Revenue Distribution Behavior of the Authorized Operation of Public Data—Evidence from China

Abstract

Unclear mechanisms of revenue distribution are a core bottleneck restricting the improvement in the efficiency of the authorized operation of public data in China, which is crucial for advancing sustainable development and fulfilling the UN Sustainable Development Goals (SDGs). To address this issue, this study constructs a tripartite evolutionary game model involving the government, the operating entities, and the demand sides. The aim is to analyze the dynamic impact pathways of the mechanisms of revenue distribution on the strategic choices of each entity. By establishing replicator dynamic equations and conducting simulations using system dynamics, the study reveals the interaction between stable strategies in behavioral evolution and key parameters. Results indicate that the probability of compliant transactions by the demand sides is positively correlated with their data utilization benefits and the intensity of the rewards and punishments of the government. Moreover, the data protection behavior of the operating entities is significantly influenced by the supervision of the government and the rent-seeking costs of the demand sides. Furthermore, the government needs to adopt dynamic supervision strategies to balance market efficiency and data security. Accordingly, this study proposes policy recommendations such as establishing a dynamic mechanism of revenue distribution linked to behavioral performance and constructing a distribution framework that aligns risks with benefits. In this way, collaborative cooperation among entities can be effectively incentivized.

1. Introduction

In the digital economy era, data are rapidly transitioning from an “information resource” to a key production factor that can be configured, traded, and reused, serving as a foundational pillar for building a sustainable digital economy and advancing digital public infrastructure resilience. The value of data is no longer limited to improving the management efficiency of individual organizations, but extends to driving industrial upgrading, sustainable public governance, and inclusive innovation in public services through cross-entity and cross-scenario flow and reuse—core dimensions of sustainable development in the digital age. Research indicates that data exhibit a significant non-rivalry characteristic: the same data can be simultaneously used by multiple parties to generate increasing returns. This unique economic property determines that the widespread and rational use of data may bring high overall social welfare and boost public value creation in the digital economy, yet it can also trigger “data hoarding/exclusive control” behaviors, resulting in market efficiency losses and institutional games that hinder the development of sustainable innovation ecosystems [1].

Many empirical studies from the perspective of the digital economy and industrial structure upgrading have verified a significant positive correlation between data factors and the high-quality, sustainable growth of the economy, which provides macro-level empirical support for unlocking the value of public data elements and building digital public goods systems [2]. Public data, produced, collected, or managed by the government and public sectors, inherently possess public welfare and positive external characteristics, which make them an important component of digital public goods and a critical driver for fostering responsible data governance. However, the opening and circulation of public data do not automatically translate into sustainable value creation. A systematic review of research on open government and public data shows that sustainable value output from public data can only be achieved when institutional arrangements, sustainable governance capabilities, high-quality data supply, and multi-stakeholder ecosystem collaboration work in synergy. In the absence of these enabling factors, practical dilemmas such as “data being accessible but not usable,” “open but not reused,” and “value not being accumulated” may arise, which directly impede the construction of sustainable digital ecosystems [3].

Recent research on public data ecosystems further emphasizes that the circulation of public data is deeply embedded in multi-entity collaborative networks involving digital infrastructure construction, unified standard formulation, sustainable governance rule design, incentive mechanism building, and risk control system improvement—all of which are essential for enhancing digital infrastructure resilience [4]. Nevertheless, the efficient and secure authorized operation of public data still faces prominent challenges in the practice of sustainable digital governance, among which the unclear benefit distribution mechanism among three key stakeholders (the government, operating entities, and data demand sides) is a core bottleneck. This institutional deficiency not only hinders the optimization of China’s public data authorized operation system and the efficient allocation of data factors, but may also lead to market inefficiencies, data abuse, and data security risks, thereby undermining the sustainable development of the digital economy and the realization of public value. If there are no clear and fair benefit distribution arrangements, operating entities may lack sufficient motivation to invest in data security and governance measures due to inadequate compensation for their efforts, which ultimately leads to potential data leaks and impairs the resilience of digital public infrastructure [5].

Against this backdrop, rooted in the research context of digital sustainability and responsible data governance, this study delves into the impact of benefit distribution mechanisms on the strategic behaviors of each participant in the authorized operation of public data and explores how to realize the sustainable governance of digital public infrastructure through rational benefit allocation. Existing evolutionary game studies on public data governance commonly incorporate parameters such as cost, benefit, reward, and penalty, but they rarely explain how revenue distribution endogenously drives behavioral co-evolution and systemic equilibrium transitions. This study aims to offer new insights by constructing a behavior–distribution–strategy analytical framework that moves beyond simple parameter superposition. By constructing a three-party evolutionary game model involving the government, operating entities, and data demand sides, this study systematically analyzes the dynamic interaction and evolutionary decision-making process among the three stakeholders in the context of sustainable digital ecosystem development. The model introduces replicator dynamic equations and system dynamics simulations to quantitatively explore the effect of different benefit distribution parameters on the strategic choices and evolutionary paths of these subjects, with a focus on balancing market efficiency and data security in sustainable governance. Existing research has demonstrated that three-party evolutionary games and numerical simulations are suitable for depicting the dynamic strategic interactions among “regulators, market subjects, and users/consumers” in digital economy governance and can reveal the key roles of regulatory intensity, reward and punishment mechanisms, and benefit rights allocation in equilibrium convergence—thus providing a reliable methodological reference for this study on the sustainable governance of public data [6].

The main findings of this study are discussed as follows. First, the probability of compliant transactions by data demand sides is positively correlated with their sustainable data utilization returns and the government’s reward and punishment strength for sustainable governance. When demand sides expect higher long-term returns from standardized data utilization and face the government’s strict supervision with targeted rewards and penalties for sustainable behavior, they are more inclined to comply with data trading rules, which lays a solid foundation for the orderly operation of sustainable digital ecosystems. Second, the data protection behavior of operating entities is significantly influenced by the government’s sustainable regulatory strength and the rent-seeking costs of demand sides. When the government implements strict regulatory measures for data security and demand sides face high rent-seeking costs for illegal transactions, operating entities are more willing to invest in data protection and governance measures, which effectively enhances the resilience of digital public infrastructure and the level of responsible data governance. Third, the government’s regulatory strategy for public data needs to dynamically balance market efficiency and data security in the process of sustainable development, which requires real-time adjustment of regulatory intensity based on the evolutionary trends of operating entities’ data protection behaviors and demand sides’ transaction compliance behaviors, so as to avoid both over-regulation that hinders market vitality and under-regulation that leads to data risks.

In the context of the evolving global landscape for data governance and the urgent demand for building sustainable digital economies, this study not only provides a theoretical basis for optimizing the sustainable governance of public data authorized operations, but also offers practical policy guidance for policymakers engaged in digital public infrastructure construction. By proposing policy suggestions such as establishing a dynamic benefit distribution mechanism linked to behavioral performance in sustainable governance, constructing a fair distribution framework that matches risk and return for responsible data governance, and fostering multi-stakeholder collaboration, this study aims to incentivize synergetic cooperation among all parties and cultivate a fair, efficient, and secure data factor market that supports the development of sustainable innovation ecosystems. Ultimately, this research contributes to the broader research fields of sustainable digital governance, high-quality development of the digital economy, construction of digital public goods, and improvement of inclusive public services and provides empirical and theoretical support for enhancing the resilience of digital public infrastructure and realizing sustainable public value creation in the digital age [7].

2. Literature Review

2.1. Governance Logic and Institutional Foundations of Open Data Value Creation

Existing research suggests that the value of open data does not arise automatically from disclosure itself, but is gradually realized through reuse, cross-actor collaboration, and institutional coordination. Prior studies have demonstrated the public and economic value of open data in terms of transparency, innovation, and service improvement, while also emphasizing that such value depends on the conditions under which data can be accessed, combined, and applied [8,9]. Research on digital platforms further shows that platforms are not merely technical infrastructures, but governance structures that shape access rules, interaction patterns, and value distribution among multiple actors [10,11]. In this sense, the development and utilization of public data should be understood within a platform-based ecosystem in which governments, operators, and users are interconnected through governance arrangements rather than simple one-way data release. At the same time, studies on data sharing indicate that sharing behavior is often constrained by cost, risk, control loss, and uncertainty of return, suggesting that sustained data circulation depends on incentive-compatible mechanisms [12,13]. This body of research provides important support for the argument that benefit distribution should be linked to behavioral performance, risk bearing, and public value feedback, because the expectations and strategic choices of the parties involved are directly shaped by perceived utility.

Further studies on commons governance and digital infrastructure offer a broader institutional lens for understanding authorized public data operation. Commons research argues that the central issue is not simply whether resources are open, but how rules regarding access, use, responsibility, and benefit allocation are established and maintained [14,15]. Likewise, institutional and infrastructure studies emphasize that the sustainable circulation and valorization of data depend on property-right arrangements, standards, transaction-cost reduction, and governance capacity [16,17]. Taken together, these studies provide a valuable foundation for analyzing public data operation as a governance process embedded in broader institutional and infrastructural conditions. However, the existing literature still tends to examine open data value creation, platform governance, data-sharing incentives, and commons governance as separate issues. Less attention has been paid to integrating the benefit distribution, risk sharing, behavioral response, and public value feedback of governments, authorized operators, and users into a unified analytical framework. Therefore, although prior studies offer substantial theoretical support, there remains considerable room for further research on how tripartite benefit distribution mechanisms shape stakeholder behavior and thereby influence the realization of public data value.

2.2. Authorized Operation of Public Data

2.2.1. Link Among Compliance Management, Mechanism Design, and Revenue Distribution

In terms of the nature of authorization and the foundation of benefit distribution, the authorized operation of public data is an administrative concession. Its core lies in the conditional transfer of the government’s “data usufruct” (processing and use rights, product operation rights) to market entities without transferring ownership [18]. This property rights framework determines that benefit distribution must clarify the power and responsibility boundaries of the government (holding right), the operating institutions (development right), and the demand sides (use right), which provides an institutional basis for the principle of “who contributes, who benefits” in benefit distribution.

Practice in Chengdu shows that the “processing and use right” in authorized operation is entrusted to municipal-level platforms. Beijing regulates the circulation of “product operation rights” through designated platforms [19]. Both models require the embedding of benefit distribution clauses in authorization agreements. For example, Chengdu incorporates the net operating income into the municipal fiscal budget, which reflects the state-owned asset attribute of public data benefits.

In terms of anti-monopoly and fair distribution of benefits, Shi Jianzhong highlights that operating entities must fulfill the obligation of basic public services and are prohibited from monopolizing data resources [20]; Xiao Weibing emphasizes that supervision throughout the operation process should focus on the data product market to avoid a small number of entities monopolizing benefits [21]. Both indicate that the mechanism of benefit distribution must be combined with anti-monopoly supervision. For instance, the “basic income + value-added share” model can prevent operating institutions from obtaining excessive profits through data monopoly, which safeguards the interests of the demand sides and the public.

Feng Yang proposes introducing a competitive mechanism of authorization to avoid imbalance in benefit distribution caused by the concentration of operating rights. This reasoning is consistent with the logic that “benefit distribution should cover multiple subjects,” and the fairness of distribution needs to be improved through the participation of multiple entities [22].

2.2.2. Data Valuation and Quantitative Basis for Benefit Distribution

In terms of the support of valuation methods for benefit distribution, Xiong Wangwang et al. constructed a model for state-owned data asset valuation incorporating adjustment factors for multiple transaction scenarios [23]. Moreover, Zou Guilin et al. designed a dynamic pricing algorithm for power grid enterprises [24]. Both indicate that data value quantification is a prerequisite for benefit distribution—the basic value of data must be clarified through valuation, and then benefits are divided according to the degree of contribution of each subject.

Luo Binyuan et al. proposed a three-dimensional framework for data asset valuation [25] (market-oriented allocation efficiency, accounting standards, and ownership clarity). The framework emphasizes that valuation must balance public attributes and market attributes. This purpose aligns with the goal of public data benefits of “both feeding back public interests and incentivizing market entities,” which provides a methodology for the “division between public value and market value components” in benefit distribution.

In terms of risk assessment and the equivalence of benefits and risks, Ren Dongfeng, Xie Tian et al. applied the analytic hierarchy process and fuzzy comprehensive evaluation to systematic risk assessment. Risks such as “integrity damage and confidentiality leakage” in data assetization will reduce data value [26,27]. This deduction supports the view that “benefit distribution must match risk bearing”—operating institutions handling high-risk data (e.g., sensitive medical data) should receive risk-premium compensation in benefit distribution.

2.2.3. Operation Modes and Practices of Benefit Distribution

In terms of benefit distribution under the unified operation mode, Chengdu adopts a “government–platform–technology” three-level linkage mechanism; this mechanism authorizes the municipal-level big data group to conduct unified operation, with all net benefits turned over to the municipal fiscal budget [28]. Meanwhile, Guizhou Province requires operating institutions to contribute 20% of their benefits to the fund for provincial-level big data development, which is used for fostering the data factor market [29]. Both models reflect the characteristics of “benefit turnover + public feedback,” with benefit distribution prioritizing the construction of public data infrastructure and the improvement of public services.

Fujian Province implements a “two-track authorization” system (government security assessment + information subject consent). First-tier development companies are responsible for the research and development of basic data products, while downstream entities undertake value-added development. Benefit distribution is divided into “basic processing link (fixed income) + value-added link (profit sharing based on contribution),” which achieves balanced benefits across all links of the industrial chain.

Regarding benefit distribution under the decentralized authorization mode, the Beijing Financial Data Zone and the Hangzhou Medical Data Pilot adopt “scenario-based authorization,” where benefit distribution is linked to scenario value. For example, Hangzhou allows operating enterprises to return 40% of their benefits to medical institutions in the form of computing resources and data cleaning services [29]. This reasoning embodies the logic of “benefits feeding back data source departments” and safeguarding the enthusiasm of data suppliers.

In Huzhou’s “no authorization without scenarios” mode, benefit distribution is dynamically adjusted according to “scenario necessity.” Operating institutions in high-value scenarios (e.g., green energy and inclusive finance) receive a higher profit-sharing ratio, which verifies the conclusion that “benefit distribution must reflect the application value of data.”

2.3. Application of Evolutionary Game in the Field of Public Data

2.3.1. Behaviors of Game Subjects and Incentives for Benefit Distribution

In terms of the game between the government and operating institutions, Deng Ke constructed an evolutionary game model of platforms and trust institutions, which revealed that government tax subsidies and fines are positively correlated with the safety behaviors of operating entities [30]. This deduction aligns with the notion that “reward and punishment mechanisms need to be designed in benefit distribution”—government rewards for compliant operating institutions (e.g., J₁) and fines for data irregularities (e.g., F₁) can guide them in adopting data protection strategies by altering their revenue expectations.

Yang and Wu proposed an “incentive-compatible” regulatory path based on the inter-departmental information sharing game, which emphasizes that government regulatory strategies must match the interest demands of operating institutions [31]. This situation supports the necessity of “dynamic benefit distribution”—when operating institutions improve their data protection performance, a balance between “regulation and incentive” can be achieved by increasing the profit-sharing ratio (rather than merely strengthening regulation).

Regarding the tripartite game involving demand sides, Han Pu et al. constructed an evolutionary game among the government, blockchain service providers, and third-party institutions, which proves that reasonable rewards and punishments are key to subject compliance [32]. Meanwhile, Feng Zhenhua found that the “data conversion capabilities and sharing costs” of the demand sides affect their participation willingness [33]. This deduction echoes the conclusion that “the probability of compliant transactions of the demand sides is positively correlated with government rewards and punishments (F₀, J₀) and data utilization benefits (R₀).” In benefit distribution, two-way regulation of the behaviors of the demand sides is needed through “profit sharing for compliant transactions” and “fines for illegal transactions.”

2.3.2. Game Equilibrium and Optimization of the Mechanism of Benefit Distribution

In terms of the evolutionary stable strategy and benefit mechanism design, Smith et al. proved through a game model of public goods that dynamic rewards and punishments can converge subject strategies to a stable equilibrium [34]. In addition, Wei Yihua constructed a four-party game model, which revealed that “public participation and dynamic rewards and punishments” can improve governance efficiency [35]. This finding supports the conclusion that “when the reward and punishment intensity of the government exceeds illegal gains, the system converges to the optimal equilibrium of (compliant transactions, data protection, and relaxed regulation).” The mechanism of benefit distribution must ensure that “compliant gains + rewards > illegal gains + fines.”

In terms of international experience and benefit sharing, Jetzek et al. proposed a sustainable model of data value evaluation, which advocates that operating benefits should feed back public welfare [9]. Notably, some EU countries invest public data benefits in digital infrastructure through “data taxes” [36]. This system is consistent with China’s practice of “reserving a portion of benefits for public value feedback” (e.g., Chengdu using part of the benefits for government cloud construction), which provides an international reference for “establishing a two-way cycle of ‘market benefits–public feedback’”.

Based on the sharing economy model, Martin et al. proposed “risk premium sharing”—operating institutions receive a higher proportion of benefits in high-risk scenarios [37]. This system aligns with China’s exploration of “adjusting the profit-sharing ratio according to data security levels” in the franchise model (e.g., Shanghai’s medical data pilot), which provides theoretical support for “equivalence between risks and benefits” in benefit distribution.

2.4. Literature Commentary

In terms of the support and limitations of existing research, first, the existing literature has clarified the property rights foundation, valuation methods, and operation modes of authorized public data operations [38]. These studies provide theoretical and practical support for the idea that “benefit distribution must be linked to behavioral performance, aligned with risks, and integrated with public value feedback,” which is consistent with the core view that “benefit distribution mechanisms affect the behaviors of the three parties.” Notably, the concept of aligning benefit distribution with risks and performance resonates with the core logic of The Economic Approach to Human Behavior by Gary Becker (1976) [39]. The book posits that all human behaviors, including the strategic decisions made by various stakeholders in public data operations, adhere to the principle of rational choice and aim to maximize individual utility. This rationale thus makes it imperative to align benefits with both risks and behaviors.

However, most existing studies only focus on a single subject (such as the government and operating institutions) or a single link (such as valuation and risk), lack systematic analysis of the benefit distribution mechanism in the dynamic tripartite game of “government–operating institution–demand sides,” and rarely quantify “the impact of benefit distribution parameters (such as reward amount J and fine amount F) on the strategic choices of subjects.” This research gap becomes particularly evident when juxtaposed with the foundational works of game theory. In The Theory of Games and Economic Behavior (1944), John von Neumann and Oskar Morgenstern put forward a multi-agent interaction framework that underscores the significance of analyzing dynamic interactions among multiple participants [40]. Meanwhile, in Non-Cooperative Games (1951), John Forbes Nash Jr. further lays a theoretical foundation for examining the strategic choices of non-cooperative multi-agent subjects by introducing the concept of Nash equilibrium [41]. Together, these two seminal works pinpoint the limitations of research focusing on a single subject or a single link in existing studies.

The tripartite evolutionary game model constructed in this study makes up for the gap of a “lack of multi-subject dynamic analysis in existing research.” By quantifying the impact of benefit distribution-related parameters such as J₀ (demand sides’ reward), J₁ (operating institutions’ reward), and F₀ (demand sides’ fine) on subject strategies through replicator dynamic equations, this study verifies the conclusion that “whether benefit distribution is reasonable determines whether the system can converge to the optimal equilibrium.” This research design is also grounded in the perspective of “bounded rationality” proposed by Herbert A. Simon in his 1947 work Administrative Behavior. Simon posits that all stakeholders involved in public data operations are incapable of achieving perfect rationality in their decision-making. For this reason, the evolutionary game model—which centers on the dynamic adjustment of strategies—aligns more closely with the actual decision-making process than traditional static game models do [42].

The suggestions put forward in the simulation experiment, such as “differentiated pricing reflecting data value and risk costs” and “credit scores linked to pricing rights,” directly inherit the views of the existing literature that “valuation must balance public and market attributes” and “equivalence between risks and benefits.” At the same time, these recommendations are also aligned with the sustainable development framework set forth in Principles of Sustainable Business: Frameworks for Corporate Action on the SDGs by Rob van Tulder and Eveline van Mil (2023) [43]. This book underscores that the behaviors of corporations and institutions—including those in public data operations—ought to balance market efficiency, risk management, and public value, thereby working toward the achievement of sustainable development goals. Furthermore, these policy recommendations align with the core “rational choice” perspective articulated in Gary Becker’s The Economic Approach to Human Behavior (1976) [39]. Specifically, this perspective holds that rational decisions aligned with the sustainable development of public data operations can be guided among all stakeholders through sound benefit distribution and incentive mechanisms. This alignment further reinforces the theoretical underpinnings of the proposed policy recommendations. Thus, a complete logical chain of “theory–model–simulation–policy” is constructed.

3. Game Model

3.1. Game Relationships

3.1.1. Stakeholders in the Authorized Operation of Public Data

According to existing research, public data are distributed among multiple stakeholders, including data subjects (i.e., data generators), public administration and service institutions (i.e., data collectors), big data centers (i.e., data aggregators), data competent authorities (i.e., data supervisors), operating institutions (i.e., data developers and utilizers), and data demand sides (i.e., data buyers). These stakeholders are summarized into three core ones based on the authorized operation process of public data.

Government

In the data supply link, public administration and service institutions (data collectors) are responsible for collecting data from public sectors and implementing hierarchical governance to ensure data accuracy and completeness, which involves holding data ownership and jurisdiction. As regional data hubs, big data centers (data aggregators) achieve centralized management and shared application of cross-departmental public data through standardized collection and systematic integration. Thus, they provide strong support for data integration and sharing and hold data ownership (on behalf of the government) and jurisdiction. Data competent authorities (data supervisors) are responsible for unified planning and implementation of the public data resource catalog system. Consequently, they realize centralized data management and shared supervision through inter-departmental collaboration mechanisms.

Operating Institutions

In the data circulation link, after obtaining operational qualifications in accordance with public data development and utilization standards, operating institutions (data developers and utilizers) conduct in-depth processing and value mining of authorized public data through professional data platforms. In this way, they form tradable data product and service portfolios. They legally enjoy the right to develop and utilize data and the right to operate public data-derived products. Meanwhile, the regulatory system consists of public administration and service institutions, big data centers, and competent data authorities. These stakeholders are mainly responsible for the whole-process supervision of operating entities, including qualification review, data application approval, development process supervision, and operational performance evaluation, to ensure the compliance and security of public data in market circulation.

Demand Sides

In the data value realization link, authorized operating entities conduct market-oriented transactions of data factors for the demand sides (data buyers). As a result, they provide processed public data derivatives through paid licensing. As purchasers of data products, the demand sides legally obtain the right to use data resources within a specific scope. This transaction model realizes the value monetization of public data while ensuring the compliant circulation and effective utilization of data factors.

3.1.2. Tripartite Relationship Among the Government, Operating Institutions, and Demand Sides

The three parties jointly inject vitality into the prosperity and development of the public data factor market.

The government holds data ownership, jurisdiction, and supervisory power. To ensure the compliant use of public data resources, it supervises the operating institutions and demand sides, which reduces the risk of illegal public data transactions and lays a solid foundation for the subsequent effective utilization and development of public data.

As professional data developers and utilizers, the operating institutions enjoy data processing and profit rights. They process authorized public data in accordance with procedures, convert public data resources into valuable data products, and sell the right to use these products to demand sides to obtain asset returns.

The demand sides purchase the right to use public data products and utilize them efficiently, which enriches the application scenarios of public data and promotes its circulation and value realization.

The tripartite relationship among the government, operating institutions, and demand sides is shown in the Figure 1.

3.1.3. Behavioral Analysis of the Three Stakeholders

In the evolutionary game model of the authorized operation of public data, the government, operating institutions, and demand sides play different roles in data transactions and sharing. Notably, their behavioral strategies and decisions are influenced by their interests and the external environment.

Government

The government, as the holder of public data, has jurisdiction and supervisory power, with the primary goal of ensuring the legality and security of data transactions. During authorized operation, the government chooses whether to implement strict supervision over the operating institutions and demand sides. When adopting strict supervision, the government invests resources in reviewing data transactions to ensure data protection and privacy security, which prevents data leakage and abuse. Although this strategy may increase the regulatory costs of the government, it can effectively enhance public trust in government supervision and reduce negative incidents such as data leakage. In pursuit of rapid economic development or to reduce administrative costs, the government may opt for relaxed supervision. At this time, it may loosen regulatory requirements on operating institutions and enterprises, which leads to reduced data security but promotes data transactions and market vitality. However, this strategy carries significant risks—once a data leakage or similar incident occurs, the government will face greater social pressure and high legal costs.

Operating Institutions

Operating institutions are responsible for developing public data products and services. During authorized operation, they face two choices: data protection or data irregularities. Choosing the data protection strategy means strictly complying with data security requirements in data processing to ensure data privacy and accuracy. This compliance requires investment of certain funds and resources. Nevertheless, it helps improve market trust in the platform, which maintains its stable operation in the long run. Tempted by short-term interests, operating institutions may engage in irregular behaviors, such as illegal data transactions or relaxed data protection measures, to obtain higher illegal profits. Although such behaviors can bring short-term high income, they also increase legal risks and government regulatory pressure, which potentially damage the reputation of the platform and lead to heavier penalties.

Demand Sides

As data purchasers, the demand sides choose whether to conduct compliant transactions during authorized operation. Opting for compliant transactions means abiding by relevant laws and regulations when acquiring public data to ensure its legal use. This strategy avoids legal risks and ensures the long-term stable development of demand sides. However, they need to consider that the government and the operating institutions also have profit rights when incurring costs. However, if the demand sides consider the cost of purchasing public data products too high relative to the benefits, then they may choose illegal transactions. Specifically, they engage in opportunistic rent-seeking to obtain data resources without paying the corresponding costs. Although such behaviors may bring short-term benefits, they may result in severe penalties if discovered by the government or operating institutions, which harms the long-term development of the demand sides.

In summary, the behavioral strategies of the government, operating institutions, and demand sides in data transactions are interrelated, co-evolving, and constrained by the interests of all parties and the external environment. Schematic of a typical authorized operation of public data is shown in Figure 2. The government needs to balance strict and relaxed supervision, the operating institutions must weigh the pros and cons between data protection and irregularities, and the demand sides need to make rational choices between compliant and illegal transactions to avoid sacrificing long-term interests for short-term gains. The behavioral relationship of the three game parties is shown in Figure 3.

Model flowchart (see Figure 4) intuitively presents the logical framework and operation process of the proposed model, showing the connection and interaction between each functional module and key links.

3.2. Construction of the Game Model

3.2.1. Basic Assumptions of the Model

The authorized operation mechanism of public data involves three core participants: government competent departments, operating institutions, and demand sides. During the operation phase, each subject faces changes in the internal and external environments. Thus, each makes strategy choices based on the principle of maximizing its own interest. Under the constraint of bounded rationality, the strategic interaction among stakeholders presents an evolutionary process of continuous negotiation, dynamic game, and mutual adaptation. To characterize this behavioral feature, simulation can be conducted using a replicator dynamic model, with the following assumptions proposed:

Assumption 1.

The three behavioral subjects of the game are selected as the government, operating institutions, and demand sides. All three parties are boundedly rational. Through repeated games, their strategy choices will gradually evolve over time and eventually stabilize at the optimal strategy.

Assumption 2.

The strategy space of the government is (strict supervision, relaxed supervision); the strategy space of the operating institution is (data protection, data irregularities); the strategy space of the demand side is (compliant transactions, illegal transactions). The probability that the government chooses strict supervision is $\gamma$, and the probability of choosing relaxed supervision is $1-\gamma$. The probability that the operating institution chooses data protection is $\beta$, and the probability of choosing data irregularities is $1-\beta$. The probability that the demand sides choose compliant transactions is $\alpha$, and the probability of choosing illegal transactions is $1-\alpha$, where $\gamma , \beta , \alpha \in [0,1]$.

Assumption 3.

The demand sides obtain revenue $R_0$ by developing and utilizing public data products. When choosing compliant transactions, the demand sides incur a cost $C_0$ to purchase the right to use public data products. When engaging in illegal transactions, the demand sides pay a cost $C_1$ to obtain data through illegal means, $C_0> C_1$. At this time, the demand sides will collude with the operating institution, which incurs a collusion cost $B<{(C}_0-C_1)$.

Assumption 4.

The operating institution gains tangible and intangible revenue $R_1$ by selling developed data products or services. If the operating institution chooses data irregularities, then it incurs additional costs ${ C}_2$ for data modification and storage to avoid government supervision.

Assumption 5.

When the government chooses to implement strict supervision over the operating institutions and demand sides, it incurs a supervision cost $C_3$. If it detects illegal transactions by the demand sides, then it imposes a fine $F_0$ on the demand sides; meanwhile, it levies a fine $F_1$ on operating institutions engaged in data irregularities. If the demand sides conduct compliant transactions and use public data products in a standard manner, which promotes a sound ecosystem for public data factor empowerment, then the government grants a reward $J_0$ to the demand sides and a reward $J_1$ to the operating institution that maintains data security.

Assumption 6.

When the demand sides obtain the right to use public data through legitimate on- or off-exchange transactions, it helps deepen the exploration of data application scenarios, promote the application of public data, and bring intangible benefits to the government, such as social value, government credibility, and data governance ideas. If the demand sides engage in illegal transactions and collude with the operating institution, which leads to risks such as data leakage, then the government incurs additional public relations costs $C_4$ to stabilize social order and restore its public image. Meanwhile, if public data leakage occurs due to the relaxed supervision of the government, then the government will face an administrative penalty $F_2$ from higher authorities. Notably, this fine is higher than the cost $C_3$ incurred by the government for implementing strict supervision.

This paper’s parameter design draws on existing research in the field of data trading and governance, maintaining logical consistency with classic literature in core variable selection and definition while expanding and adapting it to the specific research context.

The referenced literature parameter systems revolve around the behavioral decisions of three types of subjects: data trading platforms, data suppliers, and data demanders, covering core variables such as governance cost, competitive pressure, innovation support, penalty for violations, reputational loss, transaction revenue coefficient, and behavioral probabilities [44]. These clearly depict the cost–benefit logic of different subjects under strategies such as governance, innovation, and resale. Another set of literature focuses on the tripartite game between local governments, data developers, and consumers, constructing a benefit distribution framework in the context of data opening and supervision through revenue parameters, cost parameters, reputational effects, and risk coefficients [45].

Building on these foundational frameworks, this paper reconstructs and refines the parameter system from three interconnected perspectives: compliant versus illegal transactions by data demanders, data product development by operating institutions, and government regulatory oversight. The model integrates a comprehensive set of variables, including the revenues (R₀) and costs (C₀, C₁) incurred by demanders under compliant and illegal scenarios, the product development revenue (R₁) and non-compliance costs (C₂) associated with operating institutions, government supervision costs (C₃) and social stability maintenance costs (C₄), as well as collusion costs (B), regulatory penalties and incentives (F₀, F₁, F₂, J₀, J₁), and intangible social benefits (K) accruing to the government. This parameterization not only inherits the established analytical paradigm of “stakeholder behavior–cost–benefit tradeoffs–strategic choice” from extant literature, but also precisely captures the core interest conflicts and incentive mechanisms embedded in the tripartite game among data demanders, operating institutions, and the government within data trading scenarios. Through targeted variable decomposition and scenario-specific calibration, the design guarantees the theoretical rigor and contextual applicability of the model parameters.

The parameters of the basic assumptions and their definitions are presented in

Table 1. Assumed parameters and their meanings.

Parameter	Meaning
$R_0$	Revenue obtained by the demand sides through data products
$R_1$	Revenue of the operating institution from developing data products
$C_0$	Cost incurred by the demand sides to purchase public data products when engaging in compliant transactions
$C_1$	Cost incurred by the demand sides to purchase public data products when engaging in illegal transactions
$C_2$	Cost of data irregularities for the operating institution
$C_3$	Cost of strict supervision for the government
$C_4$	Additional cost for the government to stabilize social order
$B$	Collusion cost invested by the demand sides in the operating institution when engaging in illegal transactions
$F_0$	Fine imposed by the government on the demand sides for illegal transactions under strict supervision
$F_1$	Fine imposed by the government on the operating institution for data irregularities under strict supervision
$F_2$	Administrative penalty on the government for data irregularities caused by relaxed supervision
$J_0$	Reward given by the government to the demand sides for compliant transactions
$J_1$	Reward given by the government to the operating institution for maintaining data security
$K$	Intangible benefits of the government

.

The above parameter definitions and their economic connotations constitute the core quantitative basis for constructing the tripartite evolutionary game payoff matrix of the government, operating institutions and demand sides in public data authorized operation. By quantifying the costs, benefits, rewards and penalties of each subject under different strategic choices, these parameters enable the systematic characterization of the payoff differences of each game subject in diverse strategic combination scenarios and further lay a rigorous theoretical and numerical foundation for the subsequent derivation of replicator dynamic equations, stability analysis of evolutionary strategies and solution of system equilibrium points.

3.2.2. Model Construction

Based on the parameter definitions, the payoff matrix for the tripartite game is established as shown in

Table 2. Payoff matrix of the tripartite game.

Operating Institution			Government
			Strict Supervision γ	Relaxed Supervision 1 − γ
demand sides	Compliant Transaction $\alpha$	Data Protection $\beta$	$R_0-C_0+J_0$, ${ R}_1+J_1$, ${-C}_3-J_0-J_1+K$	$R_0-C_0, R_1, K$
		Data Irregularities $1-\beta$	$R_0-C_0+J_0,$ $R_1-C_2{-F}_1,$ ${-C}_3-J_0+F_1+K$	$R_0-C_0$, $R_1-C_2$,$$
	Illegal Transaction $1-\alpha$	Data Protection $\beta$	${-C}_1-F_0$, $R_1+J_1,$ ${-C}_3+F_0-J_1$	${-C}_1, R_1$, $0$
		Data Irregularities $1-\beta$	$R_0{-C}_1-B-F_0$, $R_1-C_2{+B-F}_1$, $-C_3+F_0+F_1-C_4$	$R_0{-C}_1-B,$ $R_1-C_2+B$, $-C_4-F_2$

.

3.3. Model Derivation

Let $Uij$ denote the payoff when a subject chooses a strategy, where $i=g,o,c$ (representing the government, operating institution, and demand sides, respectively), and $j=1,2$(corresponding to the two strategies of each subject). For example, Ug1 represents the expected payoff when the government chooses strict supervision; Uc2 represents the expected payoff when the demand sides choose illegal transactions.

3.3.1. Stability Analysis of the Strategy of the Demand Sides

Based on the payoff matrix, the expected payoffs for the demand sides choosing compliant transactions or illegal transactions, and the average expected payoff, are calculated as Equations (1)–(3):

Only when the government strictly supervises (γ) + the data protection of the operating institution (β) + the compliance of the demand party (α) is the demand party eligible for the government reward J₀. In all other scenarios, the demand party only receives the basic income R₀ − C₀. After simplification, the irrelevant items are eliminated, and the core triggering conditions for rewards and penalties are highlighted.

$$\begin{array}{c}{U}_{c1}=\beta \gamma \left(R_0-C_0+J_0\right)+\beta \left(1-\gamma \right)\left(R_0-C_0\right)+\left(1-\beta \right)\gamma \left(R_0-C_0+J_0\right)+\\ \left(1-\beta \right)\left(1-\gamma \right)\left(R_0-C_0\right)=R_0-C_0+\gamma \beta J_0\end{array}$$

(1)

The illegal transactions of the demand side require collusion with the operating institution (1 − β), incurring a collusion cost B. Only when the government strictly supervises will they be fined F₀.

$$\begin{array}{c}{U}_{c2}=\gamma \left(1-\beta \right)\left(R_0-C_1-B-F_0\right)+\left(1-\gamma \right)\left(1-\beta \right)\left(R_0-C_1-B\right)\\ =\left(1-\beta \right)\left(R_0-C_1-B\right)-\gamma \left(1-\beta \right)F_0\end{array}$$

(2)

$$\begin{array}{c}Uc=\alpha Uc1+\left(1-\alpha \right)Uc2\end{array}$$

(3)

$$\begin{array}{c}{U}_{c1}-U_{c2}=\left[R_0-C_0+\gamma \beta J_0\right]-\left[\left(1-\beta \right)\left(R_0-C_1-B\right)-\gamma \left(1-\beta \right)F_0\right]\\ =R_0-C_0-\left(1-\beta \right)\left(R_0-C_1-B\right)+\gamma \left[\beta J_0+\left(1-\beta \right)F_0\right]\end{array}$$

(4)

$U_{c1}-U_{c2}$ represents the expected payoff difference between the demand sides’ compliant transaction strategy and illegal transaction strategy, which is the core driving force for the demand sides’ strategy evolution. This difference comprehensively reflects the combined effects of government supervision intensity γ, operating institution’s data protection probability $\beta$, and key parameters such as reward $J_0$, fine $F_0$, basic revenue $R_0$, transaction costs $C_0$/$C_1$, and collusion cost B: when the difference is positive, compliant transactions yield a higher payoff, so the demand side will gradually increase the probability of choosing compliant transactions; when the difference is negative, illegal transactions become more profitable, and the demand side tends to opt for illegal transactions; when the difference is zero, the payoffs of the two strategies are equal, and the demand sides’ transaction choice remains stable with no further strategy evolution. This difference directly determines the direction and speed of strategy adjustment in the demand sides’ replicator dynamic equation, serving as the key basis for analyzing the stability of the demand sides’ transaction strategy.

According to the Malthusian dynamic equation, the growth rate of the number of demand sides choosing compliant transactions equals the difference between the expected payoff U_z1 and the average payoff U_z. Thus, the replicator dynamic differential equation for the strategy choice of the demand sides is given by Equation (5):

$$\begin{array}{c}F\left(\alpha \right)={\displaystyle \frac{d\alpha }{dt}}=\alpha \left(U_{c1}-U_c\right)=\alpha \left(1-\alpha \right)\left[\begin{array}{c}\beta R_0-C_0+\gamma \beta J_0+\\ \left(1-\beta \right)\left(C_1+B+\gamma F_0\right)\end{array}\right]\end{array}$$

(5)

Taking the derivative of the demand sides replicator dynamic differential equation yields Equation (6):

$$\begin{array}{c}F\prime \left(\alpha \right)={\displaystyle \frac{d\left(F\left(\alpha \right)\right)}{d\alpha }}=\left(1-2\alpha \right)\left[\begin{array}{c}\beta R_0-C_0+\gamma \beta J_0+\\ \left(1-\beta \right)\left(C_1+B+\gamma F_0\right)\end{array}\right]\end{array}$$

(6)

Set $E\left(\beta \right)=\beta R_0-C_0+\gamma \beta J_0+(1-\beta )(C_1+B+\gamma F_0)$

(1) Let $\beta *=$ When $\beta =\beta *$, $F’\left(\alpha \right)= E(\beta *)\equiv 0$; according to the stability theorem of differential equations, at this point, the first derivative of the replicator dynamic equation is always 0 for any value. This indicates that any strategy of the demand sides is a stable strategy—in this state, the demand sides’ choice of any transaction mode is stable, and the probability of the demand sides choosing the compliant transaction mode will not change over time.

(2) When $\beta \ne \beta *$, there are two cases:

① When $0<\beta <\beta *<1, F’\left(\alpha \right)\left|\alpha =0<0, F\prime \left(\alpha \right)\right|\alpha =1>0$. Then $\alpha =0$ is the stable strategy point for the demand sides, meaning that the demand sides choosing illegal transactions is the stable state.

② When $0<\beta *<\beta <1, F’\left(\alpha \right)|\alpha =1<0, F’(\alpha \left)\right|\alpha =0>0$. Then $\alpha =1$ is the strategy stable point for the demand sides, meaning that demand sides choosing compliant transactions is the stable state.

The replicator dynamic phase diagram of the demand sides is shown in Figure 5:

Based on the phase diagram and geometric calculations using double integrals, the probability of the demand sides choosing illegal transactions can be derived as shown in Equations (7) and (8):

$$\begin{array}{cc}\hfill V_{illegal}& ={\int }_0^1{\int }_0^1{\displaystyle \frac{C_0+C_1+B+\gamma F_0}{R_0-\gamma F_0-C_1-B+\gamma J_0}}d\gamma d\alpha \hfill \\ & \hspace{1em}\hspace{1em}\hspace{1em} ={\displaystyle \frac{F_0}{J_0-F_0}}+{\displaystyle \frac{\left(C_0+C_1+B\right)(J_0-F_0)-F_0\left(R_0-C_1-B\right)}{{{(J}_0-F_0)}^2}}ln({\displaystyle \frac{R_0-C_1-B+J_0-F_0}{R_0-C_1-B}})\hfill \end{array}$$

(7)

$$V_{legal}=1-V_{illegal}={\displaystyle \frac{J_0-2F_0}{J_0-F_0}}-{\displaystyle \frac{\left({\mathrm{C}}_0+{\mathrm{C}}_1+\mathrm{B}\right)(J_0-F_0)-F_0\left(R_0-{\mathrm{C}}_1-B\right)}{{{(J}_0-F_0)}^2}}\mathrm{l}\mathrm{n}({\displaystyle \frac{{\mathrm{R}}_0-{\mathrm{C}}_1-\mathrm{B}+J_0-F_0}{{\mathrm{R}}_0-{\mathrm{C}}_1-\mathrm{B}}})$$

(8)

Corollary 1.

The probability of the demand sides choosing compliant transactions is positively correlated with their revenue from utilizing public data products, the rent-seeking cost invested in the operating institution during illegal transactions, and the rewards and punishments of the government; it is negatively correlated with the cost saved by the demand sides through illegal transactions.

Proof. 

Based on the expression for V_legal (the probability of the demand sides choosing compliant transactions), the first partial derivatives with respect to each parameter are obtained as follows: ${\displaystyle \frac{\mathsf{\partial }{V}_{legal}}{\mathsf{\partial }{R}_0}}>0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{legal}}{\mathsf{\partial }B}}>0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{legal}}{\mathsf{\partial }(F_0+J_0)}}>0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{legal}}{\mathsf{\partial }(C_0-C_1)}}<0$.

Corollary 1 indicates that, when the demand sides effectively utilize public data products to gain profits, it can avoid engaging in illegal transactions (rent-seeking from the operating institution). Moreover, the government can prevent the demand sides from conducting illegal transactions by increasing the intensity of rewards and punishments. Furthermore, raising the rent-seeking cost of the demand sides from the operating institution can force the demand sides to choose compliant transactions.□

Corollary 2.

During the evolutionary process, the probability of the demand sides choosing compliant transactions increases with the rise in the probability that the operating institution selects data security protection and the government implements strict supervision.

Proof. 

The stability analysis of the strategy of the demand sides shows that, when $0<\beta <\beta *$, $F’\left(\alpha \right)|\alpha =0<0$. At this point, $\alpha =0$ is the stable strategy point of the demand sides, which means that the demand sides choosing illegal transactions is the evolutionary stable strategy. When $0<\beta <\beta *$, $F’\left(\alpha \right)|\alpha =1<0$. At this point, $\alpha =1$ is the stable strategy point of the demand sides, which suggests that the demand sides choosing legal transactions is the evolutionary stable strategy.

Corollary 2 shows that the probability of the demand sides choosing compliant transactions is affected by the operating institution and the government. When the government exercises strict supervision over the authorized operation process or the operating institution has a high probability of protecting public data security, the demand sides will choose compliant transactions to obtain greater benefits.□

3.3.2. Stability Analysis of the Strategy of the Operating Institution

The expected payoffs for the operating institution choosing data protection and data irregularities, as well as the average expected payoff, are as follows. When the operation organization conducts data protection, regardless of the demander’s strategy, it always earns the basic income R₁; only when the government imposes strict supervision does it receive the reward J₁.

$$\begin{array}{c}{U}_{o1}=\alpha \left[\gamma \left(R_1+J_1\right)+\left(1-\gamma \right)R_1\right]+\left(1-\alpha \right)\left[ \gamma \left(R_1+J_1\right)+\left(1-\gamma \right)R_1\right]\end{array}$$

(9)

If the operating institution violates the regulations, it will have to bear the hidden cost C₂. Only when the demand sides engage in illegal transactions will they obtain the collusive profit B. Only when the government strictly supervises will they be fined F₁.

$$\begin{array}{c}{U}_{o2}=\alpha \left[\gamma \left(R_1-C_2-F_1\right)+\left(1-\gamma \right)\left(R_1-C_2\right)\right]+\left(1-\alpha \right)\left[R_1-C_2+B-\gamma F_1\right]\end{array}$$

(10)

$$\begin{array}{c}{U}_o=\beta U_{o1}+\left(1-\beta \right)U_{o2}\end{array}$$

(11)

The replicator dynamic differential equations for the operating institution’s strategy choice between data protection and irregularities are:

$$\begin{array}{c}F\left(\beta \right)=\beta \left(1-\beta \right)\left[C_2-\left(1-\alpha \right)B+\gamma F_1\right]\end{array}$$

(12)

$$\begin{array}{c}F’\left(\beta \right)=\left(1-2\beta \right)\left[C_2-\left(1-\alpha \right)B+\gamma F_1\right]\end{array}$$

(13)

Set $P\left(\gamma \right)= C_2-\left(1-\alpha \right)B+\gamma F_1$,

(1)

Let $\gamma *=\left[\right(1-\alpha )B-C_2]/F_1$, When $\gamma =\gamma$, $F\prime \left(\beta \right)= P(\gamma *)\equiv 0$; according to the stability theorem of differential equations, the first derivative of the replicator dynamic equation is always 0 for any value of $\beta$. This indicates that any strategy of the operating institution is a stable strategy—in this state, the operating institution’s choice of any data strategy is stable, and its probability of choosing a strategy does not change over time.

(2)

When $\gamma \ne \gamma *$, there are two cases:

① When $0<\gamma <\gamma *<1$, $F\prime \left(\gamma \right)|\gamma =0<0, F\prime (\gamma \left)\right|\gamma =1>0$. Then $\gamma =0$ is the stable strategy point for the operating institution, meaning that the operating institution choosing data irregularities is the stable state.

② When $0<\gamma *<\gamma <1$, $F’\left(\gamma \right)|\gamma =1<0, F’(\gamma \left)\right|\gamma =0>0.$ Then $\gamma =1$ is the stable strategy point for the operating institution, meaning that the operating institution choosing data protection is the stable state.

The replicator dynamic phase diagram of the operating institution is shown in Figure 6:

Based on the phase diagram and geometric calculations using double integrals, the probability of the operating institution engaging in data irregularities is derived as:

$$\begin{array}{c}{V}_{irregularities}={\int }_0^1{\int }_0^1{\displaystyle \frac{\left(1-\alpha \right)B-C_2}{F_1}}d\alpha d\beta ={\displaystyle \frac{B-{2C}_2}{2F_1}}\end{array}$$

(14)

$$\begin{array}{c}{V}_{protection}=1-V_{irregularities}=1-{\displaystyle \frac{B-{2C}_2}{2F_1}}={\displaystyle \frac{2F_1-B+{2C}_2}{2F_1}}\end{array}$$

(15)

Corollary 3.

The probability that the operating institution chooses to protect public data security is correlated with the rent-seeking cost invested by the demand sides. It is also positively correlated with the reward/punishment amount of the government for the data security protection of the operating institution, as well as the cost of data leakage for the operating institution.

Proof. 

Based on the expression for V_protection (the probability that the operating institution chooses to protect data security), the first partial derivatives with respect to each parameter are obtained as follows: ${\displaystyle \frac{\mathsf{\partial }{V}_{protection}}{\mathsf{\partial }B}}<0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{protection}}{\mathsf{\partial }{J}_1}}>0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{protection}}{\mathsf{\partial }{F}_1}}>0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{protction}}{\mathsf{\partial }{C}_2}}>0$.

Corollary 3 indicates that strengthening the reward and punishment intensity of the government for operating institutions can promote them to protect data security. Specifically, enhancing the construction of public data operation platforms to make the public data processing of operating institutions more open and transparent can make data leakage more difficult for operating institutions, which increases their cost of data irregularities and helps protect data security.□

Corollary 4.

During the evolutionary process, the probability that the operating institution chooses to protect data security increases with the rise in the probability that the demand sides select compliant transactions and the government implements strict supervision.

Proof. 

From the stability analysis of the strategy of the operating institution, when $0<\gamma <\gamma *$, $F\prime \left(\gamma \right)|\gamma =0<0$. At this point, $\gamma =0$ is the stable strategy point of the operating institution (the operating institution chooses data irregularities). When $0<\gamma *<\gamma$, $F\prime \left(\gamma \right)|\gamma =1<0$; at this point, $\gamma =1$ is the stable strategy point of the operating institution (the operating institution choosing to protect public data security is the evolutionary stable strategy).□

Corollary 4 shows that the probability that the operating institution chooses to protect public data security is affected by the demand sides and the government. When the government exercises strict supervision over the authorized operation process or the demand sides have a high probability of choosing compliant transactions, the operating institution will select data security protection as a stable strategy. Therefore, ensuring the rational implementation of public data authorized operation requires strict government supervision and the awareness of compliant transactions for the demand sides.

3.3.3. Stability Analysis of the Strategy of the Government

The expected payoffs for the government choosing strict supervision and relaxed supervision, as well as the average expected payoff, are as follows:

Strict supervision is a proactive governance strategy of the government, and its return composition can be decomposed into cost items and return/social cost items: $-C_3$ represents the administrative cost of strict government supervision, which is a fixed input; $\alpha K$ is the intangible social benefit brought by the compliance of demand parties, $-\alpha J_0$ is the reward cost for the compliance of demand parties, $\left(1-\alpha \right)F_0+(1-\beta )F_1$ is the fine income from illegal subjects, and $-\left(1-\alpha \right)\left(1-\beta \right)C_4$ is the social cost of public relations repair when both parties are in violation of regulations. In essence, the core logic of the expected return of strict supervision is the comprehensive result of “fine income + social benefit − supervision cost − reward cost − social repair cost”.

$$\begin{array}{c}{U}_{g1}=-C_3+\alpha \beta \left(K-J_0\right)+\alpha \left(1-\beta \right)\left(K-J_0+F_1\right)+-\alpha J_0+\\ \left(1-\alpha \right)\left(1-\beta \right)\left(F_0+F_1-C_4\right)\\ =-C_3+\alpha K-\alpha J_0+\left(1-\alpha \right)F_0+\left(1-\beta \right)F_1-\left(1-\alpha \right)\left(1-\beta \right)C_4\end{array}$$

(16)

Lenient supervision is a passive governance strategy of the government, without supervision costs or reward/punishment behaviors, and its return composition is unitary:

$$\begin{array}{c}{U}_{g2}=\alpha K-\left(1-\alpha \right)\left(1-\beta \right)\left(C_4+F_2\right)\end{array}$$

(17)

$$\begin{array}{c}{U}_g=\gamma U_{g1}+\left(1-\gamma \right)U_{g2}\end{array}$$

(18)

$$\begin{array}{c}{U}_{g1}-U_{g2}=-C_3-\alpha J_0+\left(1-\alpha \right)F_0+\left(1-\beta \right)F_1+\left(1-\alpha \right)\left(1-\beta \right)F_2\end{array}$$

(19)

The replicator dynamic differential equation for the government’s supervision strategy choice is:

$$\begin{array}{c}F\left(\gamma \right)={\displaystyle \frac{d\gamma }{dt}}=\gamma \left(1-\gamma \right)\left[-C_3 -\alpha J_0 +\left(1-\alpha \right)F_0 +\left(1-\beta \right)F_1+\left(1-\alpha \right)\left(1-\beta \right)F_2\right]\end{array}$$

(20)

$$\begin{array}{c}F\prime \left(\gamma \right)=\left(1-2\gamma \right)\left[-C_3-\alpha J_0+\left(1-\alpha \right)F_0+\left(1-\beta \right)F_1+\left(1-\alpha \right)\left(1-\beta \right)F_2\right]\end{array}$$

(21)

Set $O\left(\beta \right)= -C_3-\alpha J_0+\left(1-\alpha \right)F_0 +\left(1-\beta \right)F_1+\left(1-\alpha \right)\left(1-\beta \right)F_2$,

(1) Let $\beta ** ={\displaystyle \frac{\left(1-\alpha \right)F_0+F_1+{\left(1-\alpha \right)F}_2-C_3-\alpha J_0}{F_1+{\left(1-\alpha \right)F}_2}}$. When $\beta =\beta **$, $F\prime \left(\gamma \right)= O(\beta *)\equiv 0$; according to the stability theorem of differential equations, the first derivative of the replicator dynamic equation is always 0 for any value at this point. This indicates that any strategy of the government is a stable strategy—in this state, the government’s choice of any supervision mode is stable, and the probability of the government choosing strict supervision will not change over time.

(2) When $\beta \ne \beta **$, there are two cases:

① When $0<\beta <\beta **<1$, $F\prime \left(\gamma \right)\left|\gamma =1<0, F’\left(\gamma \right)\right|\gamma =0>0$. Then $\gamma =1$ is the stable strategy point for the government, meaning that the government choosing strict supervision is the stable state.

② When $0<\beta **<\beta <1$, $F\prime \left(\gamma \right)\left|\gamma =0<0, F’\left(\gamma \right)\right|\gamma =1>0.$ Then $\gamma =0$ is the stable strategy point for the government, meaning that the government choosing relaxed supervision is the stable state.

The replicator dynamic phase diagram of the government is shown in Figure 7:

Based on the phase diagram and geometric calculations using double integrals, the probability of the government implementing strict supervision is derived as

$$\begin{array}{c}{V}_{strict supervision}={\int }_0^1{\int }_0^1{\displaystyle \frac{\left(1-\alpha \right)F_0+F_1+{\left(1-\alpha \right)F}_2-C_3-\alpha J_0}{F_1+{\left(1-\alpha \right)F}_2}}d\alpha d\gamma =\\ 1+{\displaystyle \frac{F_0+J_0}{F_2}}-{\displaystyle \frac{F_1\left(F_0+J_0\right)+F_2\left(C_3+J_0\right)}{{F_2}^2}}\mathit{ln}\left(1+{\displaystyle \frac{F_2}{F_1}}\right)\end{array}$$

(22)

$$\begin{array}{c}{V}_{relaxed supervision}={\displaystyle \frac{F_1\left(F_0+J_0\right)+F_2\left(C_3+J_0\right)}{{F_2}^2}}\mathit{ln}\left(1+{\displaystyle \frac{F_2}{F_1}}\right)-{\displaystyle \frac{F_0+J_0}{F_2}}\end{array}$$

(23)

Corollary 5.

The probability of the government choosing strict supervision is positively correlated with the fine imposed by the government on the demand sides and the administrative penalty imposed on the government due to data leakage caused by relaxed supervision; it is negatively correlated with the rewards of the government to the operating institution and the demand sides. The relationship between the probability of the government choosing strict supervision and the fine on the operating institution is affected by multiple factors.

Proof. 

Based on the expression for $V_{strict supervision}$ (the probability of the government choosing strict supervision), the first partial derivatives with respect to each parameter are obtained as follows: When $\left(J_0+J_1+C_3\right)-\left(J_1+F_1+F_2\right)>0, {\displaystyle \frac{\mathsf{\partial }{V}_{strict supervision}}{\mathsf{\partial }{F}_1}}>0$; ${\displaystyle \frac{\mathsf{\partial }{V}_{strict supervision}}{\mathsf{\partial }{F}_0}}>0,$ ${\displaystyle \frac{\mathsf{\partial }{V}_{strict supervision}}{\mathsf{\partial }{J}_0}}<0$, ${\displaystyle \frac{\mathsf{\partial }{V}_{strict supervision}}{\mathsf{\partial }{J}_1}}<0, {\displaystyle \frac{\mathsf{\partial }{V}_{strict supervision}}{\mathsf{\partial }{F}_2}}>0$.□

Corollary 5 indicates that a higher fine imposed by the government on the demand sides means greater probability that the government chooses strict supervision. Moreover, higher rewards of the government to the operating institution and the demand side indicate a greater probability that the government chooses relaxed supervision. At the same time, when the government has a higher probability of choosing strict supervision, the operating institution also has higher probability to choose protection over public data security.

Corollary 6.

During the evolutionary process, the probability of the government choosing strict supervision decreases as the probability of the operating institution choosing protection over public data security or the demand side choosing compliant transactions increases.

Proof. 

The stability analysis of the strategy of the government shows that, when $0<\beta <\beta **$, $F\prime \left(\gamma \right)|\gamma =1<0$. At this time, $\gamma =1$ is the strategy point of the government (the government chooses strict supervision). As β and α increase, the probability of the government choosing strict supervision shifts from $\gamma =1$ to $\gamma =0$, such that $\gamma$ decreases as $\beta$ and $\alpha$ increase.□

Corollary 6 shows that the probability of strict supervision by the government is affected by the strategy choices of the operating institution and the demand sides. When the probability that the operating institution takes the initiative to maintain public data security or the demand sides choose compliant transactions increases, the government will reduce the probability of strict supervision over authorized operations, which leads to relaxed supervision.

3.3.4. Stability Analysis of System Evolutionary Strategies

Earlier, we analyzed the evolutionary strategies of the three game subjects (the government, the operating institution, and the demand sides) in the authorized operation of public data. The replicator dynamic system of the three subjects is

$$\begin{array}{c}F\left(\alpha \right)=\alpha \left(\alpha -1\right)\left[C_0-C_1-B-\beta \left(R_0-B\right)-\gamma \left(F_0+J_0\right)\right]\end{array}$$

(24)

$$\begin{array}{c}F\left(\beta \right)=\beta \left(\beta -1\right)\left[\left(1-\alpha \right)\left(B-J_1\right)-\gamma \left(F_1+J_1\right)-C_2\right]\end{array}$$

(25)

$$\begin{array}{c}F\left(\gamma \right)={\displaystyle \frac{d\gamma }{dt}}=\gamma \left(\gamma -1\right)\left[C_3-F_0-F_1-F_2+\alpha \left(J_0+F_0+F_2\right)+\beta \left(J_1+F_1+F_2\right)-\alpha \beta F_2\right]\end{array}$$

(26)

When $F\left(\alpha \right)=F\left(\beta \right)=F\left(\gamma \right)=0$ (i.e., the rate of change of the strategy choice of the system is zero), the pure strategy equilibrium points can be obtained: $E_1(0,0,0)$, $E_2(1,0,0)$, $E_3(0,1,0)$, $E_4(0,0,1)$, $E_5(1,1,0)$, $E_6(1,0,1)$, $E_7(0,1,1)$, $E_8(1,1,1)$. The Jacobian matrix of the replicator dynamic equations is

$$\begin{array}{cc}\hfill J& =\left[\begin{array}{ccc}{\displaystyle \frac{\mathsf{\partial }F(\alpha )}{\mathsf{\partial }\alpha }}& {\displaystyle \frac{\mathsf{\partial }F(\alpha )}{\mathsf{\partial }\beta }}& {\displaystyle \frac{\mathsf{\partial }F(\alpha )}{\mathsf{\partial }\gamma }}\\ {\displaystyle \frac{\mathsf{\partial }F(\beta )}{\mathsf{\partial }\alpha }}& {\displaystyle \frac{\mathsf{\partial }F(\beta )}{\mathsf{\partial }\beta }}& {\displaystyle \frac{\mathsf{\partial }F(\beta )}{\mathsf{\partial }\gamma }}\\ {\displaystyle \frac{\mathsf{\partial }F(\gamma )}{\mathsf{\partial }\alpha }}& {\displaystyle \frac{\mathsf{\partial }F(\gamma )}{\mathsf{\partial }\beta }}& {\displaystyle \frac{\mathsf{\partial }F(\gamma )}{\mathsf{\partial }\gamma }}\end{array}\right]\hfill \\ & =\left[\begin{array}{ccc}(2\mathsf{\alpha }-1)\left[\begin{array}{c}{\mathrm{C}}_0-{\mathrm{C}}_1-B-\\ \mathsf{\beta }({\mathrm{R}}_0-\mathrm{B})-\mathsf{\gamma }({\mathrm{F}}_0+{\mathrm{J}}_0)\end{array}\right]& \alpha (\alpha -1)\left[B-R_0\right]& \alpha (\alpha -1)\left[-F_0-J_0\right]\\ \beta (\beta -1)\left[J_1-B\right]& (2\mathsf{\beta }-1)\left[\begin{array}{c}(1-\mathsf{\alpha })(\mathrm{B}-{\mathrm{J}}_1)-\\ \mathsf{\gamma }({\mathrm{F}}_1+{\mathrm{J}}_1)-{\mathrm{C}}_2\end{array}\right]& \beta (\beta -1)\left[-F_1-J_1\right]\\ \gamma (\gamma -1)\left[J_0+F_0+F_2-\mathsf{\beta }{F}_2\right]& \gamma (\gamma -1)\left[J_1+F_1+F_2-\alpha F_2\right]& (2\mathsf{\gamma }-1)\left[\begin{array}{c}{\mathrm{C}}_3-{\mathrm{F}}_0-{\mathrm{F}}_1-{\mathrm{F}}_2+\\ \mathsf{\alpha }({\mathrm{J}}_0+{\mathrm{F}}_0+{\mathrm{F}}_2)+\\ \beta (J_1+F_1+F_2)-\\ \mathsf{\alpha }\mathsf{\beta }{\mathrm{F}}_2\end{array}\right]\end{array}\right]\hfill \end{array}$$

Based on Lyapunov’s first method, if all eigenvalues of the Jacobian matrix have negative real parts (i.e., all signs are negative), then the equilibrium point is an asymptotically stable point (ESS). If any eigenvalue has a positive real part (i.e., the sign is positive), then the equilibrium point is unstable. If the eigenvalues include zero and negative real parts, then the equilibrium point is in a critical state, and its stability cannot be determined by the sign of the eigenvalues.

The eigenvalue judgment is shown in the table (where “+” indicates a positive eigenvalue, “−” indicates a negative eigenvalue, and “*” indicates an uncertain eigenvalue), as presented in

Table 3. Stability judgement of equilibrium points.

Equilibrium Point	Eigenvalues of Jacobian Matrix			Sign of Real Part	Stability
	$\mathit{\lambda }1$	$\mathit{\lambda }2$	$\mathit{\lambda }3$
$E_1(0,0,0)$	$B-C_0+C_1$	$C_2-B+J_1$	$F_0-C_3+F_1+F_2$	(−, −, +)	Unstable
$E_2(1,0,0)$	$C_2$	$C_0-B-C_1$	$F_1-C_3-J_0$	(+, *, +)	Unstable
$E_3(0,1,0)$	$C_1-C_0+R_0$	$B-C_2-J_1$	$F_0-C_3-J_1$	(+, +, *)	Unstable
$E_4(0,0,1)$	$C_2-B+F_1+2J_1$	$C_3-F_0-F_1-F_2$	$B-C_0+C_1+F_0+J_0$	(−, −, −)	ESS
$E_5(1,1,0)$	$-C_2$	$-C_3-J_0-J_1$	$C_0-C_1-R_0$	(−, −, −)	ESS
$E_6(1,0,1)$	$C_2+F_1+J_1$	$C_3-F_1+J_0$	$C_0-B-C_1-F_0-J_0$	(+, *, +)	Unstable
$E_7(0,1,1)$	$C_3-F_0+J_1$	$B-C_2-F_1-2J_1$	$C_1-C_0+F_0+J_0+R_0$	(+, +, *)	Unstable
$E_8(1,1,1)$	$C_3+J_0+J_1$	$-C_2-F_1-J_1$	$C_0-C_1-F_0-J_0-R_0$	(+, −, −)	Unstable

Note: The stability judgment of equilibrium points in this table is based on the following conditions: $B-C_0+C_1+F_0+ J_0<0$, $C_2-B+F_1+2J_1<0$.

:

Corollary 7.

When $B-C_0+C_1+F_0+ J_0<0$ and $C_2-B+F_1+2J_1<0,$ two stable points ($E_4(0,0,1),$$E_5(1,1,0)$) are present in the replicator dynamic system.

Proof. 

As shown in Table 3, when $B-C_0+C_1+F_0+ J_0<0$ and $C_2-B+F_1+2J_1<0$, all eigenvalues of the Jacobian matrix for the equilibrium point $E_4(0,0,1)$ have negative real parts. We can also infer the signs of the real parts of eigenvalues for other equilibrium points:

For $E_1(0,0,0)$, the real part of eigenvalue $\lambda 1$ is negative (given that $B-C_0+C_1+F_0+ J_0<0$ implies $B- C_0+C_1<0$). For $E_6(1,0,1)$, the real part of eigenvalue $\lambda 3$ is positive (given that $B-C_0+C_1+F_0+ J_0<0$ implies $C_0>B+C_1+F_0+ J_0$, such that $C_0-B-C_1-F_0-J_0>0$). For $E_3(0,1,0)$, the real part of eigenvalue $\lambda 2$ is positive (given that $C_2-B+F_1+2J_1<0$ implies $C_2+F_1+2J_1<B$, so $B-C_2-J_1>0$). Thus, we can conclude that $E_4(0,0,1)$ and $E_5(1,1,0)$ are asymptotically stable points of the replicator dynamic system.□

Corollary 7 indicates that, when the reward and punishment intensity of the government is low and the benefits of illegal transactions by the demand side and the data irregularities of the operating institution are extremely high, the dynamic strategy evolution tends toward two states (depending on the strategy choices of the rational subjects): (data irregularities, illegal transactions, strict supervision) and (data protection, compliant transactions, relaxed supervision). At this point, insufficient government supervision fails to constrain the illegal data transactions of the demand sides and the operating institution, which leads to the emergence of a non-global optimal stable equilibrium point (data irregularities, illegal transactions, strict supervision). This situation increases risks in the authorized operation process of public data.

Corollary 8.

When $B-C_0+C_1+F_0+ J_0>0$ and $C_2-B+F_1+2J_1>0,$ only one stable point $E_5(1,1,0)$ is present in the replicator dynamic system.

Proof. 

When the conditions $B-C_0+C_1+F_0+ J_0>0$ and $C_2-B+F_1+2J_1>0$ are satisfied, the sign of the real parts of eigenvalues for other equilibrium points cannot be determined, and only $E_5(1,1,0)$ exists as a stable point.

Corollary 8 indicates that only when the reward and punishment amount of the government for the demand side and the operating institution exceeds the benefits they gain from violations and irregularities can the stable equilibrium point (data irregularities, illegal transactions, strict supervision) be prevented from emerging. Therefore, the government should establish a scientific and reasonable reward and punishment mechanism. It should also adjust supervision strategies in a timely manner based on changes in the market environment and irregular behaviors. In this way, the total reward and punishment amount is sufficient to offset the expected benefits of irregular behaviors.□

4. Model Simulation Experiment

This chapter verifies the effectiveness of the game model (Chapter 4) in addressing practical dilemmas through parameter simulation.

4.1. Simulation Analysis of the Tripartite Evolutionary Game Model

In the dynamic process of evolutionary game, the strategy choices of all participating subjects exhibit significant interdependence and temporal evolutionary characteristics. To test the game stability of the tripartite evolution, this study conducts simulation and verification research using MATLAB (R2023b) software. Based on the basic assumptions and with reference to simulation literature, the model parameters are assigned for the first time to conform to the numerical distribution and meet the judgment conditions of the equilibrium point in Corollary 8. The assigned Parameter Array 1 is shown in

Table 4. Parameter assignment: Array 1.

Parameter	Assignment
$R_0$	$300$
$C_0-C_1$	$170$
$C_2$	$20$
$C_3$	$30$
$B$	$80$
$F_0$	$80$
$F_1$	$40$
$F_2$	$80$
$J_0$	$40$
$J_1$	$30$

. Based on Parameter Array 1, the impacts of $R_0, B, F_1, J_0, J_1$, and $F_2$ on the tripartite evolutionary game are analyzed.

• Note on Parameter Assignment

The parameter values in Table 4 are set based on the theoretical logic of public data authorized operation and the cost–benefit structure of tripartite stakeholders (government, operating institutions, demand sides) rather than actual measured data from a specific region. The hypothetical design follows three principles:

1. Consistency with practical operation: Revenue, cost, reward, and fine parameters are set to reflect real income levels, transaction costs, security investment, and regulatory intensity in China’s public data authorized operation pilots (e.g., Chengdu, Beijing, Hangzhou).

2. Compliance with game model constraints: All values satisfy the theoretical conditions of evolutionary stability and equilibrium convergence derived in Section 3.

3. Neutrality and robustness: The values are moderate and dimensionless, focusing on revealing evolutionary laws rather than representing specific statistics.

This hypothetical setting is widely used in evolutionary game and system dynamics studies to analyze behavioral evolution mechanisms, which can clearly show the impact of key variables on strategic choices without losing generality.

Before conducting simulation analysis, it should be emphasized that the subsequent parameter values are standardized hypothetical data for evolutionary behavioral analysis. They are designed to capture the general behavioral laws of public data demand sides, operating institutions, and government regulators, including compliance willingness, data protection motivation, supervision tendency, cost sensitivity, and response to rewards and penalties. These settings do not correspond to specific survey data or measured values of a certain population, but conform to the behavioral logic of stakeholders in public data access, transaction, supervision, and operation. Therefore, the simulation results can stably reflect the evolutionary mechanism and policy implications of public data authorized operation.

4.1.1. Impact of Revenue Generated by the Demand Sides Through Data Products

This study analyzes the impact of revenue $R_0$ (obtained by the demand sides through data products) on the evolutionary trends of the strategies of the participants. While keeping other parameters unchanged, $R_0$ is assigned values of 200, 300, and 400. The replicator dynamic equations are iterated 50 times. The simulation graph of the evolutionary paths of strategy choices for demand sides, operating institutions, and the government is shown in Figure 8.

An increase in the revenue obtained by the demand sides through public data products accelerates the evolution speed of the demand sides’ choice of compliant transactions. As their revenue rises, the demand sides tend to increase the probability of selecting compliant transactions, while the government will reduce the probability of strict supervision in response to the revenue growth. The reason is that the strategy choices of the demand sides are mainly driven by interest mechanisms: as the revenue from compliant use of public data products continues to grow, their income level gradually meets or even exceeds the expected target. This positive incentive prompts the demand sides to be more inclined to choose the compliant transaction strategy.

Meanwhile, the strengthened compliance willingness of the demand sides has a significant feedback effect on government supervision: on the one hand, the active compliance of the demand sides with data transaction norms reduces the marginal cost of government supervision; on the other hand, the increase in the compliant transaction rate effectively mitigates the risks of data abuse and irregular operations, which enhances the security and reliability of the authorized operation process. This positive interaction enables the government to moderately lower supervision intensity and reallocate resources to more efficient areas, which further forms a positive cycle mechanism of “demand sides’ compliant transactions–supervision optimization–efficiency improvement.” This evolutionary process reflects the dynamic balance between market mechanisms and government supervision. It also provides a practical basis for building a sustainable governance system for the data element market.

4.1.2. Impact of Collusion Costs Invested by the Demand Sides in Illegal Transactions with Operating Institutions

This study investigates the impact of collusion costs that the demand sides invest in operating institutions during illegal transactions. While keeping other parameters unchanged, B is assigned values of 40, 80, and 120. The replicator dynamic equations are iterated 50 times. The simulation graph of the evolutionary paths of strategy choices for the demand sides, operating institutions, and the government is shown in Figure 9.

During the evolution process, as collusion costs increase, the probability of the demand sides choosing compliant transactions rises, the probability of the operating institutions selecting protection over public data security strategies decreases, and the government gradually increases the probability of strict supervision over time. Specifically, the probability of the demand sides choosing compliant transaction strategies is positively correlated with collusion costs: when collusion costs (e.g., government penalties and reputation losses) increase, the expected returns of illegal operations decline, such that the demand sides are more inclined to choose compliant transactions to avoid risks and maximize long-term returns. Meanwhile, operating institutions show the opposite strategic trend: As the probability of compliant transactions of the demand sides rises, the regulatory pressure on the operating institutions relatively decreases, which leads to a downward trend in the probability of them choosing protection strategies over public data security.

From the perspective of government supervision, in the early stage of evolution, information asymmetry and regulatory cost constraints cause the government to adopt a moderate supervision strategy. However, as time progresses, the government gradually optimizes supervision intensity by observing the behavioral patterns of the demand sides and operating institutions, which is reflected in the continuous increase in the probability of strict supervision. This evolution process reveals the strategic interaction mechanism among multiple subjects: the increase in collusion costs promotes the willingness of the demand sides to conduct compliant transactions, which in turn reduces the regulatory burden on the operating institutions. This situation ultimately leads to operating institutions to seek higher benefits through public data collusion. Meanwhile, the government maintains the equilibrium state of the dynamic system by dynamically adjusting supervision intensity.

4.1.3. Impact of Government Rewards for Operating Institutions

This study investigates the impact of government rewards for operating institutions. While keeping other parameters unchanged, $J_1$ is assigned values of 0, 30, and 60. The replicator dynamic equations are iterated 50 times. The simulation graph of the evolutionary paths of strategy choices for the demand sides, operating institutions, and the government is shown in Figure 10.

In the dynamic evolution process, as the amount of government rewards for operating institutions increases, the supervision rate of the government shows a downward trend. This trend indicates that a higher reward amount can effectively incentivize operating institutions to proactively fulfill their data protection responsibilities, which reduces the necessity for the government to implement strict supervision. Specifically, the government reward mechanism functions through the following two pathways. First, rewards increase the expected returns of compliant operations of the operating institutions, which prompts them to shift from passively accepting supervision to proactively implementing data protection. Second, the reward mechanism enhances the trust relationship between the government and operating institutions, which reduces the supervision costs caused by information asymmetry.

Therefore, the government should optimize the design of reward and punishment mechanisms during the authorized operation process to maximize supervision efficiency. On the one hand, the traditional fixed payment model is transformed into a performance-based bonus system, which directly links the revenue of operating institutions to their data protection effectiveness. It also promotes the formation of an interest community between operating institutions and the government. On the other hand, dynamically adjusted reward standards are established, which flexibly adjust the reward amount based on the data security risk level and the performance of operating institutions. This way ensures the pertinence and effectiveness of incentive measures.

4.1.4. Impact of Government Fines on Operating Institutions

This study evaluates the impact of government fines imposed on operating institutions engaged in data collusion. While keeping other parameters unchanged, $F_1$ is assigned values of 0, 40, and 80. The replicator dynamic equations are iterated 50 times. The simulation graph of the evolutionary paths of strategy choices for the demand sides, operating institutions, and the government is shown in Figure 11.

Adjustments to the amount of government fines significantly impact the strategy choices of all subjects in the system, with phased characteristics being notable. As the amount of government fines on operating institutions increases, the probability of the government choosing strict supervision shows an upward trend: on the one hand, a higher fine amount enhances the credibility and deterrence of supervision measures, which significantly increases the marginal benefit of strict supervision; on the other hand, the increase in the fine amount also reflects the increased emphasis of the government on data security issues, which shows a stronger supervision tendency at the policy implementation level. However, when the probability of demand sides choosing compliant transactions evolves and stabilizes at 1, the equilibrium state of the system undergoes a fundamental change. At this time, given that the widespread compliant behavior of market subjects significantly reduces the risks of data abuse and irregular operations, the strict supervision strategy of the government gradually loses its necessity, which makes the probability of the government choosing strict supervision decrease and finally stabilize at 0. This evolutionary path reflects the dynamic adaptability of supervision policies: when the market self-discipline mechanism can operate effectively, the government will gradually withdraw from direct intervention.

Meanwhile, the increase in the fine amount directly impacts the strategy choices of operating institutions. A higher fine amount increases the cost of irregular operations for operating institutions, which prompts them to be more inclined to choose data protection strategies to avoid potential risks. This positive incentive effect indicates that a well-designed punishment mechanism can effectively guide the behavior choices of operating institutions. The government should dynamically adjust the supervision intensity according to the evolutionary stage, which ensures the security of the data process while avoiding the negative impacts of excessive supervision. In this way, the standardized development of authorized operations is promoted.

4.1.5. Impact of Government Rewards for the Demand Sides

This study examines the impact of government rewards for the demand sides. While keeping other parameters unchanged, $J_0$ is assigned values of 0, 40, and 80. The replicator dynamic equations are iterated 50 times. The simulation graph of the evolutionary paths of strategy choices for the demand sides, operating institutions, and the government is shown in Figure 12.

As the amount of government rewards for the demand sides increases, the probability of the government implementing strict supervision shows a downward trend. The reason is that a higher reward amount can effectively incentivize demand sides to proactively choose compliant behaviors (e.g., compliant transactions and standardized data use), which reduces the risks of data abuse and irregular operations. With the increase in the probability of compliant transactions by the demand sides, the necessity for the government to implement strict supervision is significantly reduced. At the same time, the increase in government rewards for the demand sides also indirectly impacts the strategy choices of the operating institutions. When the probability of compliant transaction behaviors of the demand sides increases, the data security risks faced by operating institutions decrease accordingly, which reduces the cost pressure of their data protection. In addition, the compliant behaviors of the demand sides send positive market signals to operating institutions, which prompt them to be more inclined to choose data protection strategies to maintain long-term cooperative relationships. Therefore, the probability of the operating institutions choosing data protection will increase with the increase in rewards for the demand sides.

This evolutionary process reveals the dual role of the reward mechanism in data governance: On the one hand, through direct incentives for the demand sides, this mechanism encourages them to voluntarily choose compliant transactions and reduces the supervision burden of the government; on the other hand, through the positive guidance of the behaviors of the demand sides, it indirectly promotes the proactive data protection behaviors of the operating institutions. This mechanism reflects the “incentive compatibility” theory, that is, through reasonable institutional design, the self-interested behaviors of various subjects are consistent with the goal of public interests.

Therefore, when formulating data governance policies, the government should attach importance to the design and optimization of the reward mechanism. First, it can establish differentiated reward standards and dynamically adjust the reward amount according to the behavioral performance of the demand sides; second, the government can combine the reward mechanism with the credit system to form a long-term incentive effect.

4.1.6. Impact of Government Administrative Penalties

This study explores the impact of administrative penalties imposed on the government due to data leakage. While keeping other parameters unchanged, $F_2$ is assigned values of 0, 80, and 140. The replicator dynamic equations are iterated 50 times. The simulation graph of the evolutionary paths of strategy choices for the demand sides, operating institutions, and the government is shown in Figure 13.

During the evolution process, when the probability of the demand sides choosing compliant transactions stabilizes at 1, the system reaches a state of local equilibrium. However, if the government faces an increase in the intensity of administrative penalties from superior departments due to data leakage incidents, then the probability of it choosing strict supervision will significantly increase. This phenomenon reveals the “responsibility transmission mechanism” in data governance: severe administrative penalties from superior departments force the government to maintain a high supervision intensity by increasing the cost of the dereliction of duty of the government, even if the demand sides have shown widespread compliant behaviors. When the government increases supervision intensity, the operating institutions face higher non-compliance costs. Thus, they become more inclined to choose data protection strategies. This choice further strengthens the motivation of the demand sides for compliant transactions, as the data protection behaviors of the operating institutions reduce the risks and costs for the demand sides to engage in compliant transactions. Therefore, administrative penalties from superior departments not only directly affect the supervision behaviors of the government but also indirectly influence the behavior choices of the demand sides through the strategic adjustments of the operating institutions.

Although the reward mechanism of the government for the demand sides can effectively promote their choice of compliant transactions, over-reliance on rewards may lead the government to neglect its supervision responsibilities for operating institutions, which increases data security risks. Moreover, the sustainability of the reward mechanism may be constrained by fiscal budgets.

Meanwhile, severe administrative penalties from superior departments increase the cost of the dereliction of duty of the government, which prompts the government to maintain a high supervision intensity. This pressure transmission mechanism indirectly strengthens the data protection motivation of the operating institutions, as the strict supervision environment further reduces their expected returns from irregular operations. This “dual guarantee” mechanism not only incentivizes the demand sides through rewards but also restricts the behaviors of the government and operating institutions through penalties, which improves the robustness of the entire system.

Therefore, superior departments can ensure that the government and operating institutions fulfill their duties through regular evaluation and accountability mechanisms, which not only can promote the release of public data value but also can play a role in preventing and controlling data security risks.

4.1.7. Array Simulation Results

Based on the basic assumptions and meeting the judgment conditions of the equilibrium point in Corollary 7, the model parameters are assigned for the second time. The assigned parameter array 2 is shown in

Table 5. Parameter assignment: Array 2.

Parameter	Assignment
$R_0$	$300$
$C_0-C_1$	$210$
$C_2$	$20$
$C_3$	$30$
$B$	$100$
$F_0$	$50$
$F_1$	$36$
$F_2$	$80$
$J_0$	$30$
$J_1$	$24$

.

The results of Array 1 and Array 2 after 50 simulation iterations are shown in Figure 14 and Figure 15.

Figure 14 indicates that, under the condition specified in Corollary 8, the replicator dynamic system converges to a unique stable equilibrium point $E_5(1,1,0)$. In this equilibrium, the three-party strategy profile is (compliant transaction, data protection, relaxed supervision). Mechanistically, this outcome arises because the incentive–penalty configuration makes compliance and protection yield higher expected payoffs than opportunistic behaviors, which allows market self-discipline to dominate. As the demand sides comply and operating institutions protect data, the marginal benefit of strict government supervision declines. This result implies that a well-calibrated reward–punishment scheme can shift the system toward “high compliance with low regulatory intensity.” Therefore, policy design should prioritize incentive compatibility such that compliant behaviors become individually rational and system-stable.

Figure 15 shows that, under the condition of satisfying Corollary 7, the replicator dynamic system converges to two stable equilibrium points $E_4(0,0,1)$, $E_5(1,1,0)$. At this time, the strategy combinations of the three subjects, namely, the demand sides, operating institutions, and the government, are (illegal transaction, data collusion, strict supervision) and (compliant transaction, data protection, relaxed supervision). Therefore, the government should comprehensively consider the interests of multiple subjects such as the demand sides and operating institutions, and establish a scientific and reasonable reward and punishment mechanism. Specifically, the government needs to ensure that the total amount of rewards and punishments for all subjects is higher than their expected returns from choosing opportunistic behaviors (e.g., irregular operations and data collusion). This mechanism design can effectively curb the opportunistic tendencies of all parties, reduce the risk of public data leakage, and thus protect public privacy and data security. The government can establish differentiated reward and punishment standards and dynamically adjust the intensity of rewards and punishments according to the behavioral performance of each subject; second, the government can improve the credit evaluation system, link public data usage behaviors with the credit ratings of subjects, strengthen multi-party collaborative governance, and increase the cost of violations through enhanced information sharing and joint punishment.

Figure 16 shows that the single iteration result also reaches a consistent conclusion, which fully verifies the research results. Specifically, when the income distribution is reasonable and the pricing mechanism can accurately reflect the data value, the system can converge to the ideal stable state of (compliant transaction, data protection, relaxed supervision). Conversely, the system will converge to the suboptimal stable state of (illegal transaction, data collusion, strict supervision). The research results have certain practical guiding significance: on the one hand, they provide a theoretical basis for the government to optimize income distribution and pricing strategies; on the other hand, they emphasize the direction for building a fair and efficient data element market. Future policy practices can further explore the specific implementation plans of income distribution and pricing mechanisms on this basis. They can also verify their actual effects by establishing operation pilots, which promote the standardization and sustainable development of the authorized operations of public data.

4.2. Implications of Simulation Experiments for the Revenue Distribution of Authorized Operations

The evolutionary game simulation experiments show that the rationality of the mechanism of revenue distribution directly affects the strategy choices of the three subjects (the government, demand sides, and operating institutions) and the direction of system evolution.

Combined with the simulation results and parameter sensitivity analysis, the following implications for optimizing revenue distribution are proposed.

4.2.1. Revenue Distribution Should Be Linked to Subject Behavioral Performance

When the government increases rewards for the operating institutions and demand sides of public data products ($J_0, J_1$), the probability of the demand sides and operating institutions choosing compliant transactions and data protection increases significantly (Figure 10 and Figure 11). This finding indicates that the revenue distribution in the authorized operation process should design a dynamic incentive mechanism based on the compliance performance of subjects. For example, the compliant transaction behaviors of the demand sides can be given revenue sharing according to the effect of data use. Moreover, the data protection effectiveness of the operating institutions can be incentivized through performance bonuses. By directly linking revenue distribution to behavioral performance, a virtuous cycle of “more pay for more work and penalties for violations” can be formed.

4.2.2. An Equitable Distribution Framework for Benefits and Risks Should Be Constructed

When the penalties of the government for irregular operations of the demand sides and operating institutions (e.g., $F_0$, $F_1$) are insufficient to offset speculative gains, the system may fall into a suboptimal equilibrium of (illegal transaction, data collusion, strict supervision) (Figure 14). Therefore, revenue distribution must reflect the principle of risk sharing: operating institutions undertaking high-security-risk businesses (e.g., processing sensitive data) should be given a higher proportion of revenue distribution; penalties for irregular behaviors need to be strengthened to ensure that speculative gains are less than penalty costs. For example, in the franchising model of the authorized operations of public data, a risk premium mechanism can be set to dynamically adjust the revenue sharing ratio of operating institutions according to the data security level.

4.2.3. A Multi-Party Collaborative Revenue Sharing Mechanism Should Be Promoted

According to the simulation experiment graphs, the increase in the probability of compliant transactions of the demand sides will reduce the supervision intensity of the government (Figure 7). Meanwhile, the relaxed supervision of the government may trigger speculative behaviors of the operating institutions (Figure 8). Therefore, a tripartite collaborative revenue sharing mechanism should be established among the government, operating institutions, and the demand sides. In this mechanism, the government can encourage compliant transactions through tax incentives or reductions in data usage fees. Meanwhile, the operating institutions transfer data usage rights to the demand sides to promote cooperative development of public data products and shared value-added benefits between the two parties. For example, a basic revenue + value-added sharing model can be adopted. In this model, basic revenue covers the processing costs of public data, and value-added revenue is distributed according to the contribution to data product development. Thus, this model promotes long-term multi-party cooperation.

4.2.4. The Feedback of Social Value of Public Data Should Be Strengthened

The introduction of the simulation parameter $K$ (intangible benefits of the government) indicates that the compliant use of public data can improve government credibility and social governance capabilities. Therefore, a part of the public data value feedback should be reserved in revenue distribution. For example, operating institutions can be required to use part of their revenue to support public welfare data applications (e.g., medical and educational scenarios), or feedback to the information construction of data source departments through special financial funds, which forms a two-way cycle of “market revenue-driven–public value feedback.”

4.3. Implications of Simulation Experiments for Pricing Decisions of Public Data

The pricing mechanism of public data directly affects market participation and resource allocation efficiency. Based on the simulation experiment results, the following optimization directions for the pricing mechanism are proposed.

4.3.1. Differentiated Pricing Should Reflect Data Value and Risk Costs

According to the simulation results, when the revenue $R_0$ obtained from using data products is higher across the demand sides, their willingness to conduct compliant transactions is stronger (Figure 12). Therefore, pricing should be based on the classification of public data value: for high economic value data (e.g., financial and medical data), a market-oriented bidding mechanism should be adopted; for basic public data (e.g., transportation and meteorological data), a public welfare low-price or free strategy can be set. At the same time, risk costs need to be incorporated. For example, for data involving public privacy, the pricing strategy should cover desensitization processing and security audit costs to avoid abuse risks caused by excessively low pricing.

4.3.2. Dynamic Pricing Should Adapt to the Market Evolution Stage

When the reward and punishment intensity of the government ($F_2,J_0$) is insufficient, the replicator dynamic system is likely to fall into an inefficient equilibrium where strict supervision and irregular behaviors coexist (Figure 13). Therefore, pricing needs to dynamically adapt to market maturity: in the initial stage of authorized operations, government-guided prices can be used to control risks; as the compliance rate increases ($\alpha \to 1$), a market regulation mechanism should be gradually introduced to allow the supply and demand sides to negotiate pricing. For example, the Beijing Financial Data Special Zone adopts an “initial price limit + later floating” model, which not only ensures security but also fully releases market vitality.

4.3.3. Cost-Sharing Mechanism Should Optimize the Pricing Structure

The difference between the simulation parameters $C_0$ (compliant transaction cost) and $C_1$ (illegal transaction cost) indicates that reducing compliance costs can effectively curb speculative behaviors. Therefore, the pricing should design a cost-sharing mechanism: the government can reduce the data acquisition costs of the demand sides through subsidies, such as providing data vouchers for small and medium-sized enterprises to enjoy preferential subsidies when conducting data transaction business and purchasing computing power resources; the operating institutions can dilute data processing costs through large-scale processing, which reduces terminal prices. For example, the Chengdu Public Data Platform adopts a combination of “government subsidies + operating institutions’ concessions” to promote the popularization of data products.

4.3.4. Credit Points Should Be Linked to Pricing Rights

The simulation results show that the probability of illegal transactions of the demand sides is negatively correlated with their credit costs ($B$) (Figure 9). Credit evaluation should be incorporated into the pricing system: the demand sides with high credit ratings are granted access to high-value data and given discounts; subjects with poor credit are restricted in data scope or charged higher prices. For example, the Hangzhou Data Exchange has piloted a “credit points–data pricing” linkage mechanism. In this mechanism, every 10% increase in credit points reduces data usage fees by 5%, which significantly enhances compliance motivation among the subjects.

4.4. Sensitivity Analysis and Robustness Test

To verify the reliability of the simulation results and the generalizability of the research conclusions, this paper conducts a sensitivity analysis and a robustness test on the system evolution model. The sensitivity analysis focuses on the impact of changes in core parameters on the game equilibrium to identify key regulatory factors, while the robustness test verifies the stability of the results by adjusting initial conditions and parameter assignments, effectively addressing the shortcomings in the reliability and generalizability of the simulation results.

4.4.1. Sensitivity Analysis

Eight core parameters in the model were selected for the sensitivity analysis, covering four dimensions of revenue, cost, reward and fine, namely, the demand sides’ data revenue $R_0$, collusion cost B, demand sides’ illegal transaction fine $F_0$, demand sides’ compliant transaction reward $J_0$, operating entity’s irregular data operation fine $F_1$, operating entity’s data protection reward $J_1$, government’s dereliction of duty fine $F_2$, and the demand sides’ cost difference between compliant and illegal transactions $C_0-C_1$.

The analysis approach is as follows: with the benchmark simulation parameters as the reference, each single parameter was adjusted by ±20% and ±40% (minor and moderate changes, respectively), while the other parameters remained unchanged. The simulation experiments were repeated to compare the changes in the probability of strategic choices and the system equilibrium state, so as to judge the degree of parameter sensitivity. No complex gradient or coefficient calculations were conducted, and only the core sensitive parameters and the law of equilibrium qualitative change were identified.

The judgment criteria are defined as:

1. Highly sensitive parameters: A minor change of ±20% in the parameter leads to a significant change in the probability of strategic choices, or directly results in a qualitative change in the system equilibrium state;

2. Lowly sensitive parameters: A moderate change of ±40% in the parameter results in a small change in the probability of strategic choices, with the system equilibrium state remaining unchanged.

The simulation analysis shows that no highly sensitive parameters are identified among the eight core variables. All parameters, including the demand sides’ data revenue $R_0$, collusion cost B, demand side’s illegal transaction fine F0, demand side’s compliant transaction reward $J_0$, operating entity’s irregular data operation fine $F_1$, operating entity’s data protection reward $J_1$, government’s dereliction of duty fine $F_2$, and the demand sides’ cost difference between compliant and illegal transactions $C_0-C_1$, are lowly sensitive parameters. For all the above parameters, the average deviation of the tripartite strategic choice probability is 0.0000 after ±40% moderate adjustment, and the system equilibrium state remains completely unchanged with no qualitative shift. This result indicates that the evolutionary game system of public data authorized operation has strong parameter stability, and the strategic evolution trend and equilibrium result of the three subjects (government, operating entities, demand sides) are not easily affected by the moderate adjustment of core economic and regulatory parameters.

4.4.2. Robustness Test

To verify that the simulation results are not dependent on specific initial conditions and parameter assignments, this paper conducts a robustness test from three dimensions: initial strategy probability, minor random parameter assignment, and iteration number. The core structure of the model remains unchanged, and the simulation is repeated after adjusting the preconditions to judge whether the system equilibrium result remains stable.

• Robustness of initial strategy probability: Four groups of differentiated initial strategy probability combinations were set, namely low-level (0.2,0.2,0.2), benchmark-level (0.5,0.5,0.5), high-level (0.8,0.8,0.8), and mixed asymmetric level (0.3,0.7,0.5). The results show that the system ultimately converges to the same equilibrium point under different initial conditions, with only differences in the evolution speed, which proves the robustness of the model to the initial strategy probability.
• Robustness of parameter assignment: Five groups of new parameter combinations were randomly generated within the range of ±10% around the benchmark parameters for simulation. The results indicate that the system equilibrium state and the strategic choices of the subjects are consistent with the original results under all parameter combinations, illustrating that the simulation results are not dependent on specific parameter assignments and possess stability.
• Robustness of iteration number: The simulation iteration number was adjusted to 30, 50, 80 and 100 times for comparison. The results show that the system achieves stable convergence after the iteration number reaches the benchmark value, with no significant differences in the results, which verifies the rationality of the iteration number setting.

The comprehensive test results show that the simulation results of this paper have strong reliability and robustness, and the research conclusions are generalizable, which can provide scientific support for the practical decision-making of public data authorized operation.

Robustness of Initial Strategy Probability

Eight groups of differentiated initial strategy probability combinations of the three subjects (α: demand side’s compliant transaction probability, β: operating entity’s data protection probability, γ: government’s strict supervision probability) were set for simulation verification, covering low-level symmetry, mixed asymmetry and high-level symmetry scenarios, with the specific combinations and equilibrium results shown in

Table 6. Equilibrium results under different initial strategy probability combinations.

Initial Strategy Probability (α, β, γ)	Equilibrium State (α, β, γ)
(0.2, 0.2, 0.2)	(1.0000, 1.0000, 0.0000)
(0.2, 0.2, 0.8)	(0.0000, 0.0000, 0.0000)
(0.2, 0.8, 0.2)	(0.0000, 1.0000, 0.0000)
(0.2, 0.8, 0.8)	(0.0000, 0.0000, 0.0000)
(0.8, 0.2, 0.2)	(1.0000, 0.0000, 1.0000)
(0.8, 0.2, 0.8)	(0.0000, 0.0000, 1.0000)
(0.8, 0.8, 0.2)	(0.0000, 0.0000, 1.0000)
(0.8, 0.8, 0.8)	(0.0000, 0.0000, 1.0000)

.

The test results show that the system equilibrium state is highly dependent on the initial strategy probability combination of the three subjects, and different initial strategic choices lead to distinct evolutionary convergence results, without converging to a unified equilibrium point. Specifically, only the low-level symmetric initial condition (0.2,0.2,0.2) converges to the ideal equilibrium state of (compliant transaction, data protection, relaxed supervision), while all other initial combinations converge to different non-ideal equilibrium states such as (illegal transaction, data irregularities, no supervision) and (illegal transaction, data irregularities, strict supervision). This indicates that the initial behavioral tendencies of the government, operating entities and demand sides have a decisive impact on the evolutionary direction of the public data authorized operation system.

Robustness of Parameter Assignment

Five groups of new parameter combinations were randomly generated within the range of ±10% around the benchmark parameters for simulation verification, covering the random adjustment of revenue, cost, reward and fine parameters. The results indicate that the system equilibrium state and the strategic choice trend of the three subjects are completely consistent with the original results under all five groups of parameter combinations, with no qualitative change in the evolutionary convergence direction. This illustrates that the simulation results are not dependent on the specific numerical assignment of benchmark parameters within a reasonable range, and the model has strong parameter assignment stability.

Robustness of Iteration Number

The simulation iteration number was adjusted to 30, 50, 80 and 100 times for comparative analysis, with other model settings and parameters remaining unchanged. The results show that the system achieves stable convergence when the iteration number reaches 50 times, and the equilibrium state and strategic probability values do not change with the increase in iteration number (80/100 times). No significant differences are found in the convergence results of different iteration numbers, which verifies the rationality and sufficiency of the benchmark iteration number (50 times) setting in the study.

Comprehensive Robustness Conclusion

The comprehensive test results show that the evolutionary game model of public data authorized operation has strong parameter assignment stability and iteration number stability, but the system equilibrium state is highly sensitive to the initial strategy probability of the three subjects. This characteristic implies that the initial behavioral norms and supervision orientation of the government, operating entities and demand sides are the key factors determining the evolutionary direction of the public data authorized operation system. The research conclusions of the model still have good reliability and generalizability, and can provide targeted scientific support for the practical decision-making of public data authorized operation, especially for the guidance of initial behavioral intervention and supervision strategy formulation of the three subjects.

5. Conclusions

5.1. Significant Impact of the Mechanisms of Revenue Distribution on Subject Behaviors

From the perspective of the behavioral logic of the demand sides, the probability of compliant transactions of the demand sides is positively correlated with their revenue from using data products (R0) and the reward and punishment intensity of the government (F0, J0). Meanwhile, it is negatively correlated with the cost saved by illegal transactions (C0 − C1). When compliant benefits (i.e., government rewards) exceed illegal benefits (i.e., rent-seeking cost savings), the demand sides will take the initiative to choose compliant transactions; if the rent-seeking cost (B) increases, then the expected returns of illegal behaviors will further decrease, and compliance willingness will be significantly enhanced. From the perspective of the behavioral logic of the operating institutions, the probability of data protection of the operating institutions is positively correlated with government rewards and punishments (F1, J1) and data collusion costs (C2). Meanwhile, it is negatively correlated with the rent-seeking costs of the demand sides (B). When the fines for data collusion imposed by the government (F1) are higher, the rewards for data protection (J1) are more generous, or when the cost for operating institutions to tamper with or hide data (C2) is higher, the probability of them choosing data protection is also higher; on the contrary, if the rent-seeking costs of the demand sides are low, then the operating institutions are prone to choose data collusion driven by short-term interests. From the perspective of the regulatory behavioral logic of the government, the probability of its strict supervision is positively correlated with its own dereliction of duty penalties (F2) and fines for the violations of the demand sides (F0). Meanwhile, it is negatively correlated with the rewards for the subjects (J0, J1). When the superior departments increase penalties (F2) for data leakage caused by the relaxed supervision of the government, or when the illegal gains of the demand sides are high, the government will strengthen supervision; when the compliance rate of the demand sides and the data protection rate of the operating institutions increase, the government can reduce supervision intensity to achieve a dynamic balance between “supervision and market.”

5.2. Stable Equilibrium Conditions for System Evolution

The optimal equilibrium state of system evolution is when the reward and punishment amount of the government (F0 + J0, F1 + J1) is greater than the illegal gains of the demand sides (C0 − C1 − B) and the collusion gains of the operating institutions (B − C2), the system converges to the optimal equilibrium of (compliant transaction, data protection, relaxed supervision) (E5). At this time, the demand sides take the initiative to comply, the operating institutions consciously protect data, and the government does not need high-intensity supervision. As a result, a balance is achieved between data security and market efficiency. The suboptimal equilibrium risk of system evolution is that if the reward and punishment intensity is insufficient (e.g., F0 + J0 < C0 − C1 − B), then the system may fall into the suboptimal equilibrium of (illegal transaction, data collusion, strict supervision) (E4). At this time, the government needs to continuously invest high supervision costs (C3). However, eradicating illegal behaviors is difficult, which leads to low circulation efficiency of data factors and hindered release of public data value.

5.3. Optimization Directions for Revenue Distribution and Pricing Mechanisms

From the perspective of the optimization principles of revenue distribution, a distribution framework of “performance linkage, risk equivalence, multi-party collaboration, and social feedback” needs to be constructed. For the demand sides with compliant transactions, revenue sharing should be given according to the effect of data use. Meanwhile, for the operating institutions handling high-risk data (e.g., medical and financial data), risk premium compensation should be set. At the same time, the operating institutions should be required to use part of their revenue to feed back public data infrastructure (e.g., the information construction of data source departments), which forms a two-way cycle of “market revenue–public value.”

From the perspective of the adaptation strategy of the pricing mechanism, pricing should reflect data value and risk costs, and adopt differentiated and dynamic strategies. High economic value data (e.g., financial data) should adopt market-oriented bidding. Then, basic data (e.g., transportation and meteorological data) should be set at public welfare low prices. In the initial stage of authorized operations, government-guided prices should be used to control risks, and market pricing should be gradually opened up after the compliance rate increases. Moreover, pricing should be linked to credit points (e.g., demand sides with high credit can enjoy discounts on data usage fees) to strengthen the compliance motivation of the subjects.

6. Suggestions and Discussion

6.1. Improve the Targeted Incentive and Constraint Mechanism for Main Players

Based on the behavioral logic of the government, operating institutions and data demand sides, a differentiated incentive and constraint system with positive revenue incentives and rigid violation restrictions is established to shape the expectation of “benefits from compliance and high costs for violation” and guide compliant behavior at the source.

For data demand sides: Build a linkage mechanism between compliance benefits and credit ratings, implement phased revenue sharing based on the economic and social value of data application, and increase the ratio for green development and livelihood fields. Record illegal transactions in credit files, set multiple-based fines, and restrict the public data access rights of untrustworthy subjects (e.g., AAA-level subjects get fee discounts and priority access to customized products, while illegal subjects are disqualified for a certain period).

For operating institutions: Implement the risk-equivalent compensation principle, accrue risk compensation funds for high-risk data operation and subsidize data protection technology investment. Strengthen multiple accountability for data collusion with fines linked to collusion gains and leakage losses, and take data protection rate and compliant transaction rate as core assessment indicators for authorization renewal and revenue sharing (e.g., 30% technical subsidies for high-risk data protection, and priority cross-regional operation rights for excellent institutions).

For the government supervision side: Consolidate supervision responsibilities and include public data governance effectiveness in performance assessment, with hierarchical penalties for supervision negligence leading to data leakage. Optimize supervision cost allocation, feed back the saved costs from high compliance rate scenarios to public data infrastructure construction, and introduce third-party institutions to share supervision tasks and reduce government burden.

6.2. Optimize the Scientific Revenue Distribution and Pricing System

Centering on the principles of performance linkage, risk equivalence, multi-party collaboration and social feedback, a quantifiable and dynamic win-win revenue distribution framework is constructed, and a differentiated pricing strategy matching data attributes and operational laws is implemented to promote rational revenue distribution and market-oriented value release.

Multi-party collaborative revenue distribution system. Clarify the principal status of the government, data source departments, operating institutions and compliant demand sides, set basic distribution ratios, and introduce performance, compliance and public value adjustment coefficients for dynamic adjustment. Strengthen the public value feedback mechanism, requiring operating institutions to extract a fixed proportion of revenue for infrastructure upgrading to form a market revenue–public value two-way cycle (e.g., basic ratio: government 30%, data source departments 20%, operating institutions 30%, demand sides 20%; 1.2 times public value coefficient for rural revitalization data application with higher revenue sharing).

Differentiated and dynamic pricing strategy: Classify pricing by data attributes—market-oriented bidding for high-value commercial data (e.g., financial data), public welfare low prices for basic public data (e.g., transportation data), and cost + risk premium for high-risk livelihood data (e.g., medical data). Adjust pricing leading power by operation maturity: government-guided prices in the initial stage to control risks, and gradual market-oriented pricing with improved compliance rate. Establish a pricing-credit point linkage mechanism to strengthen the compliance motivation of demand sides.

6.3. Perfect the Integrated Governance and Guarantee System

Focusing on the core support needs of public data authorized operation, an integrated governance and guarantee system is built from supervision mode innovation, data resource improvement, and technical and institutional support to solve practical pain points such as data islands and low quality and lay a solid foundation for the implementation of revenue distribution mechanisms and compliant operation.

Intelligent and diversified supervision mode. Transform government supervision from high-intensity comprehensive supervision to precise and intelligent supervision, build a smart supervision platform with big data, AI and blockchain for real-time monitoring, abnormal early warning and whole-process traceability. Implement hierarchical and classified dynamic supervision by demand sides’ credit, institution assessment and data risk level. Establish a collaborative governance system of government supervision + industry self-discipline + social supervision + third-party evaluation, set up industry associations, build reporting platforms, and entrust third-party institutions to evaluate revenue distribution and data protection independently.

Public data resource integration and quality improvement: Break inter-departmental and inter-regional data barriers, build a provincially coordinated cross-regional public data resource pool with standardized collection, cleaning and integration. Establish a data quality responsibility system, clarify the responsibilities of data source departments, and link quality assessment results with revenue sharing and performance assessment to force quality improvement.

Technical and institutional support: Increase R & D investment in core technologies such as data security protection and blockchain traceability, and set up special funds to support universities and enterprises. Promote standardized application of nationally certified technologies for public data processing, especially high-risk data. Accelerate the introduction of normative documents to clarify the rights and obligations of all players, establish a dispute mediation mechanism, and strengthen the training of compound talents to improve the professional capacity of the whole industry.

6.4. Research Implications and Practical Prospects

The core implication of this study for practice is that the key to the authorized operation of public data lies in making compliant behavior of all main players a rational choice through scientific revenue distribution and reward and punishment mechanisms, rather than relying solely on high-intensity government supervision. In practice, the development of authorized operation of public data must adhere to the sustainable development orientation, put data security in first place, and balance market efficiency and public value.

Compared with international data governance frameworks, this study’s revenue distribution mechanism based on the tripartite evolutionary game presents both convergence and differentiation with typical global models. The EU’s data governance system emphasizes cross-border public data sharing, mandatory data access for specific sectors, and a “data tax” for public welfare feedback, which is consistent with the “public value feedback” principle in this paper’s distribution framework. However, the EU framework focuses more on legal compliance and cross-national coordination, while this study targets China’s centralized authorization model and highlights dynamic performance linkage and risk-benefit matching for government–operating entity–demand side. In addition, Singapore’s “safe return + value sharing” public data operation model shares similarities with our “basic income + value-added share” design, but our mechanism further integrates reward-punishment parameters and behavioral evolution simulation, making it more adaptable to large-scale public data operation scenarios with multiple stakeholders. The tripartite evolutionary game model and revenue distribution logic constructed in this paper have certain universal applicability for countries or regions promoting public data authorized operation. However, it should be noted that the model’s parameter settings are calibrated based on China’s institutional environment and pilot practices. When applied to countries with distinct legal systems, market maturity, and data governance traditions, targeted parameter correction and scenario adaptation are required to ensure the effectiveness of the mechanism.

In the future, it is possible to further make refined adjustments to the revenue distribution ratio and the intensity of rewards and punishments in combination with the characteristics of public data operation in different regions and fields, and continuously explore the application of digital technologies in data governance and supervision. It is expected to promote the transformation of public data from opening up to efficient operation and value release, so that public data can become an important support for promoting the high-quality development of the digital economy and building a sustainable digital ecosystem.

The practical recommendations of this study are based on model deduction and empirical analysis conclusions, with both theoretical logic and practical operability, which can provide direct reference for the mechanism design and policy formulation of authorized operation of public data in various regions, and promote the transformation of research results into practical effects.