Evolutionary game analysis of scientific research data sharing under the open science context

1 Introduction

The rapid advancement of big data technologies has positioned scientific research data sharing as a key driver of scientific innovation and socioeconomic development [1]. Open access to research data fosters academic collaboration and improves the utilization efficiency of scientific resources. Yet multiple systemic challenges hinder the global practice of data sharing. On the supply side, providers remain reluctant to share due to escalating marginal costs of data curation, intellectual property concerns, and reputational risks. On the demand side, users grapple with trust-related dilemmas stemming from inconsistent data quality, heterogeneous metadata standards, and restricted access rights. Privacy vulnerabilities, data security threats, interorganizational coordination costs, and regulatory resource constraints further compound the complexity of the data-sharing ecosystem.

At the heart of these challenges lie the divergent interests of stakeholders, creating a classic game-theoretic setting in which the participants hold heterogeneous objectives and only partially observe one another’s actions. Data providers prioritize profit maximization and risk mitigation; users emphasize accessibility and usability; government agencies balance public welfare against regulatory expenditure; and sharing platforms focus on operational sustainability. This multi-stakeholder structure makes it difficult for conventional unidirectional incentive models to align these competing interests. A systematic theoretical framework that captures the strategic decision-making and interactive dynamics of these actors is therefore of considerable importance.

Evolutionary game theory offers a powerful modeling tool well suited to this task. It has been widely applied to strategic interactions in multi-agent systems [2], and its treatment of social dilemmas provides valuable insights for settings in which cooperative behavior must emerge under bounded rationality [3]. In this study, we employ evolutionary game theory to construct a novel quadripartite model encompassing data providers, data users, government agencies, and sharing platforms. Unlike classical game theory, the evolutionary framework captures the strategic adaptation of boundedly rational agents through payoff-driven selection and strategy imitation at the population level, converging to a stable equilibrium [4]. Methodologically, we formulate payoff matrices across sixteen strategy combinations, derive replicator dynamic equations [5], and assess equilibrium stability via Jacobian matrix analysis.

This study makes three principal contributions. First, the four-population model extends beyond traditional bilateral analyses and provides a structured way to examine strategic adjustment among providers, users, government agencies, and platforms, while explicitly acknowledging that the platform payoff is simplified as exogenous to the strategies of the other three populations. The framework therefore captures a three-way coupled governance subsystem alongside an independently evolving platform component rather than a fully symmetric four-way co-evolutionary system. Second, it clarifies the relationship between regulatory intensity and lower-intensity, incentive-sustained coordination, yielding evidence-based guidance for phased policy design. Third, computational simulations identify conditions for a target cooperative system state and quantify the directional effects of policy packages, privacy risk, and platform incentives within the analytical model.

The remainder of the paper proceeds as follows. Section 2 reviews the literature on data sharing mechanisms and evolutionary game theory, identifying research gaps. Section 3 constructs the quadripartite model, defines parameters and assumptions, establishes the payoff matrix, derives replicator dynamic equations, and evaluates equilibrium stability. Section 4 presents numerical simulations examining key determinants of system stability. Section 5 summarizes the conclusions, discusses limitations, and outlines directions for future research.

2 Related work

Investigating the strategic challenges inherent in scientific research data sharing necessitates a critical engagement with two largely independent strands of literature. The first strand, situated within the domains of open science and data governance, examines the principles, platforms, incentive mechanisms, and regulatory frameworks that shape data sharing behavior across disciplines. However, this body of work has seldom adopted formal game-theoretic approaches to capture the coupled strategic dynamics among multiple stakeholder populations. The second strand, grounded in evolutionary game theory, offers rigorous analytical tools for modeling strategic adaptation in multi-agent systems and has recently been extended to four-party (quadripartite) settings in contexts such as energy policy and environmental regulation. Nevertheless, it has yet to be applied to the specific payoff structures and policy trade-offs that characterize scientific data governance. The remainder of this section reviews each strand in turn before synthesizing the findings to delineate the research gaps that motivate the present study.

2.1 Scientific data sharing: principles, platforms, and governance

The sharing of scientific research data has become a central imperative in the open science movement. Conceptually, the FAIR Guiding Principles, which mandate that data be Findable, Accessible, Interoperable, and Reusable, serve as the normative foundation for contemporary data stewardship. Building on this framework, Rocca-Serra et al. [6] provide actionable implementation guidance through the FAIR Cookbook, aiming to bridge the persistent gap between aspirational FAIR objectives and practical execution across diverse scientific domains. Taking a broader conceptual view, Umbach [7] frames Open Access, Open Data, FAIR principles, and Open Science as an interconnected “openness quartet,” analyzing both the synergies among these paradigms and the institutional barriers that impede their full realization. Empirically, large-scale surveys reveal considerable heterogeneity in data-sharing practices across disciplines. For instance, Khan et al. [8], in a survey of 3,257 researchers spanning 20 Scopus-indexed disciplines, found that data sharing remains far from universal in any discipline. Similarly, Gregory et al. [9] identified distinct disciplinary clusters in data-citation behavior, suggesting that the reputational incentives driving data sharing operate through markedly different mechanisms across fields.

Beyond conceptual and empirical foundations, a variety of technological platforms and institutional infrastructures have been developed to facilitate secure and efficient data exchange. Emerging technical solutions include blockchain-based architectures that ensure transparent traceability and dynamic licensing [10], smart contract systems designed to automate contribution evaluation and reward distribution [11], and federated learning frameworks that balance computational efficiency with privacy preservation [12]. Despite these technological advances, institutional coordination remains a critical bottleneck. Borgman and Bourne [13] contend that sustainable data sharing depends not on compliance by individual researchers alone, but on concerted investment across a network of institutional actors, including libraries, IT services, research administration offices, and disciplinary repositories. Corroborating this view, Borgman and Brand [14] document how universities systematically underutilize their own research data assets, exposing a structural disconnect between the ambitions of data-sharing policies and actual institutional capacity.

Complementing infrastructural development, the alignment of multi-stakeholder incentives and the design of robust governance frameworks are equally critical. To sustain long-term platform participation, Jaiman et al. [15] propose smart contract-based pricing mechanisms coupled with reputation scoring, while Yang and Huang [16] apply Shapley value analysis to achieve equitable benefit allocation among heterogeneous data contributors. Governance and ethical considerations present additional complexities. A systematic review of 972 studies by Wilmes et al. [17] revealed pervasive under-reporting of informed consent, data anonymization, and FAIR compliance, with none of the reviewed studies demonstrating full adherence to FAIR principles. Addressing the societal dimensions of data governance, Kraft et al. [18] examine the tensions between open science mandates and health justice, advocating for community-informed protections for marginalized populations. Taken together, this body of literature underscores that effective data sharing necessitates coordinated mechanisms that span normative principles, technological platforms, incentive structures, and governance protocols. However, existing research has predominantly examined these dimensions in isolation or within bilateral analytical frameworks. How sharing behaviors dynamically co-evolve among multiple stakeholder populations under coupled policy interventions and privacy constraints remains insufficiently understood.

2.2 Evolutionary game theory

Evolutionary game theory analyzes strategic interactions among populations of agents who adapt through learning and selection. It has been applied across biology, economics, and sociology, yielding deep insights into collective behavior and evolutionary dynamics.

In dyadic settings, Li et al. [19] model community reciprocity in social networks and demonstrate that community structures enhance the spread of cooperation. Abadi and Ataee-pour [20] show that properly designed reward and punishment mechanisms steer cooperation in public-private partnerships and offer quantitative tools for regulatory design. Lu et al. [21] find that dynamic government subsidies outperform fixed incentives in promoting green building adoption. Hussain et al. [22] verify the applicability of evolutionary game theory to cross-regional environmental governance, revealing equilibria between cooperative motives and policy conflicts.

In tripartite games, Fargetta and Scrimali [23] construct a platform-contractor-consumer model for live-stream e-commerce incorporating contractual penalties, explaining divergent short-term and long-term market dynamics. Eghbali et al. [24] demonstrate that full-chain government intervention stimulates synergy among technology firms, startups, and incubators in green innovation. Xia et al. [25] and Chang [26] further illustrate the value of tripartite models in sustainability policy research.

For games with four or more participants, Quan et al. [27] highlight the role of multi-level and multi-stage interactions in shaping cooperative evolution, while Wang et al. [28] show that adaptive strategy-update rules can substantially affect evolutionary outcomes in social dilemmas. Na et al. [29] incorporate large consumers into renewable energy quota systems and predict regulatory slack via four-agent dynamics. Zhang et al. [30] quantify ecological compensation in transboundary water pollution through a quadrilateral evolutionary game model. Li et al. [31] analyze photovoltaic market interactions under inclusive finance, yielding differentiated renewable energy incentives. These contributions extend evolutionary game theory toward higher-dimensional complex systems, enabling multi-agent governance methodologies.

2.3 Literature synthesis and research gap

The preceding review reveals two largely parallel streams. The data-sharing literature has established that effective sharing requires coordinated FAIR-aligned principles, secure platforms, institutional infrastructure, multi-stakeholder incentives, and privacy-aware governance frameworks; large-scale surveys further document persistent gaps between aspiration and practice across disciplines. Concurrently, evolutionary game theory has progressed from dyadic and tripartite models to quadripartite applications in domains such as renewable energy regulation and transboundary pollution control, demonstrating its capacity to capture coupled multi-agent dynamics.

However, studies bridging these two streams remain scarce. Existing game-theoretic approaches to data sharing predominantly adopt bilateral or tripartite frameworks and have not engaged with the empirical insights on disciplinary barriers, FAIR implementation challenges, and governance trade-offs documented in the recent open-science literature. Conversely, higher-dimensional evolutionary game models have been applied to energy and environmental governance but not to scientific data sharing, where the interplay of privacy risk, subsidy intensity, and platform incentives generates distinct strategic tensions.

Three gaps emerge. First, a four-party evolutionary game model tailored to scientific research data sharing, capturing strategic interplay among providers, users, government, and platforms, is absent. Second, the transition from government-driven regulation to lower-intensity, incentive-sustained coordination has not been formalized within a multi-agent data governance framework. Third, threshold effects of subsidies, privacy risks, and penalties on system stability remain unquantified in this domain. Table 1 positions this study against representative works. To address these gaps, this study constructs a four-party evolutionary game framework under explicit simplifying assumptions, derives cooperative equilibrium conditions, and systematically examines parametric sensitivity through numerical simulation.

TABLE 1. Comparison of this study with representative literature across the two research streams.

3 Model construction

3.1 Model framework

Digital transformation and the open science movement have elevated the academic value and application potential of scientific research data, making data sharing a widely accepted priority. Advances in big data and artificial intelligence have further amplified both the scale and value of research data. Yet intensifying scientific competition has encouraged some providers to prioritize rapid release over rigorous quality assurance, resulting in lax quality control.

Research on scientific data sharing in China currently centers on intellectual property stakeholders and IP-related policies, with an emphasis on institutional-level exchange. Although data trading platforms have emerged, a comprehensive online system for data quality evaluation and transmission remains under development, even as the construction of standardized sharing platforms advances.

Data sharing platforms serve as critical infrastructure for the efficient circulation of data in academic fields. As key nodes in the research data lifecycle, they integrate data submission, quality control, and access management. These platforms are expected to act as gatekeepers of data quality while strengthening cooperation with regulatory institutions to maintain a healthy sharing ecosystem.

However, conflicts of interest among platforms, providers, and users, combined with the limited supervisory capacity of research management institutions, pose serious risks to data quality and sharing efficiency. To address these challenges, this study constructs a multi-agent game model of data quality governance. The interactive relationships among the four participants are illustrated in Figure 1.

3.2 Model assumptions

Hypothesis 1 (Participants): The four-party evolutionary game involves data providers, data users, government regulatory authorities, and platform institutions. All four populations are assumed to be boundedly rational and to adjust their strategy shares through payoff-monotonic imitation and learning. The resulting replicator dynamics may converge to a locally asymptotically stable rest point; convergence to a globally optimal outcome is not assumed.

Hypothesis 2 (Strategy spaces): Data providers choose between active provision (probability x, 0 ≤ x ≤ 1) and passive provision ( 1 − x ). Data users choose between trusting use (probability y) and questioning use ( 1 − y ). The government chooses between strong supervision (probability z) and weak supervision ( 1 − z ). The platform chooses between active participation (probability k) and passive participation ( 1 − k ).

Hypothesis 3 (Data providers): Providers hold data whose quantity and quality are jointly captured by the aggregate C. Their baseline revenue is W. The active-provision cost coefficient is t 1. Passive provision is normalized to the baseline payoff W in the payoff matrix; the coefficient t 2 is retained only as a descriptive reference for the higher ad-hoc preparation and remediation burden associated with passive provision, with t 1 < t 2. Providers also earn reputational benefits G from data sharing, while facing potential losses from privacy breaches and data inaccuracies, captured by the coefficient E.

Hypothesis 4 (Data users): Users access a platform-mediated data resource with quantity-quality aggregate B, where B < C reflects transmission, screening, and filtering losses relative to the data held by providers. To keep the analytical model tractable, B is treated as an exogenous accessible-data aggregate rather than a function of the current provider strategy share x; this abstraction is revisited in the limitations. Users earn a baseline revenue W from research activities, with research benefit coefficient D. The coefficients h 1 and h 2 denote the verification and preprocessing costs borne by trusted users under active and passive platform support, respectively, with h 1 < h 2; questioning use is normalized to the baseline payoff W.

Hypothesis 5 (Government): The government’s comprehensive benefit encompassing credibility and socioeconomic value is denoted by L. Supervision costs are f 1 (strong) and f 2 (weak), with f 2 < f 1. The government provides subsidies to incentivize data sharing, at rates s 1 (strong supervision) and s 2 (weak supervision), where s 2 < s 1. Social benefits from data provision and usage are captured by coefficients P and Q, respectively. Platforms that participate passively face a penalty F, while potential negative losses from weak supervision paired with active platform participation are denoted by O.

Hypothesis 6 (Platforms): The platform’s baseline operational income is T. Active participation incurs cost m 1 and yields potential revenue n 1 plus government reward A. Passive participation incurs lower cost m 2 and yields lower revenue n 2, where m 2 < m 1 and n 2 < n 1. It is further assumed that the platform’s payoff depends on its own participation level and government-imposed rewards and penalties, but is invariant with respect to the strategies of data providers and data users. This simplification keeps the model analytically tractable.

3.3 Parameter definitions

The parameters defined in Hypotheses 1–6 are organized into four thematic categories and summarized in Table 2. (a) Data provider cost–benefit structure (C, W, G, E, t 1, t 2): The net benefit G − E governs providers’ willingness to share, while t 2 − t 1 is used as a descriptive efficiency-gap indicator rather than as a term in the current selection gradient. (b) Data user cost–benefit structure (B, D, h 1, h 2, W), where h 1 and h 2 represent trusted-use verification costs under active and passive platform support. (c) Government fiscal and regulatory instruments (L, f 1, f 2, s 1, s 2, P, Q, F, A, O). (d) Platform investment and operational structure (T, m 1, m 2, n 1, n 2). The parameter inequalities that govern which equilibrium ultimately emerges are not imposed here as assumptions; rather, they are derived from the eigenvalue analysis in Section 3.5 and are previewed at this point only to aid interpretation. As that analysis will show, the platform participates actively when A + F > m 1 − m 2 − n 1 + n 2; trusted usage becomes locally stable under strong supervision when D > h 1 − s 1; and the government’s stable regulatory strategy depends on the tradeoff among f 1 − f 2, s 1 − s 2, and O.

TABLE 2. Definitions of model parameters.

Government subsidies serve as the principal regulatory mechanism. Under strong supervision ( s 1 ), higher subsidy rates incentivize both active data provision and trusted usage. Under weak supervision ( s 2 ), subsidy levels decline, reflecting a shift toward lower-intensity public involvement rather than a complete withdrawal from governance. The penalty F deters passive platform participation, while the reward A encourages active engagement. The potential loss O captures reputational and operational risks when weak supervision coincides with active platform participation. Several inherent parameter relationships hold throughout: (i) proactive provision and active platform support are assumed to reduce effective verification or preparation burdens, hence t 1 < t 2, h 1 < h 2, and m 2 < m 1; (ii) active platform participation yields higher returns, so n 2 < n 1; and (iii) strong supervision entails higher fiscal expenditure but greater intervention intensity, implying f 2 < f 1 and s 2 < s 1.

3.4 Payoff matrix

The four-party evolutionary game model yields 2 4 = 16 strategy combinations based on the binary choices of each agent. Drawing on the assumptions and parameter definitions established above, the complete payoff matrix is presented in Table 3.

TABLE 3. Payoff matrix.

To illustrate the payoff structure, consider the strategy profile in which providers choose active provision, users choose trusted use, the government adopts strong regulation, and the platform participates actively. The provider’s payoff comprises the baseline revenue W plus the net benefit from data provision: the data quantity-quality aggregate C multiplied by the sum of reputational benefit G and strong-supervision subsidy s 1, minus provision cost t 1 C and privacy risk loss E C, yielding W + ( G + s 1 − t 1 − E ) × C.

Three features of this payoff structure follow from the simplifying assumptions and should be made explicit, since they shape the interpretation of the results that follow. First, passive provision is modeled as yielding only the baseline revenue W with no additional preparation cost, so the passive-provision cost coefficient t 2 does not enter the payoff matrix or the resulting selection gradient; it is retained solely as a reference coefficient that characterizes the efficiency gap t 2 − t 1 between active and passive provision. Second, the user cost coefficients h 1 and h 2 enter the trusted-use payoff according to the platform’s state—trusted users bear h 1 when the platform participates actively and h 2 when it participates passively—so that h 1 and h 2 represent the verification burden faced by trusted users under active versus passive platform support, while questioning use is normalized to the baseline payoff W. Third, the platform’s payoff in every profile depends only on its own participation level and on the government’s fixed reward and penalty, and is invariant to the strategies of providers and users. These are deliberate simplifications adopted for analytical tractability; their consequences are discussed in Section 5.2.

3.5 Stability analysis of individual strategies

3.5.1 Data providers

The expected payoff for scientific research data providers who opt for the “active” strategy is denoted as U 1, whereas the expected payoff for those who select the “passive” strategy is defined as U 2. The average expected payoff for scientific research data providers is represented as U. The mathematical expressions that correspond to U 1, U 2, and U are presented as follows:

U 1 = C G + s 1 − t 1 − E + W y z k + C G + s 1 − t 1 − E + W 1 − y z k + C G + s 2 − t 1 − E + W y 1 − z k + C G + s 2 − t 1 − E + W 1 − y 1 − z k + C G + s 1 − t 1 − E + W y z 1 − k + C G + s 1 − t 1 − E + W 1 − y z 1 − k + C G + s 2 − t 1 − E + W y 1 − z 1 − k + C G + s 2 − t 1 − E + W 1 − y 1 − z 1 − k (1)

U 2 = W y z k + W 1 − y z k + W y 1 − z k + W 1 − y 1 − z k + W y z 1 − k + W 1 − y z 1 − k + W y 1 − z 1 − k + W 1 − y 1 − z 1 − k (2)

U = x U 1 + 1 − x U 2 (3)

F x = x U 1 − U = C x 1 − x G + z s 1 − s 2 + s 2 − t 1 − E (4)

d F x d x = C 1 − 2 x G + z s 1 − s 2 + s 2 − t 1 − E (5)

Let g ( z ) = G + z ( s 1 − s 2 ) + s 2 − t 1 − E. According to the stability theorem of differential equations, a boundary point of the provider is locally asymptotically stable when F ( x ) = 0 and d d x ( F ( x ) ) < 0. The equilibrium points of the evolutionary process are as follows:

• When z = z * = t 1 + E − G − s 2 s 1 − s 2, g ( z ) = 0 and F ( x ) ≡ 0 for every x. This is a non-hyperbolic (neutrally stable) case: the replicator equation is stationary for any provider share, and the strategy of the scientific data provider does not change over time, but no restoring force drives x toward a particular value.
• When z > z *, for F ( x ): If x = 1, then d d x ( F ( x ) ) < 0, at this point, x = 1 is the locally asymptotically stable equilibrium, meaning the provider will tend to choose the “active provision” strategy. Conversely, when z < z * and x = 0, d d x ( F ( x ) ) < 0, at this point, x = 0 is the locally asymptotically stable equilibrium, meaning the provider will tend to choose the “passive provision” strategy.

3.5.2 Data users

For scientific research data users, the expected payoff that is associated with the “trusted use” strategy of scientific research data is designated as V 1, and the expected payoff corresponding to the “questioned use” strategy is specified as V 2. The mathematical expressions that represent the average expected payoff V, along with V 1 and V 2, are provided as follows:

V 1 = B D + s 1 − h 1 + W x z k + B D + s 1 − h 1 + W 1 − x z k + B D + s 2 − h 1 + W x 1 − z k + B D + s 2 − h 1 + W 1 − x 1 − z k + B D + s 1 − h 2 + W x z 1 − k + B D + s 1 − h 2 + W 1 − x z 1 − k + B D + s 2 − h 2 + W x 1 − z 1 − k + B D + s 2 − h 2 + W 1 − x 1 − z 1 − k (6)

V 2 = W x z k + W 1 − x z k + W x 1 − z k + W 1 − x 1 − z k + W x z 1 − k + W 1 − x z 1 − k + W x 1 − z 1 − k + W 1 − x 1 − z 1 − k (7)

V = y V 1 + 1 − y V 2 (8)

Following the standard replicator dynamics formulation [5], the replication dynamic equation F ( y ) of available scientific research data users is sorted out as follows:

F y = y V 1 − V = B y 1 − y z s 1 − s 2 + k h 2 − h 1 + s 2 − h 2 + D (9)

The first-order derivative of the function f ( y ) with respect to y is then expressed as:

d F y d y = B 1 − 2 y z s 1 − z s 2 + k h 2 − k h 1 + s 2 − h 2 + D (10)

Let j ( z ) = z ( s 1 − s 2 ) + k ( h 2 − h 1 ) + s 2 − h 2 + D. Therefore, according to the stability theorem of differential equations, a boundary point of the user is locally asymptotically stable when F ( y ) = 0 and d d y ( F ( y ) ) < 0. The equilibrium points of the evolutionary process are as follows:

• When z = z 1 * = k ( h 2 − h 1 ) + s 2 − h 2 + D s 2 − s 1, the expression j ( z , k ) vanishes and F ( y ) ≡ 0 for every y. This is a non-hyperbolic (neutrally stable) case: the replicator equation is stationary for any user share and no restoring force selects a particular y. The threshold z 1 * is meaningful only when it falls within [ 0,1 ]; otherwise one strategy dominates over the entire feasible domain.
• Since ∂ j / ∂ z = s 1 − s 2 > 0, the function j ( z , k ) is strictly increasing in z. When z < z 1 *, j ( z , k ) < 0 and d F ( y ) d y y = 0 < 0, so y = 0 (questioning use) is locally asymptotically stable. Conversely, when z > z 1 *, j ( z , k ) > 0 and d F ( y ) d y y = 1 < 0, so y = 1 (trusted use) is locally asymptotically stable.

3.5.3 Government

For the government, the expected payoff that corresponds to the “strong supervision” strategy in scientific research data sharing is denoted as W 1, and the expected payoff associated with the “weak supervision” strategy is defined as W 2. To avoid a symbol clash with the baseline revenue W of providers and users, the government’s average expected payoff is denoted W ̄ g. The mathematical expressions for W ̄ g, together with W 1 and W 2, are presented as follows:

W 1 = B Q − s 1 + C P − s 1 + L − A − f 1 x y k + L − A − f 1 1 − x y k + C P − s 1 + L − A − f 1 x 1 − y k + L − A − f 1 1 − x 1 − y k + B Q − s 1 + C P − s 1 + L + F − f 1 x y 1 − k + L + F − f 1 1 − x y 1 − k + C P − s 1 + L + F − f 1 x 1 − y 1 − k + L + F − f 1 1 − x 1 − y 1 − k (11)

W 2 = B Q − s 2 + C P − s 2 + L − A − O − f 2 x y k + L − A − O − f 2 1 − x y k + C P − s 2 + L − A − O − f 2 x 1 − y k + L − A − O − f 2 1 − x 1 − y k + B Q − s 2 + C P − s 2 + L + F − f 2 x y 1 − k + L + F − f 2 1 − x y 1 − k + C P − s 2 + L + F − f 2 x 1 − y 1 − k + L + F − f 2 1 − x 1 − y 1 − k (12)

W ̄ g = z W 1 + 1 − z W 2 (13)

Following the standard replicator dynamics formulation [5], the replication dynamic equation F ( z ) of government is sorted out as follows:

F z = z W 1 − W ̄ g = z 1 − z C x s 2 − s 1 + B x y s 2 − s 1 + O k + f 2 − f 1 (14)

The first-order derivative of the function F z with respect to z is then expressed as:

d F z d z = 1 − 2 z C x s 2 − s 1 + B x y s 2 − s 1 + O k + f 2 − f 1 (15)

Let h ( k ) = C x ( s 2 − s 1 ) + B x y ( s 2 − s 1 ) + O k + f 2 − f 1. A notable feature of this reduced selection gradient is that the government’s comprehensive benefit L and the social benefit coefficients P and Q cancel out in the payoff difference W 1 − W 2, as do the reward A and penalty F. Consequently, the government’s stable strategy is driven only by the additional subsidy expenditure (through s 1 − s 2), the supervision cost difference f 1 − f 2, and the loss O incurred when weak supervision coincides with active platform participation; L, P, and Q affect the government’s payoff level but not its strategic selection gradient. According to the stability theorem of differential equations, a boundary point of the government is locally asymptotically stable when F ( z ) = 0 and d d z ( F ( z ) ) < 0. The equilibrium points of the evolutionary process are as follows:

• When k = k * = ( s 1 − s 2 ) ( C x + B x y ) + f 1 − f 2 O, the expression h ( k ) vanishes and F ( z ) ≡ 0 for every z. This is a non-hyperbolic (neutrally stable) case: the government share is stationary for any z and no restoring force selects a particular value. The threshold k * is meaningful only when it lies within [ 0,1 ]; otherwise one supervision strategy dominates over the entire feasible domain.
• Since ∂ h / ∂ k = O > 0, the function h ( k ) is strictly increasing in k. When k < k *, h ( k ) < 0 and d F ( z ) d z z = 0 < 0, so z = 0 (weak supervision) is locally asymptotically stable. Conversely, when k > k *, h ( k ) > 0 and d F ( z ) d z z = 1 < 0, so z = 1 (strong supervision) is locally asymptotically stable.

3.5.4 Data sharing platform

The expected payoff for the scientific research data-sharing platform that selects the “active participation” strategy is denoted as R 1. The expected payoff corresponding to the “passive participation” strategy is defined as R 2. The mathematical expressions for R 1, R 2, and the average expected payoff R are presented as follows:

R 1 = T + A + n 1 − m 1 x y z + T + A + n 1 − m 1 1 − x y z + T + A + n 1 − m 1 x 1 − y z + T + A + n 1 − m 1 1 − x 1 − y z + T + A + n 1 − m 1 x y 1 − z + T + A + n 1 − m 1 1 − x y 1 − z + T + A + n 1 − m 1 x 1 − y 1 − z + T + A + n 1 − m 1 1 − x 1 − y 1 − z (16)

R 2 = T − F + n 2 − m 2 x y z + T − F + n 2 − m 2 1 − x y z + T − F + n 2 − m 2 x 1 − y z + T − F + n 2 − m 2 1 − x 1 − y z + T − F + n 2 − m 2 x y 1 − z + T − F + n 2 − m 2 1 − x y 1 − z + T − F + n 2 − m 2 x 1 − y 1 − z + T − F + n 2 − m 2 1 − x 1 − y 1 − z (17)

R = k R 1 + 1 − k R 2 (18)

Following the standard replicator dynamics formulation [5], the replication dynamic equation F ( k ) of the scientific research data sharing platform is sorted out as follows:

F k = k R 1 − R = k 1 − k A + F + m 2 + n 1 − m 1 − n 2 (19)

The first-order derivative of the function f k with respect to k is then expressed as:

d F k d k = 1 − 2 k A + F + m 2 + n 1 − m 1 − n 2 (20)

Let l = A + F + m 2 + n 1 − m 1 − n 2. According to the stability theorem of differential equations, a boundary point of the platform is locally asymptotically stable when F ( k ) = 0 and d d k ( F ( k ) ) < 0. When l ≠ 0, the platform reaches a locally asymptotically stable state at k = 1 (active participation) if l > 0 and at k = 0 (passive participation) if l < 0. In the boundary case l = 0, F ( k ) ≡ 0 for every k ∈ [ 0,1 ], so every platform share is a non-hyperbolic (neutrally stable) rest point. Because l contains no x, y, or z terms, the platform’s stable choice is independent of the strategies of the other three agents.

3.6 Stability of strategy combinations

This study focuses on a four-party evolutionary game model that is composed of four types of participants, including scientific research data providers, scientific research data users, relevant government departments, and scientific research data sharing platforms. A replicator dynamics system is constructed for these four participants, and the replicator dynamic equations of this system are presented as follows:

F x = C x 1 − x G + z s 1 − s 2 + s 2 − t 1 − E F y = B y 1 − y z s 1 − s 2 + k h 2 − h 1 + s 2 − h 2 + D F z = z 1 − z s 2 − s 1 C x + B x y + O k + f 2 − f 1 F k = k 1 − k A + F + m 2 + n 1 − m 1 − n 2 (21)

By setting the above system of equations equal to 0 and excluding the interior (mixed-strategy) points, we obtain the 16 pure-strategy boundary vertices as candidate rest points: D 1 ( 0,0,0,0 ), D 2 ( 1,0,0,0 ), D 3 ( 0,1,0,0 ), D 4 ( 0,0,1,0 ), D 5 ( 0,0,0,1 ), D 6 ( 1,1,0,0 ), D 7 ( 1,0,1,0 ), D 8 ( 1,0,0,1 ), D 9 ( 0,1,1,0 ), D 10 ( 0,1,0,1 ), D 11 ( 0,0,1,1 ), D 12 ( 1,1,1,0 ), D 13 ( 1,1,0,1 ), D 14 ( 1,0,1,1 ), D 15 ( 0,1,1,1 ), D 16 ( 1,1,1,1 ).

These 16 vertices are candidate rest points because the x ( 1 − x ), y ( 1 − y ), z ( 1 − z ), and k ( 1 − k ) factors in the replicator equations vanish there automatically; they are not, by construction, strict Nash equilibria, and would qualify as such only where the corresponding payoff inequalities hold strictly. The stability of these candidate rest points is evaluated through the application of the Lyapunov Indirect Method and Jacobian Matrix analysis, which are widely used in dynamic system research. Specifically, the local asymptotic stability of the 16 pure-strategy candidate rest points that exist within the evolutionary system is examined, where these points are substituted into the Jacobian matrix to conduct the assessment. For high-dimensional complex evolutionary game systems such as the four-agent game constructed in this study, Jacobian matrix-based stability determination combined with dimension-reduction numerical simulation methods serves as a key technical approach [33].

A candidate rest point is locally asymptotically stable when all eigenvalues of its Jacobian matrix are negative; following the convention of the multi-population evolutionary game literature, we refer to such a point as an Evolutionarily Stable Strategy (ESS), while noting that, strictly speaking, in asymmetric multi-population games the Jacobian eigenvalue criterion establishes asymptotic stability rather than the classical single-population ESS of Maynard Smith and Price. Conversely, the point is unstable if at least one eigenvalue is positive; among unstable points, we follow common usage in labeling those with eigenvalues of mixed sign as saddle-type, whereas a point with all-positive eigenvalues is a source (unstable node). In cases where one eigenvalue equals zero while all other non-zero eigenvalues are negative, the point is non-hyperbolic and its stability cannot be determined from the linearization alone.

Based on these analytical procedures, we derive the Jacobian matrix for our study as follows:

J = J 11 = ∂ F x ∂ x J 12 = ∂ F x ∂ y J 13 = ∂ F x ∂ z J 14 = ∂ F x ∂ k J 21 = ∂ F y ∂ x J 22 = ∂ F y ∂ y J 23 = ∂ F y ∂ z J 24 = ∂ F y ∂ k J 31 = ∂ F z ∂ x J 32 = ∂ F z ∂ y J 33 = ∂ F z ∂ z J 34 = ∂ F z ∂ k J 41 = ∂ F k ∂ x J 42 = ∂ F k ∂ y J 43 = ∂ F k ∂ z J 44 = ∂ F k ∂ k (22)

The specific expression is as follows:

J 11 = C 1 − 2 x G + z s 1 − s 2 + s 2 − t 1 − E J 12 = 0 J 13 = C x 1 − x s 1 − s 2 J 14 = 0 J 21 = 0 J 22 = B 1 − 2 y z s 1 − s 2 + k h 2 − h 1 + s 2 − h 2 + D J 23 = B y 1 − y s 1 − s 2 J 24 = B y y − 1 h 1 − h 2 J 31 = z z − 1 B y + C s 1 − s 2 J 32 = B x z z − 1 s 1 − s 2 J 33 = 1 − 2 z C x s 2 − s 1 + B x y s 2 − s 1 + O k + f 2 − f 1 J 34 = O z 1 − z J 41 = 0 J 42 = 0 J 43 = 0 J 44 = 1 − 2 k A + F + m 2 + n 1 − m 1 − n 2 (23)

3.6.1 Equilibria under strong supervision

When C x ( s 2 − s 1 ) + B x y ( s 2 − s 1 ) + O k > f 1 − f 2, that is, when the difference between the costs incurred by the government for choosing strong regulation versus weak regulation in the process of scientific data sharing is less than the difference between the losses and subsidies under weak regulation and those under strong regulation, the government tends to adopt the “strong regulation” strategy. In this case, there are a total of 8 equilibrium points, and the analysis of their asymptotic stability conditions is shown in Table 4.

TABLE 4. Equilibrium point stability analysis of four-party evolutionary game.

In the initial stage of scientific research data sharing, government intervention is considered necessary to guide the implementation of relevant policies and measures that can promote data sharing. As presented in Table 4, when the government chooses the “strong regulation” strategy, four of the eight candidate rest points can become locally asymptotically stable once their respective conditions are met, while the remaining four are unstable. In the “Stability” column, “Condition i” denotes a point that is locally asymptotically stable precisely when the listed eigenvalue signs are all negative, and “Unstable” denotes a point with at least one positive eigenvalue. We follow the common convention of describing such unstable boundary points as saddle-type; strictly, a point is a saddle only when its eigenvalues are of mixed sign, and a source when they are all positive.

Condition 1: In the initial stage of scientific research data sharing, the evolutionary game agents pursue profit maximization based on bounded rationality. When data providers lack profit incentives, they tend to provide data passively; data users, due to the lack of high-quality data, tend to use it skeptically; the government, facing increasing demand, implements strong regulation to promote active platform participation. This equilibrium point requires the following conditions to be satisfied: G − E < t 1 − s 1, D < h 1 − s 1, O > f 1 − f 2, A + F > m 1 − m 2 − n 1 + n 2. When the net benefit of data providers (benefit coefficient minus privacy risk loss coefficient) is less than the net savings from passive provision (cost coefficient minus strong regulation subsidy coefficient), data providers may lack motivation to actively provide data. When the data usage benefit coefficient is less than the trusted usage cost coefficient minus the strong regulation subsidy coefficient, data users may be unwilling to use the data in a trusted manner. Strong supervision is locally stable at this point when the potential loss under weak supervision with active platform participation exceeds the additional cost of strong supervision, i.e., O > f 1 − f 2. When the platform’s active participation incentives (reward plus penalty) exceed the sum of the cost difference and benefit difference between active and passive participation, the incentives are sufficient to offset the changes, prompting the platform to participate actively. This condition corresponds to the strategy combination (0, 0, 1, 1), with the corresponding evolutionary strategy simulation results shown in Figure 2.

Condition 2: In the process of data sharing, strong regulation promotes the provision of high-quality data through subsidies, while users tend to employ skeptical usage when confronted with complex data, and platform participation is encouraged by strong regulation via subsidy and penalty mechanisms. This equilibrium requires that E − G < s 1 − t 1, D < h 1 − s 1, f 1 − f 2 < O − C ( s 1 − s 2 ), and A + F > m 1 − m 2 − n 1 + n 2. Specifically, data providers remain motivated to supply data when the difference between privacy risk loss and data provision income is less than the difference between strong regulatory subsidies and passive provision costs, which implies that subsidies can cover related costs; data usage behavior is sustainable when the income from data use is less than the difference between trusted usage cost and the subsidy; strong government regulation is locally stable when the potential weak-supervision loss, net of the additional subsidy burden associated with active provision, exceeds the supervision cost difference; and the platform is motivated to shift to active participation when its incentives (rewards plus penalties) exceed the comprehensive changes in costs and benefits. This condition corresponds to the strategy combination (1, 0, 1, 1), with the corresponding evolutionary strategy simulation results shown in Figure 3.

Condition 3: Scientific data providers struggle to maintain consistent high-quality data provision, often leading to passive attitudes and low-quality supply. Thus, data users actively seek support and ultimately choose to trust and accept available data. Under the fixed reward–penalty mechanism, data sharing platforms participate actively when platform incentives outweigh the net cost of active participation. This equilibrium requires the following conditions: G − E < t 1 − s 1, D > h 1 − s 1, f 1 − f 2 < O, A + F > m 1 − m 2 − n 1 + n 2. Specifically, under strong regulation, data providers tend to adopt passive strategies when their net benefits affected by privacy risks and low returns are lower than the costs of passive data provision. Conversely, data users are inclined toward trusted usage due to higher benefits and subsidy incentives. Meanwhile, strong regulation is locally stable when the potential loss associated with weak supervision exceeds the supervision cost differential. Platforms, the net benefits under government incentive and penalty mechanisms favor active participation. This scenario demonstrates that strong regulatory policies effectively regulate stakeholders’ behaviors, corresponding to the strategic combination (0, 1, 1, 1), with the corresponding evolutionary strategy simulation results shown in Figure 4.

Condition 4: The government will strengthen financial assistance and policy incentives in the process of scientific research data sharing, and accelerate the positive role of scientific research data sharing in social development. The providers, users and platforms of scientific research data will be affected by it, and they will choose to actively provide, trust and participate. The equilibrium point must meet the following conditions: E − G < s 1 − t 1, D > h 1 − s 1, f 1 − f 2 < O − ( B + C ) ( s 1 − s 2 ), A + F > m 1 − m 2 − n 1 + n 2. Specifically, when the net loss caused by privacy risk is less than the net subsidy under the government’s strong supervision, and the income from data use is higher than the difference between the questioning cost and the supervision subsidy, strong supervision is locally stable when the potential loss from weak supervision, net of the additional subsidy burden associated with active providers and trusted users, exceeds the supervision cost differential, and the incentive and punishment mechanism of platform participation offsets the difference between its participation cost and income, thus forming a multi-party equilibrium. This scenario demonstrates that incentive-based strong regulatory policies drive all stakeholders to adopt positive collaborative strategies, corresponding to the strategic combination (1, 1, 1, 1), with the corresponding evolutionary strategy simulation results shown in Figure 5. At this time, the government has the strongest influence on the scientific research data platform, and the evolution speed of scientific research data providers is the slowest.

3.6.2 Equilibria under weak supervision

When C x ( s 2 − s 1 ) + B x y ( s 2 − s 1 ) + O k < f 1 − f 2, that is, the difference between the cost of choosing strong supervision and the cost of weak supervision in the process of scientific research data sharing is greater than the net benefit differential between weak and strong supervision, the government tends to choose the “weak supervision” strategy. The asymptotic stability condition analysis of the corresponding eight equilibrium points of the replicator dynamic system is shown in Table 5.

TABLE 5. Asymptotic stability analysis of equilibrium point under weak government supervision strategy.

During the stable development phase of scientific research data sharing, the model suggests that lower-intensity supervision may coexist with active strategies by providers, users, and platforms when the corresponding payoff inequalities are satisfied. This statement should not be interpreted as a proof of social optimality: the model contains no explicit welfare maximization criterion. It should also be emphasized that weak supervision ( z = 0 ) does not correspond to a complete absence of intervention: the government still disburses the subsidy s 2 and reward A and enforces the penalty F, so this regime is best understood as lower-intensity involvement. As shown in Table 5, the four rows labelled “Condition” are the representative weak-supervision boundary states emphasized in the policy discussion. The rows labelled “Parameter-dependent” are not claimed to be intrinsically saddle points; their stability also depends on the signs of the listed eigenvalues and may change under alternative parameter restrictions. The equilibrium points selected for detailed interpretation, covering a gradient from full passivity to multi-party collaboration, are (0, 0, 0, 0) (0, 1, 0, 0), (0, 1, 0, 1), and (1, 1, 0, 1).

Condition 1: With the continuous development of scientific data sharing, data providers who receive no additional incentives gradually choose to contribute passively. This is accompanied by an insufficient net benefit from trusted use, making users inclined to maintain a skeptical attitude toward the shared data. Under the government’s gradual decentralization and implementation of weak supervision, scientific data platforms will also participate passively. This equilibrium requires the following conditions: G − E < t 1 − s 2, D < h 2 − s 2, f 1 > f 2, and A + F < m 1 − m 2 − n 1 + n 2. Specifically, under the weak supervision of the government, if the net income of data providers is lower than the net cost of actively providing data, they may lack enthusiasm; at the same time, if the trusted-use benefit is lower than the verification burden under passive platform support, users are more inclined to question the data; the cost of strong supervision by the government is naturally higher than that of weak supervision, because it requires more resources; in addition, if the platform incentive is not enough to offset the net cost of active participation, the platform may also lack the motivation to participate. This scenario demonstrates that weak supervision and insufficient incentives lead to all stakeholders adopting passive strategies, corresponding to the strategic combination (0, 0, 0, 0), with the corresponding evolutionary strategy simulation results shown in Figure 6.

Condition 2: When scientific research data providers opt for passive data provision, users may still choose trusted use if the normalized benefit from accessible platform-mediated data exceeds the relevant verification burden, while insufficient platform incentives keep platforms in passive participation. This equilibrium point must satisfy the following conditions: G − E < t 1 − s 2, D > h 2 − s 2, f 1 > f 2, and A + F < m 1 − m 2 − n 1 + n 2. Specifically, under weak government supervision, data providers lack enthusiasm as the net income from active data provision fails to cover the corresponding net cost, whereas data users have sufficient incentives to utilize data due to usage benefits exceeding the net cost. Meanwhile, strong government supervision incurs higher costs than weak supervision, as it requires additional resource input; additionally, government incentives received by the platform are insufficient to compensate for the net cost or income gap arising from participation strategy conversion, potentially leading to a lack of motivation to adjust its participation strategy. This scenario corresponds to the strategic combination (0, 1, 0, 0), with the corresponding evolutionary strategy simulation results shown in Figure 7.

Condition 3: When the strategic choices of scientific research data providers and users remain unchanged, the platform’s active participation is driven by the fixed reward–penalty incentive term rather than by data circulation volume in the current formulation. This equilibrium point must satisfy the following conditions: G − E < t 1 − s 2, D > h 1 − s 2, O < f 1 − f 2, and A + F > m 1 − m 2 − n 1 + n 2. Specifically, under weak government supervision, data-providing enterprises or individuals tend to adopt passive data provision when the net income from active provision is lower than the net cost of passive provision. Meanwhile, data users are more willing to trust and utilize data if the revenue from data use can cover the net cost of trusted utilization. For the government, weak supervision is locally stable here when the potential loss from weak supervision with active platform participation remains smaller than the additional cost of strong supervision. For the platform, active participation is more likely to be chosen if the total value of incentives and penalties exceeds the net cost of switching participation strategies. This scenario corresponds to the strategic combination (0, 1, 0, 1), with the corresponding evolutionary strategy simulation results shown in Figure 8.

Condition 4: With the development of scientific research data sharing, even without strong supervision, data providers act as key active contributors, providing data proactively. Research data users can easily access and trust available data. Amid the sharing system improvement, sustainable development is achievable with minimal intervention, prompting the government to adopt weak supervision. Meanwhile, research data sharing platforms achieve orderly active participation. This equilibrium must meet the following conditions: E − G < s 2 − t 1, h 1 − s 2 < D, f 2 − f 1 < ( B + C ) ( s 1 − s 2 ) − O, A + F > m 1 − m 2 − n 1 + n 2. Specifically, under weak supervision, government subsidies for active data provision cover the gap between privacy risk losses and data provision income, even accounting for active provision costs. For users, their income offsets the difference between trusted data usage costs and subsidies, sustaining motivation to use data under weak supervision. Equivalently, weak supervision is locally stable at this state when the loss from weak supervision with an active platform, O, is smaller than the combined fiscal saving and avoided strong-supervision subsidy burden, i.e., O < f 1 − f 2 + ( B + C ) ( s 1 − s 2 ). Furthermore, the combined incentive and punishment mechanism motivates platforms to opt for active participation, as total incentives and penalties exceed the gap between active and passive participation costs/benefits. This scenario corresponds to the strategic combination (1, 1, 0, 1), with the corresponding evolutionary strategy simulation results shown in Figure 9.

4 Simulation analysis

4.1 System dynamics model

To systematically trace the evolutionary dynamics of the four game participants under complex parameter interactions, we integrate evolutionary game theory with system dynamics to construct a simulation model. This approach enables intuitive visualization of how key factors influence each agent’s strategy selection probability over time. It should be noted that the system dynamics model implements the same four replicator dynamic equations derived in Section 3, and the Python simulation reported below solves the same system; the numerical results therefore constitute an internal consistency check on the analytical model, illustrating the trajectories, convergence behavior, and parameter sensitivity implied by those equations rather than an independent validation of the model assumptions, the payoff matrix, or the model’s real-world validity. Stochastic and spatial evolutionary game models provide complementary perspectives for analyzing strategic evolution in complex systems and offer a methodological reference for future extensions of the present work.

The SD model, constructed using Vensim software (Figure 10), comprises 4 stocks, 4 rate variables, 8 intermediate variables, and 25 exogenous variables. The 4 stocks correspond to the strategy probabilities of the four agents: x (providers’ active provision), y (users’ trusted usage), z (government’s strong supervision), and k (platform’s active participation). The 4 rate variables are the rates of change of these probabilities, namely, d x d t, d y d t, d z d t, and d k d t, governed by the replicator dynamic equations derived in Section 3. The 8 intermediate variables represent the expected payoffs under each strategy: U 1 and U 2 for providers choosing active and passive provision respectively; V 1 and V 2 for users choosing trusted and questioning use; W 1 and W 2 for government choosing strong and weak supervision; and R 1 and R 2 for the platform choosing active and passive participation. The 25 exogenous variables map directly to the parameters of the payoff matrix. The functional relationships among these variables are specified by the replicator dynamic equations, allowing the SD model to visually reflect the causal pathways through which parameter changes propagate to affect strategy selection probabilities.

4.2 Parameter settings

Numerical simulations are conducted to numerically illustrate the dynamic evolution implied by the analytical model and to examine how the trajectories respond to parameter variation. Since many parameters are difficult to measure precisely in practice, their assignment follows three principles to ensure broad applicability and interpretability. First, benchmark values are drawn from multiple complementary sources: (a) published literature on data sharing platforms, data governance costs, and stakeholder incentive mechanisms [12, 34]; (b) exploratory consultations with three domain specialists: a senior data manager from a provincial science and technology information institute, a policy researcher from a government IT department, and an academic researcher specializing in evolutionary game theory and data governance. Their professional judgment informed the identification of reasonable parameter ranges, and these consultations should be regarded as an exploratory calibration aid rather than a systematic empirical validation; and (c) publicly available policy documents specifying subsidy rates and regulatory cost structures for scientific data sharing pilot programs in China. Second, to illustrate convergence to the target cooperative equilibrium (1, 1, 0, 1), baseline parameter values are chosen to lie within the stability threshold conditions derived in Section 3. We note that some parameters (notably G and s 2) are set so that the analytical threshold E c = G + s 2 − t 1 equals 0.6; the associated numerical trajectories therefore visualize this analytically implied threshold and do not constitute independent confirmation of it. Third, sensitivity analyses adopt a control-variable approach, varying one parameter at a time while holding others constant wherever feasible, thereby minimizing cross-parameter interference and isolating the marginal effect of each variable; where several policy instruments are varied jointly, the corresponding experiment is interpreted as a policy-package scenario rather than a single-parameter marginal effect.

The complete parameter settings are detailed in Table 6.

TABLE 6. Source of simulation parameters.

4.3 Evolutionary path analysis

Each game participant exhibits distinct evolutionary trajectories across different stages of scientific research data sharing. To comprehensively illustrate the strategic choices within the replicator dynamic system, a simulation was implemented. For the system to converge to the target cooperative state (1, 1, 0, 1) in which all four agents participate constructively, the equilibrium must be locally asymptotically stable, which requires: E − G < s 2 − t 1, h 1 − s 2 < D, f 2 − f 1 < ( B + C ) ( s 1 − s 2 ) − O, and A + F > m 1 − m 2 − n 1 + n 2.

To examine the system’s sensitivity to initial strategic compositions, each agent’s initial strategy share was varied independently across the set { 0.1 , 0.3 , 0.5 , 0.7 , 0.9 } while the other initial shares were held at their baseline values. Specifically, subfigure (a) varies the initial provider share x ( 0 ), subfigure (b) varies the initial user share y ( 0 ), and subfigure (c) varies the initial platform share k ( 0 ). The government’s initial share z ( 0 ) is held fixed at its baseline value across all subfigures. It should be noted that because F ( k ) in Equation 19 contains no z term under the current formulation, the platform trajectory is decoupled from the government’s initial strategy composition; the platform trajectories in subfigure (c) vary because k ( 0 ) itself, rather than z ( 0 ), is being swept. The resulting evolutionary paths of providers, users, and platforms are displayed in Figure 11.

As shown in Figure 11, under the baseline parameter configuration the system approaches the target state (1, 1, 0, 1) for all explored initial shares. Because F ( k ) in Equation 19 contains no x, y, or z terms, the platform’s trajectory in subfigure (c) reflects variation in k ( 0 ) itself rather than a response to the initial strategies of other agents. In the target scenario, the government can reduce the equilibrium share of strong supervision while continuing to use lower-intensity policy instruments, enabling providers to adopt active provision, users to embrace trust-based usage, and platforms to maintain active participation.

4.4 Parameter sensitivity analysis

Building on the evolutionary path analysis, we systematically examine how key external parameters influence the system’s convergence behavior.

4.4.1 Reward and penalty mechanisms

Under weak regulation, the reward and punishment mechanism shapes convergence speed and strategy selection through distinct channels. Figure 12 illustrates the effects of jointly varying the government subsidy and penalty coefficients; because the subsidy and penalty are varied together here, this experiment is interpreted as a policy-package scenario rather than the marginal effect of any single instrument. In the current model, subsidies s 1 and s 2 directly affect providers and users and enter the government’s selection gradient through fiscal costs, whereas platform participation is governed by the separate reward–penalty term involving A and F. Within the explored grid, the non-government strategies shift toward the target state once the policy package crosses a critical range near a subsidy coefficient of 0.4 and a penalty coefficient of 0.1. Because the grid is coarse, this value should be read as the interval within which the transition occurs rather than a sharply identified single-parameter threshold. Beyond this range, further increases in intervention intensity yield diminishing marginal behavioral returns. In this mature phase, incentive mechanisms (which still include s 2, A, and F) sustain provider contributions, user trust, and platform participation under lower-intensity government involvement.

4.4.2 Impact of privacy risk

Privacy risks pose significant challenges to data sharing, particularly when datasets contain sensitive information common in medical research and other scientific domains. As privacy risks increase, researchers become more reluctant to disclose their data; conversely, a moderate perceived risk level can encourage more structured and compliant sharing practices. To examine these dynamic effects, the privacy risk coefficient E is varied from 0.2 to 0.8 at equal intervals. The simulation results (Figure 13) illustrate the sign change of the provider’s selection gradient at the analytically implied threshold E c = G + s 2 − t 1 = 0.6: when E remains below 0.6, providers actively share data, users consistently adopt trusted usage, and the platform participates actively, driving convergence to the target state (1, 1, 0, 1). When E rises to 0.8, providers shift from active to passive sharing, and the system evolves toward (0, 1, 0, 1). At exactly E = E c the provider’s selection gradient vanishes, so every interior provider share is neutrally stationary in the current formulation and the provider share retains its initial value. Because E is sampled only at a few discrete points, these trajectories illustrate the direction of change on either side of the analytically implied threshold rather than constituting a rigorous bifurcation proof, which would require a continuous parameter sweep with an explicit exchange-of-stability analysis. This transition indicates that higher privacy risks fundamentally hinder data dissemination and reduce researcher engagement. With growing public awareness of data privacy, regulatory frameworks such as the GDPR and China’s Data Security Law require further refinement to establish a balanced institutional framework that protects data privacy while facilitating the legal and efficient circulation of scientific research data.

4.4.3 Joint effects of government subsidies and provider-side parameters

Among the government’s regulatory instruments, subsidy policies directly affect the strategic choices of providers and users and enter the government’s selection gradient through fiscal terms; platform behavior is affected only when the associated platform reward or penalty terms are varied. This section examines how the joint variation of subsidies and related provider-side parameters (including the reputational benefit coefficient G and the active-provision cost coefficient t 1) shapes providers’ behavior; because several parameters are varied together, this experiment is interpreted as a joint-parameter (policy-package) analysis rather than a single-parameter marginal effect of subsidies alone.

The relevant simulation results are presented in Figure 14. When the combined policy package is set at its lowest level (subsidy coefficients s 1 and s 2 set to zero, while reputational benefit G and active-provision cost t 1 are held at their baseline values), providers face the dual pressure of high sharing costs and low expected returns, leading them to adopt a passive provision strategy. Simultaneously, under conditions of information asymmetry, users exhibit a tendency to question the authenticity and usability of shared data. As the joint parameter levels (subsidies, reputational benefits, and provision costs) are progressively adjusted, providers’ cost pressures are relieved and their net income rises, prompting a progressive shift from passive to active provision. Users’ decision-making exhibits more complex dynamics under information uncertainty; they face the challenge of evaluating massive volumes of research data and tend to adjust their strategies more conservatively. When the joint parameter package reaches the critical range identified in the explored grid, the system converges to the target equilibrium (1, 1, 0, 1), where providers actively share, users adopt trusted usage under quality assurance, and the platform actively participates to improve service efficiency. This evolutionary path indicates that a well-calibrated joint policy package, comprising subsidies, reputational incentives, and cost structures, can coordinate provider and user incentives and, when combined with appropriate platform rewards and penalties, steer the system toward the target equilibrium.

4.4.4 Joint effects of data supply and government subsidy

Figure 15 illustrates the joint dynamics of data supply and subsidy policy; because supply-side and subsidy parameters are varied together, this experiment is read as a policy-package scenario rather than a single-parameter marginal effect. In the initial stage, when the combined policy package is set at its lowest level (subsidy coefficients held at zero while other supply-side parameters remain at baseline values), providers face the dual pressure of high sharing costs and low expected returns, leading them to adopt passive provision. At the same time, under information asymmetry, data users also exhibit a tendency to question the authenticity and usability of shared data, consistent with decision-making behavior under uncertainty. As the joint supply-side and subsidy parameter levels are progressively adjusted, providers’ income rises significantly, prompting a gradual transition from passive to active provision. However, users’ cost coefficients, while reduced, are not eliminated, and they continue to exhibit conservative questioning strategies, indicating that income sensitivity outweighs expenditure sensitivity in data-sharing decisions within this configuration. When the joint policy package reaches the critical range identified in the explored grid, the system evolves toward the target equilibrium (1, 1, 0, 1), in which providers adopt active provision, users choose trusted usage under quality assurance, and the platform implements active participation, collectively establishing a cooperative and sustainable development pattern within the current model.

5 Conclusions, limitations, and future work

5.1 Conclusions

This paper developed a bounded-rationality evolutionary game framework to investigate the strategic interactions among scientific research data providers, data users, government regulatory agencies, and data sharing platforms under the open science paradigm. A payoff matrix encompassing all sixteen strategy combinations was constructed, replicator dynamics equations were derived, and local asymptotic stability was evaluated via Lyapunov’s indirect method with Jacobian eigenvalue analysis, followed by system dynamics-based numerical simulations that illustrate the trajectories implied by the analytical model.

The findings reveal that the target cooperative equilibrium (1, 1, 0, 1), in which providers actively share, users trustfully utilize, platforms actively participate, and the government maintains a low equilibrium share of strong supervision, is locally asymptotically stable under identifiable parameter constraints. This result indicates that lower-intensity government involvement can coexist with active non-government strategies when continuing policy instruments remain in place. Because the model contains no explicit social-welfare function, this equilibrium is described as the target cooperative state rather than a socially optimal or Pareto-superior one, and the state still relies on continuing policy instruments (s 2, A, and F) rather than complete regulatory withdrawal. Several critical thresholds govern this transition. The privacy risk coefficient E must satisfy E − G < s 2 − t 1; under the selected baseline calibration the provider’s selection gradient changes sign at the analytically implied threshold E c = G + s 2 − t 1 = 0.6, below which active sharing prevails, while at E = 0.8 the system shifts toward (0, 1, 0, 1). Government subsidies and platform reward–penalty mechanisms exhibit non-linear threshold effects: moderate intervention triggers active strategies, yet once the strategy probabilities approach their boundary values, further increases in the subsidy parameters produce only limited additional behavioral change within the current model. Because no explicit government budget constraint is included, fiscal sustainability itself is not evaluated here.

These results carry three policy implications. First, phased regulatory strategies should pair strong supervision with differentiated subsidies in the initial stage, transitioning to credit-based management as the ecosystem matures. Second, privacy risk governance must integrate federated learning and data classification with well-designed revenue-sharing mechanisms. Third, platform development should be incentivized through activity-based rewards and FAIR tool support, fostering inter-platform competition.

In summary, moderate and well-targeted intervention, rather than maximal subsidy intensity, is the more effective path to incentive-sustained collaboration in scientific research data sharing within the scope of the proposed model.

5.2 Limitations

Despite the theoretical contributions discussed above, several limitations of the present study should be acknowledged, each of which points to productive directions for future research.

5.2.1 Agent homogeneity and deterministic dynamics

The current model assumes homogeneous agents within each stakeholder group and deterministic replicator dynamics. In reality, providers differ substantially in their data production capacity, institutional affiliation (universities versus research institutes versus corporate laboratories), and access to data curation resources, implying heterogeneous adoption thresholds for active sharing strategies. Similarly, data users vary in their analytical capabilities and domain-specific data quality requirements, while sharing platforms exhibit diverse technological infrastructures and service models across different scientific disciplines.

5.2.2 Binary strategy simplifications

The binary strategy assumptions for all four agents (active versus passive provision, trusting versus questioning use, strong versus weak supervision, and active versus passive platform participation) represent deliberate simplifications that enable closed-form analytical solutions. In practice, these strategic choices span continuous ranges: government subsidy intensity, provider sharing effort, user trust levels, and platform investment scales are inherently multi-level or continuous decisions that the current formulation cannot fully capture.

5.2.3 Provider–user payoff abstraction

The current user payoff treats the accessible data aggregate B as exogenous rather than as a direct function of the provider strategy share x. This keeps the user replication equation analytically simple, but it abstracts from an important real-world channel: passive provision by data holders would normally reduce the volume, freshness, or quality of data available to users. Future work should allow B to vary with provider behavior and platform filtering capacity, thereby capturing provider–user coupling more directly.

5.2.4 Platform strategy independence

In the current formulation, the platform’s payoff in each strategy profile depends solely on its own action k and is invariant to the strategies of the other three agents (the platform payoff expressions R 1 and R 2 in Equations 16, 17). Consequently, the platform’s replicator dynamics equation F ( k ) contains no x, y, or z terms, implying that the platform’s evolutionary trajectory is decoupled from the behavior of providers, users, and the government. This independence follows from the simplifying assumption that platforms receive fixed operational income and incur fixed costs contingent only on their own participation level, rather than on data circulation volumes or regulatory conditions. While this assumption keeps the model analytically tractable, it limits the extent to which the framework captures genuine four-way co-evolution. Future work could enrich the platform’s payoff function by introducing terms that depend on the volume of data being shared (a function of x and y) and on the regulatory environment ( z ), thereby embedding the platform more fully within the interactive dynamics.

5.2.5 Deterministic abstraction of uncertainty

The model treats all costs, benefits, and risk parameters as deterministic and known ex ante, abstracting from the fundamental uncertainties that characterize real-world scientific data sharing. Data breach incidents, sudden policy shifts, technological disruptions in data analytics and privacy protection, and evolving stakeholder expectations introduce stochastic elements that the current replicator dynamics framework does not explicitly accommodate. While the privacy risk coefficient E partially captures data security concerns, the stochastic nature of these disruptions, including their frequency, severity, and cascading effects, remains unmodeled.

5.2.6 Empirical validation

The current study is primarily theoretical and simulation-based. Although the parameter values were calibrated with reference to published literature on data sharing platforms and evolutionary game models, augmented by expert consultations with specialists in scientific data management and policy research, systematic empirical validation has not yet been conducted. The absence of real-world data from operational scientific research data sharing platforms, longitudinal surveys of provider and user behavior, or comparative case studies of regulatory interventions limits the direct empirical grounding of the simulation results.

5.3 Future work

Based on the limitations identified above, several directions for future research are outlined below.

First, future work could relax the homogeneous-agent assumption by employing agent-based modeling with heterogeneous agent populations characterized by empirical distributions of cost structures, risk preferences, data production capacities, and institutional affiliations. Incorporating stochastic perturbations into the replicator dynamics equations would further enable analysis of the system’s resilience to random shocks arising from data breach incidents, policy changes, or technological breakthroughs. Integrating prospect theory to capture asymmetric risk attitudes, such as loss aversion where providers weigh privacy losses more heavily than equivalent sharing benefits, could yield more behaviorally realistic predictions than the expected utility framework.

Second, the binary strategy assumptions could be generalized in several directions: (a) modeling government subsidy intensity as a continuous decision variable, potentially using optimal control theory to characterize the optimal subsidy trajectory over time, including the analytical conditions for gradual phase-out as the sharing ecosystem matures; (b) introducing multi-level strategies for providers (e.g., minimal sharing, selective sharing, comprehensive sharing) and users (e.g., skeptical, conditional, full trust); and (c) extending the platform strategy space to include continuous investment levels or multi-stage deployment decisions.

Third, to address the deterministic abstraction, future research could incorporate stochastic evolutionary game theory with explicit noise processes in the payoff functions, apply fuzzy set theory or robust optimization to model the ambiguity surrounding key parameters subject to rapid technological change, or develop scenario-based simulation frameworks that evaluate strategy robustness across alternative future states defined by different privacy regulation regimes, technology adoption rates, and stakeholder cooperation scenarios.

Fourth, systematic empirical validation constitutes a critical next step. Specific approaches include: (a) Delphi studies with a larger panel of experts from scientific data management, research policy, and platform operations for systematic parameter calibration; (b) structured surveys of data providers and users across multiple scientific disciplines to empirically estimate sharing cost coefficients, trust parameters, and privacy risk perceptions; (c) in-depth comparative case studies of established scientific research data sharing platforms at different maturity stages to trace their strategic evolution paths and verify the predicted stability regime shifts; and (d) econometric analysis of platform-level data on sharing volumes, user engagement, and regulatory interventions to test the model’s equilibrium predictions against observed outcomes.

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Footnotes

Edited by: Kaipeng Hu, Yunnan University of Finance And Economics, China

Reviewed by: Huihui Nong, Guangxi University, China

Wenhua Li, Beijing Normal University, China