BenchCouncil Transactions on Benchmarks, Standards and

Evaluations, 2026

DOI: https://doi.org/10.66834/1zj2hv33

Research Article

RESEARCH ARTICLE

Endogenous Punishment-Driven Distributed

Computing Environment for Data Factor Property

Right Protection

Chuan Fu

1,∗

and Jian Ye

Institute of Computing Technology, Chinese Academy of Sciences, 100190, Beijing, China

∗

Corresponding author. chuanfu@ict.ac.cn

Received on 21 December 2025; Accepted on 23 September 2026

Abstract

The non-excludability and non-rivalry characteristics of data pose challenges to Coase’s property rights theory. Based

on Ostrom’s Common Pool Resources (CPR) Governance Theory, this study proposes deﬁning the data factor as a

six-tuple and designing a computational environment that supports the protection of data factor property rights. This

deﬁnition integrates the original dataset, transaction entities, commitments, supervision, and punishment into a uniﬁed

whole, speciﬁcally referred to as data factor. Similar to the intellectual property protection system, the six-tuple ﬁrst

endows data factors with excludability in a contractual sense. Secondly, to eﬀectively support such exclusivity, this

study proposes a distributed property rights protection computing environment with the capabilities of ”supervision-

punishment-commitment”, adopting the ”terminal-pipe-cloud” architectural template. This computing environment

better matches the self-organizing nature of data trading activities. We use evolutionary game theory to verify how the

new data factor deﬁnition promotes the development of trading markets. To provide practical reference, the simulation

focuses on two key aspects: market stability under the coexistence of multiple strategies, and the impact of the initial

conditions of the institutional environment on participants’ strategy choices.

Key words: Data Factor Property Rights Protection, Common Pool Resources Governance, Evolutionary Game,

Endogenous Punishment, Network Address Translation(NAT)

1. Introduction

The wealth value of data does not depend on ”how much” data

one possesses, but on ”how to utilize” it. However, the non-

excludability and non-rivalry of data[1],[2] pose challenges to

the property rights theory advocated by Coase. For instance,

how to address the issue that an additional copy halves

the data’s price, and how to ensure that data is reliable,

trustworthy, and usable. The property rights economic theory,

which is based on the excludability and rivalry of factors, holds

that clear property rights constitute the core prerequisite for

ensuring market collaboration and orderly transactions[3]. The

ongoing debate over the property rights of data factors precisely

indicates that data has not yet fully shed its ”pure resource”

attribute.

Unlike general factors of production, whose excludability

enables owners to sustain prices through use control, data

factors are non-excludable. Anyone who gains access can

replicate them at zero cost. This drives supply to inﬁnity, prices

toward zero, and ultimately severs the link between price and

the intrinsic value of the data.

Data open-sourcing is a typical approach to demonstrating

the value of data factors and exploring avenues for multi-

party collaboration. Among its key components, open-source

test datasets[4] serve as critical benchmarks for algorithm

validation and model training, furnishing a uniﬁed evaluation

baseline for technological iteration across diverse domains

including artiﬁcial intelligence and computer vision[5]. To

ensure stable and sustainable supply capacity, we need to

prioritize the development dilemmas of open-source datasets[6]

as well as the potential incentive mechanisms for them. The

Sponsors program rolled out by GitHub, a world-renowned

open-source platform, oﬀers valuable implications for the

development of the open-source ecosystem. Relevant study[7]

have demonstrated that even when a large number of developers

do not receive direct sponsorship after joining the program,

their enthusiasm for engaging in contributory activities such as

code optimization and vulnerability remediation is signiﬁcantly

boosted—and this constitutes the core foundation for them

to build reputation and garner trust within the open-source

community.

Chuan Fu et al.

Exploring and reﬁning incentive mechanisms for open data

sharing not only serves to fully mobilize the enthusiasm of data

contributors, but also accelerates the transformation of data

from a general-purpose resource into an economically valuable

production factor.In the context of data factors, we argue

that—much like peer-to-peer (P2P)[8]systems—distributed

environments not only oﬀer the dual advantages of minimizing

operational costs and streamlining data access, management,

and maintenance for providers, but also, by supporting

necessary game-theoretic behaviors, can endow data factors

with the core attributes of exclusivity and competitiveness,

thereby building a robust computing environment that

underpins the protection of data factor property rights.

Elinor Ostrom, the 2009 Nobel laureate in Economics,

probed into that whether a common resource (such as a

pond) can possess ”excludability” depends not only on its

inherent natural attributes but also on the costs incurred by

the appropriator(s) in attempting to prevent others from using

it[9],[10]. To align the computing environment for data factor

property rights protection with the requirements of Ostrom’s

theory of common-pool resource governance, this study deﬁnes

data factors in the form of a six-tuple denoted as <P, Q,

D, C, punish, supervisor>. Among them: P and Q represent

the objectiﬁed descriptions of transaction entities; D denotes

the transaction data; C stands for the contract signed by P

and Q regarding D, which is also an objectiﬁed description

before the entities of P and Q are determined; ”punish” refers

to the endogenous punishment or sanction function between

entities ( This punishment does not require third-party consent

or implementation ); ”supervise” represents the supervision

function between entities.

This 6-tuple indicates that when any party involved in the

transaction detects a violation related to D, the transaction

entities (i.e., P or Q) may impose punishment on the violator

in accordance with C, and such punishment or sanctions occur

directly between P and Q. The form of the 6-tuple clearly

shows that the punitive operations connoted in data factors

are intended to protect the interests of speciﬁc groups, namely

second-tier excludability[10].

Private goods achieve ”excludability” in the ﬁrst-tier

sense, whereas club goods and common-pool resources

achieve ”exclusivity” in the second-tier sense.[10]. Second-tier

excludability refers to exclusivity that is realized within a

certain scope and based on speciﬁc rules or conditions. From

the perspective of excludability, the expectation of endogenous

punishment can motivate entities involved in sharing to

proactively avoid risks and reduce the possibility of data

dissemination—similar to how patents are brought under legal

protection. On the other hand, the convenience of imposing

punishments during transactions destabilizes illegal trading

markets[11], which can minimize the number of participants

to the greatest extent.

Through the collaboration of ”punish” and ”supervise”, a

mechanism is provided for groups that have already secured

access to shared data factors, enabling them to prevent

others from using the factors at low cost. The computational

environment deﬁned by this six-tuple supports the protection

of data factor property rights and is better aligned with the

self-organizing nature of data trading activities.

Based on the six-tuple of data factors, this study proposes a

distributed property rights protection computing environment

that can supervise data factor transaction behaviors, enhance

the cooperation level of the transaction market, and features

automatic data leakage detection and autonomous contract

breach penalty imposition.The main innovations are as

follows:

1. General factors of production possess the attribute of

excludability, which enables them to unify both value

and price within a single transaction framework. Data

factors, however, lack this attribute, causing their price

to be gradually eroded during the process of value

realization. Addressing the non-excludability characteristic

of data—and shifting the analytical object accordingly—we

propose a framework that bridges economic theory with

technical implementation. By leveraging the incentives

embedded in the technical implementation to inﬂuence

transaction entities, the framework achieves the governance

eﬀects prescribed by economic theory, thereby resolving

the fundamental contradiction inherent in treating data

as a tradable factor. Resolving the non-excludability

problem would facilitate the widespread development of

data transactions.

2. Based on the CPR Governance Theory, this study

proposes a six-tuple framework for describing data factors.

Relying on the endogenous punishment mechanisms and

customized contracts within the six-tuple, it realizes

the excludability(second-tier excludability) and rivalry

required for factors, thereby providing support for

clarifying the boundaries of property rights.

3. According to the six-tuple of data factors, this study

proposes a distributed data factor transaction and

supervision system composed of ”cloud”, ”pipe”, and

”terminal”. Speciﬁcally: the blockchain serves as the

”cloud” to record transaction contracts; a virtual machine-

based sandbox is used as the execution environment

for data users, allowing data owners to monitor

whether the execution process of training programs

complies with speciﬁcations through the sandbox; by

referring to telephone call blocking and utilizing signaling

technology[12], we have realized the capability to

autonomously punish untrustworthy entities (in a NAT

(Network Address Translation) network environment) by

blocking and restricting data transmission paths.

Blocking access paths[13],[14] and isolating violators

from business cooperative relationships[15],[16] not only

reduce their actual operational capabilities but also harm

their business reputation through the industry credit

transmission mechanism.

4. To verify the role of autonomous punishment in improving

the cooperation level of the data transaction market, this

study models the autonomous punishment behavior of

traders using game theory, based on the prisoner’s dilemma

principle. On this basis, we simulate four transaction

strategy combinations using the Moran process. The

simulation results show that under the constraint of the

autonomous punishment mechanism, the probability of

individuals choosing the cooperative strategy is much

higher than that of choosing other strategies, and the

group can beneﬁt from cooperation more quickly. Such

simulations can also help policymakers understand the role

and value of each external condition in designing the initial

system of the trading market.

In terms of the service goal, this system is designed around

the theme that data trading requires promoting cooperation

among subjects, controlling the dissemination of data among

subjects, and supporting subjects in autonomously punishing

each other within a speciﬁc relationship, which is essentially

diﬀerent from systems that encourage information sharing.

To the best of our knowledge, this is the ﬁrst paper to

deﬁne data factors through an extension based on datasets;

it is also the ﬁrst paper to discuss how to construct the

excludability attribute of data factors from the perspective of

punishment; and it provides, in conjunction with the deﬁnition

of data factors, the implementation principles of a computing

environment that speciﬁcally supports factor transactions.

The remainder of this article is structured as follows:

First, it introduces the current contradictions in data

factor tradings, proposes an extended approach to deﬁning

data factors, and brieﬂy describes the innovations of this

paper. Second, it introduces the CPR Governance Theory,

and based on the six-tuple of data factors, proposes a

computing environment supporting the trading market and its

implementation mechanism. Third, drawing on simulations of

four transaction strategy combinations, it uses evolutionary

game theory to explain the important role of the mutual

restriction mechanism (supporting autonomous punishment) in

enhancing governance capabilities, maintaining the market’s

cooperation level, and maximizing cooperative beneﬁts. Fourth,

it reviews the current research status of data factors and

discusses the property rights dilemmas of various schemes.

Finally, it presents the conclusions and future work.

2. Data Factor and Property Rights Protection

Computing Environment

2.1. Theoretical Basis for Data factor Deﬁnition

Ostrom’s[9] research focuses on the governance of public

goods (e.g., forests, pastures, roads, parking lots)—which also

possess non-rivalry and non-excludability. She found that when

tackling issues such as free-riding, shirking of responsibilities,

and opportunistic behaviors, integrating mechanisms including

community rules, supervision, and hierarchical governance can

resolve the collective action dilemma, enable eﬀective resource

allocation, and achieve economic goals. The development

of data factor trading markets also faces collective action

dilemmas arising from opportunistic behaviors. Beyond

government regulation and privatization models, Ostrom’s

theory oﬀers a new perspective for deﬁning data factors and

constructing relevant trading systems.

Diﬀerent from property rights economic theory, the

governance of common pool resources (CPR)[9] is based on

the clear deﬁnition of boundaries. The core purpose of clearly

deﬁning boundaries is to clarify responsibilities, as well as

to fulﬁll obligations and obtain returns in accordance with

these responsibilities. In practice, clearly deﬁning boundaries

means that each participant makes explicit commitments to

themselves and others. Such commitments do not stem from

external imposition but must be self-implemented by the

involved parties. The governance solution proposed by Ostrom

aims to enable interdependent principals to organize themselves

autonomously and achieve sustained collective beneﬁts—even

when faced with temptations such as free-riding.

Ostrom argued that commitments and supervision must be

strategically nested: eﬀective supervision cannot be achieved

solely by relying on external forces; only by integrating

supervision and hierarchical sanctions into a complete set of

institutional principles and operating them in coordination

can strong public institutions be established or reshaped.

Supervision is crucial, yet third-party supervision is not the

only approach. When individuals commit to a contingency

strategy for abiding by rules—i.e., ”I act as others act”—they

will be motivated to supervise others to ensure that most people

comply with the rules. We argue that supervision and sanctions

(i.e., punishment) together constitute eﬀective oversight.

Based on the CPR Governance Theory, this study deﬁnes

data factors using a six-tuple framework: <P, Q, D, C, punish,

supervise>, which essentially serves to deﬁne boundaries. The

components are deﬁned as follows:

• P and Q: Objectiﬁed descriptions of transaction entities,

i.e., abstract descriptions of the entities’ characteristics.

All entities that meet the requirements are potential

counterparts to these entities (for convenience, P refers to

the data owner, and Q refers to the data user).

• D: Denotes the transaction data.

• C: Represents the contract (i.e., commitment) signed by

P and Q regarding D. Before the entities of P and Q are

determined, this contract also functions as an objectiﬁed

description.

• punish (C, punisher, defaulter): Represents the

punishment or sanction function between entities. The

return value of this function is either 0 or 1, where 0

indicates no punishment and 1 indicates the imposition of

punishment. The speciﬁc form of punishment or sanction

shall be determined in accordance with Contract C.

• supervise (D, C, proctor): Refers to the inter-entity

supervision function. The return value of this function is

either 0 or 1, where 0 indicates compliance with relevant

agreements and 1 indicates a violation of such agreements.

The speciﬁc supervision actions and rules are determined in

accordance with Data D and Contract C.

This six-tuple implies that when any party involved in the

transaction detects a violation related to D, the transaction

entity (either P or Q) can impose punishment on the violator

in accordance with C, and the punishment or sanction occurs

directly between P and Q.The values of ”punisher”, ”defaulter”,

and ”proctor” correspond to the entities represented by P or Q.

When understanding the deﬁnition of data factors from

the perspective of excludability in property rights economic

theory, the expectation of endogenous punishment can motivate

entities to proactively avoid risks and abandon the use of

relevant datasets. Endogenous punishment ﬁrst directly leads to

losses in expected beneﬁts and prior costs; second, it indirectly

aﬀects the entity’s business reputation and other ongoing

transactions involving the entity. When the total cost of

infringement exceeds the beneﬁts of infringement, punishment

measures achieve excludability by increasing various costs[17].

Data factors described by the six-tuple can exhibit the

excludability required of production factors. On the other hand,

the convenience of imposing punishments during transactions

destabilizes illegal trading markets[11], which can minimize the

number of participants to the greatest extent.

When the dataset is determined, the expression <P, ∅,

D, C(∅), punish, supervise> represents the basic data factor

released by the data owner. The customized contracts signed

by diﬀerent entities, along with the connections between

contracts formed around the same dataset, collectively endow

the six-tuple-described data factors with the characteristic of

rivalry. Based on the CPR Governance Theory, the six-tuple

data factors deﬁned in this study can externally exhibit the

characteristics of production factors that are adapted to market

transactions.

Chuan Fu et al.

2.2. Property Rights Protection Computing

Environment

To support the trading of six-tuple data factors, this study

proposes a distributed property rights protection computing

environment for data factor trading, which consists of ”cloud”,

”pipe”, and ”terminal”.

2.2.1. System Structure of the Computing Environment

The six-tuple-based computing environment consists of three

components: ”cloud”, ”pipe”, and ”terminal”, as illustrated in

Figure 1.

• Cloud: The blockchain serves as the ”cloud” to record

transaction contracts (i.e., C in the six-tuple), which

represent commitments.

• Pipe: By referring to telephone call blocking and utilizing

signaling technology[12], we have realized the capability to

independently punish untrustworthy entities (i.e., ”punish”

in the six-tuple) in a NAT (Network Address Translation)

network environment by blocking and restricting data

transmission paths.

• Terminal: This component is divided into two categories:

– Terminal systems for data usage (i.e., Q in the six-

tuple) are virtual machine-based sandboxes serving as

execution environments for data users. Data owners

monitor whether the execution process of training

programs complies with speciﬁcations through the

sandbox (i.e., ”supervise” in the six-tuple).

– Terminal systems for data owners (i.e., P in the six-

tuple) provide data access environments for data owners

and collect information about data users’ training data

usage.

Both types of terminals access the internet through NAT

devices, with data transmission paths between NAT devices

established using the SIP protocol.

Fig. 1. A computing environment supporting property rights protection.

2.2.2. Commitment and Monitoring

A distributed ﬁle system similar to IPFS is used to store

contract texts[18],[19]. When a contract text is uploaded, it is

ﬁrst hashed, and the resulting ﬁle hash value is then uploaded

to the blockchain for storage. The integration of distributed

storage and blockchain technology ensures the tamper-proof

nature of the commitments recorded in the contract, providing

traceable and reliable guarantees for enforcing punishment in

the event of infringement.

The sandbox of the ﬁrst type of terminal system (for

data usage) is capable of tracking the information ﬂow during

the training process and restricting the scope of information

diﬀusion. This type of terminal system downloads data from

the second type of terminal system (for data owners) and stores

the data in a virtual space. Drawing on the privacy-preserving

data protection methods for Android systems proposed in

References[20],[21],[22], we adopt data contamination marking

and attribute-based access control as the core mechanisms for

sandbox monitoring of data leakage. These mechanisms can

track the original data and the model parameters derived from

the original data, and restrict their diﬀusion scope.

Fig. 2. Three-space sandbox and its interaction process.

Based on the conﬁdentiality and integrity requirements

of the security access mode[23], we partition the continuous

model training environment into three mutually independent

subspaces(zone): the data provider subspace, the data user

subspace, and the intermediary service subspace—forming the

“three-space sandbox”, as illustrated in Figure 2. The data

provider subspace stores datasets, the data user subspace stores

algorithms, and the intermediary service subspace executes

model training and provides services to the outside.

The access relationships among the three subspaces are

determined based on the dataset. The dataset is conﬁrmed

as complete by both parties prior to the transaction, and this

integrity serves as the foundation for subsequent cooperation.

Based on conﬁdentiality requirements, the original data has

a higher protection level than the algorithm code; therefore,

the data provider subspace is assigned a higher level than the

data user subspace. The intermediary service subspace, which

performs auditing, has the highest level of privilege.

AI model training follows a ﬁxed data ﬂow: sample

reading, preprocessing (normalization/tensor conversion),

forward propagation, loss computation, and backpropagation.

The training programs provided by data users typically rely

on existing third-party libraries. We decompose this workﬂow

across the three subspaces and insert checkpoints at key stages.

When the data provider uploads data, the data provider

subspace generates a sample ﬁngerprint for each record in the

original dataset and stores these ﬁngerprints in a ﬁngerprint

table[24]. Upon receiving the algorithm code submitted by

the data user, the intermediary service subspace scans the

code using syntactic analysis tools and inserts integrity-

checking code before the preprocessing (normalization/tensor

conversion) stage. During execution, the integrity-checking

code computes the ﬁngerprint of the sample being processed

and compares it against the ﬁngerprint table. If no matching

record is found, the checking code triggers an alarm. The

relative privilege levels among the subspaces ensure that the

data user cannot detect the intermediary service’s inspection

of the algorithm code.

To broaden the coverage of parties participating in data

trading, the core purpose of the sandbox is supervision, not

absolute protection, and it is designed to simulate the canary in

a coal mine. In normal operation, the sandbox achieves mutual

isolation between diﬀerent subjects, as well as mutual isolation

between data and the original execution program. When a

violation occurs, the data integrity and conﬁdentiality deﬁned

by the sandbox will be breached, thereby triggering an alarm

to the data provider. This will lead the data provider to initiate

punishment. Once a violation is detected, the deterrence comes

from the endogenous punishment mechanism—the blocking of

signaling and data paths—rather than from the sandbox itself.

2.2.3. Network Environment Supporting Endogenous

Punishment

Endogenous punishment serves as the foundation for data

factors to possess excludability. Existing studies have applied

the PageRank algorithm[15],[16] to evaluate the reputation of

nodes in supply networks—nodes in an isolated state within

the network fail to obtain favorable evaluations. Therefore, we

consider restricting the punished entity’s access to the network

as a punishment measure[13],[14]. When the data transmission

path is blocked, this is equivalent to isolating the defaulter from

business cooperative relationships, which directly diminishes

their operational capacity and business reputation.

Telecom network operators can compel users with unpaid

fees to settle their payments promptly by blocking their calls.

As illustrated in Figure 3, based on the SIP protocol and

NAT devices, we propose a network environment that not only

supports data exchange between transacting parties but also

enables the autonomous implementation of punishment. Using

NAT (Network Address Translation) devices to provide internet

access services to users is a common solution for addressing

IP address shortages, and the NAT network environment

lays the foundation for us to implement punishment. When

a transaction entity accesses the public network via a NAT

device using a private address, it requires the assistance of

a third-party service deployed on the public network (i.e., a

transaction matcher) to communicate with another transaction

entity located behind a NAT device. The technical solution for

establishing data transmission channels between NAT devices

based on the SIP (Session Initiation Protocol) has been widely

adopted in the internet. Once the tunnel is established,

the two parties can perform data transmission and status

synchronization.

As illustrated in Figure 4, when services are provided to

transaction entities based on the SIP protocol, the transaction

matcher controls the mutual access capabilities of all entities. In

the aforementioned network environment, taking the scenario

where the ﬁrst type of terminal detects abnormal behavior

as an example, the punishment implementation process is as

follows:

1. In accordance with the punishment clauses speciﬁed

in the contract between the two transaction parties,

Fig. 3. Process of Establishing Data Paths Between NAT Devices

Fig. 4. Process of Implementing Punishment

the transaction matcher can conﬁgure an automatic

punishment implementation service for the transaction

entities.

2. When an entity submits a punishment request, the

automatic punishment implementation service is triggered

to restrict or block the punished entity from establishing

data transmission paths with other entities. The punished

entity may also ﬁle a reverse punishment request against

the initiator of the original punishment request. The

transaction matcher will similarly restrict the punishment

initiator in accordance with the provisions of the

punishment clauses. At this point, the ability of both

parties to access other entities in the system will be frozen

until the dispute is resolved.

3. During the freezing period, the two parties negotiate to

reach a resolution—similar to how PPP (Public-Private-

Partnership) models[25] adjust project outputs, modify

cost-sharing ratios, or even terminate cooperation through

negotiation.

4. After the two transaction parties resolve the dispute,

the initiator of the original punishment request submits

a revocation request. The transaction matcher then

automatically restores both parties’ ability to access other

entities in the network.

Under normal circumstances, a trader will not initiate a

punishment request without cause. From a game-theoretic

perspective, this is a lose-lose state and attracts attention from

multiple parties. However, it cannot be ruled out that someone

Chuan Fu et al.

may raise a false alarm or deliberately initiate punishment.

Therefore, before implementation, it is necessary to conﬁrm

that the sandbox alarm actually occurred. SIP is a protocol

with rich tags and complete call-sequence records. Because

systems behind diﬀerent NAT devices need to communicate via

the SIP protocol, and SIP has the capability to record sessions

in the call server, when a subject submits a punishment request,

the call service will check its local records to determine whether

the cooperative session exists—that is, whether the alarm

message was actually issued by the sandbox. In future work,

we will treat security issues in data trading as an independent

research problem, and analyze and study security threats

from multiple aspects, ranging from system-level attacks to

transaction-level attacks.

3. From Endogenous Punishment to

Cooperation

To analyze the role of punishment-based restraint mechanisms

in enhancing entities’ willingness to cooperate, we categorize

the strategies available to entities participating in data

transactions into four basic types: cooperation, defection, loner,

and punishment. In each round of the game, transaction

entities can independently choose a strategy based on their own

objectives.

• Cooperation Strategy: Refers to a strategy where an

entity is willing to invest resources (i.e., incur costs) in

cooperation and share the resulting beneﬁts.

• Defection Strategy: Refers to a strategy where an entity

refuses to invest resources (i.e., avoids incurring costs) in

cooperation but still seeks to share the beneﬁts.

• Punishment Strategy: Refers to a strategy where an

entity is willing to invest resources (i.e., incur costs) in

cooperation, share the resulting beneﬁts, and proactively

punish defectors upon detecting defection—while also

bearing the costs associated with the punishment itself.

• Loner Strategy: Refers to a strategy where an entity

generates value independently using its data, without

engaging in cooperation with other entities.

Based on the above strategies, we deﬁne four strategy

combinations: Cooperation-Defection, Cooperation-Defection-

Loner, Cooperation-Defection-Punishment, and Cooperation-

Defection-Loner-Punishment. Using the social prisoner’s

dilemma model as a foundation, we discuss the cooperation

tendencies of entities under various combinations by analyzing

the ﬁxation probability in evolutionary games. The so-called

ﬁxation probability refers to the probability that a strategy

spreads from a single mutant individual within a population to

eventually dominate the entire population[26],[27].

3.1. Proﬁt Analysis of Transaction Strategies in the

Game

In the data transaction market, some entities are responsible for

data collection, while others are tasked with data processing.

The beneﬁts generated from data are the result of collective

eﬀorts. Prior to cooperation, participants cannot observe the

strategies adopted by other entities in the market. For the sake

of simplicity, we assume that cooperative beneﬁts are evenly

distributed among all entities involved in the cooperation.

With reference to Hauert[28], we assume there are M entities

participating in data factor tradings in the market, including

X cooperators, Y defectors, Z loners, and W punishers (where

X + Y + Z + W = M ). From a population of M entities,

N entities are randomly selected to form a game group for

project implementation. δ represents the proﬁt of loners. c

represents the cost incurred by cooperators (or punishers). The

value created through cooperation is r times the cost c (i.e.,

r denotes the rate of return). δ provides a reference baseline

for cooperative beneﬁts—speciﬁcally, it represents the market

value that an entity can generate by using a given dataset

independently without engaging in cooperation. The value of

δ may increase with network eﬀects and decrease accordingly.

β denotes the punishment intensity coeﬃcient with which

punishers sanction defectors, or equivalently, the punishment

intensity perceived by defectors. αβ denotes the punishment

coeﬃcient with which punishers sanction entities that refuse

to participate in punishing defectors, or equivalently, the

punishment intensity perceived by those non-participating

entities.When terminals communicate via SIP signaling, the

call server that provides the service typically also oﬀers a

presence service. When a punisher initiates a punishment

request, the call server blocks all outgoing connection requests

from the punished party, and the punished party’s login status

is simultaneously set to ”dispute frozen.” Non-participating

entities can query this presence service to obtain the current

status of other nodes (e.g., online, dispute frozen, etc.). γ

and αγ represent the costs borne by punishers for the two

aforementioned punishment behaviors, respectively. We assume

N > r > (1 + δ/c) and β > γ, 1 > α > 0. Based on

the hypergeometric distribution[29],[30], the average proﬁts

corresponding to the above strategies are as follows:



N−1





M−1

N−1



δ + B(Z) − F (Z)c −

M − 1

(N − 1)G(Y )αβ



N−1





M−1

N−1



δ + B(Z) −

M − 1

(N − 1)β

= δ



N−1





M−1

N−1



δ + B(Z) − F (Z)c −

M − 1

(N − 1)γ −

M − 1

(N − 1)G(Y )αγ

(1)

where,

B(Z) = rc

X + W

M − Z − 1





1 −

N(M − Z)

(M − (Z − N + 1)



N−1





M−1

N−1







F (Z) = 1 −

M − N

M − Z − 1



N−1





M−1

N−1



(

Z + 1

M − Z − 1

r(M − Z − 2)

M − Z − 1

− 1)

G(Y ) = 1 −

M − 1

M − Y − 1



M−Y −1

N−1





M−1

N−1



(2)

Apart from the scale parameters, all game-related parameters

in this paper are illustrative parameters that reﬂect the

economic behavioral characteristics of transacting subjects,

rather than parameters of the information system.

3.2. Simulation of Game Behavior Among Data

Transaction Entities

To secure higher proﬁts, entities will adjust their strategies

based on their opponents’ strategies, environmental factors,

Table 1. Game Proﬁts of the Four Strategies

Cooperation(X) Defection(Y) Loner(Z) Punishment(W)

Cooperation(X) (r − 1)c

1 +

(X−1)(N −1)

M−1

− c (r − 1)c −

(

N−1

)

(

M−1

N−1

)

[(r − 1)c − δ] (r − 1)c

Defection(Y)

X(N −1)c

M−1

(

N−1

)

(

M−1

N−1

)

(

N−1

)

(

M−1

N−1

)

M−1

(N − 1)(

− β)

Loner(Z) δ δ δ δ

Punishment(W) (r − 1)c

(1 +

(W −1)(N−1)

M−1

) − c −

(M−W )(N−1)

M−1

γ (r − 1)c −

(

N−1

)

(

M−1

N−1

)

[(r − 1)c − δ] (r − 1)c

and game outcomes during repeated games. By integrating

environmental inﬂuences with individual strategies, we use the

Moran process to simulate the four strategy combinations. The

speciﬁc game structure is presented in Table 1.

In the Moran process, the parameter ω ∈ [0, 1]—used

to calculate ﬁtness[27]—represents the intensity of natural

selection. When ω is close to 0, the external environment

in which players operate exerts a greater impact on ﬁtness;

when ω is close to 1, the interactions between players have a

more signiﬁcant impact on ﬁtness. Fitness reﬂects the combined

eﬀect of dominance and game dynamics.

In accordance with the requirements of the Moran

process, after the population is fully mixed, four types of

entities—cooperators, defectors, loners, and punishers—engage

in random pairwise games (self-gaming is not considered). For

example, when a cooperator interacts with a defector, the proﬁt

of the cooperator is

1 +

(X−1)

(M−1)

(N − 1)

− c, denoted as

. The game proﬁts between other types of entities are

presented in Table 1.

Let x, y, z, and w represent the counts of the four types of

entities participating in the project, where N = x+y+z+w. For

convenience, we use the 3D array (x, y, z) to denote a combined

state of the four types. Based on the deﬁnition of the Moran

process, the ﬁtness values corresponding to the four types are

as follows:



x,y,z



= (1 − ω) +

N − 1

Π (3)

where,

Π =



(x − 1)P

(y)P

(z)P

(N − x − y − z)P

(x)P

Y X

(y − 1)P

Y Y

(z)P

Y Z

(N − x − y − z)P

Y W

(x)P

(y)P

(z − 1)P

(N − x − y − z)P

(x)P

W X

(y)P

W Y

(z)P

W Z

(N − x − y − z − 1)P

W W



(4)

Among them, f

x,y,z

, g

x,y,z

, h

x,y,z

, and l

x,y,z

represent

the ﬁtness of cooperators, defectors, loners, and punishers,

respectively. Based on the ﬁtness of each type of entity, we

can calculate the transition probability between diﬀerent entity

types. It is assumed that when an entity type transition

occurs, only one entity type participates in the transition,

and only one individual from this type is involved in the

transition. The transition probability is calculated as the

product of the proportion of the current entity type in the entire

population and the proportion of the target entity type in the

entire population under ﬁtness weighting.

represents the

probability that no entity type transition occurs.

yy+1

xx−1

represents the probability that one individual from entity type

x transitions to entity type y; other similar notations follow

the same interpretation. The speciﬁc calculation method is as

follows:



yy+1

xx−1

zz+1

xx−1

yy−1

xx+1

yy−1

zz+1

yy−1

zz−1

xx+1

yy+1

zz−1

xx+1

yy+1

zz+1



= µ



x y z w

y 0 0 0

z 0 0 0

w 0 0 0

0 x 0 0

0 z 0 0

0 w 0 0

0 0 x 0

0 0 y 0

0 0 w 0

0 0 0 x

0 0 0 y

0 0 0 z



xyz



(5)

where,

µ =

(xf

x,y,z

+ yg

x,y,z

+ zh

x,y,z

+ (N − x − y − z)l

x,y,z

(6)

Figure 5 illustrates a potential evolutionary outcome under

the fourth game scenario. After multiple rounds of games,

cooperators and punishers emerge as the dominant groups

within the population.

3.3. Analysis of the Evolutionary Tendency of

Transaction Entities

An evolutionarily stable strategy (ESS) refers to a strategy

adopted by the majority of a population’s members. The

beneﬁts this strategy confers on entities cannot be matched by

any other strategy. In evolutionary games involving randomness

in ﬁnite populations, ﬁxation probability is a key indicator for

analyzing whether a strategy can qualify as an evolutionarily

stable strategy.

To calculate the ﬁxation probability in multi-strategy

games, we treat the transition matrix as a process that

describes strategy transformation when an independent

strategy competes against a set of other strategies. All

strategies except the independent one form a ”super strategy.”

We use the calculation method proposed in[27] to compute

the ﬁxation probability of this independent strategy. When

calculating the ﬁxation probability of other strategies,

we sequentially adjust the independent strategy and its

corresponding super strategy. When the individual state of the

Chuan Fu et al.

Fig. 5. Population evolution process

independent strategy is 1, it corresponds to multiple individual

states of the super strategy; in such cases, we calculate the

ﬁxation probability of the independent strategy by taking the

average value.

Below, we analyze the cooperation tendencies of entities

across the four strategy combinations, based on the relationship

between the rate of return r and ﬁxation probability. Figure

6 illustrates the changes in ﬁxation probability for the four

combinations when the proﬁt of loners is 0.2. Figure 7

illustrates the changes in ﬁxation probability for the four

combinations when the proﬁt of loners is 0.5. Figure 8

illustrates the changes in ﬁxation probability for the four

combinations when the proﬁt of loners is 1. The proﬁt of loners

serves as the baseline return that individuals in the population

can obtain through independent eﬀorts.

The gray plane in each ﬁgure represents the reference

probability. For example, in the ”Cooperator-Defector-Loner-

Punisher” scenario, the probability of participants choosing

each strategy is 0.25. We consider that when the ﬁxation

probability of a particular strategy exceeds the reference plane,

this strategy exhibits a selection bias within the population.

When all strategies fall below the reference plane, the

population has no distinct preferred strategy, and individuals

tend to adopt the strategy with a relatively higher ﬁxation

probability.The parameters used in the simulations, such as

population size, punishment cost, and punishment intensity,

are based on references[31][32][33]

Figure 6 to Figure 9 indicate that when individuals select

a game strategy, they must comprehensively consider, at

minimum, factors such as the return from cooperation, the

intensity of natural selection (ω), the proﬁt of loners (δ), and

the punishment intensity exerted by punishers.

Figure 6 to Figure 8 demonstrate that, with cooperative

proﬁts held constant: as the intensity of external environmental

selection (ω) increases, the ﬁxation probability of cooperators

rises signiﬁcantly, while that of defectors decreases signiﬁcantly;

with the intensity of external environmental selection (ω) held

constant, as the rate of return (r) increases, the ﬁxation

probability of cooperators rises signiﬁcantly, while that of

defectors decreases signiﬁcantly; when the ﬁxation probability

Fig. 6. Fixation Probability (δ = 0.2). M = 120 N = 6 c = 1 1.5 <=

r <= 3.9 0.1 <= ω < 0.85 α = 0.1 β = 1.1 γ = 0.3 (1) X = 60 Y = 60

(2) X = 40 Y = 40 Z = 40 (3) X = 40 Y = 40 W = 40 0.1 <= ω < 0.5

(4) X = 30 Y = 30 Z = 30 W = 30 0.1 <= ω < 0.65

Fig. 7. Fixation Probability (δ = 0.5). M = 120 N = 6 c = 1 1.5 <=

r <= 3.9 0.1 <= ω < 0.85 α = 0.1 β = 1 γ = 0.3 (1) X = 60 Y = 60

(2)X = 40 Y = 40 Z = 40 (3) X = 40 Y = 40 W = 40 0.1 <= ω < 0.5

(4) X = 30 Y = 30 Z = 30 W = 30 0.1 <= ω < 0.65

is lower than the reference probability, it indicates high

uncertainty in the strategy selected by individuals.

By comparing (1), (2), and (3) in Figure 6: the presence

of loners and punishers leads to a rapid downward trend in

the ﬁxation probability of defectors; a comparison between

(2) and (3) shows that punishers can more eﬀectively

suppress individuals’ defection behavior in the environment,

however, under the same proﬁt conditions, punishers also

inhibit individuals’ cooperative behavior; additionally, in

the ”Cooperator-Defector-Punisher” combination, when the

intensity of external environmental selection (ω) is relatively

high, punishers will penalize all participants, resulting in

abnormal market operation.

A comparison between (2) and (4) shows that when

the investment return (r) has increased signiﬁcantly, the

ﬁxation probability of loners in the ”Cooperator-Defector-

Loner” combination remains relatively high—meaning there is

a high probability that individuals will not engage in data

transactions with one another; the trend in (4) indicates that,

in the fourth strategy combination, the ﬁxation probabilities

Fig. 8. Fixation Probability (δ = 1) M = 120 N = 6 c = 1 1.5 <= r <=

3.9 0.1 <= ω < 0.85 α = 0.1 β = 1.1 γ = 0.3 (1) X = 60 Y = 60 (2)

X = 40 Y = 40 Z = 40 (3) X = 40 Y = 40 W = 40 0.1 <= ω < 0.5 (4)

X = 30 Y = 30 Z = 30 W = 30 0.1 <= ω < 0.65

Fig. 9. Fixation Probability (δ = 0.2) M = 120 N = 6 X = 30 Y = 30

Z = 30 W = 30 0.1 <= ω < 0.65 c = 1 1.5 <= r <= 3.9 α = 0.1 γ = 0.3

0.1 <= ω < 0.85 α = 0.1 γ = 0.3 (1) β = 0.5 (2) β = 1.1

of loners and defectors are signiﬁcantly lower than those in

(2); since punishers are a special type of cooperator, the

ﬁxation probability of the population’s tendency to cooperate

is signiﬁcantly higher than that in (2); when the ﬁxation

probability of cooperators exceeds the reference plane, the rate

of return in (4) is lower than that in (2), yet the population

can obtain returns through cooperation earlier; both Figure 7

and Figure 8 exhibit this upward trend.

By comparing the fourth strategy combination across Figure

6 to Figure 8, we observe that as the proﬁt of loners

(δ) gradually increases, more eﬃcient individual productivity

delays group cooperation. Figure 9 illustrates that increasing

punishment intensity can eﬀectively suppress the tendency to

defect and accelerate the ﬁxation probability of the cooperative

tendency to exceed the reference plane.

The above simulation results demonstrate that the incentive

mechanism embedded in the technical scheme combining the

SIP protocol with the NAT network can achieve the governance

eﬀect proposed by Common Pool Resources governance

theory—namely, that the majority of individuals in the

population adopt cooperative strategies. This study provides

a technology-supported institutional system for non-excludable

data factors. Only on the basis of traders’ stable cooperation

can the value of data factors—such as non-rivalry and zero

replication cost—be realized.

4. Related Research

We believe that current research on data (factor) transactions

can be categorized into three perspectives: value chain research

centered on datasets, research on data transaction market

construction schemes, and research on governance methods

for data factor transaction markets. These studies reﬂect the

process by which data evolves from speciﬁc datasets to an

abstract concept.

The data value chain originated from enterprises’ needs

for massive data management[34] and has received widespread

attention with the development of big data technologies[35].

In industry-speciﬁc research—such as in supply chains[36],

ﬁnance[37], agriculture[38], and healthcare[39]—people have

further recognized the new value that the data value chain

brings to industries.

When data transactions need to be conducted across

organizations and countries[40], constructing transaction

environments has become a new research hotspot. Transaction

environments have evolved from cloud-based environments[41]

to distributed transaction environments[42]. Studies[42],[43],[44]

have explored how to use blockchain technology to address

security and credibility issues in data transactions within

distributed environments. Research[45],[46] aims to promote

cross-border data ﬂow and transactions through more

reasonable proﬁt distribution mechanisms.

Research on transaction environment construction schemes

has also stimulated in-depth exploration of governance

mechanisms for data factor tradings. Governance mechanisms

are divided into two types: governance centered on

organizing units or departments, and governance based on

polycentric governance theory. Governments[47],[48], internet

platforms[49], and data intermediaries[50] all play organizing

roles. In the ”platform society”[49], a large amount of data

is controlled by a few large technology platforms, making

platforms a natural dominant model for data governance. By

applying evolutionary game theory, the value of regulators in

open data governance is elaborated[51]. Attention needs to be

paid to balancing diﬀerences between individuals, and between

individuals and policymakers[52].

On the other hand, data stored dispersedly among

numerous interconnected entities forms a ”datasphere”[53]. In

environments where governments, markets, societies, and non-

governmental organizations coexist, studies[54] have discussed

how to use polycentric governance theory[55],[56] to promote

coordination and cooperation among diﬀerent entities and

establish a more eﬃcient market. While polycentric governance

theory is increasingly accepted as a governance concept,

relative diﬀerences between entities in the datasphere lead to

divergences in their governance demands.

The abstraction process directly deﬁnes data as data factors

but fails to resolve the inherent dilemmas of non-excludability

and non-rivalry in data itself. Unlike existing research, while

abstracting data, we have deﬁned new connotations for data

factors through an extended approach.

5. Conclusion and Future Work

The non-excludability of data is the core focus of our research.

Compared with data factors, other factors of production possess

excludability. The boundaries of excludable factors are easier

to deﬁne, and property-rights proof can be established through

registration and query, thereby achieving protection at both

the physical and the property-rights levels; the boundaries of

Chuan Fu et al.

non-excludable factors, by contrast, are diﬃcult to deﬁne, and

such factors cannot form eﬀective proof through themselves,

so they require an institutional system to constrain users’

behavior in order to achieve the eﬀect of protecting the factor.

Accordingly, the governance of excludable factors can rely more

on private property-rights mechanisms, whereas data factors,

because they cannot deﬁne their own boundaries, rely more

on Common-Pool Resource (CPR) governance mechanisms that

take the constraint of users’ behavior as their core.

This therefore requires that the information system be

grounded in CPR governance mechanisms, so as to control

the orderly ﬂow of data factors among speciﬁc subjects and

thereby create value. At the present stage, this research has

identiﬁed the point of convergence between economic theory

and technical solutions, linking economic and technical issues so

that the next stage of development can be applied more rapidly

to the construction of data trading markets. In terms of the

service goal, this system is essentially diﬀerent from systems

that encourage information sharing.

Building upon Ostrom’s CPR governance framework

outlined above, we deﬁne the data factor as a six-tuple.

Meanwhile, we develop a technical system embedded with the

“supervision-punishment-commitment” mechanism to enable

the governance of factor excludability. Relying on the

“terminal-pipe-cloud” architecture, this technical system

can construct an operating environment for data-factor

transactions.

To verify the role of this new data factor deﬁnition in

constructing transaction markets, we employed evolutionary

game theory to simulate two key aspects: ﬁrst, market stability

under the coexistence of strategies (i.e., cooperation, defection,

loner, and punishment); second, the impact of initial market

institutions on participants’ strategy choices. In a certain sense,

when a dataset can be converted into a six-tuple format, it can

become a tradable data factor.

The punishment behavior supported by the combination of

the SIP protocol and the NAT network—namely, connection

blocking—is essentially a pledge mechanism collateralized

by the punished party’s entire business cooperation value.

Its eﬀect directly impacts the punished party’s ongoing

and subsequent transactions, thereby eﬀectively freezing its

business relationships in the market. Compared with smart

contract slashing, the blocking approach does not require

deﬁning the relationship between the collateral value and

the transaction value, which simpliﬁes transaction rules,

reduces participation costs, and eliminates potential arbitrage

opportunities. Reputation systems can help traders select

more trustworthy counterparts; however, from a governance

mechanism perspective, reputation systems only accomplish

the ”commitment-supervision” phase and lack an eﬀective

punishment mechanism.

The primary task for the next step is to expand the

application scope of computing environments that support

factor property rights protection in data trading scenarios,

and to extend into data-driven cooperation and collaboration

ﬁelds. To improve system reliability, we will use the

SIP OPTIONS method to periodically query the status of

network elements and the platform during prototype system

development, and collect statistics on the eﬀectiveness of

the punishment mechanism. We will validate the prototype

through a multi-party data collaboration scenario, and

investigate system metrics such as the impact of ﬁngerprint

veriﬁcation on model training performance (e.g., the percentage

increase in sample reading time), the response time of the

punishment mechanism (connection blocking), and system

throughput under concurrent transaction scenarios. We also

expect to provide conﬁguration recommendations for practical

deployment by combining system performance analysis with

the scenario. Secondly, improve the training eﬃciency of data

sandboxes—for instance, by using neural networks to analyze

malicious code and reducing the number of functions that need

to be tracked.Thirdly, in real trading markets, transaction

rules constrain the connectivity relationships among traders.

Therefore, we need to investigate the impact of population

topology on the equilibrium states of the game, as well as to

study incentive mechanisms based on value distribution that

enable more entities to beneﬁt from data transactions. At the

same time, we will treat system security and business security

issues in data trading as an independent research problem.

6. Acknowledgments

This study was supported by the National Key R&D Program

of China (No.2023YFB2703900).

Ethical Statement

No ethical approval was required for this study, as it did not

involve human or animal subjects.

Funding

The authors declare the following interests: This work was

supported by the National Key R&D Program of China (Grant

No. 2023YFB2703900). The funders provided ﬁnancial support

for data collection and experiment implementation but had no

role in the study design, data analysis, decision to publish,

or preparation of the manuscript. All other authors have no

competing ﬁnancial or personal interests to declare.

Declaration of competing interests

The authors declare that they have no known competing

ﬁnancial interests or personal relationships that could have

appeared to inﬂuence the work reported in this paper.

Data Availability Statements

Data sharing is not applicable to this article as no datasets were

generated or analysed during the current study.

Credit authorship contribution statement

Chuan Fu: Conceptualization, Formal analysis, Methodology,

Software Development, Writing-original draft, Writing-review

& editing, Visualization, Validation.

Jian Ye: Funding acquisition, Project administration,

Supervision, Review & editing, Validation.

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