How to Optimize Data Sharing in Logistics Enterprises: Analysis of Collaborative Governance Model Based on Evolutionary Game Theory

Abstract

Data, as a key production factor in modern logistics systems, plays a crucial role in enhancing industry efficiency and promoting supply chain coordination. To address challenges in data sharing among logistics enterprises—such as conflicts of interest, unequal risk allocation, and insufficient security governance—this study develops a tripartite evolutionary game model involving logistics enterprises, data partners, and supervisory institutions. The payoff matrix incorporates prospect theory to account for risk attitudes, loss–gain perceptions, and subjective judgments. Stable equilibrium points are derived using the Jacobian matrix, and numerical simulations examine strategic evolution under varying parameters. Results indicate that increased returns for data partners reduce their motivation to provide truthful data, while higher enterprise profits suppress logistics enterprises’ willingness to share. Compensation levels have limited impact, whereas excessively high supervision subsidies weaken participation and oversight across all parties. Stronger penalties and higher-level enforcement significantly promote compliance and positive system evolution. Enterprise investment positively correlates with data-sharing behavior, and risk preferences of all parties accelerate convergence to stable equilibria. Conversely, excessively low risk preference in supervisory institutions may lead to an unstable “sharing–false data–non-regulation” pattern. These findings provide theoretical support and policy guidance for designing a dynamic governance mechanism that balances incentives, constraints, and collaboration, thereby facilitating secure and effective logistics data sharing and informing the development of the data factor market.

1. Introduction

Data, as a core resource of modern logistics systems, plays a critical role in enhancing industry efficiency and reducing overall social transportation costs. In recent years, with the implementation of policies such as “Digital Transportation” and “Smart Logistics”, as well as the establishment of a “National Data Factor Market”, logistics big data has been recognized as a fundamental driver in terms of optimizing supply chain collaboration and building a unified national market [1]. In the digital economy era, data is no longer regarded merely as an input or output in commercial transactions but also as an institutional asset comparable to fiscal, physical, and human capital [2]. As the primary raw material for enterprises engaged in developing and operating data-based industries, data can be deeply mined to create a wide range of information products. With the continuous emergence of innovative data services, market competition in the digital economy has become increasingly intense [3,4].

In practical applications, data is easily stored and conveniently transmitted, and its shared use more fully reflects its utility as a data asset. Governments, enterprises, and society at large all have a growing demand for data sharing, which enables the maximization of data value [5]. However, the potential value of data is not always fully realized. Conflicts often arise between the private value of data owners and the public social value of data, between data ownership and data sharing, and between data sharing and data security [6]. Moreover, due to variations in business practices and information standards across different enterprises and departments, the realization of effective data sharing remains difficult to achieve [7].

Compared with other industries, logistics enterprises exhibit distinct characteristics in the challenges they face regarding data sharing. First, the logistics business involves a long operational chain and multiple stakeholders—including carriers, warehouse operators, cargo owners, e-commerce platforms, and supervisory institutions—whose information systems vary significantly. The absence of unified data interfaces and standards hinders the smooth flow of information across transportation, warehousing, and distribution processes [8]. Second, logistics data often contain core commercial information such as customer orders, transportation routes, and cargo status, which are highly confidential and competitively sensitive. Enterprises are generally concerned that data sharing may result in the leakage of trade secrets or customer loss, thereby reducing their willingness to disclose data [9]. Third, as logistics activities typically occur in dynamic and distributed environments, the real-time accuracy of data collection is difficult to guarantee. Data from different sources often vary in timeliness, format, and reliability [10]. Finally, at the industry level, mechanisms for data security and rights protection remain underdeveloped. The absence of clear rules defining data usage boundaries and benefit distribution leads to asymmetric risks and returns in data sharing, further discouraging enterprise participation [11]. These characteristics make logistics enterprises face more complex institutional and technical barriers to promoting data sharing than those encountered in most other industries.

Given the structural barriers faced by logistics enterprises in data sharing, it is necessary to examine their formation mechanisms and strategic interactions from a multi-stakeholder perspective. Moreover, effective governance of data sharing cannot rely solely on government intervention; instead, a collaborative governance network should be established [12], whereby a system of responsibilities coordinates individual behaviors and collective duties to form a networked model of power operation. To reveal the dynamic decision-making mechanisms of different participants in benefit allocation, risk bearing, and trust building, this study develops an evolutionary game model involving logistics enterprises, supervisory institutions, and data partners. The model analyzes the evolution of strategies under varying policy incentives, cost constraints, and risk preferences. By simulating the strategic evolution of all parties, the study identifies the key conditions and equilibrium characteristics that enable stable data-sharing behaviors and governance performance, providing theoretical support and policy guidance for constructing an efficient, secure, and sustainable logistics data-sharing mechanism.

2. Literature Review

2.1. Data Sharing

Recent research on data sharing has achieved notable progress. Platform-based data-sharing mechanisms enable cross-departmental and cross-system data interoperability, enhancing collaborative capabilities. As platform users, individuals’ data must be handled in compliance with legal regulations, safeguarding consumer rights and data security. According to prior theories, individuals tend to resist information perceived as having explicit persuasive intent. In the context of platforms soliciting user data, such resistance may emerge; however, when platforms employ mechanisms such as incentives or reward points, users are more likely to provide authentic data [13,14]. Collected data are then utilized for market analysis, product recommendations, and personalized customization, ultimately aiming to improve service quality for users.

From a theoretical perspective, data flows between enterprises and government departments increasingly exhibit bidirectional patterns, gradually evolving toward comprehensive data sharing. In the European Union, data-sharing practices include government-to-business (G2B) and business-to-business (B2B) models. Systematic legislative frameworks, technical support infrastructures, and social trust-building initiatives have been established, forming an industrial ecosystem characterized by a virtuous cycle: “data sharing → improved products and services → enhanced benefits for data subjects” [15,16]. Data-sharing models can also be differentiated according to the exercise of authority by participants, determining which elements are shared, the frequency of data collection, and the applicable definitions for these elements.

Specifically, the General Data Protection Regulation grants individuals a range of enforceable rights over their personal data—including informed consent, data access, erasure, restriction, portability, and objection—and requires data controllers to adopt robust technical and organizational safeguards such as data minimization, purpose limitation, encryption, and breach notification [17]. Meanwhile, the EU Data Act further complements GDPR by mandating that users and businesses have fair access to data generated by connected products or services—including non-personal and machine-generated data—and allows them to share such data with third parties under clear, non-discriminatory contractual terms, while preserving trade-secret protections and ensuring interoperability across ecosystems [18]. This dual-layer regulatory framework provides a practical benchmark for designing a dynamic “incentive–constraint–coordination” mechanism in logistics industry data sharing, ensuring both privacy protection and legitimate data reuse.

Compared with fields such as healthcare, supervisory institutions, and law, research on data sharing in the logistics industry remains limited. While data sharing in other sectors has been widely applied to information interoperability, resource optimization, and decision support, studies in logistics are often constrained to informatization and data management, with insufficient attention to the multi-stakeholder game relationships and the evolutionary patterns of sharing mechanisms. Scholars have primarily focused on data protection, often framing data sharing within an anti-monopoly context. Defining “legitimate interests” is critical for balancing the benefits of data sharing: overly broad definitions may infringe upon the informational freedom of data subjects, whereas overly narrow definitions may impede social governance or the development of the digital economy [19]. From the perspective of different stakeholders, platform enterprises are often reluctant to share data. Conflicts of objectives or interests among enterprises lead them to withhold or refuse to accept data sharing, including documents, audiovisual materials, and multimedia resources [20]. Moreover, weak incentive mechanisms partially suppress the willingness to share, and the construction of sharing systems remains inadequate. Responsibility for data sharing is often unclear, and cross-departmental systems face technical limitations. Data-sharing standards are inconsistent, platforms are not interoperable, and the capacity of departments to provide or receive case-related data—such as system integration and data transmission—remains insufficient [21].

2.2. Evolutionary Game Theory and Prospect Theory

Compared with traditional static game models, evolutionary game theory (EGT) overcomes the assumptions of complete rationality and perfect information. By modeling repeated interactions, EGT captures how boundedly rational agents learn and adjust their strategies over time, revealing the dynamic evolutionary patterns as participants pursue marginal gains and long-term equilibrium. However, classical EGT assumptions often overlook the influence of behavioral factors on decision-making. To address this limitation, prospect theory has been integrated into evolutionary game models. Prospect theory incorporates non-rational factors, such as risk preferences and cognitive biases, into decision-making, modifying traditional risk–return calculations and relaxing the assumption of rational expected utility. This integration renders EGT more reflective of real-world behavior [22].

For example, Qiu et al. employed a prospect value function to construct a three-party evolutionary game model involving governments, farmers, and consumers. Their results indicate that participants in agricultural green transformation exhibit loss-averse behavior, and that both the risk preference coefficient and the loss-aversion coefficient in the value function significantly influence the transformation process [23]. Shen et al. applied a two-party game model integrating prospect theory to analyze interactions between local watershed governments and polluting enterprises, addressing cross-regional water pollution issues [24]. Lang et al. developed a three-party evolutionary game incorporating prospect theory to study effective governance of inland waterway pollution and provided policy recommendations for shipping environmental management [25]. Yu and Lu discussed how blockchain technology and data alliances influence enterprise data sharing by mitigating risks and transaction costs, promoting cooperation through reward and penalty mechanisms, and balancing efficiency and fairness in collaborative revenue distribution [26].

Existing studies on data-sharing behavior in logistics enterprises remain relatively limited, and most of them focus on technological solutions or institutional constraints rather than providing a dynamic depiction of decision-making processes. Prior models predominantly rely on static game settings or simplified bilateral frameworks, which prevents them from capturing the strategic feedback and evolutionary interactions among logistics enterprises, data partners, and supervisory institutions. Research incorporating behavioral factors is scarce, and where it does exist, decision-makers are typically assumed to be fully rational, overlooking real-world features such as loss sensitivity, heterogeneous risk preferences, and biased expectations regarding regulatory intensity. In contrast, this study embeds a reference-point-based value evaluation mechanism, payoff-sensitivity parameters, and context-specific payoff formulations into the evolutionary game framework, enabling the endogenous representation of strategy adjustment paths under varying distributions of benefits, exposure to risks, and regulatory interventions. This approach provides a substantive extension to existing prospect-theory-based EGT models at the level of underlying mechanisms.

In contrast, this study contributes to the literature in three key ways. First, guided by the national logistics big data strategy, a tripartite co-evolutionary model is developed involving logistics enterprises, data partners, and supervisory institutions. This framework systematically analyzes the evolution of data-sharing behaviors from the perspectives of interactive relationships and incentive–constraint mechanisms, thereby expanding the research scope of strategy design for logistics data sharing. Second, the payoff matrix of the traditional evolutionary game model is modified by incorporating the prospect theory value function and decision-weighting function, integrating psychological factors such as risk attitudes, gain–loss perception, and subjective judgment into the analytical framework, enriching the decision dimensions of data-sharing behavior. Third, numerical simulations are conducted in MATLAB 2022a to examine the effects of varying scenarios and parameter changes on the evolutionary pathways of logistics data-sharing models. Based on these findings, policy recommendations regarding institutional optimization and technological innovation are proposed, providing feasible approaches to achieve data collaboration and efficient governance in the logistics industry.

3. Multi-Agent Game Analysis of the Collaborative Supervision Model

3.1. Game Model Framework

In the logistics big-data sharing environment, data resources exhibit both private and public attributes: they constitute critical competitive assets for enterprises while simultaneously generating collaborative value and broader social benefits. Due to substantial heterogeneity in payoff objectives, risk preferences, and information endowments among stakeholders in the logistics sector, a single-agent analytical perspective is insufficient to capture the complexity of data-sharing behavior. To address this limitation, the present study models logistics enterprises, data partners (including warehousing, e-commerce, and transportation collaborators), and supervisory institutions as three distinct evolutionary agents. This triadic structure enables a realistic representation of reciprocal feedback, asymmetric information, and regulatory dependence—mechanisms that cannot be captured by the dyadic or static formulations commonly adopted in prior prospect-theory-based evolutionary game studies. In this framework, parameters associated with subsidies, penalties, and supervision intensity are designed to be adjustable, allowing the model to reflect variations in regulatory strength and governance structures across different countries and regions.

The multi-agent strategic interactions embedded in the collaborative regulatory framework for logistics big-data sharing are illustrated in Figure 1. In the absence of influences from neighboring regions or other stakeholders, the collaborative regulation of logistics data sharing can be conceptualized as a game among logistics enterprises, data partners, and supervisory institutions, with the outcomes of this game directly affecting the effectiveness of logistics big-data utilization. Based on this three-party evolutionary game system, the following assumptions are made.

3.2. Game Model Assumption and Design

Assumption 1.

In the collaborative regulatory framework for logistics big-data sharing, three types of agents participate in repeated strategic interactions: logistics enterprises (LE), data partners (DP)—including warehousing, e-commerce, and transportation collaborators—and supervisory institutions (SI). All agents are assumed to be boundedly rational and adjust their strategies through repeated interactions under incomplete information, following payoff-improving revision rules until an evolutionary stable strategy (ESS) emerges. The central data authority is assumed to possess sufficient enforcement capacity to accurately identify violations once reported, making it impossible for any agent to evade penalties through opportunistic behavior. This triadic setting departs from conventional dyadic EGT models by enabling endogenous feedback loops among enterprises, partners, and regulators, thereby capturing multi-directional incentive transmission that is intrinsic to logistics data sharing.

Assumption 2.

To better align the constructed model with practical processes, the bounded rationality of participants is adjusted by incorporating prospect theory, accounting for the influence of subjective psychological perceptions on strategy formulation. Under conditions of risk preference, the strategies adopted by participants depend on their subjective evaluation and perceived value of events, rather than solely on actual outcomes [27]. When formulating strategies, each participant first establishes a reference point of value, ${\omega }_0$, and then assesses whether the decision outcomes exceed or fall below this reference point to determine perceived value. The perceived payoff $V$ for strategy selection is jointly determined by the decision-maker’s weighting function $\pi \left(p_i\right)$ representing the perceived probability of event $p_i$, and the value function $v\left(\Delta {\omega }_i\right)$, representing the gain or loss relative to the reference point. Formally, this can be expressed as $V={\displaystyle {\sum }_i\pi \left(p_i\right)v\left(\Delta {\omega }_i\right)}$. The specific forms of the weighting function $\pi \left(p_i\right)$ and the value function $v\left(\Delta {\omega }_i\right)$ are defined as follows:

$$\pi (p_i)={\displaystyle \frac{{p_i}^{\delta }}{{\left. [{p_i}^{\delta }+{(1-p_i)}^{\delta }\right]}^{\frac{1}{\delta }}}}$$

(1)

$$v(△{\omega }_i)=\left\{\begin{array}{l}{(△{\omega }_i)}^{\alpha },△{\omega }_i\ge 0\\ -\lambda {(-△{\omega }_i)}^{\beta },△{\omega }_i<0\end{array}\right.$$

(2)

In Equation (1), $p_i$ denotes the probability of event iii occurring, and $\delta$ is a scaling parameter. Based on the assumptions of prospect theory, participants tend to underestimate high-probability events and overestimate low-probability events, with $\pi \left(1\right)=1$ and $\pi \left(0\right)=0$ [28].

In Equation (2), and $\beta$ represent the risk attitude coefficients ($0<\alpha$ and $\beta <1$), where higher values indicate greater risk preference. The parameter $\lambda$ denotes the loss-aversion coefficient ($\lambda >1$), reflecting that participants are more sensitive to potential losses than to equivalent gains. In studies integrating prospect theory with evolutionary game models, the primary focus is on how the decision-maker’s risk preferences influence strategy selection. For analytical convenience, the reference point of value is generally set to zero, i.e., ${\omega }_0=0$, such that $\Delta {\omega }_0={\omega }_i-{\omega }_0={\omega }_i$.

Assumption 3.

The strategy set for logistics enterprises is {share data, retain data}, with $x\left(0\le x\le 1\right)$ representing the proportion of enterprises that choose to share data. Logistics enterprises derive revenue from data transactions and supervisory subsidies, while platforms incur operational costs. When a logistics enterprise opts to share operational data, it incurs a cost $C_{x1}$ associated with data processing, standardization, and integration across fragmented supply chains, and obtains a revenue $R_{x1}$ derived from efficiency gains such as reduced delivery delays and optimized fleet dispatch. In addition, the enterprise receives a supervisory subsidy $G$ specifically granted to logistics enterprises for data-sharing initiatives. Conversely, enterprises that retain data bear higher costs $C_{x2}>C_{x1}$ due to redundant data acquisition, storage, and maintenance, while achieving a net payoff $R_{x2}$. Retained data do not contribute to public oversight or regulatory decision-making, and thus these enterprises are ineligible for the data-sharing subsidy.

Data-sharing enterprises emphasize the protection of sensitive information, particularly customer and shipment data. Under supervisory supervision, any breach triggers user compensation $aP$, occurring with probability $a\left(0\le a\le 1\right)$. In the absence of regulatory oversight, compensation $bP$ is independently determined by the enterprise, with $b\left(0\le b\le 1\right)$ representing the internal compensation coefficient. Moreover, sharing enterprises not only pursue their own operational improvements but also collaborate with other logistics partners, publicly disclose aggregated data to authorities and society, and gain social recognition $S$, reflecting improvements in service reliability, reputation, and societal trust. Enterprises that retain data bear the full burden of data management, fail to contribute to supply chain-wide efficiency, and, in the event of negative incidents, are responsible for resulting social losses $aS$.

Assumption 4.

The strategy set for data partners is {provide truthful/high-quality data, provide false/low-quality data}, with $y\left(0\le y\le 1\right)$ representing the proportion of data partners providing truthful or high-quality data.

During platform operations, data partners benefit from logistics enterprises’ services, including enhanced shipment tracking, route optimization support, and access to collaborative resources, resulting in higher payoffs $R_{y1}$. Partners who provide inaccurate or low-quality data face restricted access to platform functionalities and collaborative opportunities, receiving lower payoffs $R_{y2}$, with $R_{y1}>R_{y2}$.

Logistics enterprises retain discretion in interacting selectively with data partners. Partners who contribute accurate and high-quality data are eligible for additional incentives $Q$, such as priority access to scheduling tools, advanced analytics, or co-development opportunities. In contrast, partners providing false or low-quality data are limited to basic compensation determined by the enterprise, reflecting their diminished value to logistics operations.

Assumption 5.

The strategy set for supervisory institution, which may represent government authorities, independent regulatory body, or industry association is {supervise, not supervise}, with  $z\left(0\le z\le 1\right)$ representing the proportion of supervisory institutions engaging in supervision. The supervisory collects management fees from logistics enterprises, oversees enterprise operations, provides policy guidance and support, and leverages feedback data from logistics enterprises to improve management decisions.

For supervisory institutions who choose to supervise, the cost of implementing regulatory measures is denoted as $C_{z1}$. When overseeing data-sharing logistics enterprises, which control extensive user and shipment data, the supervisory institution assumes responsibility both to these enterprises and to platform users. The benefit obtained by the supervision from data-sharing enterprises is denoted as $R_{z1}$. For logistics enterprises that retain data, the corresponding regulatory cost is $C_{z2}$, and the benefit to the supervision is $R_{z2}$, with $C_{z1}>C_{z2}$ and $R_{z1}>R_{z2}$.

For supervisory institutions who choose not to supervise, no regulatory cost is incurred. However, in the event of a data breach, logistics enterprises bear full responsibility for compensating affected users. Simultaneously, the supervisory institution faces potential penalties imposed by higher-level authorities, represented by the national data authority. The penalty for failing to ensure data-sharing compliance is denoted as $N$, where $N>aP$ and $aN>bP$, reflecting stricter accountability under non-supervised scenarios.

3.3. Game Model Solution

Based on the above assumptions, the strategic payoff matrix for logistics enterprises, data partners, and supervisory institutions is presented in

Table 1. Three-party payoff matrix of logistics enterprise, data partner, and supervisory institution.

		Logistics Enterprises
		Shared Data $\mathit{x}$		$\mathbf{Exclusive} \mathbf{Data} 1-\mathit{x}$
Data partners		Provide high quality data $y$	Provide low quality data $1-y$	Providehigh quality data $y$	Provide low quality data $1-y$
Supervisory institution	Supervise $z$	$\begin{array}{l}-C_{x1}+R_{x1}+G\\ +S-V\left(aP\right)\end{array}$	$\begin{array}{l}-C_{x1}+R_{x1}+G\hfill \end{array}$	$\begin{array}{l}-C_{x2}+R_{x2}\\ -V\left(aS\right)\end{array}$	$-C_{x2}+R_{x2}$
		$R_{y1}+V\left(aP\right)+Q$	$R_{y2}$	$R_{y1}$	$R_{y2}$
		$-C_{z1}+R_{z1}-G$	$-C_{z1}+R_{z1}-G$	$-C_{z2}+R_{z2}$	$-C_{z2}+R_{z2}$
	Not supervise $1-z$	$\begin{array}{l}-C_{x1}+R_{x1}\\ -V\left(bP\right)\end{array}$	$-C_{x1}+R_{x1}$	$-C_{x2}+R_{x2}$	$-C_{x2}+R_{x2}$
		$\begin{array}{l}{R}_{y1}+V\left(bP\right)+Q\hfill \end{array}$	$R_{y2}$	$R_{y1}$	$R_{y2}$
		$V\left(-N\right)$	$0$	$V\left(-N\right)$	$0$

.

Based on the above assumptions and game model, the replicator dynamic equations and equilibrium solutions are established to analyze the evolutionary game process among logistics enterprises, data partners, and supervisory institutions. Let $U_{11}$ denote the expected payoff for logistics enterprises choosing the strategy {share data}, $U_{12}$ denote the expected payoff for choosing {retain data}, and ${\overline{U}}_1$ represent the average expected payoff of the two strategies. Then, the replicator dynamics for logistics enterprises can be expressed as:

$$\left\{\begin{array}{l}{U}_{11}=yz\left(-C_{x1}+R_{x1}+G+S+V\left(-aP\right)\right)+y\left(1-z\right)\left(-C_{x1}+R_{x1}+V\left(-bP\right)\right)\\ +z\left(1-y\right)(-C_{x1}+R_{x1}+G)+\left(1-y\right)\left(1-z\right)\left(-C_{x1}+R_{x1}\right)\\ U_{12}=yz\left(-C_{x2}+R_{x2}+V\left(-aS\right)\right)+y\left(1-z\right)(-C_{x2}+R_{x2})\\ +z\left(1-y\right)\left(-C_{x2}+R_{x2}\right)+\left(1-y\right)\left(1-z\right)\left(-C_{x2}+R_{x2}\right)\\ {\overline{U}}_1=x{U}_{11}+\left(1-x\right)U_{12}\end{array}\right.$$

(3)

Similarly, the expected payoff equations for data partners and supervisory institutions are given by:

$$\left\{\begin{array}{l}{U}_{21}=xz\left(R_{y1}+V\left(aP\right)+Q\right)+x\left(1-z\right)\left(R_{y1}+V\left(bP\right)+Q\right)\\ +z\left(1-x\right)\left(R_{y1}\right)+\left(1-x\right)\left(1-z\right)\left(R_{y1}\right)\\ U_{22}=xz{R}_{y2}+x\left(1-z\right)R_{y2}+z\left(1-x\right)R_{y2}+\left(1-x\right)\left(1-z\right)R_{y2}\\ {\overline{U}}_2=y{U}_{21}+\left(1-y\right)U_{22}\end{array}\right.$$

(4)

$$\left\{\begin{array}{l}{U}_{31}=xy\left(-C_{z1}+R_{z1}-G\right)+x\left(1-y\right)\left(-C_{z1}+R_{z1}-G\right)\\ +y\left(1-x\right)\left(-C_{z2}+R_{z2}\right)+\left(1-x\right)\left(1-y\right)\left(-C_{z2}+R_{z2}\right)\\ U_{32}=xyV\left(-N\right)+y\left(1-x\right)V\left(-N\right)\\ \overline{U_3}=z{U}_{31}+\left(1-z\right)U_{32}\end{array}\right.$$

(5)

In the above equations, $U_{21}$ represents the expected payoff for data partners choosing the strategy {provide truthful data}, $U_{22}$ represents the expected payoff for choosing {provide false data}, and ${\overline{U}}_2$ denotes the average expected payoff of the two strategies for data partners. For supervisory institutions, $U_{31}$ represents the expected payoff for choosing the strategy {supervise}, $U_{32}$ represents the expected payoff for {not supervise}, and ${\overline{U}}_3$ denotes the average expected payoff of the two strategies.

According to the replicator dynamic model proposed by Friedman [29], the replicator dynamic equations describe how the proportion of participants adopting a dominant strategy evolves over time. The replicator dynamic equations for the three-party game involving logistics enterprises, data partners, and supervisory institutions are as follows:

$$\begin{array}{l}{F}_{LE}\left(x\right)={\displaystyle \frac{dx}{dt}}=x\left(U_{11}-\overline{U_1}\right)=x\left(1-x\right)\left(U_{11}-U_{12}\right)\\ =-x\left(x-1\right)\left(C_{x2}-C_{x1}+R_{x1}-R_{x2}+Gz+Syz-V\left(-aS\right)yz\right)\end{array}$$

(6)

$$\begin{array}{l}F\left(y\right)={\displaystyle \frac{dy}{dt}}=y\left(U_{21}-\overline{U_2}\right)=y\left(1-y\right)\left(U_{21}-U_{22}\right)\\ =-y\left(y-1\right)\left(R_{y1}-R_{y2}+Qx+V\left(bP\right)x+V\left(aP\right)xz-V\left(bP\right)xz\right)\end{array}$$

(7)

$$F\left(z\right)={\displaystyle \frac{dz}{dt}}=z\left(U_{31}-\overline{U_3}\right)=z\left(z-1\right)\left(\begin{array}{l}{C}_{z2}-R_{z2}+C_{z1}x-\\ Cz2x+Gx+V\left(-N\right)y-R_{z1}x+R_{z2}x\end{array}\right)$$

(8)

Here, $V\left. [-\left(aS\right)\right]=-{\lambda }_l{(aS)}^{{\beta }_l}$, $V\left(aP\right)={(aP)}^{{\alpha }_d}$, $V\left(bP\right)={(bP)}^{{\alpha }_d}$ and $V\left(-N\right)=-{\lambda }_g{N}^{{\beta }_g}$. The replicator dynamic equations indicate that the evolution of the proportion of strategies chosen by each participant is influenced by the associated game payoffs.

4. Evolutionary Stability Analysis

4.1. Single-Agent Stability Analysis

4.1.1. Evolutionarily Stable Strategy Analysis of Logistics Enterprises

According to the stability theorem of differential equations, determining whether the strategic outcome of logistics enterprises is in a stable state requires that both conditions $F_{LE}\left(x\right)=0$ and $\partial F_{LE}\left(x\right)/\partial x<0$ are satisfied:

$${\displaystyle \frac{\partial F_{LE}\left(x\right)}{\partial x}}=\left(1-2x\right)\left(C_{x2}-C_{x1}+R_{x1}-R_{x2}+Gz+Syz-{\lambda }_l{(aS)}^{{\beta }_l}yz\right)$$

(9)

Let $M\left(y\right)$ be a function of $y$ then:

$$M\left(y\right)=\left(C_{x2}-C_{x1}+R_{x1}-R_{x2}+Gz-Syz+{\lambda }_l{(aS)}^{{\beta }_l}yz\right)$$

(10)

$$y*={\displaystyle \frac{C_{x2}-C_{x1}+R_{x1}-R_{x2}+Gz}{Sz-{\lambda }_l{(aS)}^{{\beta }_l}z}}$$

(11)

Therefore, when $y=y^{\ast }$, $M\left(y\right)=0$, and $\partial F_{LE}\left(x\right)/\partial \hspace{0.33em}x\equiv 0$, the system can reach a stable state regardless of the value of $y$, indicating that logistics enterprises have no evolutionarily stable strategy. When $y<y^{\ast }$, $M\left(y\right)>0$, and ${\left.\hspace{0.33em}\partial F_{CE}\left(x\right)/\partial x\right|}_{x=0}<0$, the system becomes stable at $x=1$, implying that the evolutionarily stable strategy (ESS) of logistics enterprises is data sharing. Conversely, when $x=0$, the ESS corresponds to data exclusivity. The replicator dynamic phase diagram of logistics enterprise strategies is illustrated in Figure 2.

Proposition 1.

The probability $x$ that logistics enterprises choose to share data is positively correlated with the data transaction benefits, supervisory subsidies, social reputation, post-compensation expenditures, penalties for data leakage, risk preference coefficient, and loss aversion coefficient. Conversely, it is negatively correlated with the implementation cost of data sharing, the cost of data exclusivity, platform management fees, and the liability-sharing coefficient. In other words, when the economic benefits, supervisory rewards, and social reputation associated with data sharing increase significantly, enterprises tend to raise the proportion of shared data. In contrast, when the sharing cost is high, the exclusivity cost is relatively low, or enterprises can mitigate risk through liability sharing, they are more likely to adopt a data exclusivity strategy. Moreover, reducing sharing costs through technological innovation, strengthening privacy protection, establishing clear compensation and penalty mechanisms, and enhancing social recognition can effectively motivate logistics enterprises to increase their willingness to share data, thereby promoting the coordinated utilization of data resources and the sustainable development of the logistics industry.

Proposition 2.

The probability $x$ that logistics enterprises choose to share data is jointly influenced by the strategic choices of data partners and supervisory regulatory authorities. Under the condition $0<y^{*}<1$ , data partners provide authentic data and supervisory supervision is in place, logistics enterprises will gradually evolve toward a data-sharing strategy and eventually reach a stable state. Conversely, when data partners prefer exclusivity or exhibit non-cooperative behavior, and supervisory supervision is weak, enterprises will gradually evolve toward a data exclusivity strategy. As the critical threshold $y^{*}$ increases, the strategic interactions of data partners and regulatory authorities exert a stronger positive effect on enterprises’ data-sharing behavior. This suggests that collaborative policy design and the promotion of active data sharing among partners can significantly enhance the willingness of logistics enterprises to share data, thereby fostering a virtuous cycle of tripartite co-governance.

4.1.2. Evolutionarily Stable Strategy Analysis of Data Partners

According to the stability theorem of differential equations, determining whether the strategic outcome of data partners is in a stable state requires that both conditions $F_{DP}\left(y\right)=0$ and $\partial F_{DP}\left(y\right)/\partial y<0$ are satisfied:

$${\displaystyle \frac{\partial F_{DP}\left(y\right)}{\partial y}}=\left(1-2y\right)\left(R_{y1}-R_{y2}+Qx+{(bP)}^{{\alpha }_d}x+{(aP)}^{{\alpha }_d}xz-{(bP)}^{{\alpha }_d}xz\right)$$

(12)

Let $L\left(z\right)$ be a function of $z$ then:

$$L\left(z\right)=\left(R_{y1}-R_{y2}+Qx+{(bP)}^{{\alpha }_d}x+{(aP)}^{{\alpha }_d}xz-{(bP)}^{{\alpha }_d}xz\right)$$

(13)

$$z*={\displaystyle \frac{R_{y1}-R_{y2}+Qx+{(bP)}^{{\alpha }_d}x}{{(aP)}^{{\alpha }_d}x-{(bP)}^{{\alpha }_d}x}}$$

(14)

Therefore, when $z=z^{*}$, $L\left(z\right)=0$, and $\partial F_{DP}\left(y\right)/\partial y\equiv 0$, the system can reach a stable state regardless of the value of $z$, indicating that data partners have no evolutionarily stable strategy. When $z<z^{*}$, $L\left(z\right)>0$, and $\partial F_{DP}\left(y\right)/\partial y\equiv 0$, and ${\left.z<z^{\ast },L\left(z\right)>0,\partial F_{LG}\left(y\right)/\partial y\right|}_{y=0}<0$, the system becomes stable at $y=0$, implying that the evolutionarily stable strategy (ESS) of data partners is to provide false data. Conversely, when $y=1$, the ESS corresponds to providing authentic data. The replicator dynamic phase diagram of data partners’ strategies is illustrated in Figure 3.

Proposition 3.

The probability $y$ that data partners provide truthful or high-quality data increases as the effective payoff from truthful provision becomes higher, and decreases when such payoff is insufficient to offset the associated costs. In other words, when the incentive level remains within a reasonable range and strong strategic motives are absent, raising the net return from truthful data generally strengthens the partner’s inclination to supply high-quality information; conversely, when the incremental benefit of truthful provision is limited, low-quality or strategic supply becomes more likely. Accordingly, incentive schemes designed within an appropriate range—enhancing the marginal return of truthful data while constraining the benefit space of low-quality data—can help improve overall data quality and enhance coordination efficiency.

Proposition 4.

The probability $y$ that data partners provide high-quality data is jointly influenced by the strategic choices of logistics enterprises and supervisory regulatory authorities. Under the condition $0<z^{*}<1$, when logistics enterprises tend to share data and supervisory supervision is in place (e.g., providing subsidies, and establishing clear penalties and liability rules), data partners gradually evolve toward a strategy of providing authentic or high-quality data. Conversely, when logistics enterprises favor data exclusivity or supervision is lax, partners are more likely to adopt a strategy of providing false or low-quality data. As the critical threshold $z^{*}$ increases, the influence of logistics enterprises’ sharing strategies and supervisory regulatory measures on partners’ behavior is strengthened. This indicates that coordinated enterprise–regulator policies and well-designed incentive mechanisms can significantly increase the probability of high-quality data provision by partners, thereby ensuring the overall value of platform data and enhancing collaborative efficiency in the logistics industry.

4.1.3. Evolutionarily Stable Strategy Analysis of Supervisory Institutions

According to the stability theorem of differential equations, determining whether the strategic outcome of logistics enterprises is in a stable state requires that both conditions $F_{SI}\left(z\right)=0$ and $\partial F_{SI}\left(z\right)/\partial z<0$ are satisfied:

$${\displaystyle \frac{\partial F_{SI}\left(z\right)}{\partial z}}=\left(2z-1\right)\left(C_{z2}-R_{z2}+C_{z1}x-C_{z2}x+Gx-{\lambda }_g{N}^{{\beta }_g}y-R_{z1}x+R_{z2}x\right)$$

(15)

Let $S\left(x\right)$ be a function of $x$ then:

$$S\left(x\right)=\left(C_{z2}-R_{z2}+C_{z1}x-C_{z2}x+Gx-{\lambda }_g{N}^{{\beta }_g}y-R_{z1}x+R_{z2}x\right)$$

(16)

$$x*={\displaystyle \frac{R_{z2}-C_{z2}+{\lambda }_g{N}^{{\beta }_g}y}{C_{z1}-C_{z2}+G-R_{z1}+R_{z2}}}$$

(17)

Therefore, when $x=x^{*}$, $S\left(x\right)=0$ and $\partial F_{SI}\left(z\right)/\partial z\equiv 0$, the system can reach a stable state regardless of the value of $x$, indicating that supervisory institutions have no evolutionarily stable strategy. When $x<x^{*}$, $S\left(x\right)<0$ and ${\left.x<x^{\ast },S\left(x\right)<0,\partial F_{SI}\left(z\right)/\partial z\right|}_{z=0}<0$, the system stabilizes at $z=1$, implying that the evolutionarily stable strategy (ESS) of supervisory institutions is to implement supervision. Conversely, when $z=0$, the ESS corresponds to not supervising. The replicator dynamic phase diagram of supervisory institutions’ strategies is illustrated in Figure 4.

Proposition 5.

The proportion $z$ of supervisory institutions adopting supervision depends on the comparison between regulatory benefits and costs. When the net benefits of supervision—including returns from data-sharing logistics enterprises and the positive social effects of policy implementation—exceed regulatory costs, the supervisory institution tends to adopt an active supervisory strategy; otherwise, it leans toward relaxed or no supervision. When the proportion of data-sharing logistics enterprises is high, the supervisory institutions, can achieve greater governance efficiency and information transparency through data feedback, thereby increasing the marginal benefits of supervision. Conversely, when data-exclusive enterprises dominate or regulatory costs are high, the supervisory institution’s willingness to supervise is suppressed. Therefore, the optimal regulatory intensity depends on the dynamic balance among regulatory costs, enterprise data openness, and the social welfare gains derived from data sharing.

Proposition 6.

The probability $z$ that supervisory institutions implement supervision is jointly influenced by the strategic choices of logistics enterprises and data partners. Under the condition $0<x^{*}<1$ , logistics enterprises tend to share data and data partners provide authentic or high-quality data, supervision gradually evolves toward an active strategy. Conversely, when logistics enterprises favor data exclusivity and data partners provide false or low-quality data, supervisory institutions are more likely to adopt a laissez-faire or non-supervisory strategy. As the critical threshold $x^{*}$ increases, the effects of enterprises’ data-sharing willingness and partners’ data quality on supervision are strengthened. This indicates that enhancing data transparency and reinforcing collaborative governance mechanisms can effectively reduce regulatory costs, improve policy implementation efficiency, and promote sustained supervisory institution efforts to safeguard data security and maintain market order.

4.2. System Stability Analysis

In the replicator dynamic system, multiple equilibrium points may exist. An equilibrium point is considered locally asymptotically stable if, starting from any nearby region, the trajectories of the system ultimately converge to that point. The combination of strategies corresponding to different equilibrium points constitutes the evolutionarily stable strategy (ESS) [30]. By setting $F_{LE}\left(x\right)=F_{DP}(y)=F_{SI}\left(z\right)=0$, eight specific equilibrium points of the replicator dynamic system are obtained: $E_1\left(0,0,0\right)$, $E_2\left(0,0,1\right)$, $E_3\left(0,1,0\right)$, $E_4\left(0,1,1\right)$, $E_5\left(1,0,0\right)$, $E_6\left(1,0,1\right)$, $E_7\left(1,1,0\right)$ and $E_8\left(1,1,1\right)$, along with four mixed-strategy equilibrium solutions. In multi-agent evolutionary games, evolutionarily stable equilibria are necessarily strict Nash equilibria, whereas mixed-strategy Nash equilibria cannot resist cumulative minor perturbations and will eventually evolve toward pure-strategy Nash equilibria. Therefore, only the asymptotic stability of the above eight specific points is discussed [31].

By substituting the eight specific equilibrium points into the Jacobian matrix, the eigenvalues corresponding to each point are obtained, as shown in

Table 2. Characteristic values and stability analysis of system equilibrium points.

Equilibrium Point	Characteristic Value and Symbol Judgment			Stability
	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$
$E_1\left(0,0,0\right)$	$R_{z2}-C_{z2}\left(+\right)$	$R_{y1}-R_{y2}\left(+\right)$	$\begin{array}{l}{C}_{x2}-C_{x1}+\\ R_{x1}-R_{x2}\left(+\right)\end{array}$	Unstable point
$E_2\left(1,0,0\right)$	$R_{z1}-G-C_{z1}\left(\times \right)$	$\begin{array}{l}{C}_{x1}-C_{x2}\\ -R_{x1}+R_{x2}\left(-\right)\end{array}$	$\begin{array}{l}Q+R_{y1}-R_{y2}\\ +{(bP)}^{{\alpha }_d}\left(+\right)\end{array}$	Unstable point
$E_3\left(0,1,0\right)$	$\begin{array}{l}{R}_{y2}-R_{y1}\left(-\right)\hfill \end{array}$	$\begin{array}{l}{\lambda }_g{N}^{{\beta }_g}-C_{z2}\\ +R_{z2}\left(+\right)\end{array}$	$\begin{array}{l}{C}_{x2}-C_{x1}+\\ R_{x1}-R_{x2}\left(+\right)\end{array}$	Unstable point
$E_4\left(0,0,1\right)$	$\begin{array}{l}{C}_{z2}-R_{z2}\left(-\right)\hfill \end{array}$	$R_{y1}-R_{y2}\left(+\right)$	$\begin{array}{l}{C}_{x2}-C_{x1}+G+\\ R_{x1}-R_{x2}\left(+\right)\end{array}$	Unstable point
$\begin{array}{l}{E}_5\left(1,1,0\right)\hfill \end{array}$	$\begin{array}{l}\begin{array}{l}{R}_{y2}-R_{y1}-Q\\ -{(bP)}^{{\alpha }_d}(\times )\end{array}\hfill \end{array}$	$\begin{array}{l}{\lambda }_g{N}^{{\beta }_g}-G\\ -C_{z1}+R_{z1}\left(\times \right)\end{array}$	$\begin{array}{l}{C}_{x1}-C_{x2}-R_{x1}\\ +R_{x2}\left(-\right)\end{array}$	Possible for ESS
$E_8\left(1,0,1\right)$	$\begin{array}{l}{C}_{z1}+G-R_{z1}\left(\times \right)\hfill \end{array}$	$\begin{array}{l}Q+R_{y1}-R_{y2}\\ +{(aP)}^{{\alpha }_d}\left(\times \right)\end{array}$	$\begin{array}{l}{C}_{x1}-C_{x2}-G\\ -R_{x1}+R_{x2}\left(-\right)\end{array}$	Possible for ESS
$E_7\left(0,1,1\right)$	$R_{y2}-R_{y1}\left(-\right)$	$\begin{array}{l}{C}_{z2}-{\lambda }_g{N}^{{\beta }_g}\\ -R_{z2}\left(-\right)\end{array}$	$\begin{array}{l}{C}_{x2}-C_{x1}+G+R_{x1}\\ -R_{x2}+S-{\lambda }_l{(aS)}^{{\beta }_l}\\ \left(+\right)\end{array}$	Possible for ESS
$E_8\left(1,1,1\right)$	$\begin{array}{l}{R}_{y2}-R_{y1}-Q\\ -{(aP)}^{{\alpha }_d}\left(\times \right)\end{array}$	$\begin{array}{l}{C}_{z1}+G\\ -{\lambda }_g{N}^{{\beta }_g}-R_{z1}\left(\times \right)\end{array}$	$\begin{array}{l}{C}_{x1}-C_{x2}-G-R_{x1}\\ +R_{x2}-S+{\lambda }_l{(aS)}^{{\beta }_l}\\ \left(-\right)\end{array}$	Possible for ESS

Note: × represents uncertain symbol.

. According to the first method of Lyapunov, the eigenvalues of the Jacobian matrix can be used to assess evolutionary stability. If all eigenvalues are negative, the corresponding equilibrium point can be identified as an evolutionarily stable strategy (ESS). Conversely, if any eigenvalue is positive, the equilibrium point cannot be considered an ESS. For some equilibrium points, the signs of the eigenvalues vary depending on parameter values, indicating differences in the system’s evolutionary trajectory. Based on the states presented in Table 2, {data sharing, providing authentic data, no supervision}, {data sharing, providing false data, supervision}, and {data sharing, providing authentic data, supervision} emerge as potential evolutionarily stable strategies, representing the ideal states for the system under study and warranting further investigation.

$$\begin{array}{l}J=\left. [\begin{array}{l}{\displaystyle \frac{\partial F(x)}{\partial x}}{\displaystyle \frac{\partial F(x)}{\partial y}}{\displaystyle \frac{\partial F(x)}{\partial z}}\\ {\displaystyle \frac{\partial F(y)}{\partial x}}{\displaystyle \frac{\partial F(y)}{\partial y}}{\displaystyle \frac{\partial F(y)}{\partial z}}\\ {\displaystyle \frac{\partial F(z)}{\partial x}}{\displaystyle \frac{\partial F(z)}{\partial y}}{\displaystyle \frac{\partial F(z)}{\partial z}}\end{array}\right]=\left. [\begin{array}{l}{J}_{11}{J}_{12}{J}_{13}\\ J_{21}{J}_{22}{J}_{23}\\ J_{31}{J}_{32}{J}_{33}\end{array}\right]=\\ \left. [\begin{array}{l}-\left(2x-1\right)\left(\begin{array}{l}{C}_{x2}-C_{x1}+R_{x1}-R_{x2}+\\ Gz+Syz-{\lambda }_l{(aS)}^{{\beta }_l}yz\end{array}\right) -Sxz\left(a+1\right)\left(x-1\right) -x\left(x-1\right)\left(G+Sy+-{\lambda }_l{(aS)}^{{\beta }_l}y\right)\\ -y\left(y-1\right)\left(Q+{(bP)}^{{\alpha }_d}+{(aP)}^{{\alpha }_d}z-{(bP)}^{{\alpha }_d}z\right) -\left(2y-1\right)\left(\begin{array}{l}{R}_{y1}-R_{y2}+Qx+{(bP)}^{{\alpha }_d}x\\ +{(aP)}^{{\alpha }_d}xz-{(bP)}^{{\alpha }_d}xz\end{array}\right) -Pxy\left(a-b\right)\left(y-1\right)\\ z\left(z-1\right)\left(C_{z1}-C_{z2}+G-R_{z1}+R_{z2}\right) -{\lambda }_g{N}^{{\beta }_g}z\left(z-1\right) \left(2z-1\right)\left(\begin{array}{l}{C}_{z2}-R_{z2}+C_{z1}x-C_{z2}x\\ +Gx-Ny-R_{z1}x+R_{z2}x\end{array}\right)\end{array}\right]\end{array}$$

Proposition 7.

When $R_{y2}-R_{y1}-Q-{(bP)}^{{\alpha }_d}<0$ and ${\lambda }_g{N}^{{\beta }_g}+R_{z1}-G-C_{z1}<0$, $E_5\left(1,1,0\right)$ represents an evolutionarily stable equilibrium point, where the net benefit of data sharing for logistics enterprises is lower than that of exclusive data usage after accounting for the penalty for exclusivity, and the sum of the superior-level penalty and supervision revenue is less than the total of supervision subsidies and enforcement costs. This indicates that when the gains from data collaboration are insufficient relative to exclusive data benefits, and the regulatory costs faced by the supervisory institutions exceed the combined returns from shared data, the evolutionarily stable strategies for the three parties are {share data, provide truthful data, do not regulate}. This suggests that under conditions of limited governmental incentives and high regulatory costs, the supervisory institution tends to reduce its regulatory intervention, allowing market mechanisms to dominate data-sharing activities. Meanwhile, logistics enterprises continue to share data based on reputation constraints and long-term cooperative expectations, and data partners tend to provide truthful information to maintain business credibility and collaborative relationships. The system exhibits a stable equilibrium centered on market self-discipline, reflecting endogenous coordination and self-organizing characteristics when the supervisory institution withdraws from active regulation.

Proposition 8.

When $C_{z1}+G-R_{z1}<0$ and $Q+R_{y1}-R_{y2}+{(aP)}^{{\alpha }_d}<0$, $E_6\left(1,0,1\right)$ represents an evolutionarily stable equilibrium point. This occurs when the sum of supervision investment costs and subsidies is less than supervision benefits, and the revenue of logistics enterprises exceeds the combined revenue of data partners, data-sharing gains, and penalty costs. This indicates that when the total regulatory cost and subsidies to sharing enterprises are lower than the gains obtained from shared data, and data partners providing authentic data receive lower overall benefits than in the case of providing false data, while logistics enterprises face relatively low compensation expenditures under supervision, the evolutionarily stable strategy for the three parties in the game is {data sharing, providing false data, supervision}. This scenario demonstrates that when supervision is supported by strong economic incentives, low regulatory costs, and sufficient returns, the supervisory institution maintains an active supervisory stance. However, under conditions of low compensation burden for enterprises and minimal costs for false-data behavior, data partners may choose to provide low-quality or false data for profit. In this context, logistics enterprises continue to share data, but the quality of shared data declines, increasing supervisory institutions pressure and resulting in a non-ideal equilibrium characterized by “supervision present but quality compromised”, reflecting a situation where incentive imbalance and moral hazard coexist.

Proposition 9.

When  $R_{y2}-R_{y1}-Q-{(aP)}^{{\alpha }_d}<0$ and $R_{y2}-R_{y1}-Q-{(aP)}^{{\alpha }_d}<0$,  $E_8\left(1,1,1\right)$ represents an evolutionarily stable equilibrium point. This occurs when the revenue of logistics enterprises is less than the combined revenue of data partners, data-sharing gains, and penalty costs, and when supervision revenue and upper-level cost savings exceed supervision investment and subsidy expenditures. This indicates that when data partners obtain higher overall benefits by providing authentic or high-quality data than by refusing to provide data, logistics enterprises can maintain data sharing with manageable privacy compensation obligations, and the supervisory institution’s net gains from supervision—including governance value obtained from sharing enterprises and reduced risk of upper-level penalties—exceed regulatory costs and subsidy expenditures, the evolutionarily stable strategy for the three parties is {data sharing, providing authentic/high-quality data, supervision}. This scenario demonstrates that when partners provide high-quality data due to sufficient marginal returns, logistics enterprises maintain data sharing under regulatory and subsidy incentives, and the supervisory institutions ensures data security and public value through supervision, the interests of all three parties are effectively coordinated. This results in a synergistic equilibrium of data quality, data security, and utilization efficiency, representing the ideal state of a collaborative governance model for logistics big data sharing.

5. Numerical Simulation and Discussion

5.1. Parameters Setting

To examine how variations in key parameters influence the evolutionary game behavior of the agents, this study employs MATLAB 2022a for simulation analysis and derives the stable strategies corresponding to Inferences 7–9. The model parameters, summarized in

Table 3. Parameter settings for game system simulation.

Array	A	B	C
$C_{x1}$	2	2	2
$C_{x2}$	1	1	1
$R_{x1}$	40	40	40
$R_{x2}$	20	20	20
$R_{y1}$	100	10	100
$R_{y2}$	85	115	85
$R_{z1}$	50	50	50
$R_{z2}$	25	25	25
$C_{z1}$	20	20	20
$C_{z2}$	10	10	10
$Q$	600	100	600
$P$	10	0	10
$S$	10	10	10
$a$	0.4	0.4	0.4
$b$	0.3	0.3	0.3
$N$	20	20	50
$G$	100	0	50
$\alpha$	0.88	0.44	0.88
$\beta$	0.88	0.44	0.88
$\lambda$	2.25	1.25	2.25

, are dimensionless. Parameters associated with logistics enterprises are determined based on existing empirical studies [1,2,8,9,10,11,12] and statistical data released by the China Logistics Association, ensuring consistency with observed operational costs, revenues, and incentives. Parameters of data-sharing partners are specified with reference to prior research findings [6,7,8,13,29], reflecting realistic variations in payoff structures and collaboration benefits. Parameters for supervisory institutions are extracted from relevant policy documents [19,20,21], capturing the regulatory scope and enforcement mechanisms in the logistics sector. For the prospect-theory component, coefficients of risk attitude and loss aversion are assigned according to the experimental results reported by Tversky and Kahneman [32].

To enhance the model’s generalizability, key parameters are designed to be adjustable, allowing the model to accommodate variations in regulatory strength and incentive mechanisms across different countries or regions. Following standard approaches in evolutionary game studies, we conducted a proportional sensitivity analysis by systematically increasing or decreasing key parameters to examine their impact on the qualitative evolutionary dynamics. The results indicate that the evolutionary stability of data-sharing strategies is generally robust to reasonable changes in parameter values. This approach ensures that the model is both empirically informed and adaptable to different governance contexts without implying extensive experimental calibration.

5.2. Game Factors Simulation and Discussion

Experiment 1: effect of data-sharing revenue $Q$ on system evolution.

To examine the impact of data-sharing revenue on the evolutionary game process and outcomes, the initial conditions were set, and $Q$ was assigned values of 300, 600, and 900. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 5.

As shown in Figure 5, during the system’s evolution toward a stable state, the willingness of logistics enterprises to share data declines slightly, while the intention of partner enterprises to provide truthful data remains relatively stable across different payoff conditions. As the returns from data sharing increase and enterprise revenues rise, high-performing logistics firms accumulate a substantial volume of data and begin to prioritize their own economic interests, platform development, and the protection of data value and user privacy, thereby reducing their willingness to share data. Heightened supervision further reinforces this cautious behavior. To encourage data-sharing under such conditions, it is necessary to strengthen both technical and organizational safeguards by improving data security technologies, reducing the cost of privacy protection, and promoting clearer data management protocols. Through these measures, platforms can facilitate data sharing while ensuring the protection of user information, enabling data to generate its intended economic and operational value.

Experiment 2: effect of logistics enterprise compensation $P$ on system evolution.

To analyze the impact of logistics enterprise compensation on the evolutionary game process and outcomes, the initial conditions were set, and $P$ was assigned values of 0, 10, and 20. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 6.

As shown in Figure 6, the compensation offered by logistics enterprises exerts no significant influence on the behavior of either data-sharing partners or the supervisory institutions. Regardless of the compensation level, partners’ willingness to provide truthful data remains largely unchanged, suggesting that their behavior is not substantially driven by monetary compensation. Likewise, compensation does not meaningfully affect the data-sharing decisions of logistics enterprises themselves, indicating that firms may prioritize factors such as regulatory pressure and privacy considerations over user-level compensation. Moreover, variations in compensation do not materially alter the effectiveness of supervision, implying that regulatory outcomes are largely independent of platform-initiated compensation measures. Under these conditions, compensation cannot be regarded as a key determinant of the behavioral dynamics among the three parties. To improve the effectiveness of incentive schemes, technical safeguards—such as enhanced data encryption and privacy-preserving data processing—and organizational measures—such as clear governance protocols and monitoring procedures—can help ensure that compensation mechanisms align with authentic data provision and overall platform objectives.

Experiment 3: effect of supervision subsidy $G$ on system evolution.

To examine the impact of supervision subsidies on the evolutionary game process and outcomes, the initial conditions were set, and $G$ was assigned values of 0, 50, and 100. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 7.

As shown in Figure 7, during the system’s evolution toward a stable state, both the partners’ provision of truthful data and the logistics enterprises’ data-sharing behavior decline, and the intensity of supervision weakens; excessively high subsidies exert a suppressive effect on all three parties. As subsidies increase, the willingness of logistics enterprises to share data shows a downward trend, ultimately constraining enterprise development. This outcome may arise because higher subsidies raise enterprise income, prompting firms to place greater emphasis on protecting platform data and preserving the economic value embedded in their data assets, thereby reducing their incentive to share. At the same time, supervision diminishes as subsidy levels rise, possibly because financial transfers reduce regulatory investment while expecting enhanced industry self-discipline. To mitigate these effects, technological solutions such as access control, real-time monitoring of data use, and automated audit mechanisms, combined with organizational measures including formal data-sharing policies and structured oversight, can help balance subsidies with effective data governance and encourage continued participation.

Experiment 4: Effect of data partner revenue $R_{y1}$ on system evolution.

To analyze the impact of data partner revenue on the evolutionary game process and outcomes, the initial conditions were set, and $R_{y1}$ was assigned values of 10, 100, and 1000. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 8.

As shown in Figure 8, during the system’s evolution toward a stable state, increased income for logistics enterprise partners strengthens the data-sharing behavior of logistics enterprises, while simultaneously reducing the partners’ willingness to provide truthful data. As partner income continues to rise, the frequency of truthful data provision declines, indicating that incentives should be maintained within a certain range. Excessive incentives may heighten partners’ defensive awareness, leading them to withhold authentic data. Additionally, higher enterprise investment in acquiring data may result in insufficient attention to data protection, thereby diminishing the provision of truthful user data. In the early stages of platform operation, logistics enterprises tend to reward user income to rapidly expand their own data pools. During this period, enterprises demonstrate strong demand for shared data, as they simultaneously increase investments to attract users and aim to leverage data sharing or exchange to access larger data markets, thereby continuously expanding their business scope. To support these strategies while safeguarding data quality and user privacy, enterprises can adopt technical measures such as secure data storage, differential privacy, and anonymization, together with organizational mechanisms like standardized reward procedures, compliance checks, and data governance frameworks, which ensure that incentive schemes effectively translate into reliable data provision and sustainable platform growth.

Experiment 5: Effect of upper-level penalties $N$ on system evolution.

To analyze the impact of upper-level penalties on the evolutionary game process and outcomes, the initial conditions were set, and $N$ was assigned values of 0, 50, and 100. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 9.

As shown in Figure 9, during the system’s evolution toward a stable state, increases in penalty amounts lead to higher levels of truthful data provision by partners, enhanced data-sharing behavior by logistics enterprises, and stronger supervision, indicating that higher-level penalties exert a significant promoting effect on all three parties. Higher penalties reflect stricter consequences for data breaches, signaling increased oversight from superior authorities, which in turn strengthens partners’ trust in logistics enterprises and encourages them to provide truthful data. Similarly, logistics enterprises’ trust in the market improves, and the increased penalty pressure incentivizes greater investment in data protection, resulting in more extensive data-sharing behavior. Superior-level penalties also have a direct effect on supervisory institution: the involvement of higher authorities enables local regulators to more effectively fulfill their supervisory responsibilities, enhance enterprise data monitoring capabilities, and implement additional coordination measures. To support these outcomes, technical measures such as real-time data monitoring, automated audit systems, and secure storage can reinforce compliance, while organizational mechanisms including clear reporting protocols, hierarchical oversight structures, and coordinated regulatory frameworks can further strengthen governance of data transactions, ensuring that increased penalties translate into improved data-sharing behavior and more effective market supervision.

Experiment 6: effect of logistics enterprise risk preferences ${\lambda }_l$ and ${\beta }_l$ on system evolution.

To analyze the impact of logistics enterprises’ risk preferences on the evolutionary game process and outcomes, the initial conditions were set, and the loss-aversion coefficient ${\lambda }_l$ was assigned values of 2.25 and 4.5, while the risk-attitude coefficient ${\beta }_l$ was assigned values of 0.44 and 0.88. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 10.

As shown in Figure 10, during the system’s evolution toward a stable state, increases in the risk attitude coefficient, loss aversion coefficient, and responsibility-sharing coefficient significantly accelerate the evolutionary process, with logistics enterprises increasingly favoring a data-sharing strategy. A higher risk attitude coefficient encourages enterprises to undertake moderate risks in uncertain environments to obtain additional benefits from data sharing. An elevated loss aversion coefficient heightens sensitivity to potential reputational damage and regulatory penalties, prompting firms to share data as a means of mitigating risks related to noncompliance and data silos. The combined effect of these risk parameters drives logistics enterprises toward data-sharing behavior and enables the system to converge more rapidly to a stable equilibrium. From a policy perspective, this suggests the need to strengthen data security safeguards, optimize data property rights mechanisms, and enhance positive incentives for sharing, thereby reducing potential risks and uncertainties in collaborative data use. In addition, establishing cross-departmental regulatory coordination, credit constraint systems, and enforcement mechanisms for firms that conceal or refuse to share data can reinforce compliance. Complementary technical measures such as secure data management platforms, real-time monitoring, and automated auditing, together with organizational mechanisms including standardized reporting procedures and interdepartmental oversight protocols, can further support enterprises in sharing data responsibly while ensuring privacy and system-wide coordination, thereby promoting full-process logistics data collaboration.

Experiment 7: effect of data partner risk-return preference ${\alpha }_d$ on system evolution.

To analyze the impact of data partners’ risk-return preferences on the evolutionary game process and outcomes, the initial conditions were set, and the risk-return coefficient ${\alpha }_d$ for data partners was assigned values of 0.22, 0.44, and 0.88. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 11.

As shown in Figure 11, during the system’s evolution toward a stable state, variations in the risk–return preferences of data-sharing partners have little effect on the evolutionary rate and do not alter the system’s outcome. This result indicates that, in the logistics data-sharing game, partners’ decisions to provide truthful or false data are not primarily determined by their individual risk preferences. Based on this finding, supervisory institutions should enhance regulatory and credit evaluation frameworks by incorporating data authenticity into industry credit assessments and public procurement standards. Joint sanctions against providers of false data can establish a dual incentive structure—high-quality data yields high returns, whereas false data incurs significant penalties—thereby stabilizing the game equilibrium and improving the overall quality and trustworthiness of the logistics data-sharing ecosystem. Complementary technical measures, such as automated verification tools and secure data auditing systems, alongside organizational mechanisms including coordinated oversight and standardized reporting protocols, can further support the effective implementation of these regulatory strategies and reinforce compliance across all participants.

Experiment 8: Effect of supervisory institutions’ risk preferences ${\lambda }_g$ and ${\beta }_g$ on system evolution.

To analyze the impact of supervisory institutions’ risk preferences on the evolutionary game process and outcomes, the initial conditions were set, and the loss-aversion coefficient ${\lambda }_g$ was assigned values of 2.25 and 4.5, while the risk-attitude coefficient ${\beta }_g$ was assigned values of 0.44 and 0.88. The replicator dynamic equations were simulated over 50-time steps, with the results presented in Figure 12.

As shown in Figure 12, during the system’s evolution toward a stable state, increases in the risk–loss preference of supervisory institution departments accelerate system evolution and encourage the adoption of more proactive regulatory strategies. Higher risk sensitivity indicates that regulators are more attuned to potential environmental and social risks, prompting stricter oversight to mitigate system instability and responsibility-related hazards. Conversely, when the regulatory departments exhibit low risk preference, the system ultimately evolves to a stable state characterized by data sharing by enterprises, provision of false data by partners, and minimal regulatory intervention. This outcome highlights that, in the absence of sufficient risk pressure or incentive constraints, market mechanisms alone are insufficient to self-correct, and false data behaviors remain unaddressed, undermining the trust foundation of the data-sharing system. From a policy perspective, it is therefore essential to establish accountability-based incentive mechanisms, introduce third-party supervision, and implement social auditing frameworks to reinforce regulators’ sense of responsibility and risk-prevention capacity. Complementary technical measures, such as automated monitoring, data integrity verification tools, and real-time reporting systems, alongside organizational mechanisms including structured oversight protocols and interdepartmental coordination, can further ensure that regulatory behavior is sustained, effective, and capable of guiding the multi-agent system toward collaborative and stable data-sharing outcomes.

5.3. Game System Simulation and Discussion

Array A satisfies the conditions of Proposition 7. As shown in Figure 13, logistics enterprises tend to engage in data sharing, and data partners are willing to provide authentic data. Under these circumstances, the platform operates effectively, and supervisory institutions tend not to intervene. The corresponding strategy profile is (1, 1, 0), i.e., {data sharing, provision of authentic data, no supervision}. This scenario typically occurs during the early stage of logistics enterprise development, when the enterprise aims to expand its user base and requires substantial data support for operations. To attract users, the enterprise invests resources and provides financial incentives to encourage data partners to supply authentic data. At this stage, the enterprise also adheres to operational norms and complies with data transaction rules, reducing the risk of data leakage. Consequently, even in the absence of active supervision, the platform can function smoothly.

Array B satisfies the conditions of Proposition 8. As shown in Figure 14, logistics enterprises tend to engage in data sharing, while data partners are inclined to withhold authentic data. Under these circumstances, supervisory institutions tend to adopt a supervisory role. The corresponding strategy profile is (1, 0, 1), i.e., {data sharing, provision of false data, supervision}. This scenario generally occurs during the mid-term of logistics enterprise operations, when data volume remains critical for business, and enterprises continue to invest resources to acquire data. At this stage, data partners’ vigilance gradually increases, and financial incentives alone are insufficient to encourage the provision of authentic data. In some cases, excessive incentives may even heighten partners’ caution, prompting them to withhold authentic data. To ensure data integrity, supervisory institutions intervene to regulate enterprise data transactions and enhance oversight of logistics enterprises’ data-sharing behavior.

Array C satisfies the conditions of Proposition 9. As shown in Figure 15, logistics enterprises tend to share data, data partners are inclined to provide authentic data, and supervisory institutions actively supervise. The corresponding strategy profile is (1, 1, 1), i.e., {data sharing, provision of authentic data, supervision}. This state represents an ideal scenario for logistics enterprises engaging in data sharing. Effective data transactions require active participation from multiple parties. Coordination among logistics enterprises, data partners, and supervisory institutions facilitates reliable data collection. Data partners provide authentic data, ensuring accuracy and reliability from the source, while supervisory institutions implement comprehensive supervision measures, supporting and safeguarding data-sharing activities at the governance level. Such a collaborative framework promotes data mining and enables data to generate substantial value for logistics enterprises and society at large.

Overall, the simulation analysis aligns with the conclusions drawn from the stability analysis of the strategies and demonstrates practical validity, offering meaningful guidance for the collaborative governance of logistics big data sharing.

6. Conclusions and Implication

6.1. Conclusions

This study focuses on data-sharing governance in logistics operations and constructs an evolutionary game model involving three parties: logistics enterprises, data partners, and supervisory institutions. System stability and equilibrium conditions are analyzed based on the Jacobian matrix, while numerical simulations conducted in MATLAB 2022 examine the influence of key parameters on the system’s evolutionary outcomes. The results reveal the behavioral logic of different stakeholders and their dynamic evolution under risk constraints, providing theoretical foundations and policy implications for data-sharing governance.

The findings indicate that increased revenue for data partners reduces their motivation to provide truthful data, while simultaneously enhancing the propensity of logistics enterprises to share data. Conversely, higher profits for logistics enterprises tend to suppress their data-sharing behavior. Compensation amounts do not significantly affect the behaviors of the three parties, whereas excessively high supervision subsidies weaken the willingness of data partners to provide truthful data, logistics enterprises to share data, and supervisory institutions to implement oversight. Increasing the enforcement intensity of higher-level authorities significantly promotes compliance across all parties.

The study further shows that in the early stage of data transactions, supervisory institutions may adopt a relatively lenient supervision strategy. At this stage, the incentives and constraints implemented by logistics enterprises can effectively regulate data partners’ behavior, enabling the system to maintain stability through internal mechanisms. As enterprises develop, however, the marginal effectiveness of incentives diminishes and may even induce strategic responses. Consequently, supervision intervention becomes necessary in the mid-to-late stages. Regulatory measures not only help restore the order of data sharing but also enhance data partners’ willingness to provide truthful data, thereby ensuring data quality and usability.

The analysis also indicates that enterprise investment is positively correlated with data-sharing behavior, whereas profit levels are negatively correlated. Data-sharing willingness varies across different stages of enterprise development: early-stage enterprises, focused on expanding collaboration and accumulating resources, tend to share data proactively; in contrast, mature enterprises, possessing sufficient internal data and reduced reliance on external sources, show lower willingness to share. At this stage, governance strategies should shift from purely financial incentives to institutional measures—such as reputation evaluation, credit constraints, and performance accountability—to strengthen corporate social responsibility and promote proactive data sharing.

From a risk perspective, the risk preferences of all three parties significantly affect the system’s evolutionary speed and stability. Increases in risk attitude coefficients, loss-aversion coefficients, and responsibility-sharing coefficients for logistics enterprises, data partners, and supervisory institutions accelerate convergence to stable equilibria. However, if supervisory institutions exhibit excessively low risk preference, the system may evolve toward an unstable state characterized by “data sharing–false data–no supervision.” Therefore, appropriately enhancing risk awareness among supervisory institutions and enterprises, while strengthening risk-sharing and accountability mechanisms, is critical for ensuring the stable operation of the data-sharing system.

6.2. Implication

Based on the research findings, this study proposes establishing a dynamic “incentive–constraint–collaboration” mechanism among logistics enterprises, data partners, and supervisory institutions. This mechanism aims to promote the stable and efficient operation of the logistics data-sharing governance system while ensuring data security and quality. Specific policy recommendations are as follows:

• Logistics Enterprises: strengthen incentive mechanisms and data security governance

Logistics enterprises should balance economic returns, risk exposure, and social responsibility in the process of data sharing. First, to obtain high-quality and authentic data, enterprises should enhance partner engagement through subsidy-based incentives and tiered reward mechanisms, designing differentiated strategies for various types of partners and expanding the data source base via platform promotion and data dissemination activities. In line with international practices, enterprises can also draw on EU approaches, such as implementing standardized consent management, differential privacy, and GDPR-compliant data processing frameworks, to ensure both legal compliance and enhanced partner trust. Second, enterprises should recognize that data sharing itself generates potential economic and social benefits; once these benefits reach a certain level, short-term private gains should not restrict data openness. Continuous data sharing should be promoted under robust privacy protection and encryption technologies to achieve revenue growth, fulfill social responsibilities, and enhance corporate reputation. Third, logistics enterprises need to establish comprehensive data risk management systems covering preemptive protection, real-time monitoring, and post-incident remediation. In the event of a data breach, immediate compensation and recovery measures should be implemented to maximize protection of user rights and corporate credibility. Overall, enterprises should integrate data-sharing behavior into their sustainable development strategies, achieving a dynamic balance between data sharing and security governance through risk alert mechanisms and compliance systems.

2.

Data Partners: enhance data authenticity and compliance awareness

As the supply side of the shared data ecosystem, partners’ behavior directly affects data quality and system evolution. Partners should prioritize cooperation with reputable and well-managed logistics enterprises, providing authentic data while safeguarding their legal rights. Drawing on EU practices such as the GDPR and Data Act, partners should adopt clear consent protocols, participate in data portability and access arrangements, and ensure compliance with privacy and security standards, thus building trust and supporting sustainable data sharing. At the same time, partners should strengthen privacy awareness, carefully review and comply with data-use and privacy protection agreements, and avoid misuse of information or infringement of rights due to asymmetric information. Any infringement or improper use of personal data should be promptly reported to regulatory authorities, with legal recourse pursued as necessary. Partners can also proactively participate in industry credit systems, linking data quality with commercial credit to obtain long-term and stable benefits. Sustainable engagement is only possible when data authenticity and economic incentives are aligned to form a positive feedback mechanism.

3.

Supervisory institutions: optimize phased supervision and collaborative governance

The supervisory institutions should perform a triple role of guidance, supervision, and coordination within the data-sharing system. During the initial phase, guidance and incentive measures should predominate, encouraging logistics enterprises and partners to self-organize a data-sharing ecosystem while avoiding excessive intervention that may generate institutional friction. In the middle and later phases, supervision should be strengthened, with a focus on data authenticity, security, and privacy compliance. International practices, such as the EU’s phased regulatory approach under GDPR and the Data Act, demonstrate the value of combining initial guidance and incentives with subsequent compliance enforcement, including sanctions for non-compliance, auditing, and standardized reporting. Regulatory policies should avoid creating dependency through excessive subsidies, instead leveraging reputational constraints, credit penalties, and tax incentives to establish a flexible incentive framework. Furthermore, supervisory institutions must maintain risk sensitivity and regulatory vigilance, continuously monitoring enterprise and industry dynamics, implementing risk alerts, and preventing systemic data security threats, ensuring that governance is effective and sustainable throughout the data-sharing lifecycle.

Moreover, data-sharing governance requires multi-level and cross-departmental coordination. A multi-stakeholder governance framework should be established, led by the national data authority, coordinated by local regulators, and involving industry associations and social organizations. This framework should facilitate policy coordination, joint enforcement, and information sharing. By constructing unified regulatory data platforms and shared credit systems, and learning from EU initiatives such as interoperable data spaces and sectoral data governance frameworks, the supervisory institutions can strengthen intergovernmental and supervisory institutions–enterprise data governance capabilities, thereby fostering a secure, transparent, and sustainable data-sharing ecosystem.

6.3. Deficiency and Future Prospect

Although this study systematically analyzes the evolutionary behaviors of logistics enterprises, data partners, and supervisory institutions in data sharing through a three-party evolutionary game model, several limitations remain. First, the model assumes certain parameters to be static and does not fully account for the potential effects of enterprise scale, industry type, or regional differences on behavioral choices. Second, the simulation analysis is conducted under specific initial conditions, whereas real-world applications may involve more complex environmental disturbances and multidimensional constraints. Future research could enrich the model by incorporating greater heterogeneity, dynamic policy adjustments, and multi-platform interaction mechanisms, thereby further exploring the evolutionary patterns of data-sharing behavior under different market structures and policy environments. Such advancements would provide more precise theoretical foundations and practical guidance for data governance in the logistics industry. In addition, the international dimension could be explored in greater depth by integrating data and policy considerations from other regions, including EU regulations such as the Data Governance Act and the Data Act, as well as OECD best practices on data sharing and governance. Such advancements would provide more precise theoretical foundations and practical guidance for data governance in the logistics industry across both domestic and international contexts.