A Tripartite Evolutionary Game Analysis of Enterprise Data Sharing Under Government Regulations

Abstract

The tripartite evolutionary game model focuses on the strategic choices and evolutionary laws of three parties in dynamic interaction. By constructing a tripartite evolutionary game model involving the government, Enterprise A, and Enterprise B, this paper analyzes the strategic choices of enterprise data sharing from the perspective of government regulation and uses the simulation method to assign and simulate the parameters of the model. Furthermore, the evolutionary trends of the behavioral strategies of the three parties are analyzed under the changes of factors such as the government’s regulation costs, government penalties, government rewards, and the compensation fees for enterprises to obtain shared data. The findings indicate that when the benefits obtained by enterprises from data sharing are relatively high, and the compensation fees incurred by enterprises to obtain the other party’s data are sufficient to compensate for the losses caused by the other party’s data sharing, enterprises will tend to choose “data-sharing”. At this time, the combined strategy of “no-regulation, data-sharing, data-sharing” reaches an equilibrium point. In this combination strategy, the initial willingness of the government and enterprises will not affect the final evolutionary result. The government’s regulation costs, government penalties, and government rewards will not affect the final behavioral strategy evolutionary result for the government and enterprises. However, the compensation fees for enterprises to obtain shared data will affect the final evolutionary direction of the three parties. When the compensation fees for enterprises to obtain shared data are low, enterprises are more inclined toward “no-data-sharing”.

1. Introduction

With the rapid development of the digital economy, the scale of data has been burgeoning, data types have become increasingly diversified, and data sources have grown more extensive. They span a wide array of fields, including but not limited to personal information, business secrets, scientific research, and the public service sectors. The manner in which people harness data has witnessed revolutionary changes, and the economic worth of data has become ever more prominent. Data are characterized by reusability, non-competitiveness, and the ability to be replicated at low cost. The utilization of data by different entities does not depreciate its value, rather, diverse forms of utilization by different entities can optimize and maximize the value inherent in the data. This implies that only through data sharing among diverse data entities can the latent value within the data be fully unleashed [1]. Enterprise data sharing pertains to the process of disseminating data resources among different departments, business systems, or organizations. In the era of big data, data-sharing activities serve as the foundation of data valorization. On the one hand, data sharing constitutes one of the preliminary processes in the data elements market. It facilitates the influx of copious amounts of data into the market, bolsters the data supply capacity, and curtails data collection expenditures. On the other hand, data sharing represents a crucial avenue for data utilization. Within the sharing context, data can undergo secondary development and repeated exploitation, thereby optimizing the release of data dividends to the fullest extent.

With the accelerating pace of digitalization, enterprise data sharing is still in the exploratory stage. Although internet companies have mastered massive amounts of data, the full potential of enterprise data value has yet to be realized. A research investigation indicated that most companies are reluctant to participate in data sharing, even if there are companies willing to participate, they will only share a small part of enterprise data [2]. This indicates that platform companies tend to retain data within the industrial organization system, shunning transactions with third-party companies outside the industrial organization. Therefore, promoting data sharing among enterprises is fraught with difficulties, given that enterprises regard data as important assets and prefer to monopolize data rather than share them externally. Government regulation, as a pivotal component of the modern national governance system, guides microeconomic activities and their behaviors. Regulatory agencies establish closer interactive relationships with platform companies, using their advantages to compensate for regulatory loopholes and eliminate gray areas in regulatory behavior, so as to achieve standardized operation of platform companies and enhance regulatory efficiency. Against this backdrop, it becomes imperative to explore how enterprises can achieve data sharing under government regulation.

In the context of enterprise data sharing, there are multiple stakeholders involved, including the government and data-sharing enterprises, and the relationships between them are intricate. Compared with traditional single or two-party game models, the tripartite evolutionary game model can comprehensively incorporate these stakeholders into the analysis framework. It fully takes into account the decision-making behaviors of all parties and their mutual influences. By constructing a game matrix and analyzing the game process, it delves deep into the logic behind these complex interest relationships, reveals the optimal strategy choices of all parties in different situations and the possible equilibrium states, and provides a more comprehensive perspective for understanding and solving enterprise data-sharing problems. In addition, the decision of enterprise data sharing is not a static one-time behavior, but a dynamic and constantly evolving process. The tripartite evolutionary game model can well depict the strategic adjustments and interactions of all parties at different stages, reflecting how each party adjusts its own strategy according to the behaviors and benefits of the other parties over time, and more realistically demonstrating the dynamic nature of data sharing problems. The existing literature may mostly study enterprise data sharing from the perspective of a single entity or the relationship between two parties. We adopt a tripartite evolutionary game model from the perspective of the interaction between the three parties, filling the gap in research from a more comprehensive perspective and providing new ideas and methods for this field. At the same time, the analysis results based on the tripartite evolutionary game model can provide more accurate theoretical support for the government to adjust regulatory policies, and guide enterprises to make decisions that are more conducive to data sharing and industry development.

Based on the above, with the aim of probing into the specific approaches for enterprises to actualize data sharing from the perspective of government regulation, this paper integrates government regulation into an evolutionary game model of enterprise data sharing. By assigning values to the model parameters in light of China’s current policies and enterprise circumstances, and carrying out simulations, this paper focuses on investigating the impact of different factor alterations on the evolutionary process under multiple scenarios, as well as the migratory trajectory of evolutionary stable points. It analyzes the influence of changes in government regulation costs, government penalties, government rewards, and the compensation fees for enterprises obtaining shared data on the evolution of enterprises and government behavior strategies. The research results provide certain references for government macro-control to promote enterprises to achieve data sharing and hold significant theoretical and practical implications for expediting the swift development of the digital economy and harnessing the full potential of data value.

The remaining sections of this study are organized as follows. Section 2 reviews the literature review. In Section 3, a tripartite evolutionary game model is established. Section 4 analyzes the stability and system equilibrium points of the tripartite evolutionary game model. Section 5 employs a system simulation model to test evolutionary stability strategies and describes the impact of main parameters on system stability and convergence trends. Finally, Section 6 presents the main conclusions and policy implications.

2. Literature Review

2.1. Enterprise Data Sharing

Enterprise data sharing refers to the process of opening, exchanging, and integrating data resources owned by different departments within or between enterprises based on common interests or business needs. Existing studies have carried out in-depth discussions on the impact of data sharing. Overall, data sharing can generate the following benefits: (1) Economic benefits. Data sharing has the potential to yield mutually beneficial outcomes for multiple parties involved. In this process, data providers stand to gain direct economic returns via such transactions, while buyers can leverage this data to bolster their business capabilities and gain a competitive edge [3]. Enterprise data sharing acts as a catalyst for the transformation of research findings into products and services [4], it facilitates the rapid entry of these results into the market, enabling them to gain a more robust competitive edge [5]. Shared data can fully unleash the value of data, serve as a guiding force for the rational allocation of industrial resources [6], optimize the layout of the energy industry [7], enhance the economic benefits of the entire industry [8], and propel sustainable economic development [9]. (2) Political and social benefits. By sharing credit and transaction data of enterprises, government departments can better maintain market order and create a fair competitive market environment. Data sharing is beneficial for enhancing government credibility, improving government governance, increasing transparency in government funding for scientific research [10], and improving government administrative efficiency and sensitivity [11]. Shared data on transportation, environment, public safety, etc., can directly improve residents’ quality of life and promote the quality of public services [12]. Open data-sharing by the government is beneficial for the public to understand the country’s scientific research [13], provide publicly funded research results to the public [14], promote public participation in scientific research, and improve public participation and satisfaction [10]. (3) Technical and operational benefits. The process of data sharing effectively prevents the duplication of work, significantly enhances open scientific research, and elevates the quality of research results [15]. Date sharing enables improved scientific transparency and accuracy, and generates higher scientific research impact [16]. Meanwhile, data sharing is conducive to encouraging cooperation and enhancing collaboration across disciplines, departments, and institutions [5], so as to maximize the research potential of new digital technologies and networks.

Enterprise data sharing confronts numerous obstacles that have been thoroughly explored in existing research. The obstacles that data sharing encounters mainly include the following aspects: (1) Data security and privacy concerns. The release of data may result in information disclosure [17]. Enterprises are concerned that during the data-sharing process, due to technical loopholes, poor management, or improper operation by partners, the enterprise’s internal core data, such as customer lists, trade secrets, financial data, etc., could be leaked, which may bring huge economic losses and reputation damage to the enterprise [18]. (2) Data ownership and benefit distribution. In the process of enterprise business operation, data generation often involves multiple links and subjects, which makes it difficult to clearly define the ownership of data. At the same time, differences may occur due to the difficulty in determining a reasonable benefit distribution scheme [19]. As a result, cooperation may fail or sustainable sharing may be difficult to achieve. (3) The data format and standard are not unified. Enterprises frequently adopt diverse formats and standards in data collection, storage, and presentation, which makes it challenging to directly integrate and utilize shared data [20]. (4) Corporate culture and organizational structure. Some enterprises regard data as their private property, lacking the cultural atmosphere and cooperation consciousness of data sharing, and are unwilling to share with other departments [21]. Each department has relatively high autonomy in data management and decision-making, and there is a lack of a unified coordination and management mechanism, which is not conducive to the promotion of data sharing [22]. (5) Limitations of digital technology and sharing costs. Enterprises may encounter compatibility problems in terms of technical platforms, database management systems, and data interfaces when sharing data [23]. Additionally, constructing a safe and efficient data-sharing platform requires a lot of capital and technical resources. For some small and medium-sized enterprises, they may not be able to afford these costs, thus restricting the development of data sharing [24].

2.2. Government Regulation and Enterprise Data Sharing

In the digital economy era, data have emerged as a crucial resource for corporate development. Nevertheless, data sharing is far from straightforward, entangling a host of issues, including data privacy, security, and rights. Enterprise data sharing confronts numerous barriers and surmounting them necessitates government regulation as a catalyst. Through the formulation and implementation of relevant laws and regulations, government regulation can offer explicit norms and guidance for enterprise data sharing. Policies and regulations play a pivotal role in the open sharing of scientific data. They offer targeted policy-oriented guidance, guaranteeing seamless access, wide dissemination, accurate replication, and reliable verification of scientific data [25]. This not only prevents the erosion of trust among stakeholders like governments, organizations, and institutions during potential data-sharing conflicts [26] but also effectively regulates and restricts the citation of scientific data, thereby fostering a favorable environment for scientific data citation [27]. The government organizes the development of unified data standards and supervises data quality, which can improve the efficiency and reliability of data sharing and guide enterprises to actively participate in data sharing [28,29]. Borycz et al. [30] based on the technology acceptance model and multi-factor analysis method, found that a trustworthy and open research environment promotes data-sharing behavior. Loenen et al. [31] analyzed the current implementation status of data sharing in the European Union and found that data regulation and review policies are key to protecting personal data security. Nugroho et al. [32] compared the open data policies of multiple countries using a cross-country comparative framework through a literature review and case studies, and pointed out that open data policies can guide and stimulate the utilization of public data. Tenopir et al. [33] and Kim and Zhang [34] posited that the provision of national policy support or technical support, such as data services, tools, and data repositories, would significantly enhance enterprises’ willingness to share scientific data. However, Fecher et al. [35] held the view that even when there is support from national policies and data management technologies, the number of researchers willing to provide scientific data remains a very small minority, and proposes that there is a need to further implement incentive policies to boost the willingness to share. Sun and Zhao [36] used the relatively novel qualitative analysis method of Meta ethnography to believe that subjective norms, policies, and incentive mechanisms for data sharing are key to scientific data sharing. Berberi and Roche [37] pointed out that an efficient and secure data-sharing environment requires support from national-level data management policies and relevant laws and regulations, and effective mechanisms to regulate the compliance of relevant parties with data-sharing policies.

2.3. Evolutionary Game Theory and Its Applications in the Field of Data Sharing

Evolutionary game theory can vividly mirror the dynamic process in which subject strategies are continuously adjusted over time. Within the framework of evolutionary game theory, we can conduct in-depth research on how various factors influence the strategic choices of each subject and how these strategies evolve as time progresses. Data sharing encompasses multiple stakeholders, and the behavior strategies of each subject are shaped by a multitude of factors. Evolutionary game theory offers a potent analytical tool for research in the data-sharing domain and has been extensively applied in data open-sharing mechanisms. Wang et al. [38] established a two-party evolutionary game model based on incomplete information dynamic game theory, analyzed the game problems between the government and the public in the open sharing of government data, and pointed out that government departments should actively open up and share government data. Xu et al. [39] constructed a tripartite evolutionary game model involving data providers, data users, and data management organizations within the context of open data sharing. Through in-depth exploration, they identified the critical factors impeding government data sharing. In response, they put forward a multi-agent collaborative “quality-trust transformation” strategy, aiming to break through existing bottlenecks and promote more efficient and high-quality government data sharing. Wei et al. [40] analyzed the government’s supervision behavior and enterprises’ sharing behavior by constructing an evolutionary game model of data sharing involving both enterprises and government participation, and discovered that the influence of government regulation on enterprises’ data-sharing strategies is relatively limited. Xiao et al. [41], based on the evolutionary game model, studied the behavioral patterns of online users and the government in data sharing and disclosure of COVID-19 prevention and control information, and analyzed the reasons for the contradiction between the privacy risks faced by online users when sharing information and the COVID-19 prevention and control work, and proposed solutions to this problem. Deng et al. [42] conducted a study on government data sharing by constructing a tripartite evolutionary game model involving the government, regulatory agencies, and technology-supporting enterprises, and proposed that increasing the benefits of active sharing and strengthening the supervision of regulatory agencies would contribute to the government’s active sharing of data. Xu et al. [43] constructed a two-party evolutionary game model to analyze the dynamic relationship between manufacturing Enterprise A and manufacturing Enterprise B; the results showed that, in the game between the two parties, manufacturing enterprises tend to adopt the strategy of sharing manufacturing resources. Feng and Pei [44] constructed an evolutionary game model for the data-sharing behaviors between platform providers and the government to study their strategic choices during the game; they found that when there is a disparity in data conversion capabilities between platform providers and the government, the choice of data-sharing behavior will be significantly promoted only when the government’s data conversion ability surpasses that of the platform providers. Sun and Xie [45] constructed a tripartite evolutionary game model involving the government and the upstream and downstream subgroups of the supply-chain network. It was found that increasing incentives for data sharing and the intensity of punishment can enhance the willingness of the upstream and downstream subgroups to share data, while reducing the marginal cost of data sharing and speculative gains can effectively curb opportunistic sharing behavior among the upstream and downstream subgroups.

In summary, the relevant literature on enterprise data sharing has important reference and guidance significance, but there are still some shortcomings. Firstly, research on enterprise data sharing from the perspective of government regulation mainly adopts static analysis, which cannot reflect the changes in the interaction between entities over a period of time. Secondly, existing research on the application of evolutionary game theory in enterprise data sharing mostly adopts single or bilateral subject analysis, and most studies only focus on the simple application of core concepts, lacking in-depth analysis of the dynamic evolution of concepts such as evolutionary stability strategies in complex data sharing scenarios. Finally, although the three-party evolutionary game model has been used to analyze the strategic interaction between government and enterprises, there are idealization issues with the model assumptions, such as the assumption of complete rationality of the subject not matching reality, insufficient basis for parameter setting, and insufficient consideration of dynamic changes in the external environment, resulting in limited explanatory power of the model in reality. This article introduces the use of a three-party dynamic evolutionary game theory to analyze the data-sharing behavior of enterprises from the perspective of government regulation. The government, Enterprise A, and Enterprise B are included in the same analysis framework, breaking through the limitations of traditional research on single or bilateral subject analysis. It can present the adjustment process of the three-party subject strategies over time and in response to environmental changes, compensating for the shortcomings of static analysis. At the same time, taking into account the interaction of multiple factors, such as government regulatory costs, benefits and losses of enterprise data sharing, and compensation costs for obtaining shared data, a more comprehensive understanding of the inherent mechanism of data sharing can be revealed. This will offer a more precise foundation for policy-making and corporate decision-making.

3. Model Assumptions and Tripartite Evolutionary Game Model Construction

3.1. Model Assumptions

3.1.1. Subjects of the Game

The process of enterprise data sharing under government regulation mainly includes three subjects: the government, Enterprise A, and Enterprise B. In the whole system, the government leads data legislation, legislates for data sharing, and is responsible for the implementation of relevant policies. Meanwhile, the government is also the direct beneficiary of policy implementation, which prompts it to take a more proactive stance in data element governance. Enterprise A and Enterprise B are mainly engaged in the collection, processing, and utilization of data for value creation, and decide whether to share data. Without considering other external factors, it is assumed that the government, Enterprise A, and Enterprise B are the three parties involved in enterprise data sharing. All three parties are bounded rationality, and there is information asymmetry among them. Each party’s behavior strategy will be influenced by the behavior strategies of the other two parties.

3.1.2. Behavioral Strategies of Subjects

The government’s behavioral strategy set is S₁ = {G₁ regulation, G₂ no-regulation}. Regulation means that the government carries out mandatory promotion of each enterprise’s data sharing, incorporates each enterprise’s data sharing into the top-level design of national data factor governance, formulates scientific strategic planning and policy guidelines, and strictly supervises the implementation of policies. No-regulation means that the government encourages the decision-making and deployment of data sharing, refrains from formulating strict rules and regulations, and simplifies administrative processes while delegating power. The behavioral strategy set of Enterprise A and Enterprise B is S₂ = {A₁ data-sharing, A₂ no-data-sharing}, S₃ = {B₁ data-sharing, B₂ no-data-sharing}. Data-sharing refers to sharing their own data with other enterprises, which allows users in different places to be able to read other enterprise’s data and carry out a variety of operational calculations and analyses. No-data-sharing means enterprises retain their own data resources and do not share their own data element resources and information with other enterprises.

3.1.3. Probability of Behavioral Strategies

Suppose that in the preliminary stage of the game among the government, Enterprise A, and Enterprise B, the probability that the government chooses regulation is p₁, and the probability that it does not is 1 − p₁. The probability that Enterprise A chooses data-sharing is p₂, and the probability that it does not data-share is 1 − p₂. The probability that Enterprise B chooses data-sharing is p₃, and the probability that it does not data-share is 1 − p₃. p₁, p₂, p₃ ϵ [0, 1].

3.1.4. Game Diagram and Parameter Setting

When the government adopts the “regulation” strategy, it incurs direct costs in terms of manpower, material resources, capital, and time for top-level design, data-sharing standardization, and digital infrastructure construction. It also bears indirect costs for verifying and monitoring the implementation of data-sharing strategies by enterprises. Under the “regulation” strategy, the government has the power to impose penalties or offer rewards regarding enterprises’ implementation of the “data-sharing” strategy. Enterprises that respond positively to the “data-sharing” policy will receive rewards in the form of incentives, while those that do not will face penalties. Accordingly, when both enterprises share data elements, it brings certain macro benefits to the government. When one enterprise shares data elements and the other does not, the government may still obtain certain macro benefits, although these benefits are smaller than those when both enterprises share data. When both enterprises choose the “no-data-sharing” strategy, the government will experience macro-governance losses.

In this paper, we assume that Enterprise A and Enterprise B are perfectly symmetric, with identical costs and benefits when choosing a “data-sharing” strategy. When the enterprise chooses the “data-sharing” strategy, it may suffer losses or adverse effects, namely data openness cost. Data sharing requires organizing, cleaning, and standardizing data formats. Hiring professional talents, such as specialized data managers and data compliance officers, to manage and promote data-sharing work demands significant investments in human resources, material resources, and time. When the enterprise chooses the “no-data-sharing” strategy, the specific advantages it acquires are known as data retention benefits. Data represents a core asset for enterprises and is fundamental to their competitive standing. By withholding data, enterprises can preserve the uniqueness of this information and thereby uphold their competitive position in the market.

When the enterprise shares its own data and the other party also shares data, the positive effects and benefits brought by this mutually beneficial data exchange can be called data cooperation benefits. By combining data from different sources through data sharing, new business opportunities can be discovered, which can bring advantages to both parties involved.

When the enterprise shares data but the other party refrains from sharing, the potential adverse effects can be referred to as data exchange imbalance loss. In such a situation, the enterprise that shares data may find that the other party uses the provided data to refine their strategies, while the sharing enterprise fails to obtain equivalent information to boost its competitiveness.

When the enterprise does not share data, but the other party shares data, it will bring certain benefits to the enterprise, which can be called data acquisition benefits. Enterprises that obtain more data can make wiser decisions, develop more competitive products or services, and gain a competitive advantage in the market.

When the enterprise does not engage in data sharing and the other party follows suit, the potential adverse effects or losses that may result from both parties maintaining a closed data state can be referred to as data closure loss. Due to the absence of data sharing, each party may make decisions based on limited information, which results in a loss for both parties.

The tripartite relationship between the government, Enterprise A, and Enterprise B is shown in Figure 1. The basic principle of the tripartite evolutionary game is grounded in the bounded–rationality assumption, studying the strategy selection and evolution of three participants in dynamic interaction. Its core idea is that participants approach a stable equilibrium through continuous strategy adjustment. The tripartite evolutionary game framework has four key components: (1) Participants: As shown in Figure 1, they are the government, Enterprise A, and Enterprise B. (2) Strategies: Options for each entity, such as government regulation and enterprises’ decisions on data sharing. (3) Interaction: It involves government–enterprise relations (regulation and enterprises’ responses), and inter-enterprise relations (data sharing, compensation, and strategy adjustment). (4) Payoff functions: They describe the benefits or costs of different strategy combinations, e.g., the cost of government regulation, as well as the benefits and compensation paid by enterprises for obtaining shared data. In the context of enterprise data sharing, the behaviors and decisions of the government, Enterprise A, and Enterprise B are mutually influential. The tripartite evolutionary game framework represents a significant advancement as it can seamlessly incorporate all three entities into a unified analysis system. Compared to models that only consider two parties, it is closer to the real market and policy environment. This framework can describe the dynamic adjustment and evolution of strategies among three parties in a long-term process. Each party will continuously adjust their strategies based on their own interests, observations, and expectations of the behavior of other parties. Through evolutionary game analysis, the trend and laws of this strategy change can be clearly demonstrated.

Nevertheless, this model does have its inherent limitations. In order to make the model analyzable, it often requires simplifying assumptions about the behavior and decisions of the three parties, which may deviate from the complex decision-making processes and behavior patterns of all parties in reality. Simultaneously, the model encompasses a multitude of parameters. Ascertaining the precise values of these parameters is often a challenging task. Given that different parameter values can result in substantial variances in the game outcomes, and obtaining these parameters accurately in practical applications proves to be quite difficult, the reliability and stability of the model are thereby affected. Against this backdrop, this article endeavors to assign values to various parameters grounded in real-world scenarios. By gathering industry reports and corporate financial data, and referring to relevant government regulatory documents, the intention is to make the parameters more reflective of real-life situations, thus enhancing the model’s practicality and accuracy.

Based on the above assumptions, the relevant parameter settings for the three subjects—government, Enterprise A, and Enterprise B—are detailed in

Table 1. Symbol setting and meaning of related parameters.

Subjects	Parameter	Hidden Meaning
Government	CG1	The cost to the government of choosing a regulation strategy
	PG1	Penalties for enterprises not sharing data during government regulation
	RG1	Incentives for enterprises to respond positively to data sharing during government regulation
	BG1	Macro benefits to the government when both enterprises engage in data sharing
	BG2	Macro benefits to the government when one enterprise shares data and the other does not
	LG1	Macro-governance losses suffered by the government when neither enterprise engages in data sharing
Enterprise	CE1	Data openness cost caused by enterprises choosing a data-sharing strategy
	BE1	Data retention benefits obtained by enterprises choosing no-data-sharing strategies
	CE2	Compensation fees for the cost paid by an enterprise to obtain shared data from another enterprise
	RE1	Data cooperation benefits from data sharing by another enterprise when this enterprise shares data
	LE1	Data exchange imbalance loss suffered by one enterprise when it shares data, while the other enterprise does not share data
	RE2	Data acquisition benefits from data sharing by another enterprise when this enterprise does not share data
	LE2	Data closure loss suffered by one enterprise when it does not share data, and the other enterprise also does not share data

.

3.2. Tripartite Evolutionary Game Model Construction

Based on the behavioral strategies of the government, Enterprise A, and Enterprise B, it is evident that these three subjects can produce eight distinct game combinations, as shown in

Table 2. Game behavior strategy combination of three parties.

Behavior Strategy	Governments	Enterprise A	Enterprise B
(G1, A1, B1)	Regulation	Data-sharing	Data-sharing
(G1, A1, B2)	Regulation	Data-sharing	No-data-sharing
(G1, A2, B1)	Regulation	No-data-sharing	Data-sharing
(G1, A2, B2)	Regulation	No-data-sharing	No-data-sharing
(G2, A1, B1)	No-regulation	Data-sharing	Data-sharing
(G2, A1, B2)	No-regulation	Data-sharing	No-data-sharing
(G2, A2, B1)	No-regulation	No-data-sharing	Data-sharing
(G2, A2, B2)	No-regulation	No-data-sharing	No-data-sharing

. This paper will take the e-commerce industry as an example to analyze these eight combination strategies. Assuming that in an e-commerce ecosystem, government, Enterprise A (a large e-commerce platform), and Enterprise B (a technology enterprise specializing in data analysis) form a tripartite game relationship.

(G₁, A₁, B₁): The government opts for the “regulation” strategy, Enterprise A selects the “data-sharing” strategy, and Enterprise B chooses the “data-sharing” strategy. The government has formulated strict data regulations to monitor data sharing. As a large e-commerce platform, Enterprise A shares data with Enterprise B, which excels in data analysis, in order to explore commercial value. This is beneficial for both parties.

(G₁, A₁, B₂): The government selects the “regulation” strategy, Enterprise A selects the “data-sharing” strategy, and Enterprise B chooses the “no-data-sharing” strategy. The government continues to strictly regulate the data field. Enterprise A hopes to collaborate with Enterprise B to develop precision marketing services through data sharing, but Enterprise B refuses to share data due to concerns about data security risks.

(G₁, A₂, B₁): The government chooses the “regulation” strategy, Enterprise A opts for the “no-data-sharing” strategy, and Enterprise B chooses the “data-sharing” strategy. The government strictly regulates to ensure data sharing. Enterprise A, due to concerns about data leakage affecting its competitiveness, refuses to share data even if Enterprise B is willing to share and provide cooperation solutions.

(G₁, A₂, B₂): The government chooses the “regulation” strategy, Enterprise A opts for the “no-data-sharing” strategy, and Enterprise B chooses the “no-data-sharing” strategy. The government vigorously regulates the data market. Both Enterprise A and Enterprise B do not share data with each other due to considerations of data security, business competition, and other factors.

(G₂, A₁, B₁): The government selects the “no-regulation” strategy, Enterprise A chooses the “data-sharing” strategy, and Enterprise B chooses the “data-sharing” strategy. The government has not strictly controlled e-commerce data due to limited manpower and energy, and Enterprise A and Enterprise B quickly reached a data-sharing cooperation in pursuit of commercial interests. Both parties quickly integrate data and develop new e-commerce services.

(G₂, A₁, B₂): The government selects the “no-regulation” strategy, Enterprise A chooses the “data-sharing” strategy, and Enterprise B chooses the “no-data-sharing” strategy. The regulatory environment is relaxed, and Enterprise A actively shares data to obtain more business opportunities. However, Enterprise B is cautious about data sharing, concerned about cooperation risks and data security, and refuses to share.

(G₂, A₂, B₁): The government chooses the “no-regulation” strategy, Enterprise A opts for the “no-data-sharing” strategy, and Enterprise B selects the “data-sharing” strategy. Government regulation is weak, Enterprise B hopes to expand its business via data sharing. Nevertheless, Enterprise A is worried about data leakage and the loss of its competitive advantage, so it is reluctant to share data.

(G₂, A₂, B₂): The government chooses the “no-regulation” strategy, Enterprise A opts for the “no-data-sharing” strategy, and Enterprise B selects the no-data-sharing” strategy. The government regulation is loose, Enterprise A has accumulated a massive amount of user consumption data but is concerned that sharing it may leak trade secrets, so it refuses to share. Enterprise B excels in data analysis; its own data also holds unique value, and it is afraid of losing its advantage after sharing, so it does not share.

Table 3. Payment benefit matrix for the behavioral strategies combination of the three subjects.

Strategic Combination	Governments	Enterprise A	Enterprise B
(G1, A1, B1)	BG1 − 2RG1 − CG1	RE1 + RG1 − CE1	RE1 + RG1 − CE1
(G1, A1, B2)	BG2 + PG1 − RG1 − CG1	RG1 + CE2 − CE1 − LE1	BE1 + RE2 − CE2 − PG1
(G1, A2, B1)	BG2 + PG1 − RG1 − CG1	BE1 + RE2 − CE2 − PG1	RG1 + CE2 − CE1 − LE1
(G1, A2, B2)	2PG1 − LG1 − CG1	BE1 − LE2 − PG1	BE1 − LE2 − PG1
(G2, A1, B1)	BG1	RE1 − CE1	RE1 − CE1
(G2, A1, B2)	BG2	CE2 − LE1 − CE1	BE1 + RE2 − CE2
(G2, A2, B1)	BG2	BE1 + RE2 − CE2	CE2 − LE1 − CE1
(G2, A2, B2)	−LG1	BE1 − LE2	BE1 − LE2

presents the payment return matrix for the behavioral strategies combination of the three subjects.

To better analyze the adjustment process of the behavioral strategies of the three parties, this study aims to construct the replicated dynamic equations of the behavioral strategies of each subject. Assuming that the expected return of the government’s “regulation” strategy is V₁₁, the return of choosing the “no-regulation” strategy is V₁₂, and the average expected return is V₁, then:

$$\begin{array}{c}{\mathrm{V}}_{11}=({\mathrm{BG}}_1-2{\mathrm{RG}}_1-{\mathrm{CG}}_1)\times {\mathrm{p}}_2\times {\mathrm{p}}_3+({\mathrm{BG}}_2+{\mathrm{PG}}_1-{\mathrm{RG}}_1-{\mathrm{CG}}_1)\times {\mathrm{p}}_2\times (1-{\mathrm{p}}_3)+({\mathrm{BG}}_2+{\mathrm{PG}}_1-{\mathrm{RG}}_1-{\mathrm{CG}}_1)\times (1-{\mathrm{p}}_2)\times {\mathrm{p}}_3\\ \hspace{1em}\hspace{1em}+(2{\mathrm{PG}}_1-{\mathrm{LG}}_1-{\mathrm{CG}}_1)\times (1-{\mathrm{p}}_2)\times (1-{\mathrm{p}}_3)\end{array}$$

(1)

$${\mathrm{V}}_{12}={\mathrm{BG}}_1\times {\mathrm{p}}_2\times {\mathrm{p}}_3+{\mathrm{BG}}_2\times {\mathrm{p}}_2\times (1-{\mathrm{p}}_3)+{\mathrm{BG}}_2\times (1-{\mathrm{p}}_2)\times {\mathrm{p}}_3+(-{\mathrm{LG}}_1)\times (1-{\mathrm{p}}_2)\times (1-{\mathrm{p}}_3)$$

(2)

$${\mathrm{V}}_1={\mathrm{p}}_1\times {\mathrm{V}}_{11}+(1-{\mathrm{p}}_1)\times {\mathrm{V}}_{12}$$

(3)

Therefore, the replicator dynamic equation for the government behavioral strategy is:

$$\begin{array}{c}\mathrm{F}({\mathrm{p}}_1)={\mathrm{dp}}_1/\mathrm{dt}={\mathrm{p}}_1\times ({\mathrm{V}}_{11}-{\mathrm{V}}_1)\\ \hspace{1em}\hspace{1em} ={\mathrm{p}}_1\times ({\mathrm{p}}_1-1)\times ({\mathrm{CG}}_1-2{\mathrm{PG}}_1+{\mathrm{PG}}_1\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_3+{\mathrm{RG}}_1\times {\mathrm{p}}_2+{\mathrm{RG}}_1\times {\mathrm{p}}_3)\end{array}$$

(4)

Similarly, assume that Enterprise A chooses the “data-sharing” strategy with expected return V₂₁, chooses the “no-data-sharing” strategy with expected return V₂₂, and has an average expected return V₂, then:

$$\begin{array}{c}{\mathrm{V}}_{21}=({\mathrm{RE}}_1+{\mathrm{RG}}_1-{\mathrm{CE}}_1)\times {\mathrm{p}}_1\times {\mathrm{p}}_3+({\mathrm{RG}}_1+{\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{LE}}_1)\times {\mathrm{p}}_1\times (1-{\mathrm{p}}_3)+({\mathrm{RE}}_1-{\mathrm{CE}}_1)\times (1-{\mathrm{p}}_1)\times {\mathrm{p}}_3\\ \hspace{1em}\hspace{1em}+({\mathrm{CE}}_2-{\mathrm{LE}}_1-{\mathrm{CE}}_1)\times (1-{\mathrm{p}}_1)\times (1-{\mathrm{p}}_3)\end{array}$$

(5)

$$\begin{array}{c}{\mathrm{V}}_{22}=({\mathrm{BE}}_1+{\mathrm{RE}}_2-{\mathrm{CE}}_2-{\mathrm{PG}}_1)\times {\mathrm{p}}_1\times {\mathrm{p}}_3+({\mathrm{BE}}_1-{\mathrm{LE}}_2+{\mathrm{PG}}_1)\times {\mathrm{p}}_1\times (1-{\mathrm{p}}_3)+({\mathrm{BE}}_1+{\mathrm{RE}}_2-{\mathrm{CE}}_2)\times (1-{\mathrm{p}}_1)\times {\mathrm{p}}_3\\ \hspace{1em}\hspace{1em}+({\mathrm{BE}}_1-{\mathrm{LE}}_2)\times (1-{\mathrm{p}}_1)\times (1-{\mathrm{p}}_3)\end{array}$$

(6)

$${\mathrm{V}}_2={\mathrm{p}}_2\times {\mathrm{V}}_{21}+(1-{\mathrm{p}}_2)\times {\mathrm{V}}_{22}$$

(7)

Therefore, the replicator dynamic equation for Enterprise A’s behavioral strategy is:

$$\begin{array}{c}\mathrm{F}({\mathrm{p}}_2)={\mathrm{dp}}_2/\mathrm{dt}={\mathrm{p}}_2\times ({\mathrm{V}}_{21}-{\mathrm{V}}_2)\\ \hspace{1em}\hspace{1em}=-{\mathrm{p}}_2\times ({\mathrm{p}}_2-1)\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-{\mathrm{LE}}_1+{\mathrm{LE}}_2+{\mathrm{LE}}_1\times {\mathrm{p}}_3-{\mathrm{LE}}_2\times {\mathrm{p}}_3+{\mathrm{PG}}_1\times {\mathrm{p}}_1+{\mathrm{RG}}_1\times {\mathrm{p}}_1+{\mathrm{RE}}_1\times {\mathrm{p}}_3-{\mathrm{RE}}_2\times {\mathrm{p}}_3)\end{array}$$

(8)

Similarly, Enterprise B’s expected return V₃₁ for choosing the “data-sharing” strategy and V₃₂ for choosing the “no-data-sharing” strategy has an average expected return of V₃, respectively:

$$\begin{array}{c}{\mathrm{V}}_{31}=({\mathrm{RE}}_1+{\mathrm{RG}}_1-{\mathrm{CE}}_1)\times {\mathrm{p}}_1\times {\mathrm{p}}_2+({\mathrm{RG}}_1+{\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{LE}}_1)\times {\mathrm{p}}_1\times (1-{\mathrm{p}}_2)+({\mathrm{RE}}_1-{\mathrm{CE}}_1)\times (1-{\mathrm{p}}_1)\times {\mathrm{p}}_2\\ \hspace{1em}\hspace{1em}+({\mathrm{CE}}_2-{\mathrm{LE}}_1-{\mathrm{CE}}_1)\times (1-{\mathrm{p}}_1)\times (1-{\mathrm{p}}_2)\end{array}$$

(9)

$$\begin{array}{c}{\mathrm{V}}_{32}=({\mathrm{BE}}_1+{\mathrm{RE}}_2-{\mathrm{CE}}_2-{\mathrm{PG}}_1)\times {\mathrm{p}}_1\times {\mathrm{p}}_2+({\mathrm{BE}}_1-{\mathrm{LE}}_2-{\mathrm{PG}}_1)\times {\mathrm{p}}_1\times (1-{\mathrm{p}}_2)+({\mathrm{BE}}_1+{\mathrm{RE}}_2-{\mathrm{CE}}_2)\times (1-{\mathrm{p}}_1)\times {\mathrm{p}}_2\\ \hspace{1em}\hspace{1em}+({\mathrm{BE}}_1-{\mathrm{LE}}_2)\times (1-{\mathrm{p}}_1)\times (1-{\mathrm{p}}_2)\end{array}$$

(10)

$${\mathrm{V}}_3={\mathrm{p}}_3\times {\mathrm{V}}_{31}+(1-{\mathrm{p}}_3)\times {\mathrm{V}}_{32}$$

(11)

Therefore, the replicator dynamic equation for Enterprise B’s behavioral strategy is:

$$\begin{array}{c}\mathrm{F}({\mathrm{p}}_3)={\mathrm{dp}}_3/\mathrm{dt}={\mathrm{p}}_3\times ({\mathrm{V}}_{31}-{\mathrm{V}}_3)\\ \hspace{1em}\hspace{1em}=-{\mathrm{p}}_3\times ({\mathrm{p}}_3-1)\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-{\mathrm{LE}}_1+{\mathrm{LE}}_2+{\mathrm{LE}}_1\times {\mathrm{p}}_2-{\mathrm{LE}}_2\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_1+{\mathrm{RG}}_1\times {\mathrm{p}}_1+{\mathrm{RE}}_1\times {\mathrm{p}}_2-{\mathrm{RE}}_2\times {\mathrm{p}}_2)\end{array}$$

(12)

4. Stability Analysis of Tripartite Evolutionary Game Theory

4.1. The Jacobi Matrix of Replicator Dynamic System

By associating the replicator dynamic equation F(p₁), F(p₂), and F(p₃), the three-dimensional dynamic evolution system between the government, Enterprise A, and Enterprise B can be obtained in the process of enterprise data sharing under government regulation, as shown in Equation (13).

$$\left\{\begin{array}{l}\mathrm{F}({\mathrm{p}}_1)={\mathrm{p}}_1\times ({\mathrm{p}}_1-1)\times ({\mathrm{CG}}_1-2{\mathrm{PG}}_1+{\mathrm{PG}}_1\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_3+{\mathrm{RG}}_1\times {\mathrm{p}}_2+{\mathrm{RG}}_1\times {\mathrm{p}}_3)\\ \mathrm{F}({\mathrm{p}}_2)=-{\mathrm{p}}_2\times ({\mathrm{p}}_2-1)\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-{\mathrm{LE}}_1+{\mathrm{LE}}_2+{\mathrm{LE}}_1\times {\mathrm{p}}_3-{\mathrm{LE}}_2\times {\mathrm{p}}_3+{\mathrm{PG}}_1\times {\mathrm{p}}_1+{\mathrm{RG}}_1\times {\mathrm{p}}_1+{\mathrm{RE}}_1\times {\mathrm{p}}_3-{\mathrm{RE}}_2\times {\mathrm{p}}_3)\\ \mathrm{F}({\mathrm{p}}_3)=-{\mathrm{p}}_3\times ({\mathrm{p}}_3-1)\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-{\mathrm{LE}}_1+{\mathrm{LE}}_2+{\mathrm{LE}}_1\times {\mathrm{p}}_2-{\mathrm{LE}}_2\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_1+{\mathrm{RG}}_1\times {\mathrm{p}}_1+{\mathrm{RE}}_1\times {\mathrm{p}}_2-{\mathrm{RE}}_2\times {\mathrm{p}}_2)\end{array}\right.$$

(13)

By solving the local stability of the Jacobi matrix, the equilibrium solution in the steady state of the evolutionary result can be obtained, with the solution shown in Equation (14). If F(p₁) = F(p₂) = F(p₃), a total of 15 equilibrium points can be calculated for the system. Among them are eight pure equilibrium points, namely E₁ (0, 0, 0), E₂ (1, 0, 0), E₃ (0, 1, 0), E₄ (0, 0, 1), E₅ (1, 1, 0), E₆ (1, 0, 1), E₇ (0, 1, 1), E₈ (1, 1, 1), and the remaining ones are mixed strategy equilibria. According to the aforementioned assumptions p₁, p₂, p₃ ϵ [0, 1], it can be seen that the mixed-strategy equilibrium points are significant only under specific conditions, and do not fall into the category of evolutionarily stable strategies. Therefore, this paper focuses on the stability of the pure-strategy equilibrium points and does not discuss the mixed-strategy equilibrium points further.

$$\left[\begin{array}{ccc}\begin{array}{l}({\mathrm{p}}_1-1)\times ({\mathrm{CG}}_1-2{\mathrm{PG}}_1+{\mathrm{PG}}_1\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_3\\ +{\mathrm{RG}}_1\times {\mathrm{p}}_2+{\mathrm{RG}}_1\times {\mathrm{p}}_3)+{\mathrm{p}}_1\times ({\mathrm{CG}}_1-2{\mathrm{PG}}_1+\\ {\mathrm{PG}}_1\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_3+{\mathrm{RG}}_1\times {\mathrm{p}}_2+{\mathrm{RG}}_1\times {\mathrm{p}}_3)\end{array}& {\mathrm{p}}_1\times ({\mathrm{PG}}_1+{\mathrm{RG}}_1)\times ({\mathrm{p}}_1-1)& {\mathrm{p}}_1\times ({\mathrm{PG}}_1+{\mathrm{RG}}_1)\times ({\mathrm{p}}_1-1)\\ -{\mathrm{p}}_2\times ({\mathrm{PG}}_1+{\mathrm{RG}}_1)\times ({\mathrm{p}}_2-1)& \begin{array}{l}-({\mathrm{p}}_2-1)\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-{\mathrm{LE}}_1+{\mathrm{LE}}_2+\\ {\mathrm{LE}}_1\times {\mathrm{p}}_3-{\mathrm{LE}}_2\times {\mathrm{p}}_3+{\mathrm{PG}}_1\times {\mathrm{p}}_1+{\mathrm{RG}}_1\times {\mathrm{p}}_1+\\ {\mathrm{RE}}_1\times {\mathrm{p}}_3-{\mathrm{RE}}_2\times {\mathrm{p}}_3)-{\mathrm{p}}_2\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-\\ {\mathrm{LE}}_1+{\mathrm{LE}}_2+{\mathrm{LE}}_1\times {\mathrm{p}}_3-{\mathrm{LE}}_2\times {\mathrm{p}}_3+{\mathrm{PG}}_1\times {\mathrm{p}}_1\\ +{\mathrm{RG}}_1\times {\mathrm{p}}_1+{\mathrm{RE}}_1\times {\mathrm{p}}_3-{\mathrm{RE}}_2\times {\mathrm{p}}_3)\end{array}& -{\mathrm{p}}_2\times ({\mathrm{p}}_2-1)\times ({\mathrm{LE}}_1-{\mathrm{LE}}_2+{\mathrm{RE}}_1-{\mathrm{RE}}_2)\\ -{\mathrm{p}}_3\times ({\mathrm{PG}}_1+{\mathrm{RG}}_1)\times ({\mathrm{p}}_3-1)& -{\mathrm{p}}_3\times ({\mathrm{p}}_3-1)\times ({\mathrm{LE}}_1-{\mathrm{LE}}_2+{\mathrm{RE}}_1-{\mathrm{RE}}_2)& \begin{array}{l}-({\mathrm{p}}_3-1)\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-{\mathrm{LE}}_1+{\mathrm{LE}}_2+\\ {\mathrm{LE}}_1\times {\mathrm{p}}_2-{\mathrm{LE}}_2\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_1+{\mathrm{RG}}_1\times {\mathrm{p}}_1+\\ {\mathrm{RE}}_1\times {\mathrm{p}}_2-{\mathrm{RE}}_2\times {\mathrm{p}}_2)-{\mathrm{p}}_3\times ({\mathrm{CE}}_2-{\mathrm{CE}}_1-{\mathrm{BE}}_1-\\ {\mathrm{LE}}_1+{\mathrm{LE}}_2+{\mathrm{LE}}_1\times {\mathrm{p}}_2-{\mathrm{LE}}_2\times {\mathrm{p}}_2+{\mathrm{PG}}_1\times {\mathrm{p}}_1+\\ {\mathrm{RG}}_1\times {\mathrm{p}}_1+{\mathrm{RE}}_1\times {\mathrm{p}}_2-{\mathrm{RE}}_2\times {\mathrm{p}}_2)\end{array}\end{array}\right]$$

(14)

4.2. Stability Analysis of Equilibrium Points

By substituting each equilibrium into the Jacobi Matrix (14), the eigenvalues for each equilibrium are calculated, and the results of the eigenvalues (λ) for each equilibrium are shown in

Table 4. Eigenvalues of each equilibrium point.

Equilibrium Point	λ1	λ2	λ3
E1 (0, 0, 0)	2PG1 − CG1	CE2 − CE1 − BE1 − LE1 + LE2	CE2 − CE1 − BE1 − LE1 + LE2
E2 (1, 0, 0)	CG1 − 2PG1	CE2 − CE1 − BE1 − LE1 + LE2 + PG1 + RG1	CE2 − CE1 − BE1 − LE1 + LE2 + PG1 + RG1
E3 (0, 1, 0)	PG1 − CG1 − RG1	BE1 + CE1 − CE2 + LE1 − LE2	CE2 − CE1 − BE1 + RE1 − RE2
E4 (0, 0, 1)	PG1 − CG1 − RG1	CE2 − CE1 − BE1 + RE1 − RE2	BE1 + CE1 − CE2 + LE1 − LE2
E5 (1, 1, 0)	CG1 − PG1 + RG1	BE1 + CE1 − CE2 + LE1 − LE2 − PG1 − RG1	CE2 − CE1 − BE1 + PG1 + RE1 − RE2 + RG1
E6 (1, 0, 1)	CG1 − PG1 + RG1	CE2 − CE1 − BE1 + PG1 + RE1 − RE2 + RG1	BE1 + CE1 − CE2 + LE1 − LE2 − PG1 − RG1
E7 (0, 1, 1)	−CG1 − 2RG1	BE1 + CE1 − CE2 − RE1 + RE2	BE1 + CE1 − CE2 − RE1 + RE2
E8 (1, 1, 1)	CG1 + 2RG1	BE1 + CE1 − CE2 − PG1 − RE1 + RE2 − RG1	BE1 + CE1 − CE2 − PG1 − RE1 + RE2 − RG1

.

By analyzing the positivity and negativity of all the eigenvalues in Table 4 and judging the stability of each local equilibrium point on this basis, the results are shown in

Table 5. Stability analysis of local equilibrium points.

Equilibrium Point	λ1	λ2	λ3	Stability	Stable Condition
E1 (0, 0, 0)	±	±	±	ESS	2PG1 < CG1,CE2 + LE2 < CE1 + BE1 + LE1
E2 (1, 0, 0)	±	±	±	ESS	CG1 < 2PG1,CE2 + LE2 + PG1 + RG1 < CE1 + BE1 + LE1
E3 (0, 1, 0)	±	+/−	−/+	Instability	/
E4 (0, 0, 1)	±	+/−	−/+	Instability	/
E5 (1, 1, 0)	±	+/−	−/+	Instability	/
E6 (1, 0, 1)	±	+/−	−/+	Instability	/
E7 (0, 1, 1)	−	±	±	ESS	BE1 + CE1 + RE2 < CE2 + RE1
E8 (1, 1, 1)	+	±	±	Instability	/

Note:“±” means the outcome of λ can be + or −, independent of other λ. “+/−” and “−/+” indicate the result of λ is affected by other λ. When λ₂ is +, λ₃ is −, and when λ₂ is −, λ₃ is +.

.

As shown in Table 5, E₁ (0, 0, 0), E₂ (1, 0, 0), and E₇ (0, 1, 1) have the potential to become stable points of the tripartite evolutionary game under certain conditions. Moreover, the conditions satisfied by these three stable points are mutually exclusive. Therefore, the results of the tripartite game among the government, Enterprise A, and Enterprise B can have at most one stable equilibrium point. Based on this, this paper discusses three scenarios.

Scenario I: When 2PG₁ < CG₁, CE₂ + LE₂ < CE₁ + BE₁ + LE₁, there exists a unique stable equilibrium point E₁ (0, 0, 0) in the replication dynamic system, and the combination of the tripartite game strategies stabilizes at “no-regulation, no-data-sharing, no-data-sharing”. The inequality 2PG₁ < CG₁ indicates that when the government enforces strict regulations, the total penalty imposed on two enterprises for not sharing data is less than the cost the government incurs in adopting a “regulation” strategy. This suggests that the potential gains from the government’s regulation might not be substantial enough to compensate for the cost. As a result, the government is inclined to opt for the “no-regulation” strategy. For enterprises, if they choose data sharing, they need to bear the data openness cost loss CE₁, the data exchange imbalance loss LE₁, and give up the data retention benefit BE₁ obtained when not sharing data. When choosing not to share data, the cost and loss are CE₂ + LE₂. The inequality CE₂ + LE₂ < CE₁ + BE₁ + LE₁ indicates that when an enterprise chooses the “no-data-sharing” strategy, the overall cost and loss are relatively lower, while the benefits are relatively higher. This situation makes the enterprises believe that maintaining the status quo of not sharing data is more advantageous.

Scenario II: When CG₁ < 2PG₁, CE₂ + LE₂ + PG₁ + RG₁ < CE₁ + BE₁ + LE₁, there exists a unique stable equilibrium point E₂ (1, 0, 0) in the replication dynamic system, and the combination of the tripartite game strategies is stable at “regulation, no-data-sharing, no-data-sharing”. The inequality CG₁ < 2PG₁ indicates that the cost incurred by the government in choosing the “regulation” strategy is less than the total penalty for not sharing data between the two enterprises. From the perspective of cost and potential benefits, it is profitable for the government to adopt the “regulation” strategy. For enterprises, if they choose the “data-sharing” strategy, the sum of losses they may suffer, including data openness cost, abandoned data retention benefits, and data exchange imbalanced loss, is CE₁ + BE₁ + LE₁. Assuming that a company chooses the “no-data-sharing” strategy, the potential losses it may suffer include the costs and losses that may be incurred if data is not shared, government penalties, and government rewards for data sharing, totaling CE₂ + LE₂ + PG₁ + RG₁. The inequality CE₂ + LE₂ + PG₁ + RG₁ < CE₁ + BE₁ + LE1 indicates that when a company chooses not to share data, the costs and losses are relatively smaller, and the benefits are relatively greater. Therefore, both Enterprise A and Enterprise B will choose the “no-data-sharing” strategy from the perspective of maximizing their own interests.

Scenario III: When BE₁ + CE₁ + RE₂ < CE₂ + RE₁, there exists a unique stable equilibrium point E₇ (0, 1, 1) in the replication dynamics system, and at this time, the combination of the tripartite game strategies is stable at “no-regulation, data-sharing, data-sharing”. This inequality suggests that when both enterprises engage in data sharing, the overall net profit of the enterprises is relatively substantial when both benefits and costs are taken into account. When enterprises opt for the “no-data-sharing” strategy, the overall net benefit is inferior to that achieved when both parties share data. In this case, both parties will choose the “data-sharing” strategies. Due to the fact that Enterprise A and Enterprise B can choose the “data-sharing” strategies based on their own profit situations if the government chooses strict “regulation” at this time, it will incur CG₁ costs. However, since the enterprise has already taken the initiative to share data, even if the government chooses the “no-regulation” strategy, it can still obtain macro benefits from enterprise data sharing and save CG₁ cost required for strict “regulation”. So, from a cost-benefit perspective, the government will choose the “no-regulation” strategy.

5. System Simulation

5.1. The Test of Evolutionary Stability Strategy

To intuitively analyze the relationships among the government, Enterprise A, and Enterprise B in the above model and the impact of relevant parameters on the game equilibrium. This part will assign values to parameters and conduct simulation analysis using Matlab 2016a software. First of all, the parameters are assigned for the above three stable scenarios, as follows:

Scenario Ⅰ: Taking practical factors into account, assign values to each parameter as CG₁ = 50, PG₁ = 20, RG₁ = 15, BG₁ = 100, BG₂ = 50, LG₁ = 50, CE₁ = 10, BE₁ = 15, CE₂ = 10, RE₁ = 80, LE₁ = 20, RE₂ = 70, LE₂ = 10. Establishing regulatory teams and purchasing necessary equipment incur expenses. CG₁ = 50 indicates that the cost of government regulation is relatively high, which is in line with the actual regulatory investment. In real-world scenarios, punishment levels are determined by the severity of violations and the enterprises’ financial capabilities. PG₁ = 20 implies that the punishment amount has a deterrent effect on enterprises without being overly punitive. RG₁ = 15 indicates that moderate rewards can effectively motivate enterprises to participate in data-sharing initiatives without imposing a heavy financial burden on the government. BG₁ = 100, BG₂ = 50, and LG₁ = 50 reflect the impact of different degrees of data sharing on the government’s macro-level benefits and losses. The benefits of data sharing between two enterprises are greater than those of data sharing by one enterprise. If neither enterprise shares data, losses will occur. CE₁ = 10 indicates that the cost loss of data openness caused by enterprises sharing data is relatively low. BE₁ = 15 means that enterprises can maintain a relatively low data retention benefit by not sharing data. CE₂ = 10 shows that enterprises need to pay a relatively small compensation fee to obtain external data from other parties. RE₁ = 80 and RE₂ = 70 suggest that when the other enterprise shares data, the benefits of an enterprise sharing data are greater than those of not sharing data. LE₁ = 20 and LE₂ = 10 imply that when the other enterprise does not share data, the losses of an enterprise sharing data are greater than those of not sharing data. The setting of the above parameters is consistent with the cost–benefit considerations of enterprises in real-world data-sharing decisions. By bringing the parameter values into the above replicator dynamic equation group and making the replicator dynamic equation evolve 100 times over time, the simulation results are shown in Figure 2. It can be found that after 100 times of evolution over time, the stability point of different initial strategy combinations turns out to be (0, 0, 0). At this time, the behavior strategy combination of the three participants is “no-regulation, no-data-sharing, no-data-sharing”.

Scenario Ⅱ: Assign the values of each parameter as CG₁ = 20, PG₁ = 20, RG₁ = 15, BG₁ = 100, BG₂ = 50, LG₁ = 50, CE₁ = 80, BE₁ = 15, CE₂ = 20, RE₁ = 80, LE₁ = 20, RE₂ = 70, LE₂ = 10. Unlike the parameter settings in scenario Ⅰ, in this scenario, CG₁ = 20, indicating that the cost of the government’s regulation is relatively low. This implies that the government’s investment in the regulatory process is minimal. At this time, the data norms in the relevant industries are clear, and the regulatory difficulty is low, so the investment is small. CE₁ = 80, suggesting that the loss of data openness costs incurred by enterprises due to data sharing is substantial. This could be due to high data security risks or the weakening of enterprises’ core competitiveness caused by sharing. CE₂ = 20, reflecting that a certain compensation fee needs to be paid to obtain data from the other party, and the fee is at a moderate level. The settings of other parameters are the same as those in scenario Ⅰ. By bringing the parameter values into the above replicator dynamic equation group and making the replicator dynamic equation evolve 100 times over time, the simulation results are shown in Figure 3. It can be found that the evolution results at this time tend to be stable at (1, 0, 0). The behavior strategy combination of the three participants is “regulation, no-data-sharing, no-data-sharing”.

Scenario Ⅲ: Assign values to each parameter as CG₁ = 30, PG₁ = 20, RG₁ = 15, BG₁ = 100, BG₂ = 50, LG1 = 50, CE₁ = 10, BE₁ = 15, CE₂ = 50, RE₁ = 80, LE₁ = 20, RE₂ = 70, LE₂ = 10. Among them, CG₁ = 30, which means that the cost for the government to implement strict control is at a moderate level. The involved regulatory processes and technological investments may have a certain degree of complexity, but they are maintained within a relatively reasonable range. CE₂ = 50 reflects that enterprises need to pay relatively high compensation fees when obtaining data from other enterprises. Such high compensation fees greatly affect enterprises’ decisions on data acquisition and sharing. The settings of other parameters are the same as those in scenario Ⅰ. By substituting the parameter values into the aforesaid replicator dynamic equation set and letting the replicator dynamic equations undergo 100 times of evolution over time, the simulation outcomes are presented in Figure 4. It can be observed that after evolving 100 times over the course of time, various initial strategy combinations reach a stable state at (0, 1, 1). At this time, the behavioral strategies of the three participants are as follows: the government chooses “no-regulation”, and Enterprise A and Enterprise B choose “data-sharing”.

The optimal case is set as the initial state for correlation analysis. In reality, the most desirable state is that the government does not regulate, and enterprises can still choose data sharing, that is, the combination strategy in scenario 3, “no-regulation, data-sharing, data-sharing”. Next, this paper takes the relevant settings in scenario 3 as the initial state and analyzes it.

5.2. The Impact of the Changes in Initial Probability

To investigate the impact of the initial inclinations of the government, Enterprise A, and Enterprise B in their choice of behavioral strategies on the evolution results, this paper sets the probabilities combination of the initial willingness (p₁, p₂, p₃) as (0.2, 0.2, 0.2), (0.5, 0.5, 0.5), (0.8, 0.8, 0.8), respectively. Here, p₁ represents the probability that the government opts for regulation, p₂ refers to the probability that Enterprise A chooses “data-sharing”, p₃ is the probability of Enterprise B choosing “data-sharing”. The values of the remaining parameters are as described in the previous section. The behavioral strategies and evolutionary trends of the three parties under different initial conditions are shown in Figure 5. It can be observed that, under the above-mentioned parameter settings and initial probability conditions, the government’s behavioral strategy gravitates towards “no regulation”, while the behavioral strategies of Enterprise A and Enterprise B tend towards “data-sharing”.

According to the previous assumption that Enterprise A and Enterprise B are completely symmetrical, this paper assigns the same initial probability to both Enterprise A and Enterprise B’s behavior strategies to analyze the impact of different enterprises’ initial willingness on the evolution trajectory of government behavior strategies. Simultaneously, this paper delves into the evolutionary trajectories of enterprises’ behavioral strategies under varying initial inclinations within the initial assessment of the government’s behavioral strategy. The results are shown in Figure 6 and Figure 7. Figure 6 shows the evolution trajectory of government behavioral strategies under different initial willingness of enterprises. It can be discerned that the initial willingness level of local enterprises’ “data-sharing” strategy will not change the evolution direction of the government’s “no regulation” behavioral strategy, but it will exert an impact on the evolution rate of the government’s behavioral strategy. Specifically, when enterprises exhibit a greater inclination towards “data-sharing”, the government’s “no-regulation” behavioral strategy becomes more pronounced, and the time required for its evolution is shorter. The rationale lies in the fact that the objective of government regulation is to achieve enterprises’ data-sharing. Thus, when enterprises demonstrate a strong inclination to share data, the government can promptly curtail the expenditure associated with its regulatory behavioral strategy. This enables the government to expedite the self-adjustment process within the data-element market.

Figure 7 shows the impact of the government’s initial willingness on the evolution of enterprises’ behavioral strategies. Since the behaviors of Enterprise A and Enterprise B are symmetric, the behavioral evolution of Enterprise A is taken as an example here. It can be observed that regardless of how the government’s initial willingness varies, the evolutionary direction of the enterprise’s behavioral strategy remains constant. However, through comparison, it becomes evident that the government’s initial willingness impacts the evolution rate of the enterprise’s behavioral strategy. Specifically, the greater the government’s initial inclination towards “regulation”, the shorter the time it takes for enterprises’ “data-sharing” behavioral strategy to evolve. This shows that an increase in the government’s initial eagerness to implement “regulation” can effectively hasten the evolution of enterprises’ behavioral strategies towards “data-sharing”.

5.3. The Influence of Key Variables on Subjects’ Evolutionary Strategies

5.3.1. The Influence of Government Regulation Cost

The cost of government regulation, denoted as CG₁, determines whether the government chooses the “regulation” strategy, which in turn affects the “data-sharing” behavioral strategy of individual enterprises. Based on this, this paper classifies the cost CG₁ incurred by the government when choosing the regulation strategy into low, medium, and high levels, with values set at 5, 30, and 100, respectively. Additionally, the initial willingness of the three parties is set to be the same (p₁ = p₂ = p₃ = 0.5). Subsequently, we analyze the impact of the government’s regulation cost on the government’s and enterprises’ behavioral strategies under the different levels of initial willingness (since Enterprise A and Enterprise B are completely symmetric, Enterprise A is taken as an example in this section). The results are shown in Figure 8, Figure 9 and Figure 10, which report the impact of the government’s regulation cost CG₁ on the evolutionary trajectory of the government, Enterprise A, and Enterprise B’s behavioral strategies from a three-dimensional perspective.

It can be observed that regardless of the different regulation costs, the government’s behavioral strategies tend to lean towards “no regulation”, while the enterprises’ behavioral strategies tend to be “data-sharing”. Under varying initial willingness levels, the increase of CG₁ will accelerate the evolution speed of the government’s “no-regulation” strategy and curtail the time of the government’s evolution to the ESS. For enterprises, as CG₁ increases, the pace of their “data-sharing” activities gradually decelerates, which will increase the evolution time of the enterprise’s behavior strategy to ESS. The lower the initial propensity of enterprises to adopt the “data-sharing” strategy, the more pronounced the impact of the augmented government regulation cost on the speed at which they evolve toward ESS. Under these circumstances, the government can appropriately cut down on the regulation cost. This not only helps in reducing fiscal expenditure but also quickens the process through which enterprises achieve data sharing.

5.3.2. The Influence of Government Penalties

With other parameters remaining unchanged, the value of PG₁, which refers to the government’s penalty for enterprises’ “no-data-sharing” under its “regulation”, is set to 2, 20, and 100, respectively, for simulation analysis. Figure 11 and Figure 12 illustrate the impact of the government’s penalty on enterprises’ “no-data-sharing” behavioral strategies of the government and enterprises, and Figure 13 demonstrates how the government’s penalty on enterprises influences the behavioral strategies evolution of the three parties from a three-dimensional perspective.

It shows that government penalties PG₁ do not change the final trend of the three subjects’ behavioral strategies. An increase in PG₁ will slow down the evolution of the government’s “no regulation” strategy but will accelerate the evolution of enterprise A and Enterprise B to the “data sharing” strategy. For the government, there is no significant difference between the evolution paths with PG₁ values of 2 and 20, indicating that an increase in PG₁ within a certain range will not have a significant impact on the government behavior strategy. When the value of PG₁ is 100, the governmental behavioral strategy initially exhibits a tendency towards “regulation” and then shifts to “no-regulation”, indicating that when PG₁ exceeds a certain range, it will prompt the government to consider adopting the “regulation” strategy and slow down the pace of the “no-regulation” strategy. Consequently, this significantly increases the evolution time of the government behavior strategy to ESS. For enterprises, when the initial willingness of “data-sharing” is relatively high, the effect of increasing PG₁ on enterprise behavioral strategy is not significant, while the initial willingness level of enterprise “data-sharing” is low, the increase of PG₁ will accelerate the evolution of enterprise to ESS. Therefore, the government can moderately increase administrative penalties in order to better promote enterprises to achieve data sharing.

5.3.3. The Influence of Government Incentives

Other parameters remain unchanged, and the government’s rewards to enterprises for “data-sharing” under its “regulation”, denoted as RG₁, are respectively assigned to 2, 20, and 100 for simulation analysis. Through this, we can obtain the impact of the government’s reward for enterprises’ positive responses to data-sharing regulation on both the government and enterprises’ behavioral strategies, and the results are shown in Figure 14, Figure 15 and Figure 16. Figure 14 and Figure 15 show the impact of RG₁ on the behavioral strategies of the government and enterprises, and Figure 16 shows how the government’s rewards for enterprises affect the evolutionary trajectories of the behavioral strategies of the three parties from a three-dimensional perspective.

It can be seen that RG₁ does not affect the final evolution trajectory of the government, Enterprise A, and Enterprise B. RG₁ does not exert a significant impact on the evolution direction and speed towards the ESS, but the increase of RG₁ will slow down the evolution speed of Enterprise A and Enterprise B to the ESS. For enterprises, the higher RG₁ is, the slower the evolution to ESS is at different initial willingness levels, and when RG₁ exceeds a certain value, it will greatly lengthen the evolution time to ESS. The reason is that the government’s incentive mechanism will not impose substantial losses on the government, while high-level incentives can effectively mitigate the costs and losses of enterprise data sharing, which makes enterprises more likely to choose the “data-sharing” strategy. Concurrently, as the enterprises’ willingness to share data grows, the government will tend to choose the “no-regulation” strategy. However, when the government’s reward for enterprise data sharing is high, enterprises will choose to slow down the pace of data sharing in order to enjoy the rewards for a longer time. Therefore, the government ought to moderately scale back the level of incentives provided to enterprises for data sharing. This approach will enable enterprises to engage in data sharing at a more rapid pace.

5.3.4. The Influence of Compensation Fees for Enterprises to Obtain Shared Data

Keeping other parameters unchanged, the compensation fees for enterprises to acquire other enterprises’ shared data, denoted as CE₂, are respectively assigned as 10, 50, and 150 for simulation analysis. The impact of CE₂ on the behavioral strategies of the government and enterprise is presented in Figure 17 and Figure 18. Figure 19 presents the result of the evolution from a three-dimensional perspective, offering a comprehensive and multi-faceted view of the evolutionary process. This enables a more in-depth analysis and understanding of how various factors interact and change over time in that particular context.

It can be observed that the CE₂ will have a greater impact on the final behavioral strategy evolution trajectory of the government, Enterprise A, and Enterprise B. When CE₂ is at a relatively low level, the government’s behavioral strategy will ultimately converge towards “regulation”, and the enterprises’ behavioral strategy will eventually shift towards “no-data-sharing”. When the CE₂ level rises to a certain critical value, the government and enterprises’ behavioral strategies will evolve to “no regulation” and “data-sharing”, respectively. From the government’s perspective, when the CE₂ level is low, enterprises will tend to hoard data, in this case, the government has to step in with regulations to compel enterprises to share data. As the CE₂ increases to a certain range, enterprises will actively choose the “data-sharing” strategy, and then the government can achieve the effect of macro-control without adopting strict monitoring measures. From the enterprises’ standpoint, when the CE₂ is at a low level, the revenue derived from sharing data is low, while the compensation fees for sharing data remain high. As a result, enterprises will tend to adopt the “no-data-sharing” strategy. As CE₂ increases, and when the compensation from data sharing can make up for the cost, enterprises will prefer data sharing. The higher the compensation, the faster the evolution of enterprises toward “data-sharing”. This approach can effectively promote mutual benefit and a win–win situation for all enterprises involved.

6. Conclusions and Policy Implications

This paper constructs a tripartite evolutionary game model involving the government, Enterprise A, and Enterprise B, and analyses how different enterprises select data-sharing behavioral strategies under government regulation. Employing a simulation approach, this paper assigns values to the model’s parameters and conducts simulations. Subsequently, it comprehensively analyzes the evolutionary trends of the behavioral strategies of these three-party subjects in the face of changes in factors such as the government’s regulation costs, government penalties, government incentives, and the cost of enterprises’ access to shared data. This study shows that when the benefits of enterprise data sharing are high and the compensation fees for enterprises to obtain shared data are enough to compensate for the losses caused by each other’s data sharing, the government does not need to carry out regulation, and enterprises are inclined to choose the “data-sharing” strategy. Moreover, under the different initial willingness levels of the behavior strategies of the government, Enterprise A, and Enterprise B, the evolution results of the three parties’ behavioral strategies will not change. In addition, the cost of government regulation, government penalties, and government incentives will not affect the final evolution of the behavioral strategy choices of enterprises and the government, whereas the compensation fees for acquiring shared data by enterprises will affect the direction of the final evolution of the three parties.

Based on these conclusions, this paper proposes the following policy recommendations:

(1)

Precisely regulate the intensity of government regulation. In the context of the “no-regulation, data-sharing, data-sharing” combination strategy, where government-related factors primarily influence the evolutionary speed, the government must adopt a proactive and well-planned approach. In the initial phase, it is crucial to formulate rational and stringent control cost budgets, penalty regulations, and reward mechanisms. For regulatory costs, a meticulous accounting of the necessary human resources, material assets, and technological investments is essential. This precision ensures that costs are neither exorbitantly high, which could strain public finances, nor too low, which might compromise the effectiveness of supervision. Penalty standards should be scientifically calibrated according to the severity of enterprises’ violations and their tolerance thresholds. This scientific approach guarantees that the penalties have sufficient deterrence without being overly punitive. The reward mechanism, on the other hand, should be designed to be highly appealing. By offering substantial incentives, such as tax breaks, preferential policies, or financial subsidies, the government can encourage enterprises to actively engage in data sharing.

(2)

Reasonably intervene in the compensation fees for enterprise data sharing. The compensation fees for enterprises to obtain shared data have a profound impact on the ultimate evolutionary direction of all three parties involved. When these fees are low, enterprises tend to be reluctant to share data. To address this issue, the government can play a guiding role. The government can introduce clear guidelines on reasonable price ranges for data-sharing compensation. By doing so, it can effectively regulate the compensation-fee market, preventing situations where enterprises abandon data sharing due to unjust or unreasonable fee structures. Additionally, the government should encourage industry associations to take the lead in constructing data-sharing cost assessment platforms, which can help enterprises calculate compensation costs accurately and fairly.

(3)

Improve the market mechanism for data sharing. The government should strengthen the institutional construction of the data-sharing market, formulate fair and transparent data-sharing rules, and prevent unfair competition among enterprises. It should prohibit dominant enterprises from monopolizing key data resources, restrict opportunities for other enterprises to access data, avoid uneven distribution of data resources, and hinder market innovation vitality. At the same time, the government should crack down severely on malicious tampering of data, false labeling of data, and other behaviors, create a good atmosphere for data sharing, enhance the willingness and confidence of enterprises in data sharing, and promote the healthy development of the entire industry’s data-sharing ecosystem.

While this study offers valuable insights, additional research is necessary. Firstly, this article did not comprehensively consider data privacy protection. Future research will balance data-sharing incentives with the need to protect sensitive information and comply with data privacy regulations. Secondly, this study focuses on the influence of local government regulation on enterprise data sharing. With globalization and more frequent cross-border data flows, future research will include international regulatory frameworks and standards in the analysis. Finally, this study did not account for the cost-cutting and efficiency-boosting effects of emerging technologies in the analysis framework. Future research will explore how emerging technologies could reduce costs and enhance trust in data-sharing mechanisms.