Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 14, No. 1, 2024 

 

70 

Study	on	Data	Supply	Chain	Pricing	Decision	
Considering	Network	Externalities	
Zhicheng Zhang1, *, Yiming Zhang2, Weibin Deng1, Guangming Liu3 

1 School of Economics and Management, Chongqing University of Posts and Telecommunications, CO 400065, China 
2 78111 troops, People's Liberation Army of China, CO 409626, China 
3 Chongqing Branch of China Tower Corporation Limited, CO 401120, China 
* Corresponding author: Zhang Zhi-Cheng (Email: 1079169190@qq.com) 

 

Abstract: Nowadays, data has become an important productive factor in the world. Data as an asset to management and 
realizing its value are important factors for its flowing smoothly. However, how to price the data scientifically and reasonably 
has been a difficult and key problem for the data element market development. After analyzing the transaction process of data 
products from data resource acquisition to production and sales, a three-level data supply chain consisting of data providers, data 
trading platforms and users is constructed. In this chain, government subsidies for data trading platforms are considered. Based 
on that, a centralized and a decentralized differential game pricing model of data supply chain under the influence of network 
externalities are proposed respectively. The impact of network externalities and government subsidy elasticity coefficients, 
among others, on the two decision models is analyzed from a theoretical perspective. 

Keywords: Data pricing, data supply chain, network externalities, government subsidies, differential game. 
 

1. Introduction 
With the widespread popularization and application of big 

data, the value of data resources is increasing. So far, dozens 
of data trading organizations have been established across the 
country, but compared with traditional resources, due to the 
intangible, variable, social and shared nature of data resources, 
resulting in a market with insufficient participants in data 
trading, low frequency of transactions, and small scale of 
transactions. Currently, research on data supply chain-based 
pricing strategies has made some progress in data supply 
chain operation, considering data quality and scale pricing. 
First, the research on the operation of data supply chain. Chen 
et al [1] optimized the profit of a two-level supply chain by 
constructing a Nash equilibrium bargaining model to achieve 
the global optimality of the supply chain. Barman et al [2] 
used the Stackelberg game model to evaluate the centralized 
and decentralized decision-making of the three-level green 
supply chain, and compared the optimal pricing of the supply 
chain with and without government subsidies. Pricing. 
Secondly, there are studies on data pricing considering data 
quality and scale. Batini et al [3] summarized data quality as 
accuracy, completeness, redundancy, readability, accessibility, 
consistency, usefulness, and trustworthiness. Taleb et al [4] 
proposed a new data quality framework that uses predefined 
quality metrics to accomplish more effective data quality 
assessment. 

However, in actual data supply chain pricing is not solely 
influenced by data characteristics. From the market level, 
consumers' willingness to purchase data products is not only 
affected by their own needs and product factors, but also 
related to the size of the users who purchase the products, i.e., 
data products in the data supply chain have network 
externalities. Network externality is generated by the 
economies of scale of users and refers to the fact that the value 
of a product to its users increases with the increase in the 
number of consumers adopting the same product [5]. Tang et 
al [6] constructed a pricing model for the competition 

between newcomer platforms and incumbent platforms by 
using the Hotelling model based on the consideration of 
cross-network externalities, and explored the future strategic 
choices of the two platforms in order to obtain more benefits. 
Zhu et al [7] explored the impact of the magnitude of network 
externalities on product quality, provider implementation 
mode and their profits. 

For the node enterprises of data supply chain, how to 
improve the quality of data products and at the same time how 
to make reasonable data pricing decisions is a very 
challenging problem, most of the previous literature on data 
supply chain pricing focuses on the supply chain's own 
operation and pricing, and fails to consider the network 
externality and the government's subsidies for data trading 
platforms. Therefore, the innovations of this paper are 
reflected in the following points: (1) network externalities as 
a decision variable in the data pricing model, and further 
analyze its impact on the operation of the data supply chain, 
which is to make the model and the conclusion of the study 
more in line with the status quo of the development of the 
network economy. (2) In the existing research on data supply 
chain pricing, little consideration has been given to the impact 
of government subsidies on the pricing of data products, 
because in the actual operation of the data supply chain, 
government subsidies can play the role of incentives for data 
trading platforms to innovate, so as to enable them to develop 
higher-quality data products and promote the development of 
the data supply chain. 

2. Problem Description and 
Assumptions 

In this paper, we consider a data supply chain with 
monopoly position consisting of a data provider and a data 
trading platform. Among them, the data provider obtains raw 
data of quality 𝑞  and size 𝑛 through a reward mechanism, 
removes personal attributes through technical processing and 
then sells them to the data trading platform at price 𝑃  The 



 

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data trading platform produces data products by processing 
the raw data obtained through its own technical resources, and 
then sells them to users at a certain price 𝑃  The government, 
in order to promote the technological innovation of the data 
trading platform, will subsidize the platform according to the 
quality of the data products it produces at a certain price 𝑃  
In the operation of this data supply chain, both data providers 
and data trading platforms incur a certain amount of data 
processing costs, and they need to consider their own 
revenues and costs in order to maximize profits. In order to 
illustrate more clearly the study of profit maximization 
decision-making of data supply chain under the consideration 
of network externality, the relevant symbols involved in the 
model construction are first defined, as shown in Table 1. 

 

Table 1. Description of relevant symbols 

Symbol Definition 

𝑃  
Price of unit quantity of data purchased from 

data providers by data trading platforms 

𝑃  
Price of data products developed by the data 

trading platform 

𝑃  
Cost of government subsidies to encourage 

technological innovation by data trading 
l f

𝑞  Quality of raw data acquired by data providers 

𝑞  
Quality of data products developed by data 

trading platforms 

𝑛 Size of raw data acquired by data providers 

α 
Cost coefficient of raw data acquired by the 

data provider, α∈(0, 1) 

𝑘  
Cost coefficient of raw data processing by the 

data provider, 𝑘 ∈（0, 1） 

𝑘  
Coefficient of data product development cost of 

the data trading platform，𝑘 ∈(0, 1) 

𝑢 Network externality， 𝑢∈（0, 10） 

𝑎 User market size 

𝜃 
Elasticity coefficient of the selling price of data 

products, 𝜃∈(0, 1） 

𝑤 
Elasticity coefficient of the cost of subsidies 

given to the platform by the government， 𝑤∈

𝑄 Market demand for the data product 

𝜋  Profit function of the data provider 

𝜋  Profit function of the data trading platform 

𝜋  Total profit function of the data supply chain 

Assumption 1 Data providers need to pay a certain cost 
when acquiring raw data, the more cost they pay, the larger 
the scale and quality of raw data they acquire, so this paper 
assumes that the cost of raw data acquisition for data 
providers is 𝛼𝑞 𝑛 , where 𝛼  denotes the cost coefficient of 
raw data acquisition for data providers. 

Assumption 2 The improvement of raw data quality and 
scale helps data trading platforms to develop higher quality 
data products, so this paper assumes that the relationship 
function of 𝑞 , 𝑞  and 𝑛 is: 

𝑞 𝑞 𝑛                 (1) 

Assumption 3 The subsidy cost of the government to 
encourage technological innovation of the data trading 
platform and the quality of data products is a linear 
relationship between the higher the quality of data products 
obtained by the user, the more government subsidies, but the 
subsidy is not an infinite increase, and the relationship 
function is: 

𝑃 𝑤𝑞 𝑤𝑞 𝑛              (2) 

 

Assumption 4 Assume that end users will only purchase 
data products on this one data trading platform, and the 
product production of the data trading platform is the market 
demand. In order to consider the impact of network 
externalities on the data supply chain, the demand function of 
the market is defined as: 

𝑄 1 𝑢 𝑎 𝜃𝑃              (3) 

 

where 𝑢 is the network externality, 𝑎 is the end-user size, 
and 𝜃 is the elasticity coefficient of the sales price of data 
products. 

Assumption 5 The profits of the data provider and the data 
trading platform are 𝜋   and 𝜋  , respectively, and the total 
profit of the data supply chain is 𝜋  . When the data scale 
increases, the data processing cost and the product 
development cost also increase, and the growth rate increases 
gradually, so this paper assumes that the data processing cost 
of the provider and the product development cost of the 
platform are 𝑘 𝑛   and 𝑘 𝑛  , respectively, where 𝑘  
denotes the original data processing cost coefficient of the 
data provider, and 𝑘  is the data product development cost 
coefficient of the data trading platform. 

The profit function of the data provider is: 

𝜋 𝑃 𝑛 𝛼𝑞 𝑛 𝑘 𝑛             (4) 

 

The data trading platform receives government subsidies 
by producing high-quality data products and also earns profits 
by selling data products. The profit function of data trading 
platform is: 

𝜋 𝑃 𝑄 𝑃 𝑛 𝑘 𝑛 𝑤𝑞 𝑛        (5) 

 

The total profit function of the data supply chain is: 

 

𝜋 𝜋 𝜋                  (6) 

 

When the size of raw data is too large, data providers and 
data trading platforms will give up the processing of raw data 
and the development of data products because the cost is 
higher than the benefit. 



 

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3. Model Construction and Analysis 

3.1. Pricing model analysis under centralized 
decision-making 

Under the centralized decision-making model, this paper is 
based on the hypothetical three-stage data supply chain, in 
which data providers charge data trading platforms the 
subscription price of raw data 𝑃  , data trading platforms 
receive government subsidies for the production of data 
products, and ultimately data trading platforms charge end 
users the price of data products 𝑃 . This study establishes the 
transaction process between data providers and data trading 
platforms as a two-stage game In this study, the transaction 
process between the data provider and the data trading 
platform is modeled as a two-stage game, where the first stage 
is for the data provider to decide the price of the original data 
𝑃 , and the second stage is for the data trading platform to 
decide the price of the data product 𝑃  . The model can be 
expressed as follows. 

 
𝜋 𝜋 𝜋 𝑃 𝑄 𝛼𝑞 𝑛 𝑘 𝑘 𝑛 𝑤𝑞 𝑛

1 𝑢 𝑎𝑃 𝜃𝑃 𝛼𝑞 𝑛 𝑘 𝑘 𝑛 𝑤𝑞 𝑛  (7) 
 

Again taking the second order partial derivative with 
respect to 𝑃  yields: 

2𝜃 0              (8) 

 
Since its second order partial derivative is less than zero, 

there exists an extreme value of 𝜋 . The optimal pricing is 
achieved when the first order partial derivative is equal to zero, 
at this time: 

𝑃 ∗                  (9) 
 

Substituting equation (9) into 𝜋  can be obtained: 
 

𝜋 𝛼𝑞 𝑛 𝑘 𝑘 𝑛 𝑤𝑞 𝑛   (10) 
 

Then the second order partial derivatives can be obtained 
for 𝑞  and 𝑛 respectively: 

 

2𝛼𝑛 0， 2 𝑘 𝑘 0  (11) 

 
One can find 𝑞  and 𝑛 respectively: 
 

𝑞 ， 𝑛           (12) 

 
The maximum profit of the data supply chain is: 
 

𝑚𝑎𝑥𝜋
𝑎 1 𝑢

4𝜃
𝑤

64𝛼 𝑘 𝑘
 

          (13) 

 
Proposition 1 Raw data quality 𝑞   is inversely 

proportional to the data acquisition cost coefficient 𝛼  and 
directly proportional to the government subsidy elasticity 
coefficient 𝑤 . Raw data size 𝑛  is inversely proportional to 
the coefficient 𝛼  as well as to the data processing cost 
coefficients 𝑘   and 𝑘  , and directly proportional to the 
government subsidy elasticity fee coefficient 𝑤. 

Proof: As can be seen from equation (12), when the 
coefficient 𝑤 increases, the original data quality 𝑞  and the 
original data size 𝑛 both increase; when the data acquisition 
cost coefficient 𝛼 increases, the original data quality 𝑞  and 
the original data size 𝑛  both decrease; when the data 
processing cost coefficients 𝑘  and 𝑘  both increase, size 𝑛 
decreases. 

Proposition 2 Both 𝜋  and the price of the data product 
𝑃  are positively affected by network externalities. 

Proof: From equation (9) and (13), and when the network 
externality is increased, the total profit of the data supply 
chain and the price of the data product 𝑃  are both increased. 

Proposition 3 The total profit of the data supply chain is 
inversely proportional to the data acquisition cost coefficient 
𝛼  and the data processing cost coefficients 𝑘  ,  𝑘  , and 
directly proportional to the elasticity coefficient of 
government subsidy 𝑤. 

Proof: From equation (13), when the coefficient 𝛼 and the 
cost coefficients 𝑘 , 𝑘  increase, the maximum total profit of 
the data supply chain decreases; when the government 
subsidy elasticity coefficient 𝑤 increases, the maximum total 
profit of the data supply chain increases, so that proposition 3 
is proved. 

3.2. Pricing model analysis under 
decentralized decision-making 

The pricing model under decentralized decision-making is 
based on the three-level data supply chain composed of data 
providers, data trading platforms and users, and a Stackelberg 
game model between data providers and data trading 
platforms is constructed by taking into account the original 
data transaction process between data providers and data 
trading platforms, and the data product transaction process 
between data trading platforms and users. The game sequence 
of the model is: the data provider first chooses the original 
data price 𝑃  to maximize its own revenue 𝜋 , and then the 
data trading platform chooses the data product sales price 𝑃  
according to the 𝑃  set by the data provider to maximize its 
revenue 𝜋 . The model can be expressed as: 

 
𝑚𝑎𝑥𝜋 𝑃 𝑛 𝛼𝑞 𝑛 𝑘 𝑛          (14) 

 
𝑛 𝑃 arg max

,
𝑃 𝑄 𝑃 𝑛 𝑘 𝑛 𝑤𝑞 𝑛   (15) 

 
This Stackelberg game model takes the data provider as the 

leader and the data trading platform as the follower, reflecting 
the important position of the owner of the data in the data 
supply chain. At the same time, the model correlates the size 
and quality of raw data with the cost of data providers and 
data trading platforms, and also considers government 
subsidies to data trading platforms, reflecting the impact of 
data characteristics on data product design and the 
government's role in promoting the data market in real life. 

The profit function of the data trading platform is: 
 

𝜋 𝑃 𝑄 𝑃 𝑛 𝑘 𝑛 𝑤𝑞 𝑛        (16) 
 

Taking the second order partial derivatives of 𝜋  for the 
data product subscription price 𝑃   and data size 𝑛 , 
respectively, yields: 

 

2𝜃 0， 2𝑘 0      (17) 



 

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It can be seen that the second order partial derivatives of 
both decision variables are less than zero, and there is a 
unique global optimal solution for 𝜋  . Let the first order 
partial derivatives be zero, it can be obtained: 

 

𝑃 ∗ 𝑤𝑞 2𝑘 𝑛， 𝑃 ∗        (18) 
 

Bringing equation (18) into (14) we can get 𝜋  is: 
 

𝜋 𝑤𝑞 2𝑘 𝑛 𝑛 𝛼𝑞 𝑛 𝑘 𝑛      (19) 
 

Then the second order partial derivatives of 𝜋   for the 
original data quality 𝑞   and the original data size 𝑛 
respectively can be obtained: 

 

2𝛼𝑛 0， 4𝑘 2𝑘 0   (20) 

 
It can be seen that the second order partial derivatives of 

both decision variables are less than zero. Therefore, there is 
a unique global optimal solution for 𝑚𝑎𝑥𝜋 . According to the 
fact that the first order partial derivatives are equal to zero, it 
can be obtained: 

𝑞 ，𝑛            (21) 

 
Therefore the original data price 𝑃 ∗ is: 
 

𝑃 ∗ 1              (22) 

 
At this point the profit function 𝜋  of the data provider is: 
 

𝜋 𝑤𝑞 𝑛 𝛼𝑞 𝑛 𝑘 2𝑘 𝑛  (23) 

 
The profit function 𝜋  of the data trading platform is: 
 

𝜋 1 𝑢 𝑎𝑃 𝜃𝑃 𝑃 𝑛 𝑘 𝑛 𝑤𝑞 𝑛 

          (24) 

 
Proposition 4 The quality of raw data 𝑞   is inversely 

proportional to the cost coefficient of data acquisition 𝛼 and 
directly proportional to the elasticity coefficient of 
government subsidy 𝑤. The size of raw data 𝑛 is inversely 
proportional to the coefficient 𝛼  as well as to the cost 
coefficients of 𝑘   and 𝑘  , and directly proportional to the 
elasticity coefficient of government subsidy 𝑤. 

Proof: From equation (21), it can be seen that when the 
coefficient 𝑤 increases, the original data quality 𝑞  and the 
original data size 𝑛 both increase; when the data acquisition 
cost coefficient 𝛼 increases, the original data quality 𝑞  and 
the original data size 𝑛  both decrease; when the data 
processing cost coefficient 𝑘   and coefficient 𝑘   both 
increase, the original data size 𝑛 decreases. 

Proposition 5 Both the profit of data trading platform and 
the price of data products 𝑃   are positively affected by 
network externalities. 

Proof: From equation (18) and (24), when the network 
externality is increased, the maximal profit of the data trading 
platform and the price of the data product 𝑃   are both 
increased. 

Proposition 6 The profit of the data trading platform is 

inversely proportional to the data acquisition cost coefficient 
𝛼 and the data processing cost coefficients 𝑘  and 𝑘 , and 
directly proportional to the elasticity coefficient of 
government subsidy 𝑤. 

Proof: From equation (24), it can be seen that when the 
data acquisition cost coefficient 𝛼 , and the data processing 
cost coefficients 𝑘  and 𝑘   are increased, the maximum 
profit of the data trading platform will be decreased, and when 
the coefficient 𝑤  is increased, the maximum profit of the 
data trading platform will be increased, so proposition 6 is 
proved. 

Proposition 7 The effects of the incentive coefficient α , 
the data processing cost coefficients 𝑘  , 𝑘   and the 
government subsidy elasticity coefficient 𝑤 on the pricing of 
unit raw data 𝑃  are as follows. 

(1) When the data acquisition cost coefficient α increases, 
𝑃  decreases; 

(2) 𝑃   decreases when the data processing cost 
coefficients 𝑘  and 𝑘  increase; 

(3) The elasticity coefficient of the government subsidy 𝑤 
paid by users to the data trading platform increases, and 𝑃  
increases. 

Proof: From equation (22), when the coefficient 𝛼 and the 
coefficients 𝑘   and  𝑘   increase, the original data pricing 
will decrease; when the government subsidy elasticity 
coefficient 𝑤  increases, the original data pricing will 
increase, so proposition 7 is proved. 

4. Conclusion  
In this paper, in the data supply chain with data providers 

and data trading platforms as the main body, parameters such 
as network externality, government subsidies, data quality, 
data scale, data acquisition and processing costs are 
introduced to analyze the optimal decision-making of data 
providers and data trading platforms in the data supply chain 
under two decision-making modes respectively, we compare 
the two decision-making models, and discuss the impacts of 
network externality and the subsidies given to data trading 
platforms by the government on the supply chain. The impact 
of network externalities and government subsidies given to 
data trading platforms on supply chain pricing is discussed. 
The study finds that: 

(1) The optimal product prices under centralized and 
decentralized decision-making are the same, and the profit of 
data trading platform, the total profit of data supply chain and 
the price of data products are positively affected by network 
externality, while the profit of data provider under 
decentralized decision-making remains unchanged with the 
increase of network externality. (2) The quality of raw data 
and data size under both decision-making modes are 
proportional to the elasticity coefficient of government 
subsidy, and the trend of government subsidy is more obvious 
under decentralized decision-making compared with 
centralized decision-making. (3) With the increase of network 
externality and government subsidy elasticity coefficient in 
both centralized and decentralized decision-making, the total 
profit of the supply chain shows a rising trend, and the overall 
profit of the supply chain under centralized decision-making 
is larger than that under decentralized decision-making. 

Acknowledgment 
This work is supported by the Chongqing Social Science 

Planning Project (2022ZDZK30) and the Chongqing 



 

74 

Technology Innovation and Application Development Project 
(CSTB2022TIAD-GPX0015). 

References 
[1] Chen J X, Chen J. Supply Chain Profit Game and Equilibrium 

Pricing[J]. Chinese Journal of Management Science, 2022, 
30(9): 128-139. 

[2] Barman A, De P K, Chakraborty A K, et al. Optimal Pricing 
Policy in a Three-layer dual-channel Supply Chain under 
Government Subsidy in Green Manufacturing[J]. Mathematics 
and Computers in Simulation, 2023, 204: 401-429. 

[3] Batini C, Scannapieco M. Data and Information Quality: 
Dimensions, Principles and Techniques[M]. Springer 
International Publishing, 2018. 

[4] Taleb I, Serhani M A, Bouhaddioui C, et al. Big Data Quality 
Framework: a Holistic Approach to Continuous Quality 
Management[J]. Journal of Big Data, 2021, 8(1): 1-41. 

[5] Li Q X, Zhang J, Huang Y M, Qi E S. Research on the 
Marketing Strategy of Community Group Buying Supply 
Chain Based on Network Externality[J/OL]. Chinese Journal 
of Management Science:1-12[2022-10-04]. 

[6] Tang F C, Guo H. Pricing Strategy of Platform Competition 
Considering Crossnetwork Externality [J/OL]. Chinese Journal 
of Management Science: 1-20 [2022-10-18]. 

[7] Zhu B X, Ma Z Q, Leon Williams. Research on Pricing and 
Quality Decision of Information Goods Based on Free Strategy 
under Piracy and Network Externalities[J]. Management 
Review,2021,33(9):143-154.