloud computing, and other information, as well as intelligent emerging technologies, to break through the barriers of fire management information integration and broaden the sources of fire information collection. Specifically, the information interoperability between the fire management sector and the transportation, health, education, commerce, and other industry management sectors should be deepened. The costs of cooperation between the fire management sector and the industry management sector can be reduced. In addition, the depth of cooperation between the fire management sector and the industry management sector in information reporting, consultation, and coordination, and social services can be continuously enhanced by relying on daily fire management and special operations for key time points and key risk areas to consolidate the trust foundation of the cross-sectoral joint fire management mode.

(3)

Expanding the scope and channels of fire information disclosure. Information disclosure is a positive measure with which to integrate fire management into the social governance environment, introduce social and public supervision, and improve the efficiency of fire management. Information disclosure can rationalize and supplement the management resources of the fire management sector and the industry management sector. Meanwhile, it is also an effective way to increase the loss perception of the industry operator. Therefore, on the one hand, the content and timeliness of fire information disclosure should be well defined, and the platform function of multiple media should be fully utilized to expand fire information disclosure channels, as well as extend the coverage of fire information. On the other hand, the fire management sector and the industry management sector can increase the information disclosure of fire risks among industry operators according to the key places and key risk types in the region as well as the industry field. In addition, a fire risk reporting mechanism can be introduced to build a bridge between the fire management sector and the public to exchange information and form a joint fire management synergy of society.