Service Pricing Decision of E-Commerce Supply Chain Members Considering Diseconomies of Scale and Network Externalities

Yuyan WANG; Ying CUI; Liang SHEN; T.E.C CHENG

doi:10.21078/JSSI-2022-425-20

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Journal of Systems Science and Information ›› 2022, Vol. 10 ›› Issue (5) : 425-444. DOI: 10.21078/JSSI-2022-425-20

Service Pricing Decision of E-Commerce Supply Chain Members Considering Diseconomies of Scale and Network Externalities

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Abstract

Considering diseconomies of scale and network externalities in the e-commerce supply chain (ECSC), we construct an e-platform-led benchmark model and derive the optimal decisions. Then, the model is extended by endogenizing the impact of service level on network externalities. Considering service investment that includes fixed and variable investments, the model is further extended. Comparing the extended models with the benchmark model, we found the following conclusions. Although the e-platform dominates the ECSC, its profit is lower than the manufacturer. The corporate profits, service level, and price increase with network externalities. Increases in diseconomies of scale decrease the corporate profits and service level, but increase the price. A high-quality service combined with network externalities can achieve synergy and improve the e-platform's economies of scale, further generating a higher profit. Improving network externalities promotes the fair profit distributionin ECSC and achieves stable development.

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e-commerce / supply chain / diseconomies of scale / network externalities / service level

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Yuyan WANG , Ying CUI , Liang SHEN , T.E.C CHENG. Service Pricing Decision of E-Commerce Supply Chain Members Considering Diseconomies of Scale and Network Externalities. Journal of Systems Science and Information, 2022, 10(5): 425-444 https://doi.org/10.21078/JSSI-2022-425-20

1 Introduction

Faced with international trade friction, epidemic blockades, and serious declines in physical sales, world trade is under severe stress. Against such a backdrop, the digital economy underpinned by e-commerce has become an important driving force of the global economy. The manufacturer can directly sell products to customers through the online platform (e-platform), forming an e-commerce supply chain (ECSC). Today, the volume of e-commerce is estimated to equal the gross value of the products sold through retail outlets five years ago. Euromonitor International found that online shopping would account for at least 50% of the growth in global resales between 2020 and 2025, equivalent to approximately fanxiexian_myfh1.4 trillion. The United Nations Conference reported that the share of online retailing in many countries had achieved a significant increase in 2021 and would continue to increase. All this shows that the ECSC has a broad market prospect and a unique competitive advantage in international trade. However, there are issues to address for the ECSC to sustain development.

In the ECSC, the manufacturer faces diseconomies of scale (DOS) whereby unit cost increases with output ^{[1, 2]}. If the firm ignores the impact of DOS, its marginal profit will decrease with the production scale and it may even suffer a significant loss ^[3]. Moreover, the manufacturer's leveraging effect inevitably makes the impact of DOS spread along the supply chain ^[4], causing an overall imbalance in the supply chain. In 2015, Konka, China's leading colour TV manufacturer, suffered its biggest profit loss since its establishment due to improper scale management. So the manufacturer should consider the negative effect of DOS to avoid losses and improve the supply chain's stability. Also, incorporating DOS into the manufacturer's decision-making is of theoretical significance.

In the ECSC, the e-platform is a typical business with network externalities, which means that the users' utility increases with the user number of the platform ^[5]. Essentially, network externalities play a vital part in improving users' willingness to use the e-platform ^[6]. As the e-platform is an Internet-based sharing-economy platform, more use of the associated Internet services will create a huge user cluster ^[7]. Therefore, network externalities enable the e-platform to achieve economies of scale ^[8]. The strength of network externalities will be further enhanced in the two-sided market formed by consumers and service providers ^[9], which benefits the e-platform considerably but the manufacturer marginally. Furthermore, the huge profit gap between the e-platform and the manufacturer will lead to a monopoly of the e-platform and the manufacturer's unfairness of profit distribution. Ultimately, network externalities will affect the manufacturer's decision-making that counters the coordination of the ECSC.

Few studies consider both DOS and network externalities. Ha, et al. analyzed how sharing information influences diseconomies of production in the supply chain ^[2]. Xu, et al. considered return policies and supply chain coordination under network externalities ^[10]. Their works do not consider the fact that DOS and network externalities exist in the ECSC simultaneously. Practical cases show that manufacturers can use e-platform's network externalities and sales services to deal with DOS and increase profits. For example, Chinese hosiery company Xinglang Trading faced a risk of DOS due to poor long-term inventory management. However, NetEase helps Xinglang rationally plan production by updating sales and inventory in real time, and promotes consumer purchases through its own network externalities. In addition, NetEase provides selected high-quality products and services to target consumers who focus on quality, resulting in a product praise rate of 99.3%, optimizing platform reputation, driving sales, and achieving a win-win situation. In this paper we incorporate DOS into the cost function to construct the e-platform-led benchmark model. Then, we endogenize the impact of the service level on network externalities and consider service investment to further analyze the ECSC's decision-making. Specifically, we address the following questions:

1) What are the manufacturer's pricing and e-platform's service decisions considering DOS and network externalities? What are the impacts on the supply chain members' profits?

2) How will the manufacturer's pricing and e-platform's service change when the impact of the service level on network externalities is considered?

3) How will the manufacturer's pricing and e-platform's service change when service investment that includes both fixed and variable investments is considered?

Our major findings are as follows:

1) Different from the finding of Shen, et al. that the dominant party receives the most benefit ^[11], we show that the manufacturer's profit from the sales scale due to network externalities is far greater than the e-platform, although the e-platform is dominant.

2) Different from the production cost function in Wang, et al. ^[12], we incorporate the impact of DOS into the cost function, which is in line with reality. We show that the manufacturer's DOS increases the "double marginalization effect" in the ECSC, reducing the manufacturer's and the e-platform's profits. On the other hand, network externalities increase consumer demand and enhance the scale advantage, increasing the manufacturer's and the e-platform's profits.

3) We find that there is synergistic utility between network externalities and the service level, which enables the ECSC to quickly respond to risks. This dual impact enables the ECSC to perform well despite fierce competition. However, the extant literature has ignored the synergistic impact of the service level and network externalities.

We organize the rest of the paper as follows: In Section 2 we review the related studies to identify the research gap and position our study in the literature. In Section 3 we introduce the model, present the notation, and discuss the assumptions. In Section 4 we analyze the e-platform-led benchmark model considering the impacts of DOS and network externalities. In Section 5 we consider two extended models, and compare them with the e-platform-led benchmark model to generate the research findings. In Section 6 we conduct numerical studies to generate managerial insights from the analytical findings. Finally, in Section 7, we conclude the paper and suggest topics for future research.

2 Literature Review

Our study is related to three research streams, namely, the ECSC's decision-making, DOS, and network externalities. In the following, we discuss the position of our work concerning these research streams.

2.1 ECSC's Decision-Making

Early research on the ECSC focuses on its structure^[13] and characteristics ^[14]. Later researchers considered the ECSC's supply chain performance, decision-making, and coordination. Li, et al. analyzed how replenishment plans influence the performance of the ECSC ^[15]. Gao, et al. studied the impact of discount frequency on the bullwhip effect in e-commerce ^[16]. Zhao, et al. analyzed the impacts of consumer loyalty, product complementarity, and market structure on the ECSC's pricing strategy ^[17]. Chen, et al. analyzed how a manufacturer uses the strategy of opening an online channel to manipulate the retailer's decision on opening a discount store ^[18]. Song, et al. developed a three-level fresh food ECSC model comprising a producer, a third-party logistics provider, and a fresh food retailing firm ^[19]. Han, et al. explored the differences between decentralized decisions and centralized decisions in the low-carbon ECSC ^[20]. Xiao, et al. studied the ECSC's decision-making under platform digital empowerment-induced demand ^[21]. Based on a closed-loop supply chain with a dual channel, He, et al. assessed the influence of consumers' free-riding behaviour on carbon emissions. They found that carbon emissions are essential for the successful management of sustainable production and consumption ^[22]. Wang, et al. studied the ECSC's decision-making and coordination under the green manufacturer's fairness concern ^[23].

However, few studies have considered both DOS and network externalities in the ECSC's model setting. Different from the general linear supply chain which relies on online platform sales, network externalities and DOS significantly affect corporate profits in the ECSC. Thus, it is desirable to consider the impacts of these two factors in research on the ECSC.

2.2 Diseconomies of Scale (DOS)

In business, the unit production cost generally increases with the output because of the inadequate production processes and management capability ^[24]. Early research on DOS focuses on the empirical study of corporate organizations. Banker, et al. used empirical methods to study the economies of scale and DOS in the development of new software products ^[1]. Zenger empirically explored the relationship between DOS and employment contracts in R & D departments ^[25]. Considering DOS in production cost ^[26], later researchers tried to solve DOS by supply chain management. Ha, et al. discussed how DOS affects vertical information sharing in a competitive supply chain ^[2]. Shang, et al. analyzed competing manufacturers' information sharing in the supply chain. They found that the retailer's motivation to share information depends on DOS, the competition intensity, and the information payment contract ^[27]. Shao studied a competitive model in which suppliers with flexible resources face DOS ^[28]. Kokott, et al. studied the diseconomies of the demand segmentation auction scale in the procurement market ^[29].

The above studies mainly focus on the offline traditional supply chain and ignore the impact of DOS on the e-commerce firm's decision-making. We incorporate DOS into the production cost in our ECSC model, yielding results that reflect real practice more.

2.3 Network Externalities

Early research on network externalities focuses on mobile communications ^[30-32]. With the rise of the internet and e-commerce, researchers attach importance to network externalities in decision-making. Zhao, et al. explored the impact of network externalities on enhancing Weibo users' perceptual interactivity, satisfaction, and continuing willingness to use^[33]. Zhou, et al. proposed a duopoly competitive supply chain model to study decentralized and centralized decision-making with consideration of the network effect ^[8]. Luo, et al. studied an information product's inter-temporal hybrid bundling strategy with network externalities ^[34]. Kung, et al. analyzed the three pricing strategies for platform delivery under network externalities which resulted in the same number of shoppers and profits ^[35]. Yi, et al. analyzed the impacts of network externalities on the retailer's evolutionary stability strategies, wholesale pricing, and supply chain members' profits. They found that network externalities affect the decision on the dealer price, so changing the retailer's marketing goal ^[36]. Xu, et al. analyzed the return strategy and supply chain coordination under network externalities ^[10]. Yi, et al. found that when developers sell products directly to consumers, the substitution effect and network effect jointly decide the optimal strategies ^[37]. Zhu, et al. studied the pricing and competition mechanism of a monopoly platform based on bilateral market theory. They analyzed the impacts of network externalities, service differentiation, and matching efficiency between groups on the price of electronic waste recycling ^[38].

The extant literature has extensively studied the impact of network externalities. But the related studies only discuss the external influence at the enterprise-enterprise or enterprise-consumer level, ignoring the endogenous impact of network externalities on corporate decision-making. In contrast, we explore in this research the synergy between the service level and network externalities to help the e-platform make rational decisions and achieve economic advantages. Specifically, we consider the impacts of such factors as DOS and network externalities, the interaction between the service level and network externalities, and the composition of the service level. We summarize the main differences between our study and other related works in Table 1.

Table 1 Differences between our study and other literature

Literature	ECSC's Decision-making	DOS	Network externalities	Interaction between service level and network externalities	Composition of service level
^[15]	√
^[17]	√
^[20]	√
^[23]	√
^[28]		√
^[2]		√
^[29]		√
^[30]		√
^[34]			√
^[35]			√
^[37]	√		√
^[38]	√		√
Our study	√	√	√	√	√

3 Model Description and Assumptions

The model considers ECSC composed of a single manufacturer and a single e-platform, whose structure is shown in Figure 1. In ECSC, the manufacturer is responsible for the production and publishes the relevant sales information through the online sales channels provided by the e-platform. Consumers browse product information through the e-platform. They purchase the product and the e-platform generates the corresponding order. After the order is generated, the manufacturer posts the product to the consumer through self-operated logistics or third-party logistics. After the consumer receives the goods and confirms that it is correct, the e-platform deducts the commission and sends the remaining payment to the manufacturer, and the product transaction is completed.

Figure 1 The model structure of the ECSC

Full size|PPT slide

The manufacturer's profit is

\begin{array}{rcl} π_{m} = (p - ρ) q - c . \end{array}

(1)

The e-platform's profit is

\begin{array}{rcl} π_{e} = (ρ + μ) q - k s^{2} / 2. \end{array}

(2)

The notation and their descriptions used in the model are in Table 2.

Table 2 Descriptions of the notation

Notation	Description
p	The product price, a decision variable of the manufacturer.
s	The service level, a decision variable of the e-platform. Following Wang, et al.^[12], we assume that the service cost is C(s) = ks²/2, where k(k > 0) represents the service cost parameter.
q	Market demand for the product, which is related to the price and service level. Following Wang, et al.^[12], we assume that q = α − βp + γs, where α (α > 0) represents the market size, β(β > 0) represents the price influencing parameter, and γ(γ > 0) represents the service level influencing parameter.
c	The production cost. For a direct-sale manufacturer, the production cost has DOS. Following Ha, et al.^[2], we assume that c = mq + nq², where m(m > 0) represents the variable cost coefficient and n(n > 0) represents the DOS parameter.
ρ	The commission for unit sale. It should satisfy 0 < ρ < p − c.
μ	The network externalities strength.
Remarks	1) The e-platform's profit from providing the selling and promotion services includes two aspects: One is the commission income generated by selling the product; the other is the total value of network externalities created by customers. Following Lee, et al.^[39], Li, et al.^[40], and Tomak, et al.^[41], we assume that network externalities are μq_e. Following Katz, et al., q = q_e under consumers' rational expectations^[5]. The network externalities utility is μq. 2) To make sense, our model should satisfy the conditions β > γ and k > γ. This shows that the consumer pays more attention to the price than the service level and the e-platform pays more attention to service cost than the service level.

4 E-Platform-Led Benchmark model

In the ECSC, as rational economic entities, the members make decisions to maximize their profits, constituting a Stackelberg game. The e-platform first sets the service level

s

, followed by the manufacturer setting the product price

p

. We use the backward induction approach to derive the optimal decisions and corporate profits in the ECSC.

s^{*} = \frac{γ (μ + ρ)}{2 k △}

p^{*} = \frac{(1 + 2 n β) γ^{2} (μ + ρ) + 2 k △ H_{4}}{4 k β △^{2}}

q^{*} = \frac{γ^{2} (μ + ρ) + 2 k △ H_{3}}{4 k △^{2}}

π_{m}^{*} = \frac{[γ^{2} (μ + ρ) + 2 k △ H_{3}]^{2}}{16 k^{2} β △^{3}}

π_{e}^{*} = \frac{(μ + ρ) [γ^{2} (μ + ρ) + 4 k △ H_{3}]}{8 k △^{2}}

△ = 1 + n β, H_{4} = α + 2 n β α + β (m + ρ), H_{3} = α - β (m + ρ)

Proof The optimal decisions of the e-platform-led benchmark model.

From Equation (1), we have

\frac{\partial^{2} π_{m}}{\partial p^{2}} = - 2 (1 + n β) < 0

, so

π_{m}

is a concave function in

p

. Solving

\frac{\partial π_{m}}{\partial p} = 0

yields

\begin{array}{rcl} p = \frac{α + m β + 2 n α β + s γ + 2 n s β γ + ρ β}{2 β △} . \end{array}

(3)

Substituting Equation (3) into Equation (2), we have

\frac{\partial^{2} π_{e}}{\partial s^{2}} = - k < 0

, so

π_{r}

is a concave function in

s

. Solving

\frac{\partial π_{r}}{\partial s} = 0

yields

\begin{array}{rcl} s^{*} = \frac{γ (μ + ρ)}{2 k △} . \end{array}

(4)

The optimal decisions are as follows:

s^{*} = \frac{γ (μ + ρ)}{2 k △}

p^{*} = \frac{(1 + 2 n β) γ^{2} (μ + ρ) + 2 k △ H_{4}}{4 k β △^{2}}

q^{*} = \frac{γ^{2} (μ + ρ) + 2 k △ H_{3}}{4 k △^{2}}

π_{m}^{*} = \frac{[γ^{2} (μ + ρ) + 2 k △ H_{3}]^{2}}{16 k^{2} β △^{3}}

π_{e}^{*} = \frac{(μ + ρ) [γ^{2} (μ + ρ) + 4 k △ H_{3}]}{8 k △^{2}}

△ = 1 + n β, H_{4} = α + 2 n β α + β (m + ρ), H_{3} = α - β (m + ρ)

According to the optimal decisions and profits, we derive the following conclusions.

Proposition 1

\frac{\partial p^{*}}{\partial n} > 0, \frac{\partial s^{*}}{\partial n} < 0, \frac{\partial {π_{m}}^{*}}{\partial n} < 0, a n d \frac{\partial {π_{e}}^{*}}{\partial n} < 0

Proof The optimal decisions of the e-platform-led benchmark model.

\frac{\partial p^{*}}{\partial n} = \frac{k △ H_{3} - n β γ^{2} (μ + ρ)}{2 k △^{3}} > 0,

similarly,

\frac{\partial s^{*}}{\partial n} < 0, \frac{\partial {π_{m}}^{*}}{\partial n} < 0

, and

\frac{\partial {π_{e}}^{*}}{\partial n} < 0

From Proposition 1, the market demand, corporate profits, and service level are all negatively related to the DOS coefficient. The price is positively related to the DOS coefficient. With an increase in DOS, the manufacturer will increase the price to compensate for the increased cost. But the consumers sensitive to price will purchase other homogenous products. As a result, the product's market demand decreases. Moreover, the increased profit due to a higher price is lower than the loss caused by the decreased market demand, so the members' profits decrease, causing a decrease in the service level. Proposition 1 shows that DOS strengthens the "double marginalization effect" in the ECSC, which reduces the supply chain's profit even to the extent of "harming others without benefiting itself". For example, LYFen, the founder of the chain business model in China, faced a crisis of "increasing volume and decreasing profit" owing to blind extension and poor management in 2018. Thus, from the perspective of ECSC's internal management, the manufacturer with DOS should communicate with the e-platform promptly, accurately grasp market trends, adjust production, avoid blind extension, and reduce cost retention, thereby reducing members' profit losses.

Proposition 2

\frac{\partial p^{*}}{\partial γ} > 0, \frac{\partial s^{*}}{\partial γ} > 0, \frac{\partial q^{*}}{\partial γ} > 0, \frac{\partial {π_{m}}^{*}}{\partial γ} > 0, a n d \frac{\partial {π_{e}}^{*}}{\partial γ} > 0

Proof The same as Proposition 1.

From Proposition 2, the market demand, the price, service level, and members' profits are positively related to

γ

. This is because the e-platform can provide differentiated services for users based on data analytics, realizing precise marketing. These services can effectively attract consumers' attention and increase sales. Thereby, the members' profits increase. In 2016, Lin's Wood pioneered the practice of no packaging for furniture online shopping. They not only sold packaged furniture but also promised to return goods without reason within three months. Ultimately, they made a profit over RMB 100 million in the off-season.

Proposition 3

\frac{\partial p^{*}}{\partial μ} > 0, \frac{\partial s^{*}}{\partial μ} > 0, \frac{\partial q^{*}}{\partial μ} > 0, \frac{\partial {π_{m}}^{*}}{\partial μ} > 0, a n d \frac{\partial {π_{e}}^{*}}{\partial μ} > 0

Proof The same as Proposition 1.

From Proposition 3, the price, market demand, service level, and members' profits are positively related to

μ

because network externalities increase the consumers' and enterprises' utilities in the supply chain. Specifically, higher network externalities are, better are consumer satisfaction and user experience. Then, the e-platform has the motivation to improve the service level to attract more consumers. In this way, the e-platform's market share will increase, achieving economies of scale. Meanwhile, the sales volume and the manufacturer's profit will increase. Proposition 3 shows that network externalities have a positive impact on the service level and enable the e-platform to achieve economies of scale. Finally, the members' profits increase, and the ECSC realizes Pareto improvement. In the operation of ECSC, when consumers shop on the platform, they often compare the sales and evaluation of products. Those products with high sales and high praise rates are more likely to attract consumers' to make purchasing decisions. So merchants should increase the types of related commodities to improve the network externalities of commodities.

Proposition 4

π_{m}^{*} > π_{e}^{*}

, and with the increase of

μ

and

n

, the profit gap between the manufacturer and e-platform is decreasing.

Proof The proof of Proposition 4.

G = γ^{2} (μ + ρ) + 2 k H

π_{m}^{*} - π_{e}^{*} = \frac{G^{2} - 2 k β △ (μ + ρ) [G + 2 k H △]}{16 k^{2} β △^{3}} > 0

\frac{\partial {π_{m}}^{*}}{\partial μ} > \frac{\partial {π_{e}}^{*}}{\partial μ}, \frac{\partial {π_{m}}^{*}}{\partial n} > \frac{\partial {π_{e}}^{*}}{\partial n}

Unlike the traditional supply chain, the e-platform is essentially a shared platform. Its profit comes from the commissions paid by the manufacturer and network externalities utility. However, we only consider a single manufacturer in our model, which cannot lead the e-platform to achieve economies of scale. On the contrary, the manufacturer will sell plenty of products through the e-platform. Moreover, to ensure the ECSC's long-term development, the commission per unit product is small. Specifically, the commission does not exceed 30% of the retail price ^[42], which causes the e-platform's profit to be lower than the manufacturer's. And as network externalities increase, the e-platform's profit increases faster. As the DOS increases, the manufacturer's profit decreases faster. So whether it is

μ

n

increases, the profit gap between the manufacturer and e-platform will narrow. This suggests that increasing the network externalities strength can also prompt the fair profit distribution in ECSC and achieve the coordination and stability of ECSC.

5 Model Extensions and Analysis

5.1 Endogenous Network Externalities Model (ENE Model)

According to Proposition 2, product sales and the user utility increase with the service level, leading to the enhancement of network externalities. To examine the impact of the service level on network externalities, we consider the ENE model. Specifically, we assume that the network externalities level is a proportional function of the service level as follows:

\begin{array}{rcl} μ = l s_{1} + μ_{0}, \end{array}

(5)

where

l (0 < l < 1)

represents the influencing parameter of the service level on network externalities and

μ_{0} (0 < μ_{0} < 1)

represents the network externalities strength when the service level is 0.

So the market demand is

\begin{array}{rcl} q_{1} = α - β p_{1} + γ s_{1} . \end{array}

(6)

To make sense, our model should satisfy

k + k n β - l γ > 0

, which implies that product sale is more affected by the service level and price than network externalities.

Hence, the manufacturer's profit is

\begin{array}{rcl} π_{1 m} = (p_{1} - ρ) q_{1} - c . \end{array}

(7)

The e-platform's profit is

\begin{array}{rcl} π_{1 e} = (ρ + l s_{1} + μ_{0}) q_{1} - k s_{1}^{2} / 2. \end{array}

(8)

The solving procedure for the ENE model is the same as that for the e-platform-led benchmark model. The e-platform first sets the service level

s_{1}

, followed by the manufacturer setting the product price

p_{1}

. We use the backward induction approach to derive the optimal decisions and profits of the ECSC members.

s_{1}^{*} = \frac{l H_{3} + γ (μ_{0} + ρ)}{2 H_{1}}

p_{1}^{*} = \frac{2 k △ H_{4} - γ l [H_{4} + 2 △ β (m + ρ)] + γ^{2} (1 + 2 n β) (ρ + μ_{0})}{4 β H}

q_{1}^{*} = \frac{γ H_{2} + 2 k △ H_{3}}{4 H}

π_{1 m}^{*} = \frac{[γ^{2} H_{2} + 2 k △ H_{3}]^{2}}{16 β H_{1} H}

π_{1 e}^{*} = \frac{(μ_{0} + ρ) [γ^{2} (μ_{0} + ρ) + 4 k △ H_{3} + l^{2} H_{3}^{2} - 2 l γ H_{3}]}{8 H}

H = (1 + n β) (k + k n β - l γ), H_{1} = k + k n β - l γ, H_{2} = - l α + l β (m + ρ) + γ (ρ + μ_{0})

Comparing the optimal decisions and corporate profits under the e-platform-led benchmark model and ENE model, we obtain the following result.

Proposition 5

\frac{\partial {p_{1}}^{*}}{\partial γ} > \frac{\partial p^{*}}{\partial γ} > 0, \frac{\partial {s_{1}}^{*}}{\partial γ} > \frac{\partial s^{*}}{\partial γ} > 0, \frac{\partial {π_{1 m}}^{*}}{\partial γ} > \frac{\partial {π_{m}}^{*}}{\partial γ} > 0, a n d \frac{\partial {π_{1 e}}^{*}}{\partial γ} > \frac{\partial {π_{e}}^{*}}{\partial γ} > 0.

From Proposition 5, in line with the e-platform-led benchmark model, the members' profits, price, and service level are positively related to

γ

under the ENE model. Furthermore, the sensitivities of members' profits, service level, and price to

γ

all increase. This is because network externalities are higher in the ENE model due to the positive effect of the service level. And then, consumers will raise their willingness to purchase products due to higher utilities created by network externalities. Thus, consumers' sensitivity to the service level increases, and the increasing rates with

γ

become higher.

Proposition 6

\frac{\partial p^{*}}{\partial n} > \frac{\partial {p_{1}}^{*}}{\partial n} > 0, \frac{\partial {s_{1}}^{*}}{\partial n} < \frac{\partial s^{*}}{\partial n} < 0, \frac{\partial {π_{1 m}}^{*}}{\partial n} < \frac{\partial {π_{m}}^{*}}{\partial n} < 0, a n d \frac{\partial {π_{1 e}}^{*}}{\partial n} < \frac{\partial {π_{e}}^{*}}{\partial n} < 0.

Proof The same as Proposition 1.

From Proposition 6, in line with the e-platform-led benchmark model, the members' profits and service level are negatively related to DOS in the ENE model, and the price is positively related to DOS. Furthermore, the sensitivities of members' profits and the service levelto DOS are higher, while the price's sensitivity to DOS is lower. Proposition 6 shows that the ECSC can quickly respond to the negative impact of DOS and has higher flexibility in operation. This is because consumers are more sensitive to the service level which is shown in Proposition 5. Although the service level and members' profits decrease with DOS, consumer behaviour changes more and the e-platform can adjust its sale plan promptly, making the ECSC more flexible in sales.

Proposition 7

s_{1}^{*} > s^{*}, p_{1}^{*} > p^{*}, π_{1 m}^{*} > π_{m}^{*}, π_{1 e}^{*} > π_{e}^{*} .

Proof The same as Proposition 1

From Proposition 7, the member' profits, price, and service level in the ENE model are higher than those in the e-platform-led benchmark model. This is because Proposition 5 shows that a higher service level increases user utilities and network externalities. Then, it increases consumers' purchase motivation, product sales, and the ECSC members' profits. In addition, Proposition 7 shows that the ECSC can adjust its sale plan effectively to deal with the negative effect of DOS. Therefore, the ECSC's profitability is improved.

From Propositions 5, 6, and 7, in the ECSC, increasing the service level can enhance network externalities, attract consumers' more attention to the shopping experience, and increase the market share. Furthermore, increasing the service level helps the e-platform quickly change its sale plan and respond to customers' demands when faced with DOS, ultimately improving the ECSC's flexible supply capacity and profit margin. The conclusion reveals a huge demand for customer service in sales service. The e-platform should attach great importance to the construction of its service system and builds a friendly user service mechanism.

5.2 Endogenous Service Investment Model (ESI Model)

In reality, service investment includes both fixed and variable investments. Despite that the e-platform has made a huge initial fixed investment, the service investment per unit sale can be reduced by economies of scale later, e.g., JD.com (www.JD.com) and Suning.com (www.suning.com). To examine changes in the ECSC members' decisions when the service investment consists of fixed and variable investments, we consider the ESI model. Specifically, we assume that

s_{2} = s_{0} + ε q_{2}

and

s_{0} >> ε

, where

s_{0}

represents the fixed investment and

ε

represents the variable investment of unit sale.

So the market demand is

\begin{array}{rcl} q_{2} = \frac{α - β p_{2} + γ s_{0}}{1 - γ ε} . \end{array}

(9)

To make sense, the model should satisfy

γ (ρ + μ) - k s_{0} (1 + n β) > 0

, which implies that product sale is more affected by the service level than the price.

Hence, the manufacturer's profit is

\begin{array}{rcl} π_{2 m} = (p_{2} - ρ) \frac{α - β p_{2} + γ s_{0}}{1 - γ ε} - c . \end{array}

(10)

and the e-platform's profit is

\begin{array}{rcl} π_{2 e} = (ρ + μ) \frac{α - β p_{2} + γ s_{0}}{1 - γ ε} - \frac{k [s_{0} (1 - γ ε) + α ε - β p_{2} ε + γ ε s_{0}]^{2}}{2 (1 - γ ε)^{2}} . \end{array}

(11)

In the ESI model, the e-platform again occupies the dominant position. Under this model, the e-platform determines

ε

, followed by the manufacturer setting the product price

p_{2}

. We use the backward induction approach to derive the optimal decisions and corporate profits.

ε_{2}^{*} = \frac{2 △ [γ (μ + ρ) - s_{0} k △]}{△_{1}}

p_{2}^{*} = \frac{k △ (H_{4} + s_{0} γ) + 2 n β γ^{2} (μ + ρ)}{2 k β △^{2}}

q_{2}^{*} = \frac{△_{1}}{2 k △^{2}}

π_{2 m}^{*} = \frac{(α - m β + s_{0} γ - β ρ) △_{1}}{4 k β △^{2}}

π_{2 e}^{*} = \frac{(μ + ρ) [△_{1} - γ^{2} (μ + ρ)]}{2 k △^{2}}

△_{1} = k (1 + n β) (α - m β + s_{0} γ - β ρ) + 2 γ^{2} (μ + ρ)

According to the optimal decisions and profits of the e-platform-led benchmark model and ESI model, we obtain the following result.

Proposition 8

\frac{\partial {p_{2}}^{*}}{\partial μ} > \frac{\partial p^{*}}{\partial μ} > 0, \frac{\partial {s_{2}}^{*}}{\partial μ} > \frac{\partial s^{*}}{\partial μ} > 0, \frac{\partial {π_{2 m}}^{*}}{\partial μ} > \frac{\partial {π_{m}}^{*}}{\partial μ} > 0, a n d \frac{\partial {π_{2 e}}^{*}}{\partial μ} > \frac{\partial {π_{e}}^{*}}{\partial μ} > 0.

Proof The same as Proposition 1.

From Proposition 8, in line with the e-platform-led benchmark model, the members' profits, service level, and price are positively related to network externalities in the ESI model. Furthermore, the sensitivities of members' profits and service level to network externalities increase, while the price's sensitivity to network externalities decreases. This is because network externalities enhance consumers' purchase motivation and user utilities, which renders that changes in the price have a smaller impact on customer satisfaction. Therefore, the sale price is less sensitive to network externalities. As the variable investment is sensitive to changes in the sale volume, the sensitivities of members' profits and service level to network externalities all increase.

Proposition 9

\frac{\partial p^{*}}{\partial n} > \frac{\partial {p_{2}}^{*}}{\partial n} > \frac{\partial {p_{1}}^{*}}{\partial n} > 0, \frac{\partial {s_{1}}^{*}}{\partial n} < \frac{\partial {s_{2}}^{*}}{\partial n} < \frac{\partial s^{*}}{\partial n} < 0, \frac{\partial {π_{1 m}}^{*}}{\partial n} < \frac{\partial {π_{2 m}}^{*}}{\partial n} < \frac{\partial {π_{m}}^{*}}{\partial n} < 0, a n d \frac{\partial {π_{1 e}}^{*}}{\partial n} < \frac{\partial {π_{2 e}}^{*}}{\partial n} < \frac{\partial {π_{e}}^{*}}{\partial n} < 0.

Proof The same as Proposition 1.

From Proposition 9, in line with the benchmark model and the ENE model, the manufacturer's profit, the e-platform's profit, and service level are negatively correlated with DOS in the ESI model, and the price is positively correlated with DOS. However, the manufacturer's profit, the e-platform's profit, and the service level are more sensitive to the DOS in the ENE model. This is because the ENE model has higher network externalities. As a result, the e-platform can change the sales plan promptly to deal with uncertain risks, making the supply chain more flexible in operation. This suggests that the attention to variable service per sale improves the ECSC's ability to cope with DOS. But it can't ignore the network externalities caused by the service.

Proposition 10

s_{2}^{*} > s_{1}^{*} > s, p_{1}^{*} > p_{2}^{*} > p^{*}, π_{1 m}^{*} > π_{2 m}^{*} > π_{m}^{*}, π_{2 e}^{*} > π_{1 e}^{*} > π_{e}^{*} .

Proof The same as Proposition 4.

From Proposition 10, it can be seen that in the ENE model, there are a higher e-platform's profit and a higher service level. In the ESI model, the manufacturer's profit and price are higher. The e-platform is a shared platform, its service level depends on the fixed investment

s_{0}

, and variable investment

ε

in the later stage is very small. In the ESI model, the e-platform focuses on both variable service investment and fixed investment. Therefore, compared with the ENE model, the service level in the ESI model is higher, and the e-platform is more profitable. In the ENE model, there is a synergistic effect between the service level and the network externalities, and consumers can accept higher sale prices. So the manufacturer's profit in the ENE model is higher than that in the ESI model. Proposition 10 shows that the essence of network externalities is to attract and consolidate customer sources. Firms should let sales service play the role of maintaining customers to expand customer demand. In addition, the e-platform must realize that the advantage of network externalities require a certain price. The fixed cost will not cause a qualitative leap in the service level, but it cannot be ignored. Many small and medium-sized firms will not take big risks considering the return of funds. From a long-term perspective, the fixed investment serves for the platform's rapid development and can not be reduced for the immediate interests. It can be further obtained that the manufacturer and e-platform have conflicting preferences to maximize their profits. The manufacturer prefers the e-platform to improve the service level (i.e., model ENE). The e-platform pays more attention to the fixed investment (i.e., model ESI). In the supply chain composing a manufacturer and an e-platform, the e-platform occupies a dominant position and has more right to speak. Therefore, when the number of manufacturers on the platform is small and the profit is low in the early stage, the e-platform always focuses on the fixed investment. Only when the number of manufacturers on the platform is large and commissions are enough can the e-platform ignore the profit difference, and it will improve the service level.

6 Numerical Studies

We conducted numerical studies to verify the analytical findings and ascertain the impacts of different model parameters on the optimal decisions.

Following Zhang, et al. ^[43], we set

α = 200, β = 0.8, k = 2, ρ = 4, μ_{0} = 0.01, l = 0.04

, and

m = 0.1

in the e-platform-led benchmark model and the ENE model, while treating

n

and

γ

as independent variables. We set

n \in [0.02, 0.08]

and

γ \in [0.45, 0.65]

to draw the diagram of optimal decisions changing with DOS and the service level influencing factor, as shown in Figures 2~5.

In addition, we set

α = 200, β = 0.8, k = 0.1, ρ = 4, γ = 0.55, μ_{0} = 0.01, s_{0} = 15

, and

m = 0.1

in the e-platform-led benchmark model and the ESI model, while treating

n

and

μ

as independent variables. We set

n \in [0.02, 0.08]

and

μ \in [0.01, 0.04]

to draw the diagram of optimal decisions changing with DOS and network externalities, as shown in Figures 6~9.

**Figure 6 Changes of π_m^* with n and μ**

Full size|PPT slide

**Figure 7 Changes of π_e^* with n and μ**

Full size|PPT slide

**Figure 8 Changes of p^* with n and μ**

Full size|PPT slide

**Figure 9 Changes of s^* with n and μ**

Full size|PPT slide

As shown in Figures 2~5, the members' profits, service level, and price in the ENE model are all higher than those in the e-platform-led benchmark model. With the increase in the service level influencing parameter, each decision's increasing rate in the ENE model is higher than that in the e-platform-led benchmark model. With the increase in DOS, the decreasing rates of members' profits and service level in the ENE model are higher than those in the e-platform-led benchmark model. The price's increasing rate in the ENE model is lower. This is because the e-platform is a typical industry with network externalities, and a high-quality service level will indirectly increase network externalities strength. Thus, the impact of network externalities on each decision significantly increases, which strengthens the integration of the ECSC and improves the ECSC's profit. These results demonstrate the robustness of the conclusion given in Propositions 5, 6, and 7.

As shown in Figures 6~9, the service level, price, and members' profits in the ESI model are all higher than those in the e-platform-led benchmark model. With the increase in network externalities, the increasing rates of members' profits and service level are higher, while the price's increasing rate is lower. With the increase in DOS, the decreasing rates of members' profits and service level are higher, while the price's increasing rate is lower. This is because increasing network externalities enhances the e-platform's scale advantage, which renders the service investment per sale a downward trend. When the e-platform provides high-quality and flexible service, the manufacturer and e-platform make more profits, realizing a virtuous cycle of the ECSC.

We set

α = 200, β = 0.5, k = 0.03, γ = 0.15, ρ = 4, μ = 0.45, l = 0.03, n = 0.1, c = 1

, and

m = 10

in the ENE model and ESI model, while treating

ε

and

s_{0}

as independent variables. We set

ε \in [0.01, 0.04]

and

s_{0} \in [20, 70]

to draw the diagram of optimal decisions changing with the fixed investment and the variable investment of unit sale, as shown in Figure 10.

Figure 10 Changes of optimal decisions with ε and s₀

Full size|PPT slide

Figure 10(a) shows that the price in the ENE model is higher than that in the ESI model. Figure 10(b) shows that the service level in the ESI model is higher than that in the ENE model. In Figure 10(c), the manufacturer has a higher profit in the ENE model. Figure 10(d) shows that the e-platform has a higher profit in the ESI model. This is because, in the ESI model, the e-platform attaches great importance to the huge fixed investment in the initial stage. Compared with the ENE model, the e-platform in the ESI model provides better services and makes more profits. Under the ENE model, the synergy between network externalities and the service level can maintain customers. Consumers can accept higher prices, so the manufacturer's profit in the ENE model is higher than that in the ESI model. In addition, from Figure 10(d) we can see that the e-platform's profit difference between the two models is very small. This verifies that the e-platform improves the service level only when the number of manufacturers on the platform is large and the commission is sufficient, which allow the e-platform to ignore the profit difference between the two models.

7 Conclusions

With the improvement of global e-commerce, the manufacturer selling products directly through online platforms has become a mainstream practice of the ECSC. The ECSC member's decision-making has become a new research hotspot. In this study, we construct an e-platform-led benchmark model considering DOS and network externalities. Then, we extend the model by endogenizing the impact of the service level on network externalities. We further extend the model by considering the service investment that includes both fixed and variable investments. We compare the e-platform-led benchmark model with the two extended models to derive the following findings.

1) Similar to the traditional supply chain, DOS harm the manufacturer's profit in the ECSC. The ECSC's leveraging effect will make this adverse impact spread to the node firms, increasing the "double marginalization effect". As a result, the service level and members' profits will decrease with DOS. Different from the traditional supply chain, network externalities have a positive impact on the ECSC, creating scale advantage and improving production to meet demand. In this way, the e-platform's profit, the manufacturer's profit, and the service level increase.

2) Different from the finding of Shen et al. that the dominant party receives the most benefit^[11], we show that the manufacturer's profit from the sales scale due to network externalities is far greater than the e-platform, although the e-platform is dominant. This is because the e-platform cannot achieve economies of scale, but the manufacturer will use the e-platform to sell a large volume of the product and obtain a huge profit.

3) There is a synergy between network externalities and the service level. On the one hand, a high-quality service level can increase sale and network externalities. On the other hand, network externalities can form a huge user cluster, making the service investment per sale decline and realizing more flexible service. When faced with the negative effects of DOS, the synergy allows the ECSC to adjust its sale plan promptly according to changes in consumer demand. Ultimately, the ECSC can enhance its flexibility to cope with risks and enhance profitability.

4) The e-platform can improve the strength of network externalities, and increase the fairness of profit distribution in ECSC. The manufacturer earns much higher profits, and the dominant e-platform inevitably feels unfair in profit distribution. By increasing the strength of network externalities, the profit gap between the two parties can be narrowed, and the conflict of interest caused by profit distribution among members can be effectively alleviated.

Specifically, the management implications of our research findings are as follows:

1) Different from the traditional linear supply chain, the losses caused by the manufacturer's DOS in ECSC are much higher. Therefore, the manufacturer should pay attention to the problems in their operations, and communicate with the e-platform promptly, accurately grasp market trends, reasonably control the scale of production, and should not expand blindly. Avoiding the phenomenon of "increase in volume and decrease in profit" to ensure the profits of supply chain cooperation members.

2) As the dominant party, the e-platform must be aware that homogeneous products' prices have become more similar. In a competitive market, consumers have gradually shifted from being price-oriented to being service-oriented. The members of the ECSC should provide not only high-quality products but also high-quality services to ensure consumers' loyalty and promote the ECSC's operations. As the dominant enterprise, the e-platform must realize that when consumers shop on the platform, products with high sales and evaluation rates are more likely to make consumers purchase. Therefore, merchants should increase the types of related products to improve the network externality of products. Give full play to the role of its brand reputation, and accurately grasp the brand characteristics of the platform to attract more consumers. Also, the price of homogeneous products has become more similar. In the competitive market, consumers have gradually shifted from price-oriented to service-oriented. Not only high-quality products but also high-quality services, including technical services for merchants, etc., the platform should strengthen the qualification review of merchants, create an online shopping environment. Realize the synergy between service levels and network externalities, and promote the healthy operation of ECSC.

3) The e-platform should also pay attention to the fixed investment in the early stage. The acquisition of network externality advantages requires a certain price. From a long-term perspective, the huge investment in the early stage is for the rapid development of the platform, and the investment in fixed capital in the early stage cannot be reduced or ignored for the sake of immediate interests.

4) Improve the cooperation mechanism between the manufacturer and e-platform. The manufacturer should conduct in-depth cooperation with the e-platform to meet the deeper needs and create a new customized market. The manufacturer can increase consumer stickiness and enhance consumer loyalty by improving product quality and after-sales service. On the other hand, the e-platform can build a good brand reputation, accurately locate brand characteristics, and enhance user stickiness. Based on the background of China's 2025 manufacturing strategy, the ECSC should focus on improving the core competitiveness and brand building capabilities, to maximize the profits of all members and reduce the injustice caused by the profit gap.

We only consider the ECSC members' decision-making problem with a single manufacturer in this paper. In reality, the e-platform usually faces multiple competing manufacturers, which is a topic worthy of future research.

References

Publishing order | Descend order by publishing year | Descend order by cited within

1	Banker R D, Kemerer C F. Scale economies in new software development. IEEE Transactions on Software Engineering, 1988, 15 (10): 1199- 1205. Cited in this article [2]

2	Ha A Y, Tong S, Zhang H. Sharing demand information in competing supply chains with production diseconomies. Management Science, 2011, 57 (3): 566- 581. https://doi.org/10.1287/mnsc.1100.1295 Cited in this article [5]

3	Beccalli E, Rossi L. Economies or diseconomies of scope in the EU banking industry?. European Financial Management, 2020, 26 (5): 1261- 1293. https://doi.org/10.1111/eufm.12261 Cited in this article [1]

4	van Blokland W W A B, FiksiȽski M A, Amoa S O B, et al. Measuring value-leverage in aerospace supply chains. International Journal of Operations Production Management, 2012, 32 (8): 982- 1007. https://doi.org/10.1108/01443571211253155 Cited in this article [1]

5	Katz M L, Shapiro C. Network externalities, competition, and compatibility. The American Economic Review, 1985, 75 (3): 424- 440. Cited in this article [2]

6	Bao Z. Exploring continuance intention of social networking sites: An empirical study integrating social support and network externalities. Aslib Journal of Information Management, 2016, 68 (6): 736- 755. https://doi.org/10.1108/AJIM-05-2016-0064 Cited in this article [1]

7	Cheng Y M. Why do customers intend to continue using internet-based sharing economy service platforms? Roles of network externality and service quality. Journal of Asia Business Studies, 2020, 15, 128- 152. https://doi.org/10.1108/JABS-05-2019-0142 Cited in this article [1]

8	Zhou R, Ma R, Jin M. Research on competitive strategy of dynamic supply chain with network effect. Journal of Difference Equations and Applications, 2017, 23, 334- 349. https://doi.org/10.1080/10236198.2016.1229315 Cited in this article [2]

9	Kumar M, Basu P, Avittathur B. Pricing and sourcing strategies for competing retailers in supply chains under disruption risk. European Journal of Operational Research, 2018, 265 (2): 533- 543. https://doi.org/10.1016/j.ejor.2017.08.019 Cited in this article [1]

10	Xu L, Li Y, Govindan K, et al. Return policy and supply chain coordination with network-externality effect. International Journal of Production Research, 2018, 56 (10): 3714- 3732. https://doi.org/10.1080/00207543.2017.1421786 Cited in this article [2]

11	Shen L, Fan R, Wang Y. Decisions of e-commerce supply chain under consumer returns and different power structures. Mathematical Problems in Engineering, 2020. https://doi.org/10.1155/2020/8884963 Cited in this article [2]

12	Wang Y, Yu Z, Shen L. Study on the decision-making and coordination of an e-commerce supply chain with manufacturer fairness concerns. International Journal of Production Research, 2019, 57 (9): 2788- 2808. https://doi.org/10.1080/00207543.2018.1500043 Cited in this article [3]

13	Pant S, Sethi R, Bhandari M. Making sense of the e-supply chain landscape: An implementation framework. International Journal of Information Management, 2003, 23 (3): 201- 221. https://doi.org/10.1016/S0268-4012(03)00025-2 Cited in this article [1]

14	Sherer S A. From supply-chain management to value network advocacy: Implications for e-supply chains. Supply Chain Management: An International Journal, 2005, 10 (2): 77- 83. https://doi.org/10.1108/13598540510589151 Cited in this article [1]

15	Li J, Ghadge A, Tiwari M K. Impact of replenishment strategies on supply chain performance under e-shopping scenario. Computers & Industrial Engineering, 2016, 102, 78- 87. https://doi.org/10.3969/j.issn.1001-3695.2016.01.018 Cited in this article [2]

Gao D, Wang N, He Z, et al. The bullwhip effect in an online retail supply chain: A perspective of price-sensitive demand based on the price discount in e-commerce. IEEE Transactions on Engineering Management, 2017, 64 (2): 134- 148.

https://doi.org/10.1109/TEM.2017.2666265

Cited in this article [1]

17	Zhao J, Hou X, Guo Y, et al. Pricing policies for complementary products in a dual-channel supply chain. Applied Mathematical Modelling, 2017, 49, 437- 451. https://doi.org/10.1016/j.apm.2017.04.023 Cited in this article [2]

18	Chen J, Pun H, Li W. Using online channel to defer the launch of discount retailing store. Transportation Research Part E: Logistics and Transportation Review, 2018, 120, 96- 115. https://doi.org/10.1016/j.tre.2018.10.012 Cited in this article [1]

19	Song Z, He S, Xu G. Decision and coordination of fresh produce three-layer e-commerce supply chain: A new framework. IEEE Access, 2018, 7, 30465- 30486. Cited in this article [1]

20	Han Q, Wang Y. Decision and coordination in a low-carbon e-supply chain considering the manufacturer's carbon emission reduction behavior. Sustainability, 2018, 10 (5): 1686. https://doi.org/10.3390/su10051686 Cited in this article [2]

21	Xiao D, Kuang X, Chen K. E-commerce supply chain decisions under platform digital empowerment-induced demand. Computers & Industrial Engineering, 2020, 150, 106876. Cited in this article [1]

22	He R, Xiong Y, Lin Z. Carbon emissions in a dual channel closed loop supply chain: The impact of consumer free riding behavior. Journal of Cleaner Production, 2016, 134, 384- 394. https://doi.org/10.1016/j.jclepro.2016.02.142 Cited in this article [1]

23	Wang Y, Fan R, Shen L, et al. Decisions and coordination of green e-commerce supply chain considering green manufacturer's fairness concerns. International Journal of Production Research, 2020, 58 (24): 7471- 7489. https://doi.org/10.1080/00207543.2020.1765040 Cited in this article [2]

24	Mollick A V. Production smoothing in the Japanese vehicle industry. International Journal of Production Economics, 2004, 91 (1): 63- 74. https://doi.org/10.1016/j.ijpe.2003.07.001 Cited in this article [1]

25	Zenger T R. Explaining organizational diseconomies of scale in R&D: Agency problems and the allocation of engineering talent, ideas, and effort by firm size. Management Science, 1994, 40 (6): 708- 729. https://doi.org/10.1287/mnsc.40.6.708 Cited in this article [1]

26	Eichenbaum M S. Some empirical evidence on the production level and production cost smoothing models of inventory investment. 1988, 79(4), DOI: 10.3386/w2523. Cited in this article [1]

27	Shang W, Ha A Y, Tong S. Information sharing in a supply chain with a common retailer. Management Science, 2016, 62 (1): 245- 263. https://doi.org/10.1287/mnsc.2014.2127 Cited in this article [1]

28	Shao L. Competition under diseconomies of scale: The role of subcontracting and single-sourcing commitment. Decision Sciences, 2018, 49 (1): 154- 179. https://doi.org/10.1111/deci.12268 Cited in this article [2]

29	Kokott G M, Bichler M, Paulsen P. The beauty of Dutch: Ex-post split-award auctions in procurement markets with diseconomies of scale. European Journal of Operational Research, 2019, 278 (1): 202- 210. https://doi.org/10.1016/j.ejor.2019.04.003 Cited in this article [2]

30	Sobolewski M, Czajkowski M. Network effects and preference heterogeneity in the case of mobile telecommunications markets. Telecommunications Policy, 2012, 36 (3): 197- 211. https://doi.org/10.1016/j.telpol.2011.12.005 Cited in this article [2]

31	Wei P S, Lu H P. Why do people play mobile social games? An examination of network externalities and of uses and gratifications. Internet Research, 2014, 24 (3): 313- 331. https://doi.org/10.1108/IntR-04-2013-0082

32	Zhou T, Lu Y. Examining mobile instant messaging user loyalty from the perspectives of network externalities and flow experience. Computers in Human Behavior, 2011, 27 (2): 883- 889. https://doi.org/10.1016/j.chb.2010.11.013 Cited in this article [1]

33	Zhao L, Lu Y. Enhancing perceived interactivity through network externalities: An empirical study on micro-blogging service satisfaction and continuance intention. Decision Support Systems, 2012, 53 (4): 825- 834. https://doi.org/10.1016/j.dss.2012.05.019 Cited in this article [1]

34	Luo X, Li M, Feng H, et al. Intertemporal mixed bundling strategy of information products with network externality. Computers & Industrial Engineering, 2017, 113, 369- 381. https://doi.org/10.3969/j.issn.1001-3695.2017.02.011 Cited in this article [2]

35	Kung L C, Zhong G Y. The optimal pricing strategy for two-sided platform delivery in the sharing economy. Transportation Research Part E: Logistics and Transportation Review, 2017, 101, 1- 12. https://doi.org/10.1016/j.tre.2017.02.003 Cited in this article [2]

36	Yi Y, Yang H. Wholesale pricing and evolutionary stable strategies of retailers under network externality. European Journal of Operational Research, 2017, 259 (1): 37- 47. https://doi.org/10.1016/j.ejor.2016.09.014 Cited in this article [1]

37	Yi Z, Li F, Ma L. The impact of distribution channels on trial-version provision with a positive network effect. Omega, 2019, 85, 115- 133. https://doi.org/10.1016/j.omega.2018.06.002 Cited in this article [2]

38	Zhu X, Li W. Research on the pricing strategy of "Internet+" recycling platforms in a two-sided network environment. Sustainability, 2020, 12 (3): 1001. https://doi.org/10.3390/su12031001 Cited in this article [2]

39	Lee D, Mendelson H. Adoption of information technology under network effects. Information Systems Research, 2007, 18 (4): 395- 413. https://doi.org/10.1287/isre.1070.0138 Cited in this article [1]

40	Li X, Chen Y. Corporate IT standardization: Product compatibility, exclusive purchase commitment, and competition effects. Information Systems Research, 2012, 23 (4): 1158- 1174. https://doi.org/10.1287/isre.1110.0412 Cited in this article [1]

41	Tomak K, Keskin T. Exploring the trade-off between immediate gratification and delayed network externalities in the consumption of information goods. European Journal of Operational Research, 2008, 187 (3): 887- 902. https://doi.org/10.1016/j.ejor.2006.04.049 Cited in this article [1]

Liu W, Yan X, Li X, et al. The impacts of market size and data-driven marketing on the sales mode selection in an internet platform based supply chain. Transportation Research Part E: Logistics and Transportation Review, 2020, 136, 101914.

https://doi.org/10.1016/j.tre.2020.101914

Cited in this article [1]

43	Zhang F, Wang C. Dynamic pricing strategy and coordination in a dual-channel supply chain considering service value. Applied Mathematical Modelling, 2018, 54, 722- 742. https://doi.org/10.1016/j.apm.2017.10.006 Cited in this article [1]

Funding

the National Natural Science Foundation of China(71971129)

the Science and Technology Support Program for Youth Innovation of Colleges and Universities in Shandong Province(2019RWG017)

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Abstract
Key words
Cite this article
1 Introduction
2 Literature Review
2.1 ECSC's Decision-Making
2.2 Diseconomies of Scale (DOS)
2.3 Network Externalities
Table 1 Differences between our study and other literature
3 Model Description and Assumptions
Figure 1 The model structure of the ECSC
Table 2 Descriptions of the notation
4 E-Platform-Led Benchmark model
5 Model Extensions and Analysis
5.1 Endogenous Network Externalities Model (ENE Model)
5.2 Endogenous Service Investment Model (ESI Model)
6 Numerical Studies
Figure 2 Changes of πm* with n and γ
Figure 3 Changes of πe* with n and γ
Figure 4 Changes of p* with n and γ
Figure 5 Changes of s* with n and γ
Figure 6 Changes of πm* with n and μ
Figure 7 Changes of πe* with n and μ
Figure 8 Changes of p* with n and μ
Figure 9 Changes of s* with n and μ
Figure 10 Changes of optimal decisions with ε and s0
7 Conclusions
References
Funding

Received	Accepted	Published
2021-11-18	2022-05-17	2022-10-25
Issue Date
2022-11-04

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Abstract

Key words

Cite this article

1 Introduction

2 Literature Review

2.1 ECSC's Decision-Making

2.2 Diseconomies of Scale (DOS)

2.3 Network Externalities

Table 1 Differences between our study and other literature

3 Model Description and Assumptions

Figure 1 The model structure of the ECSC

Table 2 Descriptions of the notation

4 E-Platform-Led Benchmark model

5 Model Extensions and Analysis

5.1 Endogenous Network Externalities Model (ENE Model)

5.2 Endogenous Service Investment Model (ESI Model)

6 Numerical Studies

**Figure 2 Changes of π_m^* with n and γ**

**Figure 3 Changes of π_e^* with n and γ**

**Figure 4 Changes of p^* with n and γ**

**Figure 5 Changes of s^* with n and γ**

**Figure 6 Changes of π_m^* with n and μ**

**Figure 7 Changes of π_e^* with n and μ**

**Figure 8 Changes of p^* with n and μ**

**Figure 9 Changes of s^* with n and μ**

Figure 10 Changes of optimal decisions with ε and s₀

7 Conclusions

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References

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Funding

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Abstract

Key words

Cite this article

1 Introduction

2 Literature Review

2.1 ECSC's Decision-Making

2.2 Diseconomies of Scale (DOS)

2.3 Network Externalities

Table 1 Differences between our study and other literature

3 Model Description and Assumptions

Figure 1 The model structure of the ECSC

Table 2 Descriptions of the notation

4 E-Platform-Led Benchmark model

5 Model Extensions and Analysis

5.1 Endogenous Network Externalities Model (ENE Model)

5.2 Endogenous Service Investment Model (ESI Model)

6 Numerical Studies

Figure 2 Changes of πm* with n and γ

Figure 3 Changes of πe* with n and γ

Figure 4 Changes of p* with n and γ

Figure 5 Changes of s* with n and γ

Figure 6 Changes of πm* with n and μ

Figure 7 Changes of πe* with n and μ

Figure 8 Changes of p* with n and μ

Figure 9 Changes of s* with n and μ

Figure 10 Changes of optimal decisions with ε and s0

7 Conclusions

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{{custom_sec.title}}

References

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Footnotes

Funding

**Figure 2 Changes of π_m^* with n and γ**

**Figure 3 Changes of π_e^* with n and γ**

**Figure 4 Changes of p^* with n and γ**

**Figure 5 Changes of s^* with n and γ**

**Figure 6 Changes of π_m^* with n and μ**

**Figure 7 Changes of π_e^* with n and μ**

**Figure 8 Changes of p^* with n and μ**

**Figure 9 Changes of s^* with n and μ**

Figure 10 Changes of optimal decisions with ε and s₀