Regulatory Effect on Information Sharing of Industrial Internet Platforms Based on Three Differentiated Game Scenarios

Abstract

This study constructs a regulatory system for information sharing on industrial internet platforms from a technical and socio-legal perspective. A differentiated game is used to construct decentralized, centralized, and cost-sharing contract decision-making scenarios to obtain the optimal level of efforts for information-sharing regulation. Through a comparative analysis, the optimal solutions under the three scenarios were derived. These solutions were then analyzed through numerical simulations using Matlab2016a. Our research demonstrates the following: (1) Centralized decision-making is most beneficial to the development of information-sharing regulatory systems. (2) Beyond a critical value for the local government cost subsidy coefficients, changes in these coefficients have a more pronounced effect on improving the economic efficiency of the regulatory system, and vice versa. That is, when the cost subsidy coefficient is higher than 1/2, increasing the cost subsidy coefficient has a more pronounced effect on improving the economic efficiency of the information-sharing regulatory system. (3) In all scenarios, an increase in the regulatory effort can effectively enhance the reputation of the information-sharing regulatory system. This study further extends the research on information-sharing regulations and provides a practical guide to industrial internet platforms.

1. Introduction

The industrial internet is a product of the deep integration of new-generation information technology and enterprises [1], and it was first proposed by General Electric [2]. The industrial internet can not only penetrate into all stages of the industrial chain, such as research, production, and trade, but can also facilitate the digital transformation of enterprises through the interconnection of data [3,4]. With continuous architectural improvement, several industrial internet platforms have emerged, such as COSMOplat and Predix [5]. These platforms can provide digital intelligence services to enterprises to maximize their production potential [6], optimize their resource allocation, and help them achieve sustainable development [7]. Therefore, it is an inevitable trend for enterprises to join industrial internet platforms and improve their position in the market [8].

However, industrial internet platforms still face issues in the process of digital empowerment. First, dangers such as information security threats and the presence of cyber hackers hinder the development of industrial internet platforms, leading to increasing information security issues and regulatory problems [9]. Increasing amounts of enterprise data on these platforms end up expanding the attack surface for data theft and leakage. In China, industrial internet information security vulnerabilities have exploded since 2010 [10]. According to a survey in 2021, there were nearly 800 industrial information-related vulnerabilities of industrials in the first half of 2020, with about 500 high-risk vulnerabilities, accounting for 61.7%, compared to only 32 vulnerabilities in 2010 [11]. These growing vulnerabilities are highly susceptible to exploitation by hackers, resulting in the risk of data leakage. Specifically in 2019, China’s industrial internet platforms, such as OneNET, COSMOPlat, and JiZhiYun, suffered several cyberattacks from outside of China, with an average of 90 attacks per day [12]. Similarly, in March 2022, the Samsung IoT platform in South Korea was hacked and nearly 190 GB of confidential data were leaked [13]. These examples show that the data security of industrial internet platforms, domestically and internationally, is seriously threatened. If and when industrial internet platforms are threatened by information security, stable operations will get significantly disrupted and trigger a series of production security accidents, which is inconducive to the sustainable development of enterprises and platforms.

In addition, problems such as information leakage and lack of regulations on industrial internet platforms have discouraged enterprises from joining them and reduced the quality of information sharing. In recent years, more than a hundred manufacturing industries, including General Motors and Ford, have suffered breaches of vital information on their industrial platform [14]. This phenomenon led to the reluctance of many automakers to disclose their supply chain information during the chip crisis of 2021 in the US, further triggering problems such as stalled automobile production [15]. On this basis, many industrial internet platforms lack valid data and cannot take advantage of integrated information sources. The overall information utilization of enterprises between platforms has been ineffective so far, slowing down their process of digital transformation. In order to further enable these enterprises to join industrial internet platforms and create social value, studying the regulation of information sharing on these platforms is of great practical significance.

In the era of the industrial internet, the regulation of information security sharing is a technical as well as socio-legal issue [16]. For the former, relying on technical support or clear contractual provisions may solve part of the information regulatory problem [5]. For the latter, local governments play a role in extending existing legal framework for information security to improve the legal conditions. To a certain extent, they can reduce the incidents of information leakage and enhance the reputation of information sharing and supervision on these platforms [17]. In addition, local governments can introduce policies to alleviate some of the inactive information sharing and data security problems by encouraging enterprises to join the industrial internet platforms [18]. In this work, we consider local governments, enterprises, and industrial internet platforms as a complete and self-sustaining regulatory system, and explore the issue of information-sharing regulations on these platforms from the technical and socio-legal perspectives.

When these three organizations share information as a complete regulatory system, it can lead to situations of cooperation or non-cooperation [19]. In November 2021, the Industrial Internet Innovation and Development Forum was conducted in Beijing, China, with the participants including scholars and platform company representatives. The following is a non-exhaustive list of answers by the company representatives, when they were asked if they were willing to create value together with industrial internet platforms: “each enterprise body thinks only about its own interests and how to surpass its competitors”; “we are willing to find partners on the platform to achieve a balance between industrial enterprises”; and “We would be more willing to work with an industrial internet platform if there were more incentives and guarantees from outside”. Following from this context, our study focuses on three scenarios to explore the issue of information-sharing regulations on industrial internet platforms:

(1)

Decentralized decision-making: This refers to the three participant entities taking decisions with the objective of maximizing the profits of their own interests, respectively [20].

(2)

Centralized decision-making: This refers to the three participant entities taking decisions with the goal of maximizing their overall interests, rather than just maximizing their own interests [21].

(3)

Cost-sharing contract decision-making: In this scenario, the local government bears part of the costs for the enterprise and the industrial internet platform [22].

Based on these three scenarios, this study focuses on the following questions:

(1)

Which of the three scenarios is most conducive to the development of an optimal information-sharing regulatory system?

(2)

Is it feasible for the local government to incentivize, through cost subsidies, technological improvements in industrial internet platforms and active participation of enterprises in sharing their data? Is there an optimal cost subsidy factor?

(3)

What are the relevant factors and how do they affect the regulatory system under the three scenarios?

The differentiated game approach was motivated by the fact that it is well suited for continuous and dynamic systems, such as information sharing on industrial internet platforms [23]. In addition, differential game research has already been shown to be effective in the context of the industrial internet era [24]. After constructing each scenario, we explored multiple facets, such as the optimal level of effort, the trajectory of the regulatory system’s reputation, and the benefits of the three main bodies. Finally, the results of the three scenarios were compared and analyzed to explore the core factors affecting the regulatory efforts and the effectiveness of the industrial internet platform information-sharing and supervision systems.

In this study, we draw the following conclusions: first, by comparing the three scenarios, we find that the centralized decision is the most beneficial to the development of an information-sharing regulatory system, the cost-sharing contract decision is the second most beneficial, and the decentralized decision is the lowest. Second, under certain conditions, the cost-sharing contract decision incentivizes industrial internet platforms and enterprises. When the local government subsidy coefficient is greater than the critical value of 1/2, the higher the cost subsidy coefficient, the more pronounced the improvement effect of the economic benefits of the regulatory system. Third, in the three scenarios, the increased level of regulatory effort from the three primary entities can effectively enhance the information-sharing regulatory system’s reputation. It is conducive to enhancing the social welfare effect and promoting the digital transformation of enterprises for value sharing. In contrast, the increase in cost coefficient, discount rate, and decay rate will hinder the enhancement of the information-sharing regulatory system.

The contribution of this paper is three-fold: First, this paper adopts a differentiated game approach to investigate the dynamic and continuous nature of information sharing, in stark contrast to the static approach of previous studies. Second, this paper builds a regulatory system for local governments, industrial internet platforms, and enterprises, the highlight of which is the combination of technical and socio-legal perspectives to explore the regulation of information sharing on industrial internet platforms. Third, this paper establishes decentralized decision-making, centralized decision-making, and cost-sharing contract decision-making to study the information-sharing regulatory system in three contexts. Our study hopes to provide help to solve the problems of data security and inactive information sharing, and to promote the digital transformation of enterprises through external data for collaborative development. Recommendations are provided to promote the widespread use of information-sharing regulations on industrial internet platforms, with important implications for management practices.

The remainder of this paper is organized as follows: We provide the literature review in Section 2. Section 3 presents the problem description and model assumptions. In Section 4, we develop an information-sharing model for the three scenarios. In Section 5, we present a comparative analysis of the results for the three scenarios. In Section 6, we perform numerical simulations and sensitivity analysis. We discuss the analysis and highlight the relevant management implications in Section 7, and we provide the conclusions in Section 8. Some proofs are provided in the Appendix A, Appendix B, Appendix C, Appendix D, Appendix E and Appendix F.

2. Literature Review

Here, we provide a literature review on two aspects of information-sharing regulations and industrial internet platforms.

2.1. Information-Sharing Regulations

Information-sharing regulations refer to the sharing of information between different information systems and social entities [25], and the regulation of the risks in the intermediary processes to prevent problems such as information leakage. Studies on information-sharing regulations have covered the fields of healthcare, finance, and supply chain [26]. Scholars often use a game-theoretic approach to study the regulation by building a two-sided, three-sided, or multi-sided monitoring model and conducting stability analyses [27,28,29,30,31,32,33,34]. Equilibrium strategies have been analyzed and effective ways to enhance information regulation have been proposed. However, most of the aforementioned studies have modelled this in terms of evolutionary games, static/dynamic games, or repeated games, and have not yet considered information sharing as a dynamic process undergoing continuous changes over time.

2.2. Industrial Internet Platforms

As industrial internet platforms continue to improve, they have attracted widespread attention [35]. Industrial internet platforms allow companies to share data and allow analysts on the platforms to process relevant data and provide them with data services [36]. The essence of industrial internet platforms is a high degree of information integration and optimal allocation of resources, while promoting the deep integration and reconfiguration of data sources [37]. Zhang et al. divided the technical architecture of an industrial internet platform into a software layer, a platform layer, a cloud infrastructure layer, and an edge layer [38]. These layers help enterprises visualize their business processes in different aspects, assisting them in making accurate predictions and analyses. Regarding the theoretical framework of industrial internet platforms, scholars have explored the perspectives of organizational behavior, industry, economics, technology, and management [39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. Unfortunately, these theories have not been explored together from a technical and socio-legal perspective.

Industrial internet platforms are able to integrate enterprise information resources and solve problems, such as mismatch between demand and supply [54]. Du Yong et al. found that the resource storage and data activation on industrial internet platforms can help manufacturing enterprises cross the digital divide in upgrading [55]. Menon et al. argued that industrial internet platforms promote deep integration and facilitate a fusion of industrialized thinking, methods, and models with new-generation information technologies, such as cloud computing, big data, and artificial intelligence [56]. For solving the demand–supply mismatch, Zhang Yanhua proposed a Q-learning computing method to optimize the resource allocation problem based on the industrial internet platform [14]. Li et al. further proposed an energy-saving resource allocation framework [57].

In summary, this study differs from these studies in three important ways. First, we adopt a differential game approach to study the problem of continuous information sharing in a dynamic context rather than static information sharing. This approach improves the study of the dynamic dimension of information-sharing regulation. Second, this study constructs a regulatory system for information sharing on industrial internet platforms from a technical and socio-legal perspective, rather than being limited to cooperation between enterprises and industrial internet platforms. Thus, we enrich the research perspective. Finally, this study compares the information-sharing regulatory schemes in three scenarios and provides corresponding insights. It is of great managerial significance to comply with the trend of collaborative data development and diversified information interaction in the industrial internet era.

3. Problem Description and Model Assumptions

3.1. Model Description

This paper considers an information-sharing regulatory system constituted by local governments, industrial internet platforms, and enterprises (collectively known as the “three entities”). We explore the impact of different cooperation models on the information-sharing and supervision system of the industrial internet platforms under decentralized, centralized, and cost-sharing contract decision-making scenarios. The relationship between the subjects of the three-entity system (Figure 1) is described as follows: Enterprises upload their data onto the industrial internet platforms, which, in turn, provide authentication and data security services. Local governments monitor information leakage and information trafficking on these platforms by enacting their policies and laws. They demand the implementation of stricter information security technologies through administrative means and regulate the information sharing quality. By adopting policies such as cost subsidies, they encourage (1) industrial internet platforms to enhance information technology innovation and (2) enterprises to strengthen the quality of information sharing, by improving the former’s reputation. Through these steps, increasingly more enterprises will join these platforms. Subsequently, this will reduce problems such as data insecurity and inactive information sharing, accelerating the development of digital synergy among enterprises. Simultaneously, the digital transformation of enterprises will generate more revenue, promote local economic growth, and increase social welfare benefits.

3.2. Model Assumptions

The classical goodwill model proposed by Nerlove and Arrow suggests that the products of a company with a better goodwill bring it excess profits [58]. This theory also applies to the regulation of information sharing on industrial internet platforms [1]. The good reputation of an information-sharing and supervision system will attract more companies to join the platform and generate more revenue. To establish a good reputation for the regulatory system, the following requirements must be fulfilled: local governments must actively enact their policies, enterprises must share real and valid information, and industrial internet platforms must provide high-quality data services. Let us denote reputation by $S(t)$. Reputation is affected by the degree of regulation of local governments, industrial internet platforms, and enterprises, along with the goodwill decay coefficient. Now, let us consider Hypothesis 1.

Hypothesis 1.

The differentiated evolution equation for the reputation of the information-sharing regulatory system is

$$\left\{\begin{array}{l}\frac{dS(t)}{dt}={\alpha }_1{E}_G(t)+{\alpha }_2{E}_P(t)+{\alpha }_3{E}_E(t)-\beta S\\ S(0)=S_0\ge 0\end{array}\right.$$

(1)

From Schumpeter’s point of view, it is clear that the cost of effort in shaping a good reputation, and that the cost of that effort, increases gradually [59]. To improve the reputation of the information-sharing and supervision systems, all three entities face regulatory costs. It is costly for local governments to control the access threshold of industrial internet platforms through policy guidance [5]. Industrial internet platforms need to invest in information-sharing devices and technologies to reduce information leakage and theft issues [60]. Enterprises have to invest in promoting the authenticity of information sharing in order to access value-added information services on these platforms and enhance brand awareness [1]. Therefore, drawing on Chen et al.’s study, which assumes the cost of regulatory effort increases with their quality, Hypothesis 2 is proposed [61].

Hypothesis 2.

The cost of regulatory efforts for the local governments, industrial internet platforms, and enterprises at time$t$are given as

$$C_G(t)=\frac{1}{2}{k}_G{E}_G^2(t); C_p(t)=\frac{1}{2}{k}_p{E}_p^2(t); C_E(t)=\frac{1}{2}{k}_E{E}_E^2(t)$$

(2)

The value co-creation theory proposed by Prahalad and Ramaswamy suggests that a value co-creation system between producers and consumers is conducive to improved business performance [62]. Applying this theory to the regulation of information sharing, we found that the quality of regulation and information sharing is beneficial to the development of society. For enterprises, data resource sharing facilitates centralized risk control and resource allocation, maintains service quality, and improves customer satisfaction [3]. Information regulation will further optimize the operations of enterprises, promote their digital transformation, and create business benefits. Information regulation will also reduce the information security risks and enhance the reputation, occupancy, and revenue of industrial internet platforms [63]. These combined factors will also increase the benefits for local governments by bringing in a huge social welfare effect [5]. Therefore, Hypothesis 3 is proposed.

Hypothesis 3.

The social welfare effect of improved regulations by local governments and industrial internet platforms, and the improved quality of information sharing by enterprises can be expressed as

$$Q_t=Q_0+{\gamma }_G{E}_G(t)+{\gamma }_p{E}_p(t)+{\gamma }_E{E}_E(t)+\epsilon S(t)$$

(3)

Enterprises improve the quality of information sharing to promote the sharing of data resources and to increase social welfare [5]. Information symmetry due to information sharing will make the products produced by enterprises more popular with consumers, further increasing social welfare [6]. Let the coefficient of social welfare effect on local governments and industrial internet platforms due to improved supervision, and on enterprises due to improved information sharing quality, be denoted as $\omega$ ($\omega >0$), then the total benefit of the three is $\omega Q(t)$.

Hypothesis 4.

Following Akdil’s work [64], the benefits of data sharing are distributed between local governments, industrial internet platforms, and enterprises. The benefit coefficients of local governments, enterprises, and industrial internet platforms are ${\lambda }_1$(${\lambda }_1>0$),${\lambda }_2$(${\lambda }_2>0$), and $1-{\lambda }_1-{\lambda }_2$(${\lambda }_1+{\lambda }_2<1$), respectively.

The specific model symbols and meanings are displayed in

Table 1. Model symbols and their meanings.

Symbol	Meaning	Symbol	Meaning
$S(t)$	Reputation of information-sharing supervision systems at time t.	$E_E^{}(t)$	Level of effort by enterprises to improve the quality of information sharing.
${\alpha }_1$	Coefficient for the degree of influence of local government regulations on the reputation of the information-sharing regulatory system, ${\alpha }_1>0$	$Q_0$	Initial state of social welfare effects when neither local governments nor industrial internet platforms regulate information and when companies have not improved the quality of information sharing, $Q_0>0$
${\alpha }_2$	Coefficient for the degree of influence of industrial internet platform regulations on the reputation of the information-sharing regulatory system, ${\alpha }_2>0$	${\gamma }_G$	Coefficient for the degree of influence of local government regulations on the social welfare effect, ${\gamma }_G>0$
${\alpha }_3$	Coefficient for the degree of influence of enterprise efforts to improve the quality of information sharing on the reputation of the regulatory system, ${\alpha }_3>0$	${\gamma }_p$	Coefficient for the degree of influence of regulation of industrial internet platforms on social welfare effects, ${\gamma }_p>0$
$\beta$	Decay rate of the information-sharing regulatory system’s reputation, $\beta >0$	${\gamma }_E$	Coefficient for the degree of influence of enterprise efforts to improve the quality of information sharing on the social welfare effect, ${\gamma }_E>0$
$C_G(t)$	Cost of information-sharing regulatory efforts by local governments at time t.	$\epsilon$	Coefficient for the degree of influence of enterprise efforts to improve the quality of information sharing on the social welfare effect, $\epsilon >0$
$C_p(t)$	Cost of information-sharing regulatory efforts by industrial internet platforms at time t.	$\omega$	Coefficient of the social welfare effect on local government, industrial internet platform, and firm returns, $\omega >0$
$C_E(t)$	Cost of improving the quality of information-sharing efforts by enterprises at time t.	${\lambda }_1$	Benefit coefficient of local governments, ${\lambda }_1>0$
$k_G$	Information-sharing regulatory cost coefficient for local governments, $k_G>0$	${\lambda }_2$	Benefit coefficient of enterprises, ${\lambda }_2>0$
$k_p$	Information-sharing regulatory cost coefficient for industrial internet platforms, $k_p>0$	$\rho$	Discount rate, $\rho >0$
$k_E$	Cost coefficient for enterprise efforts to improve the quality of information sharing, $k_E>0$	${\mu }_P$	Subsidy coefficient provided by local governments to industrial internet platforms, $0<{\mu }_P<1$
$E_G^{}(t)$	Degree of effort put into information regulation by local governments	${\mu }_E$	Subsidy coefficient provided by local governments to enterprises, $0<{\mu }_E<1$
$E_p^{}(t)$	Degree of effort put into information regulation by industrial internet platforms

.

4. Model Formulation and Solution

4.1. Decentralized Decision Making (Model N)

In this scenario, the local government, the industrial internet platforms, and the enterprises aim to maximize the profits of their stakeholders and take their own independent decisions [20]. The process is as follows: First, the enterprises take the initiative to share accurate information on the industrial internet platforms to obtain value-added services and accelerate their digital transformation process [5]. Then, the industrial internet platforms provide improved information services and information protection for enterprises to increase their benefits [65]. Finally, the local government supervises the authenticity of the information being shared by the enterprises and the effectiveness of information defense on the industrial internet platforms, at which point the decision problems of the three parties can be described as

$$\underset{E_G}{\max }{J}_G^N={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left[{\lambda }_1\omega (Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S)-\frac{1}{2}{k}_G{E}_G^2\right]dt$$

(4)

$$\underset{E_p}{\max }{J}_p^N={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left[(1-{\lambda }_1-{\lambda }_2)\omega (Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S)-\frac{1}{2}{k}_p{E}_p^2\right]dt$$

(5)

$$\underset{E_E}{\max }{J}_E^N={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left[{\lambda }_2\omega (Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S)-\frac{1}{2}{k}_E{E}_E^2\right]dt$$

(6)

Theorem 1.

(1) In this scenario:

The optimal level of regulatory effort by the local government is

$$E_G^{N*}=\frac{{\lambda }_1\omega \left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}{k_G(\rho +\beta )}$$

(7)

The optimal level of regulatory effort for an industrial internet platform is

$$E_P^{N*}=\frac{(1-{\lambda }_1-{\lambda }_2)\omega \left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}{k_P(\rho +\beta )}$$

(8)

The optimal level of effort to improve the quality of information sharing for an enterprise is

$$E_E^{N*}=\frac{{\lambda }_2\omega \left[{\gamma }_E\left(\rho +\beta \right)+{\alpha }_3\epsilon \right]}{k_E(\rho +\beta )}$$

(9)

(2) In this scenario, the optimal trajectory for the reputation of the information-sharing regulatory system is given as

$$E\left[S^N(t)\right]=\frac{{\mathsf{\Omega }}_1}{\beta }+e^{-\beta t}(S_0-\frac{{\mathsf{\Omega }}_1}{\beta })$$

(10)

where,

$${\mathsf{\Omega }}_1=\frac{{\alpha }_1{}^2{\lambda }_1\omega \left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}{k_G(\rho +\beta )}+\frac{{\alpha }_2{}^2\omega (1-{\lambda }_1-{\lambda }_2)\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}{k_P(\rho +\beta )}+\frac{{\alpha }_3{\lambda }_2\omega \left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}{k_E(\rho +\beta )}$$

(11)

(3) In this scenario, the optimal benefit for the local government is

$$\begin{array}{l}{V}_G^{N*}(S)=\frac{{\lambda }_1\omega \epsilon }{\rho +\beta }S+\frac{{\lambda }_1\omega Q_0}{\rho }+\frac{{\lambda }_1{}^2{\omega }^2{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{2\rho k_G{(\rho +\beta )}^2}+\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\frac{(1-{\lambda }_1-{\lambda }_2){\omega }^2{\lambda }_1{\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{\rho k_P{(\rho +\beta )}^2}+\frac{{\omega }^2{\lambda }_1{\lambda }_2{\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{\rho k_E{(\rho +\beta )}^2}\end{array}$$

(12)

In this scenario, the optimal benefit for an industrial internet platform is

$$\begin{array}{l}{V}_P^{N*}(S)=\frac{(1-{\lambda }_1-{\lambda }_2)\omega \epsilon }{\rho +\beta }S+\frac{(1-{\lambda }_1-{\lambda }_2)\omega Q_0}{\rho }+\frac{(1-{\lambda }_1-{\lambda }_2){\omega }^2{\lambda }_1{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{\rho k_G{(\rho +\beta )}^2}\\ \hspace{1em}\hspace{1em}\hspace{1em} +\frac{{(1-{\lambda }_1-{\lambda }_2)}^2{\omega }^2{\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{2\rho k_P{(\rho +\beta )}^2}+\frac{{\lambda }_2(1-{\lambda }_1-{\lambda }_2){\omega }^2{\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{\rho k_E{(\rho +\beta )}^2}\end{array}$$

(13)

The optimal benefit for an enterprise is

$$\begin{array}{l}{V}_E^{N*}(S)=\frac{{\lambda }_2\omega \epsilon }{\rho +\beta }S+\frac{{\lambda }_2\omega Q_0}{\rho }+\frac{{\lambda }_1{\lambda }_2{\omega }^2{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{\rho k_G{(\rho +\beta )}^2}\\ \hspace{1em}\hspace{1em}\hspace{1em} +\frac{(1-{\lambda }_1-{\lambda }_2){\omega }^2{\lambda }_2{\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{\rho k_P{(\rho +\beta )}^2}+\frac{{\lambda }_2{}^2{\omega }^2{\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{2\rho k_E{(\rho +\beta )}^2}\end{array}$$

(14)

The optimal benefit of an information-sharing regulatory system is

$$\begin{array}{l}{V}_{G,P,E}^{N*}(S)=\frac{\omega \epsilon }{\rho +\beta }S+\frac{\omega Q_0}{\rho }+\frac{\left(2-{\lambda }_1\right){\lambda }_1{\omega }^2{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{2\rho k_G{(\rho +\beta )}^2}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\frac{(1-{\lambda }_1-{\lambda }_2)(1+{\lambda }_1+{\lambda }_2){\omega }^2{\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{2\rho k_P{(\rho +\beta )}^2}+\frac{(2-{\lambda }_2){\lambda }_2{\omega }^2{\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{2\rho k_E{(\rho +\beta )}^2}\end{array}$$

(15)

Proof. 

See Appendix A. □

Corollary 1.

Comparative statistical analysis of critical parameters for decentralized decision-making (

Table 2. Comparative statistical analysis of critical parameters for decentralized decision-making.

	$\mathit{\gamma }$	$\mathit{\rho }$	$\mathit{\beta }$	$\mathit{\epsilon }$	$\mathit{k}$	${\mathit{\alpha }}_3$
$G^N$	↑	↓	↓	↑	↓	↑
$P^N$	↑	↓	↓	↑	↓	↑
$E^N$	↑	↓	↓	↑	↓	↑

Note: ↑ indicates a positive correlation, ↓ indicates a negative correlation.

).

From Corollary 1, it can be seen that, under decentralized decision-making, local governments, industrial internet platforms, and enterprises have the same trends for each parameter. As the regulatory efforts by the local governments and the industrial internet platforms increase, along with the degree of effort by the enterprises to improve the quality of information sharing, the coefficient of influence on the social welfare effect will increase and the optimal benefits for the three entities will rise. This further enhances the optimal benefits for the three entities. It indicates that local governments will pay more attention to the access threshold of industrial internet platforms, while regulating their safe operation, and ensure the quality of information sharing among enterprises through legal policies. The platforms, in turn, focus on information authenticity and security, regulate the entry of enterprises, and also provide relevant value-added information services. Member enterprises on the platforms can check the information they need in real time and use the information gap to improve their business operations. Simultaneously, they can deliver high-quality information to the platforms in real time. It is conducive to forming an excellent closed loop of information and using value-added information services to promote the digital transformation of enterprises and give back to the society.

The impact of improving information sharing quality on its reputation would further accelerate the value added to the information, helping enterprises improve operational efficiency and reduce costs. The optimal benefits for enterprises will rise.

As the discount rate, the regulatory system’s reputation decay rate, and the cost coefficients of the three entities increase, the benefits to local governments, industrial internet platforms, and enterprises will start reducing. An increase in these discount and decay rates reduces the liquidity of corporate cash flows and the coefficient for the impact of the system’s reputation on social welfare effects, respectively, thereby reducing corporate benefits. An increase in the cost coefficients of all three entities will directly impact their benefits.

4.2. Centralized Decision Making (Model C)

In this scenario, the local government, industrial internet platforms, and enterprises work together to make a centralized decision to maximize the overall benefit [21]. In this case, the decision-making process is as follows: Firstly, a central decision maker is selected in the information-sharing and supervision system [66], who decides the degree of effort to be made by all the three entities to improve the quality of information sharing and maximize the overall benefit [60]. The centralized decision-making problem is

$$\underset{E_G,E_p,E_E}{\max }{J}_{G,P,E}^C={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left\{\omega \left[Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S\right]-\frac{1}{2}{k}_G{E}_G^2-\frac{1}{2}{k}_p{E}_p^2-\frac{1}{2}{k}_E{E}_E^2\right\}dt$$

(16)

Theorem 2.

(1) In this scenario, the optimal level of regulatory effort for the local government is

$$E_G^{C*}=\frac{\omega \left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}{k_G(\rho +\beta )}$$

(17)

The optimal level of regulatory effort for an industrial internet platform is

$$E_P^{C*}=\frac{\omega \left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}{k_P(\rho +\beta )}$$

(18)

The optimal level of effort to improve the quality of information sharing for an enterprise is

$$E_E^{C*}=\frac{\omega \left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}{k_E(\rho +\beta )}$$

(19)

(2) In this scenario, the optimal trajectory for the reputation of the information-sharing regulatory system is

$$E\left[S^C(t)\right]=\frac{{\mathsf{\Omega }}_2}{\beta }+e^{-\beta t}(S_0-\frac{{\mathsf{\Omega }}_2}{\beta })$$

(20)

where

$${\mathsf{\Omega }}_2=\frac{{\alpha }_1{}^2\omega \left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}{k_G(\rho +\beta )}+\frac{{\alpha }_2{}^2\omega \left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}{k_P(\rho +\beta )}+\frac{{\alpha }_3{}^2\omega \left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}{k_E(\rho +\beta )}$$

(21)

(3) The optimal benefit of an information-sharing regulatory system is

$$V_{G,P,E}^{\mathrm{C}*}(S)=\frac{\omega \epsilon }{\rho +\beta }S+\frac{\omega Q_0}{\rho }+\frac{{\omega }^2{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{2\rho k_G{(\rho +\beta )}^2}+\frac{{\omega }^2{\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{2\rho k_P{(\rho +\beta )}^2}+\frac{{\omega }^2{\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{2\rho k_E{(\rho +\beta )}^2}$$

(22)

Proof. 

The proof is similar to Theorem 1. □

Corollary 2.

Comparative statistical analysis of critical parameters for centralized decision making (

Table 3. Comparative statistical analysis of critical parameters for centralized decision making.

	$\mathit{\gamma }$	$\mathit{\rho }$	$\mathit{\beta }$	$\mathit{\epsilon }$	$\mathit{k}$	$\mathit{\alpha }$
${(G+P+E)}^C$	↑	↓	↓	↑	↓	↑

Note:↑ indicates a positive correlation, ↓ indicates a negative correlation.

).

From Corollary 2, it can be seen that, in the context of centralized decision making, the overall benefit of the three entities rises as a whole as the degrees of regulation on the social welfare effect rise. It indicates that the three entities work together to raise the quality of information-sharing regulatory efforts, create a secure information-sharing environment, and prompt the enterprises to willingly share real-time information. The flow of enterprise information can break down information barriers and use the information gap to optimize business practices and improve their services, thereby creating more corporate profits and bringing in social welfare.

The increasing reputation of the regulatory system on social welfare positively affects the overall benefits. This indicates that a rise in this reputation would attract more enterprises to join the industrial internet platforms. Enterprises will take the initiative to access the platform’s value-added information services, sharing and accessing data pertaining to other enterprises. Data resource sharing can fully function in various fields, promoting the rise of business benefits. The increase in discount rate, regulatory system reputation decay rate, and supervision costs will all impact the overall economic benefits and hinder the development of enterprises.

4.3. Cost-Sharing Contract Decision (Model D)

This scenario is based on the condition that the benefit coefficient of local governments accounts for more than one-third of the total benefits ($1/3<{\lambda }_1<1$), and local governments are willing to share the costs between industrial internet platforms and enterprises [22]. The local government subsidy coefficient ${\mu }_P$ bears part of the IT innovation costs of industrial internet platforms. The local government encourages these platforms to break the technical barriers of information regulation, build a solid data protection wall, and improve the platform’s information-carrying capacities [67]. The local government ${\mu }_E$ bears part of the enterprises’ cost of joining the industrial internet platforms. The local government encourages enterprises to actively join and share accurate information on the platforms, and to reduce the impact of information asymmetry on their digital transformation process. The decision-making process is as follows: First, the local government proposes a cost-sharing contract, and then the three entities decide on the level of regulatory effort, respectively. Once the contract expires, the local government will share the costs of the industrial internet platforms and enterprises in corresponding proportion. At this point, the cost-sharing contract decision problem is

$$\underset{E_G}{\max }{J}_G^D={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left[{\lambda }_1\omega (Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S)-\frac{1}{2}{k}_G{E}_G^2-\frac{1}{2}{\mu }_P{k}_p{E}_p^2-\frac{1}{2}{\mu }_E{k}_E{E}_E^2\right]dt$$

(23)

$$\underset{E_p}{\max }{J}_p^D={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left[(1-{\lambda }_1-{\lambda }_2)\omega (Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S)-\frac{1}{2}(1-{\mu }_P)k_p{E}_p^2\right]dt$$

(24)

$$\underset{E_E}{\max }{J}_E^D={{\displaystyle {\int }_0^{\infty }e}}^{-\rho t}\left[{\lambda }_2\omega (Q_0+{\gamma }_G{E}_G+{\gamma }_p{E}_p+{\gamma }_E{E}_E+\epsilon S)-\frac{1}{2}(1-{\mu }_E)k_E{E}_E^2\right]dt$$

(25)

Theorem 3.

(1) In this scenario, the optimal level of regulatory effort for the local government is

$$E_G^{D*}=\frac{{\lambda }_1\omega \left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}{k_G(\rho +\beta )}$$

(26)

The optimal level of regulatory effort for an industrial internet platform is

$$E_P^{D*}=\frac{(1-{\lambda }_1-{\lambda }_2)\omega \left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}{k_P(1-{\mu }_P)(\rho +\beta )}$$

(27)

The optimal level of effort to improve the quality of information sharing for an enterprise is

$$E_E^{D*}=\frac{{\lambda }_2\omega \left[{\gamma }_E\left(\rho +\beta \right)+{\alpha }_3\epsilon \right]}{k_E\left(1-{\mu }_E\right)(\rho +\beta )}$$

(28)

(2) In this scenario, the optimal trajectory for the reputation of the information-sharing regulatory system is

$$E\left[S^D(t)\right]=\frac{{\mathsf{\Omega }}_3}{\beta }+e^{-\beta t}(S_0-\frac{{\mathsf{\Omega }}_3}{\beta })$$

(29)

where

$${\mathsf{\Omega }}_3=\frac{{\alpha }_1{\lambda }_1\omega \left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}{k_G(\rho +\beta )}+\frac{{\alpha }_2(1-{\lambda }_1-{\lambda }_2)\omega \left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}{k_P(1-{\mu }_P)(\rho +\beta )}+\frac{{\alpha }_3{\lambda }_2\omega \left[{\gamma }_E\left(\rho +\beta \right)+{\alpha }_3\epsilon \right]}{k_E\left(1-{\mu }_E\right)(\rho +\beta )}$$

(30)

(3) In this scenario, the optimal benefit to the local government is

$$\begin{array}{ll}{V}_c^{D^{*}}\left(S\right)& =\frac{{\lambda }_1\omega \epsilon }{\rho +\beta }S+\frac{{\lambda }_1\omega Q_0}{\rho }+\frac{{\lambda }_1^2{\omega }^2{\left[{\gamma }_G\left(\rho +\beta \right)+{\alpha }_1\epsilon \right]}^2}{2\rho k_G{(\rho +\beta )}^2}+\frac{\left(1-{\lambda }_1-{\lambda }_2\right){\omega }^2\left[{\lambda }_1\left(2-{\mu }_P\right)-{\mu }_P\left({\lambda }_2-1\right)\right]{\left[{\gamma }_P\left(\rho +\beta \right)+{\alpha }_2\epsilon \right]}^2}{2\rho k_P{\left(1-{\mu }_P\right)}^2{(\rho +\beta )}^2}\\ & +\frac{{\lambda }_2{\omega }^2\left[2{\lambda }_1\left(1-{\mu }_E\right)-{\mu }_E{\lambda }_2\right]{\left[{\gamma }_E\left(\rho +\beta \right)+{\alpha }_3\epsilon \right]}^2}{2\rho k_E{\left(1-{\mu }_E\right)}^2{(\rho +\beta )}^2}\end{array}$$

(31)

The optimal benefit for an industrial internet platform is

$$\begin{array}{ll}{V}_P^{{\mathrm{D}}^{*}}\left(S\right)& =\frac{\left(1-{\lambda }_1-{\lambda }_2\right)\omega \epsilon }{\rho +\beta }S+\frac{\left(1-{\lambda }_1-{\lambda }_2\right)\omega Q_0}{\rho }+\frac{\left(1-{\lambda }_1-{\lambda }_2\right){\omega }^2{\lambda }_1{\left[{\gamma }_G\left(\rho +\beta \right)+{\alpha }_1\epsilon \right]}^2}{\rho k_Q{(\rho +\beta )}^2}\\ & +\frac{{\left(1-{\lambda }_1-{\lambda }_2\right)}^2{\omega }^2{\left[{\gamma }_P\left(\rho +\beta \right)+{\alpha }_2\epsilon \right]}^2}{2\rho k_P\left(1-{\mu }_P\right){(\rho +\beta )}^2}+\frac{{\lambda }_2\left(1-{\lambda }_1-{\lambda }_2\right){\omega }^2{\left[{\gamma }_E\left(\rho +\beta \right)+{\alpha }_2\epsilon \right]}^2}{\rho k_E\left(1-{\mu }_E\right){(\rho +\beta )}^2}\end{array}$$

(32)

The optimal benefit for an enterprise is

$$\begin{array}{l}{V}_E^{D*}(S)=\frac{{\lambda }_2\omega \epsilon }{\rho +\beta }S+\frac{{\lambda }_2\omega Q_0}{\rho }+\frac{{\lambda }_1{\lambda }_2{\omega }^2{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{\rho k_G{(\rho +\beta )}^2}\\ \hspace{1em}\hspace{1em}\hspace{1em} +\frac{(1-{\lambda }_1-{\lambda }_2){\omega }^2{\lambda }_2{\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{\rho k_P(1-{\mu }_P){(\rho +\beta )}^2}+\frac{{\lambda }_2{}^2{\omega }^2{\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{2\rho k_E(1-{\mu }_E){(\rho +\beta )}^2}\end{array}$$

(33)

The optimal benefit of the information-sharing regulatory system is

$$\begin{array}{l}{V}_{G,P,E}^{D*}(S)=\frac{\omega \epsilon }{\rho +\beta }S+\frac{\omega Q_0}{\rho }+\frac{{\omega }^2{\left[{\gamma }_G(\rho +\beta )+{\alpha }_1\epsilon \right]}^2}{2\rho K_G{(\rho +\beta )}^2}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\frac{{\omega }^2(1-{\lambda }_1-{\lambda }_2)(1+{\lambda }_1+{\lambda }_2-2{\lambda }_2{\mu }_P){\left[{\gamma }_P(\rho +\beta )+{\alpha }_2\epsilon \right]}^2}{2\rho k_P(1-{\mu }_P){(\rho +\beta )}^2}+\frac{{\lambda }_2{\omega }^2(2-2{\mu }_E-{\lambda }_2){\left[{\gamma }_E(\rho +\beta )+{\alpha }_3\epsilon \right]}^2}{2\rho k_E{(\rho +\beta )}^2}\end{array}$$

(34)

Proof. 

The proof is similar to Theorem 1. □

Corollary 3.

Comparative statistical analysis of critical parameters under cost-sharing contract decisions (

Table 4. Comparative statistical analysis of critical parameters under cost-sharing contract decisions.

	$\mathit{\gamma }$	$\mathit{\rho }$	$\mathit{\beta }$	$\mathit{\epsilon }$	$\mathit{k}$	${\mathit{\alpha }}_{}$	${\mathit{\mu }}_{\mathit{P}}$	${\mathit{\mu }}_{\mathit{E}}$
$G^D$	↑	↓	↓	↑	↓	↑	↑	↑
$P^D$	↑	↓	↓	↑	↓	↑	↑	↑
$E^D$	↑	↓	↓	↑	↓	↑	↑	↑

Note:↑ indicates a positive correlation, ↓ indicates a negative correlation.

).

From Corollary 3, by looking at the increase in $\gamma$, $\epsilon$, and $\alpha$, and the decrease in $\rho$, $\beta$, and $k$, we find the trend in the change of parameters under a cost-sharing decision to be roughly the same as that under a centralized decision. With the increase in ${\mu }_P$ and ${\mu }_E$, the benefits to the local government, industrial internet platforms, and enterprises under the cost-sharing contract decision would further improve. This indicates that, as the local government bears higher costs of technological innovation, the willingness of the industrial internet platforms to push their technological limits also increases. The information security, value-added information processing services, and data holding capacities of the platforms vastly improve, attracting more enterprises to the platform. As the local government bears higher cost coefficients for the enterprises, their probability of joining the industrial internet platforms effectively increases. With guaranteed information security, the willingness of the enterprises to actively share accurate information is further enhanced, eliminating free-riding and other information-acquisition behaviors. By safeguarding the information security supervision on the industrial internet platforms, the reputation of the overall information-sharing and supervision system improves. This effectively promotes the sustainable development of enterprises, enhancing the corresponding business profits and social welfare.

5. Comparative Analysis

Comparing Theorems 1–3 under the decentralized, centralized, and cost-sharing contract decision-making scenarios, the following corollaries are drawn:

Corollary 4.

The level of optimal regulatory efforts by local governments and industrial internet platforms, along with the level of information-sharing quality improvement efforts by enterprises, shows an increase under a centralized decision-making scenario compared to a decentralized one. That is, $E_G^{N*}<E_G^{C*}$,$E_P^{N*}<E_P^{C*}$, and$E_E^{N*}<E_E^{C*}$.

Proof. 

See Appendix B. □

Corollary 4 shows that, compared to the centralized decision-making scenario, the regulatory system under the decentralized decision-making scenario is likely to produce double marginal effects. That is, local governments, industrial internet platforms, and enterprises only consider maximizing their interests when making decisions but ignore the marginal benefits of other members. Therefore, when faced with the distribution of benefits of the information regulatory system, the economic decision of any one entity will affect the market demand. This, in turn, damages the interests of every subject in the information regulatory system. Therefore, decentralized decision-making can only achieve partial benefit optimization, and not a global one. Local governments, industrial internet platforms, and enterprises, under the centralized decision-making scenario, keep each other in check to maximize the overall benefits, increase social welfare, and promote Pareto improvement.

Corollary 5.

Compared to the decentralized decision, the cost-sharing contract decision satisfies the following conditions: $E_G^N{}^{*}=E_G^D{}^{*}$,$E_P^N{}^{*}<E_P^D{}^{*}$, and$E_E^N{}^{*}<E_E^D{}^{*}$. The level of regulatory effort by local governments remains unchanged under the cost-sharing contract decision, while that of both the industrial internet platforms and enterprises increases.

Proof. 

See Appendix C. □

Corollary 5 shows that, compared to the decentralized decision, the optimal regulatory effort of the industrial internet platforms and enterprises under the cost-sharing contract decision is positively correlated with the cost subsidy coefficients ${\mu }_P$ and ${\mu }_E$. The increase in the subsidy coefficient can effectively promote the platforms to invest more in technological innovation and strengthen the function of regulatory technology. This effectively improves the initiative of enterprises to share accurate and high-quality information. The cost-sharing contract decision results in a Pareto improvement in the level of information regulatory efforts of the three main entities in the information-sharing and supervision system, including the local governments, industrial internet platforms, and enterprises. That is, the decision is effective.

Corollary 6.

The three scenarios for the optimal trajectory of the reputation of an industrial internet platform information-sharing and supervision system can be expressed as$E\left[S^N(t)\right]\le E\left[S^D(t)\right]\le E\left[S^C(t)\right]$and$\underset{t\to +\infty }{\lim }E\left[S^N(t)\right]\le \underset{t\to +\infty }{\lim }E\left[S^D(t)\right]\le \underset{t\to +\infty }{\lim }E\left[S^C(t)\right]$.

Proof. 

See Appendix D. □

From Corollary 6, it can be seen that the optimal trajectory of the reputation of the industrial internet platform information-sharing and supervision system under the centralized decision-making scenario is the best, followed by that under the cost-sharing contract and decentralized decision-making scenarios. From the government’s perspective, adopting cost subsidies or joint participation with industrial internet platforms and enterprises are both conducive to improving this reputation.

Corollary 7.

Compared to the decentralized decision-making scenario, the optimal benefit situation for the information-sharing and supervision systems under the cost-sharing contract decision-making scenario is better when we have$1/3<{\lambda }_1<1$. That is, we have$V_G^N{}^{*}(S)<V_G^D{}^{*}(S),$$V_P^N{}^{*}(S)<V_P^D{}^{*}(S),$$V_E^N{}^{*}(S)<V_E^D{}^{*}(S),$$V_{G,P,E}^{N*}(S)<V_{G,P,E}^{D*}(S)$under centralized decision making, resulting in the highest optimal benefit for the three entities.

Proof. 

See Appendix E. □

From Corollary 7, it can be seen that the economic benefits reach the Pareto optimal state under the centralized decision-making scenario and reach the sub-Pareto optimal state under the cost-sharing contract decision-making scenario. From the game perspective, to maximize social welfare and increase the overall economic benefits, we must choose between the cost-sharing contract or centralized decision-making scenarios. By sharing the costs or cooperating with the government, we can reduce the free-riding behavior of the three entities and strengthen the information supervision. This will help attain high-quality overall benefits of the information-sharing and supervision system.

Corollary 8.

The magnitude of the impact of the local government subsidy coefficient on the economic efficiency of the system under the cost-sharing contract decision is minor when$0<\mu <1/2$($1/3<{\lambda }_1<1$), and the magnitude of the impact of the local government subsidy coefficient on the economic efficiency of the system under the cost-sharing contract decision is significant when$1/2<\mu <1$($1/3<{\lambda }_1<1$).

Proof. 

See Appendix F. □

From Corollary 8, it can be seen that the local government cost subsidies promote the growth of economic benefits for the industrial internet platform information-sharing and supervision system. However, the growth rate changes as a function of $\mu$ in two specific manners. When $1/2<\mu <1$ ($1/3<{\lambda }_1<1$), the local government, under the cost-sharing contract decision, gives the industrial internet platforms and enterprises corresponding cost subsidies. This promotes innovations in platform supervision technology and value-added services. Cost subsidies motivate major enterprises to join the industrial internet platforms; share accurate, valid, and secure data; and accelerate the flow of information. This will allow the economic benefits of the enterprises and the social welfare to grow, improving the status of the local government. Therefore, when local governments provide cost subsidies (within a reasonable range) to industrial internet platforms and enterprises, they will achieve Pareto improvement. The opposite is true when $0<\mu <1/2$ ($1/3<{\lambda }_1<1$).

6. Simulation Analysis

Solving the models for differentiated games is complicated, as it is difficult to visualize and dynamically present the results of research to the reader. Numerical simulation techniques can provide further insights into the development of local and global dynamics by defining individual behavioral rules and interaction mechanisms. In order to visualize the evolution of the model under different constraints, the Matlab2016a simulation platform was used to simulate the evolution of the regulatory system strategy under the three decision-making scenarios.

Based on the equations and constraints of the decision problem, numerical simulations were carried out in Matlab2016a to draw comparative graphs for the reputation of the information-sharing regulatory system, the optimal benefits of the three entities, and the impact of $\mu$ on the optimal benefits of the system. Based on the relevant literature [14,25,26,27,31] and considering the actual situation, the parameters of this paper were set as follows: $k_G=k_P=k_E=2,$ ${\alpha }_1=0.7,$ ${\alpha }_2=0.6,$ ${\alpha }_3=0.6,$ $\beta =0.1,$ ${\gamma }_G=0.35,$ ${\gamma }_P=0.35,$ ${\gamma }_E=0.3,$ ${\mu }_P={\mu }_E=0.5,$ $\epsilon =0.7,$ $Q_0=5,$ $\omega =10,$ ${\lambda }_1=0.4,$ ${\lambda }_2=0.3,$ and $\rho =0.9$.

In all three scenarios, the change in the reputation of the information-sharing and supervision system over time reflects a fast and then steady growth (Figure 2). This trend shows a positive change, which means that, as time advances, the three entities gradually increase their efforts to supervise the system. Hence, the reputation of the information-sharing regulatory system grows rapidly and then flattens out. Figure 2 also shows that the reputation is highest under the centralized decision, followed by the cost-sharing contract decision, and lowest under the decentralized decision. It indicates that the centralized decision achieves Pareto optimality and fully motivates the three entities in the information-sharing regulatory system.

As displayed in Figure 3, Figure 4 and Figure 5, the optimal benefits for all three entities under the cost-sharing contract decision are higher than those under the decentralized decision. They all show a trend of a fast, followed by a steady, growth period. During the same period under the cost-sharing contract decision, the absolute value of benefits for local governments is higher than that for industrial internet platforms and enterprises. It indicates that, under the cost-sharing contract decision, based on the condition $1/3<{\lambda }_1<1$, local governments, as the dominant player, are willing to bear part of the costs for the industrial internet platform and enterprises. Local governments provide subsidies for the cost of technological innovation for the industrial internet platforms and promote the industrial internet platforms to improve their information regulatory capacity, information value-added service capacity, and information integration capacity. Moreover, local governments provide subsidies for enterprises to join the industrial internet platforms, stimulating the enterprises to join the industrial internet platforms to share information, break the information silo and other bullwhip effects, reduce irregular information sharing, information leakage, and other problems, and accelerate the digital transformational process of enterprises. This regulatory system promotes local economic growth, brings in higher taxes for local governments, and creates revenue for industrial internet platforms, leading to a value-sharing effect that increases social welfare. Here, the absolute value of benefits to local governments is higher than that of industrial internet platforms and enterprises, in the same time period. From Figure 6, it can be seen that the optimal benefits of the system are the highest under the centralized decision-making scenario, followed by the cost-sharing contract and decentralized decision-making scenarios, which is consistent with Corollary 7.

As displayed in Figure 7 and Figure 8, under the cost-sharing contract decision, the influence of local government cost subsidy coefficients ${\mu }_P$ and ${\mu }_E$ on the system’s optimal benefit is (1) minor, when we have $0<{\mu }_P<1/2$ and $0<{\mu }_E<1/2$, and (2) positive, when we have $1/2<{\mu }_P<1$ and $1/2<{\mu }_E<1$. This indicates that, when the cost subsidy coefficient is greater than the critical value of 1/2, the local government will increase its supervision, give the industrial internet platforms sufficient funds to improve their technical service capacity, and motivate the enterprises to standardize their own information-sharing behavior. Hence, the three entities will jointly improve the quality of information sharing and enhance the optimal benefits of the system under collaborative cooperation, as consistent with Corollary 8.

7. Discussion

In order to solve the problem of data security and inactive information sharing of enterprise information due to issues such as information leakage, this study constructs an optimal information-sharing regulatory system. In response to the three decision-making (cooperation) scenarios, this study draws some conclusions through model building, comparative analysis, and numerical simulation to provide a standard structure. We found the centralized decision–making scenario to be the optimal scenario, followed by the cost-sharing contract and decentralized decision-making scenarios. Specifically, the centralized decision improves the optimal information regulatory efforts by all three entities. By means of government subsidies, the cost-sharing contract decision provides better optimal regulatory efforts, reputation, and optimal benefits for the three entities compared to the decentralized decision. The cost-sharing contract decision mechanism can effectively regulate the information-sharing regulatory strategy of industrial internet platforms under decentralized decision making.

In addition, this study examines the reputation of the information-sharing and supervision system of the industrial internet platforms under three scenarios. Comparative analysis and numerical simulations revealed the reputation in centralized decision making to be the highest and that of decentralized decision making to be the lowest. All of them displayed a trend of positive and rapid growth, followed by a gradual saturation. This result demonstrated that, irrespective of the decision-making scenario, reputation follows a positive trend after the establishment of a regulatory system for information sharing on industrial internet platforms. However, the variations in the reputation trend across the three scenarios are not surprising. Particularly, if local governments, industrial internet platforms, and enterprises adopt decentralized decision making, it is difficult to create a synergy due to the short-sightedness of the three actors, who are only concerned with their own interests, after building the regulatory system from a technical and socio-legal perspective. Problems such as information asymmetry and poor communication will slow down the development of the system’s reputation. If the three entities adopt a cost-sharing contractual decision-making scenario, with the government’s incentive, the strategies under decentralized decision making are, to a certain extent, optimally coordinated. This promotes close ties among the three entities and, thus, enhances the development of the information-sharing regulatory system. If a centralized decision-making scenario is adopted, the three entities make the best use of the available resources in a collaborative manner to the greatest extent. The development of the reputation of the regulatory system is promoted with the overall benefit as the goal.

Furthermore, this study examines the optimal benefits of the three entities and the system under the three scenarios, and performs a sensitivity analysis of the government subsidy coefficient. Compared to the decentralized decision, the optimal benefits of all three main actors are better under the cost-sharing contract decision. Moreover, in the same period under the cost-sharing contract decision, the local government has the highest absolute value of benefits, followed by the enterprises and the industrial internet platforms. This suggests that local governments adopt a cost-subsidy approach to reduce irregular information sharing and information leakage by motivating enterprises to join industrial internet platforms. In turn, this will accelerate the digital transformational process of enterprises, promote local economic growth, and increase governmental benefits. In addition, the sensitivity analysis reveals that, when the cost subsidy coefficient is greater than 1/2, the system’s optimal benefits are more sensitive to local government subsidies. In other words, when the local government cost subsidy coefficient is less than 1/2, the degree of incentive for the information-sharing regulatory system is sub-optimal. This finding is consistent with the incentive principle and suggests that government subsidies should be clearly targeted towards enterprises and industrial internet platforms as per their requirements.

7.1. Practical Implications

The results of this study have some practical contributions to information-sharing regulatory systems and managers of industrial internet platforms. First, our study shows that centralized decision making is the most favorable to developing an information-sharing regulatory system for industrial internet platforms in all three scenarios, with cost-sharing contract decision making being the next most favorable and decentralized decision making being the least favorable. Centralized decision making is optimal for regulating information sharing on industrial internet platforms. Specifically, decentralized decision making is prone to double marginal effects and cannot achieve global optimality. In addition, decentralized decision making cannot follow the principle of timeliness and is prone to information asymmetry, resulting in poor regulatory coordination of industrial internet platforms. Therefore, decentralized decision making is undesirable in industrial internet platforms’ information-sharing and supervision systems. Local governments, industrial internet platforms, and enterprises cannot ignore long-term development in favor of their short-term interests. Therefore, it is essential for local governments, as the leading player in the construction of the industrial internet, to establish a suitable coordination mechanism and actively enhance the degree of cooperation among the three major players. Specifically, local governments can strengthen legal regulation to reduce dangers, such as information leakage. Industrial internet platforms can strengthen technological innovation, reduce channels for network hacking through technical improvements, and upgrade enterprise data service systems. Enterprises are actively enrolled in industrial internet platforms to share accurate and valid information and access industrial internet platform information services to facilitate their digital transformation. However, some enterprises may still have a solid profit-oriented mindset [68]. Therefore, local governments need to regulate through legal means and broaden the channels for enterprises and industrial internet platforms to make their voices heard. An information-sharing and regulation system always aims to maximize the overall benefit and promote industrial primary data’s all-round and continuous development.

Second, our results show that the magnitude of the effect of the local government cost subsidy coefficient on the optimal benefits of the system is larger and the absolute value of the optimal benefits is larger when the cost subsidy coefficients are $1/2<{\mu }_P<1$ and $1/2<{\mu }_E<1$, conditional on $1/3<{\lambda }_1<1$, as used in the cost-sharing contract decision. Conversely, the opposite is true. This result gives local governments ideas on how to give cost subsidies to enterprises and industrial internet platforms. In China, government cost subsidies can be used as a compelling incentive to stimulate the growth of industrial internet platforms and enterprises to a certain extent. Unfortunately, a more significant cost subsidy coefficient is not better, and the influence of the corresponding parameters still needs to be considered. Therefore, under the cost-sharing contract decision, in order to better realize the growth of the benefits of the regulatory system, local governments should dynamically adjust the subsidy coefficients according to the development needs of the information-sharing regulatory system. Specifically, when the development trend of the industrial internet platform information-sharing and supervision system is good, local governments can appropriately reduce the cost subsidy coefficient, which can be less than 1/2. In contrast, when the reputation of the industrial internet platform information-sharing and supervision system is damaged, and the overall situation of the information-sharing and supervision system is terrible, the local government’s subsidy coefficient can be greater than 1/2. In addition, to guarantee compliance with the use of cost subsidies, supervision and reporting channels need to be provided for enterprises and industrial internet platforms to give full play to the marginal benefits of cost subsidies.

Finally, our study shows that, in all three scenarios, the optimal benefits of the three main entities and the information-sharing and supervision system of the industrial internet platforms increase as the parameter $\gamma , \epsilon , \alpha$ increases. As the parameter $k, \rho , \beta$ increases, the optimal effectiveness of the three main entities and the information-sharing regulatory system of the industrial internet platforms decreases. The costs should not be ignored for the information-sharing and supervision system while improving the degree of information-sharing and supervision efforts to promote the development of the system. The overall benefits of the regulatory system will be low if the benefits are only enhanced while the costs are ignored [5]. Therefore, an information-sharing regulatory system must continue to have an optimal level of effort from all three, thereby enhancing the reputation of the information-sharing regulatory system. However, it also needs to reduce related costs. Specifically, local governments need to shape an excellent regulatory environment through legal means. Industrial internet platforms provide a secure information-sharing platform. Enterprises use data-sharing platforms to collect data intelligently and promote the effective use of data to enhance their self-transformational capabilities. In addition, appropriately reducing the regulatory costs of the three is a boost to the system’s effectiveness. If the costs are too high, local governments can adopt measures, such as fines, to restrain them.

7.2. Limitations and Future Research Directions

There are a few limitations to this study. Firstly, when constructing the regulatory system, this study only considers local governments, industrial internet platforms, and enterprises, ignoring other influential subjects. Future research can include more subjects, such as the banking industry and media, to form a more inclusive and complete regulatory system for industrial internet platforms.

Secondly, under the cost-sharing contract decision, this study only considers the game situation under the premise of $1/3<{\lambda }_1<1$, which cannot fully reflect the development of a regulatory system. Future research can further consider the premise where $0<{\lambda }_1<1/3$, to further improve the completeness and robustness of this study.

Finally, in exploring local government incentives, this study considers the cost-subsidy approach. Incentives can also include revenue sharing and tax incentives, which future research could include to analyze their impact on the regulatory system.

8. Conclusions

To explore the dynamic optimization of information-sharing regulatory systems consisting of local governments, industrial internet platforms, and enterprises, this study uses a differentiated game approach. We construct three scenarios to solve the problems and conduct numerical simulations. The results demonstrate that, firstly, the centralized decision is the most favorable to the development of the information-sharing regulatory system, followed by the cost-sharing contract and decentralized decisions. Secondly, under certain conditions, when the local government subsidy coefficient in the cost-sharing contract decision is greater than the critical value of 1/2, the increase in this coefficient has a more obvious effect on the improvement of the economic efficiency of the regulatory system. Finally, an increase in the regulatory effort of the three entities can effectively enhance the reputation of the information-sharing regulatory system. This would further improve the social welfare effect and promote the digital transformation of enterprises to achieve value sharing.