research article comparison of dual-channel supply chain...

Research ArticleComparison of Dual-Channel Supply Chain Structures:E-Commerce Platform as Different Roles

Cong Wang,1 De-li Yang,1 and Zhao Wang2

1Faculty of Management and Economics, Dalian University of Technology, Dalian 116024, China2Bank of Dalian Co. Ltd., Dalian 116001, China

Correspondence should be addressed to Cong Wang; [email protected]

Received 22 February 2016; Revised 26 July 2016; Accepted 7 August 2016

Academic Editor: Laura Gardini

Copyright © 2016 Cong Wang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

E-commerce platforms can act as an e-tailer or a third-party intermediary that charge a commission and allow manufacturersto sell products on their platform directly. These two forms of dual-channel supply chain structures have different impacts ondecisions and profits of manufacturers and traditional retailers. This paper establishes different Stackelberg game models for bothdual-channel supply chain structures and achieves the equilibrium results. The results state that both structures can increase theconsumer surplus and social welfare. More importantly, when the platform acts as an e-tailer, the manufacturer and the traditionalretailer can form a “win-win” situation. Nevertheless, when the platform acts as a third-party intermediary allowingmanufacturersto sell products on the platform directly, it is bound to harm the interests of the traditional retailer.

1. Introduction

With the development of e-commerce, many manufacturers,such as IBM and Nike, have added a direct e-channel toadopt dual-channel strategy. In addition, many researchershave verified that the dual-channel strategy can make moreprofit for manufacturers in some conditions (e.g., [1, 2]).However, most of the studies are based on the platformsthat are owned by manufacturers. In practice, the majority ofmanufacturers do not have the ability to build e-commerceplatforms or their platforms cannot compete with promi-nent e-commerce platforms. Hence, these manufacturershave to use a third-party e-commerce platform when theyadopt the dual-channel strategy. For example, IMB alsosells on Amazon even though it has its own sales website.Therefore, there is a theoretical gap in the dual-channelstrategy whose electronic channel is based on a third-partyplatform.

Recently, the large e-commerce platforms such as Ama-zon and Sears have broken through the traditional resellingformat and embraced the agency model [3]. It means that aplatform owner can either act as an e-tailer or an agent whoauthorizes manufacturers to sell products on the platformdirectly. Due to funding constraints and other reasons,

the platform enterprise only chooses some kinds of productsto sell by itself but earns the commission as an agent with vastmajority of products.This study is motivated by the followingtwo questions:

(1) If the platform enterprise does not choose the prod-uct to sell by itself, will the manufacturer acceptthe commission policy to join in the platform andsell products directly or only reserve the traditionalchannel?

(2) How do the different roles of the platform enterpriseinfluence the operating decisions and business perfor-mances of themanufacturers and traditional retailers?And what about the consumer surplus and socialwelfare?

This study provides the performance comparisons of sup-ply chain members between the two different dual-channelsupply chain structures and the single channel structure. Weuse the game theory approach to develop two dual-channelsupply chain structures where the e-commerce owner canact as an e-tailer (𝐸 Structure) or an agent authorizingthe manufacturer to sell products on the platform directly(𝑃 Structure). In order to get some implications to promote

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016, Article ID 3831624, 10 pageshttp://dx.doi.org/10.1155/2016/3831624

2 Mathematical Problems in Engineering

the development of e-commerce, we also compare the con-sumer surplus and social welfare in different supply chainstructures through numerical experiments.

The rest of this paper is organized as follows. Aftersummarizing the related literature in Section 2, two formsof dual-channel supply chain structurers based on third-party e-commerce platforms are introduced in Section 3.The equilibrium results in different supply chain structuresare provided in Section 4. After the comparison analysis ofthe equilibrium results, the consumer surplus and the socialwelfare are calculated in Section 5. Section 6 describes theadditional numerical experiments. The conclusion and somemanagement implications are presented at the end of thispaper.

2. Literature Review

This paper focuses on dual-channel supply chain structuresbased on third-party e-commerce platform.Thus, the relatedliterature includes the areas of dual-channelmanagement ande-commerce platform.

The literature about dual-channel management mainlyinvolves channel competition, pricing strategy, and dual-channel supply chain coordination. A large amount of liter-ature focuses on channel competition and pricing strategy ofthe dual-channel supply chain. Chiang et al. [4] demonstratedthat the manufacturer would like to add a direct channelto the existing traditional retail channel and reported azone where the manufacturer and the traditional retailercan be both better off than in the single channel structure.Croom [5] reported that operating in dual-channel supplychain has become an effective means of competition betweensupply chains members and different supply chains with thedevelopment of e-commerce. Baye [6] provided insights intothe competition between a pure play e-tailer and a bricks-and-clicks e-tailer and found out that the pure play e-taileralways had a lower equilibrium price. Park and Keh [7]pointed out that the profits of themanufacturer and thewholesupply chain will be better but the traditional retailer’s profitwill be worse when the manufacturer adds a direct channel.Lu and Liu [8] discussed the influence on the supply chainfor the manufacturer opening the electronic channel andput forward the necessary conditions for the manufacturer.Li et al. [9, 10] discussed the pricing strategy of the dual-channel supply chain for small and medium sized enterprisesand supply chain with a risk-averse retailer, respectively. Theliterature about dual-channel supply chain coordination isalso quite comprehensive. A lot of the observed papers focuson the coordination of dual-channel supply chain by differentcontracts [11–14]. And there are some other cooperationstrategies to get a win-win state for the manufacturer and theretailer, such as incentive schemes [15], service cooperation[16], and advertising cooperation [17].

The literature about e-commerce platform is basicallyfocused on the platform pricing, mainly paying attentionto fixed fees, proportional fees, or two-part tariffs [18–20].Muthers and Wismer [21] demonstrated that proportionalfees offer more advantages to avoid the risk of moral hazard

and attract more participants in comparison with two-parttariffs. Wang and Wright [22] extended the area of theproportional fees with price discrimination. The literatureabout the influence of e-commerce platforms on supply chainhas also been concerned bymany scholars in recent years.Themost relevant literature to this paper is whether the rolemodeof the platform in supply chain is a “merchant” mode or a“two-sided platform.” Hagiu [23] demonstrated the choice ofthe market intermediation between a “merchant” mode anda “two-sided platform” mode with different influence factors.Abhishek et al. [3] provided that the mode choice of theplatform enterprise between agency selling and reselling wasrelevant to the effect of sales in the electronic channel on thedemand in the traditional channel. Mantin et al. [24] foundout that e-tailer’s power of bargaining with the manufacturercould be increased after he built the platform and it benefitedthe consumers, but it would decrease the consumers’ benefitsif the power is too big. Jiang et al. [25] used “Mid Tail” theoryto analyze themode selection problemof the platform e-tailerand suggested that the e-tailer might select different modesfor different kinds of products.

Based on the literature above, this paper assumes thatthe manufacturer does not have the ability to build an e-commerce platform or his platform cannot compete withprominent e-commerce platforms. Thus, the manufacturermust add the electronic channel through a third-party e-commerce platform if he adopts a dual-channel strategy.Then, we analyze the supply chain members’ operationdecisions and their performance in different supply chainstructures caused by different roles of the platform.

3. Model Assumptions and Notations

A system analyzed in this paper consists of a manufacturer, atraditional retailer, and an e-commerce platform owner.Theycan be composed of two kinds of supply chain structuresaccording to the different roles of the platform owner in thesupply chain. For simplicity, we describe two structures, “𝐸Structure” and “𝑃 Structure,” in Figure 1.

Without loss of generality, we normalize the potentialmarket size to 1 and the marginal cost of a unit product to0. We let V denote the perceived value of products in thetraditional channel. It is uniformly distributed in the interval[0, 1]. At the same time, we denote the perceived value ofproducts in the electronic channel as 𝛿V (0 < 𝛿 < 1), where𝛿 denotes the perceptual coefficient of the electronic channelcoming from the consumers and it reflects the substitutabilityof the electronic channel to the traditional channel.

Then, we consider the demand of two channels, where theprices of the traditional channel and the electronic channelare separately 𝑝

𝑅and 𝑝

𝐷. Consumers whose perceived value

meets the condition V ∈ {V | V − 𝑝𝑅≥ 𝛿V − 𝑝

𝐷, V − 𝑝

𝑅≥

0} will purchase the products from the traditional channel,and consumers whose perceived value meets the conditionV ∈ {V | 𝛿V − 𝑝

𝐷> V − 𝑝

𝑅, 𝛿V − 𝑝

𝑅≥ 0} will purchase

the product from the electronic channel. Other consumerswill not purchase anything. Therefore, through simple cal-culations, demand functions for the traditional channel and

Mathematical Problems in Engineering 3

Manufacturer

Traditional retailer Platform owner asan e-tailer

Consumers oftraditional channel

Consumers ofelectronic channel

(a) 𝐸 Structure

Manufacturer

Traditional retailer Platform owner asan intermediary

Consumers oftraditional channel

Consumers ofelectronic channel

(b) 𝑃 Structure

Figure 1: Two dual-channel supply chain structures.

the electronic channel are, respectively, as follows: 𝑄𝑅=

(1 − 𝛿 − 𝑝𝑅+ 𝑝𝐷)/(1 − 𝛿) and 𝑄

𝐷= (𝛿𝑝

𝑅− 𝑝𝐷)/(𝛿(1 −

𝛿)). Furthermore, based on the above demand functions, theinverse demand functions of two channels are, respectively,𝑝𝑅= 1 − 𝑄

𝑅− 𝛿𝑄𝐷and 𝑝

𝐷= 𝛿(1 − 𝑄

𝑅− 𝑄𝐷).

In order to express the content easily and conveniently, weuse superscripts “𝐸”, “𝑃,” and “𝑁” to represent “𝐸 Structure,”“𝑃 Structure,” and single channel structure, and we usesubscript “𝑀,” “TR,” and “𝑃” to represent the manufacturer,the traditional retailer, and the e-commerce platform.

4. Model Analysis

4.1. E Structure-Platform Owner as an e-Tailer. In the 𝐸Structure, the e-commerce platform owner acts as an e-tailer.He and the traditional retailer sell products through theirrespective channels. It is assumed that the manufacturer andtwo channel retailers obey a two-stage Stackelberg game andthe manufacturer is the leader. The sequence of events is asfollows: firstly, the manufacturer determines the wholesaleprice of the products 𝑤; secondly, according to the wholesaleprice 𝑤, the traditional retailer and the e-tailer determinethe supply quantity of the traditional channel 𝑄

𝑅and the

electronic channel 𝑄𝐷, respectively.

The decision problems of the manufacturer, the tradi-tional retailer, and the e-tailer are as follows, respectively:

max𝑤Π𝐸

𝑀= 𝑤 (𝑄

𝑅+ 𝑄𝐷) , (1)

max𝑄𝑅

Π𝐸

TR = (𝑝𝑅 − 𝑤)𝑄𝑅, (2)

max𝑄𝐷

Π𝐸

𝑃= (𝑝𝐷− 𝑤)𝑄

𝐷. (3)

According to the relation between𝑄𝑅and𝑄

𝐷and 𝑝

𝑅and

𝑝𝐷, the objective functions of the two channel retailers can be

simplified only about 𝑤, 𝑄𝑅, and 𝑄

𝐷as follows:

max𝑄𝑅

Π𝐸

TR = (1 − 𝑄𝑅 − 𝛿𝑄𝐷 − 𝑤)𝑄𝑅,

max𝑄𝐷

Π𝐸

𝑃= (𝛿 (1 − 𝑄

𝑅− 𝑄𝐷) − 𝑤)𝑄

𝐷.

(4)

When the wholesale price is determined, two channelretailers decide sales volume simultaneously. The secondderivatives of the two channel retailers’ profits about theirsales volume are, respectively, 𝜕2𝜋𝐸TR/𝜕𝑄

2

𝑅= −2 < 0 and

𝜕2𝜋𝐸

𝑃/𝜕𝑄2

𝐷= −2𝛿 < 0, so 𝜋𝐸TR and 𝜋𝐸

𝑃are both concave

functions about each sales volume. Sequentially, making thefirst derivative of the profits of the two channel retailers abouteach sales volume be zero, we can get the reaction function ofthe sales volume about the wholesale price 𝑤, as follows:

𝑄𝑅=2 − 𝛿 − 𝑤

4 − 𝛿,

𝑄𝐷=𝛿𝑤 + 𝛿 − 2𝑤

𝛿 (4 − 𝛿).

(5)

Taking the above results into the decision problem ofthe manufacturer, the decision function can be rewritten asfollows:

max𝑤𝜋𝐸

𝑀=𝑤 (2 − 𝛿 − 𝑤)

4 − 𝛿+𝑤 (𝛿 + 𝛿𝑤 − 2𝑤)

(4𝛿 − 𝛿2). (6)

The second derivative of 𝜋𝐸𝑀

about 𝑤 is 𝜕2𝜋𝐸𝑀/𝜕𝑤2=

−4/(𝛿(4 − 𝛿)) < 0, so 𝜋𝐸𝑀

is concave functions about thewholesale price𝑤. Sequentially, making the first derivative ofthe profit of the manufacturer be zero, we can get the optimalwholesale price. All equilibrium results are summarized inTable 1.

4.2. P Structure-Platform Owner as an Intermediary Agency.In the 𝑃 Structure, the e-commerce platform owner acts asan intermediary agent. The platform enterprise charges themanufacturer a commission of𝛼 according to the turnover onthe platform and allows the manufacturer to sell on his plat-form directly. The manufacturer and the traditional retailerobey a two-stage Stackelberg game and the manufacturer isthe leader. The sequence of events is as follows: first, themanufacturer determines the wholesale price of the products𝑤; second, according to the wholesale price𝑤, the traditionalretailer and the manufacturer determine the supply quantityof the traditional channel 𝑄

𝑅and the electronic channel 𝑄

𝐷,

respectively.


Table 1: Equilibrium results in different structures.

Variable 𝐸 Structure 𝑃 Structure Single channel

𝑤𝛿 (3 − 𝛿)

4

8 − 4𝛿 + 𝛿2− 2𝛿𝛼

2 (8 − 3𝛿 + 𝛿𝛼)

1

2

𝑝𝑅

(8 + 5𝛿 − 6𝛿2+ 𝛿3)

4 (4 − 𝛿)

(2 − 𝛿) (6 − 𝛿)

2 (8 − 3𝛿 + 𝛿𝛼)

3

4

𝑝𝐷

𝛿 (5 − 𝛿)

2 (4 − 𝛿)

𝛿 (6 − 𝛿)

2 (8 − 3𝛿 + 𝛿𝛼)/

𝑄𝑅

(8 − 7𝛿 + 𝛿2)

4 (4 − 𝛿)

2 − 2𝛿 + 𝛿𝛼

8 − 3𝛿 + 𝛿𝛼

1

4

𝑄𝐷

(5𝛿 − 𝛿2− 2)

4 (4 − 𝛿)

6 − 𝛿

2 (8 − 3𝛿 + 𝛿𝛼)/

𝜋𝑀

𝛿 (3 − 𝛿)2

8 (4 − 𝛿)

4 + 𝛿2− 4𝛿𝛼

4 (8 − 3𝛿 + 𝛿𝛼)

1

8

𝜋TR(𝛿2− 7𝛿 + 8)

2

16 (4 − 𝛿)2

(2 − 2𝛿 + 𝛿𝛼)2

(8 − 3𝛿 + 𝛿𝛼)2

1

16

𝜋𝑃

𝛿 (𝛿2− 5𝛿 + 2)

2

16 (4 − 𝛿)2

𝛿𝑎 (𝛿 − 6)2

4 (8 − 3𝛿 + 𝛿𝛼)2

/

The decision problems of the manufacturer and thetraditional retailer are as follows, respectively:

max𝑤,𝑄𝐷

𝜋𝑃

𝑀= 𝑤𝑄

𝑅+ (1 − 𝛼) 𝑝𝐷𝑄𝐷, (7)

max𝑄𝑅

𝜋𝑃

TR = (𝑝𝑅 − 𝑤)𝑄𝑅. (8)

According to the relation of 𝑄𝑅and 𝑄

𝐷and 𝑝

𝑅and 𝑝

𝐷,

we include the inverse demand functions 𝑝𝑅= 1 −𝑄

𝑅− 𝛿𝑄𝐷

and 𝑝𝐷= 𝛿(1 − 𝑄

𝑅− 𝑄𝐷) into the objective function of the

manufacturer and the traditional retailer. Then, the objectivefunctions can be simplified only about 𝑤, 𝑄

𝑅, and 𝑄

𝐷as

follows:

max𝑤,𝑄𝐷

𝜋𝑃

𝑀= 𝑤𝑄

𝑅+ 𝛿 (1 − 𝛼) (1 − 𝑄𝑅 − 𝑄𝐷) 𝑄𝐷,

max𝑄𝑅

𝜋𝑃

TR = (1 − 𝑄𝑅 − 𝛿𝑄𝐷 − 𝑤)𝑄𝑅.(9)

The second derivatives of the profits of the traditionalretailer and the manufacturer about their sales volume are𝜕2𝜋𝑃

TR/𝜕𝑄𝑃

𝑅= −2 < 0 and 𝜕2𝜋𝑃

𝑀/𝜕𝑄2

𝐷= −2𝛿(1 − 𝛼) < 0,

respectively, so 𝜋𝑃TR and 𝜋𝑃

𝑀are both concave functions about

each sales volume. Sequentially, making the first derivative ofboth the profits about each sales volume be zero, we can getthe reaction function of the sales volume about the wholesaleprice 𝑤 as follows:

𝑄𝑅=2 − 𝛿 − 2𝑤

4 − 𝛿,

𝑄𝐷=𝑤 + 1

4 − 𝛿.

(10)

After taking the above results into the decision function ofthemanufacturer, then the decision function can be rewrittenas follows:

max𝑤𝜋𝑃

𝑀=𝑤 (2 − 𝛿 − 2𝑤)

4 − 𝛿+𝛿 (1 − 𝛼) (1 + 𝑤)

2

(4 − 𝛿)2. (11)

The second derivative of 𝜋𝑃𝑀

about 𝑤 is 𝜕2𝜋𝑃𝑀/𝜕𝑤2=

−2(8−3𝛿+𝛿𝛼)/(4−𝛿)2< 0, so 𝜋𝑃

𝑀is concave functions about

wholesale price𝑤. Sequentially, making the first derivative ofthe profits of themanufacturer be zero, we can get the optimalwholesale price. All equilibrium results are summarized inTable 1.

5. 𝐸 Structure versus 𝑃 Structure

Before the comparison analysis, we summarized the equilib-rium results for the single channel structure in Table 1. Andall the proofs of the propositions are shown in the Appendix.

5.1. Comparison of Equilibrium Decisions and Profits

Proposition 1. The equilibrium wholesale price and the retailprice in the traditional channel satisfy𝑤𝐸 < 𝑤𝑁 and 𝑤𝑃 < 𝑤𝑁and 𝑝𝐸

𝑅< 𝑝𝑁

𝑅and 𝑝𝑃

𝑅< 𝑝𝑁

𝑅.

Proposition 1 shows that the competition effect of chan-nels in the dual-channel structure makes the sale price of thephysical channel lower than that in the single channel struc-ture. In order to ease the channel conflict, the manufacturerdecreases the wholesale price to the traditional retailer.

Proposition 2. The equilibrium wholesale price satisfies 𝑤𝐸 <𝑤𝑃, if the commission rate of the platform 𝛼 < ��

1≡ (3𝛿2−7𝛿+

4)/𝛿(𝛿 + 1).

In dual-channel structure, the profit of the manufacturercomes from two channels. In𝐸 Structure, themarginal profitswhich the manufacturer gets from both channels are unitwholesale price. In 𝑃 Structure, the marginal profit whichthe manufacturer gets from the electronic channel equalsthe unit price minus the unit pay on commission. Thus,the commission rate 𝛼 is a significant factor for the manu-facturer weighing the traditional channel and the electronicchannel. The higher the commission rate 𝛼 is, the more thecommission is paid and the lower the marginal profit of themanufacturer is gotten from the electronic channel. It meansthat when the commission rate 𝛼 is high sufficiently, themanufacturer is more dependent on the traditional channelthan on the electronic channel.

Proposition 3. The equilibrium retail price in traditionalchannel satisfies𝑝𝐸

𝑅< 𝑝𝑃

𝑅, if the commission rate of the platform

𝛼 < ��2≡ (3𝛿4−28𝛿3+87𝛿2−104𝛿+32)/𝛿(8+𝛿

3−6𝛿2+5𝛿).The

equilibrium retail price in electronic channel satisfies 𝑝𝐸𝐷> 𝑝𝑃

𝐷.


Proposition 3 shows that, in 𝑃 Structure, 𝛼 is the cost ofthe manufacturer adding the electronic channel. The higherthe cost is, the higher the retail price in electronic channel isand the higher the retail price is in traditional channel whichcompetes with the electronic channel. When the commissionrate 𝛼 exceeds the threshold ��

2, the retail price in 𝑃 Structure

is higher than that in 𝐸 Structure.

Proposition 4. The equilibrium sales volume in the twostructures satisfies 𝑄𝐸

𝑅> 𝑄𝑃

𝑅and 𝑄𝐸

𝐷< 𝑄𝑃

𝐷.

Proposition 4 states that, for the traditional channel, theequilibrium sales volume hasmore advantages in𝐸 Structure.The reason is that, in𝐸 Structure, the traditional retailer’s rivalof the game is the e-tailer and consumer perception of theelectronic channels is smaller than the traditional channels.In 𝑃 Structure, the traditional retailer’s rival of the game isthe manufacturer, but the traditional retailer has less powerin the game as the manufacturer is the game leader. For theelectronic channel, the lower retail price in 𝑃 Structure leadsto bigger sales volume.

Proposition 5. The equilibrium profits of traditional retailerin the two structures satisfy 𝜋𝐸

𝑇𝑅> 𝜋𝑃

𝑇𝑅, and the equilibrium

profits of the manufacturer in the two structures satisfy 𝜋𝐸𝑀≤

𝜋𝑃

𝑀, if the commission rate of the platform 𝛼 < ��

3≡ (32−80𝛿+

83𝛿2− 28𝛿

3+ 3𝛿4)/𝛿(32 + 𝛿 − 6𝛿

2+ 𝛿3).

Proposition 5 illustrates that the traditional retailer earnsmore money in 𝐸 Structure than in 𝑃 Structure.The reason isthat, in 𝐸 Structure, the traditional retailer’s rival of the gameis the e-tailer and the consumer perception of the electronicchannel is lower than the traditional channel. However, in𝑃 Structure, the traditional retailer’s rival of the game is themanufacturer, and the traditional retailer has less power inthe game as the manufacturer is the game leader. For themanufacturer, in 𝑃 Structure, the commission rate 𝛼 is thecost spent on the electronic channel. When 𝛼 < ��

3, the

manufacturer’s marginal profit in 𝑃 Structure is higher thanin 𝐸 Structure, so the manufacturer will prefer 𝑃 Structure.When 𝛼 > ��

3, the case is opposite.

Proposition 6. (1) In 𝐸 Structure, when 2−√2 < 𝛿 < 3−√5,the manufacturer and the traditional retailer will form a “win-win” situation; when 3 − √5 < 𝛿 < 1, the manufacturer andthe traditional retailer will form a “win-lose” situation; when0 < 𝛿 < 2 − √2, the manufacturer and the traditional retailerwill form a “lose-win” situation.

(2) In 𝑃 Structure, when 𝛼 ≤ (3 + 2𝛿)/9, the manufacturerand the traditional retailer will form a “win-lose” situation.Otherwise, the manufacturer and the traditional retailer willform a “lose-lose” situation.

Proposition 6 illustrates that, in 𝐸 Structure, when theconsumer perception of the electronic channel is modest,the manufacturer and the traditional retailer form a “win-win” situation, and when the consumer perception of theelectronic channel is high, 𝐸 Structure harms the interests of

the traditional retailer. Finally, when the consumer percep-tion of the electronic channel is low, rational manufacturerwill not adopt 𝐸 Structure to develop the electronic channel.Dual-channel supply chain strategy always harms the inter-ests of the traditional retailer if the manufacturer adopts 𝑃Structure. At the same time, the manufacturer will considerthe relationship of the commission rate and the consumerperception of the electronic channel. If the commission raterelative to the consumer electronics channel perception is toohigh, rational manufacturers will not adopt 𝑃 Structure todevelop the electronic channel.

5.2. Calculation of Consumer Surplus and Social Welfare.Referencing the study of Orsdemir et al. [26], we denote theconsumer surplus and the social welfare as

CS = ∫1−𝑄𝑅

1−𝑄𝑅−𝑄𝐷

(𝛿V − 𝑝𝐷) 𝑑V + ∫

1

1−𝑄𝑅

(V − 𝑝𝑅) 𝑑V,

SW = ∫1−𝑄𝑅

1−𝑄𝑅−𝑄𝐷

𝛿V 𝑑V + ∫1

1−𝑄𝑅

V 𝑑V.

(12)

According to the calculation formulas and the equilib-rium results above, we can easily get the consumer surplusand the social welfare in the single channel structure asCS𝑁 =1/32 and SW𝑁 = 7/32. At the same time, we can get theconsumer surplus and the social welfare in 𝐸 Structure andin 𝑃 Structure, as follows:

CS𝐸 = 64 − 140𝛿 + 153𝛿2− 75𝛿

3+ 15𝛿

4− 𝛿5

32 (4 − 𝛿)2

,

CS𝑃

=

(16 + 52𝛿 − 52𝛿2+ 9𝛿3) + 4 (4 + 2𝛿 − 𝛿

2) 𝛿𝛼 + 4𝛿

2𝛼2

8 (8 − 3𝛿 + 𝛿𝛼)2

,

SW𝐸 = 192 − 212𝛿 + 111𝛿2− 5𝛿3− 7𝛿4+ 𝛿5

32 (4 − 𝛿)2

,

SW𝑃

=

(112 − 108𝛿 + 20𝛿2+ 𝛿3) + 8 (8 − 3𝛿) 𝛿𝛼 + 4𝛿

2𝛼2

8 (8 − 3𝛿 + 𝛿𝛼)2

.

(13)

The expressions of the consumer surplus and the socialwelfare in 𝐸 Structure and in 𝑃 Structure are complicated.Therefore, we analyze them using the numerical analysis inthe next section.

6. Numerical Analysis

In this section, in order to verify the aforementioned analysisand to study the change of the consumer surplus andthe social welfare in different supply chain structures, weconduct several numerical studies. Andwe set the parametersvariation range as shown in Table 2.

The changes of the profits, the consumer surplus, andthe social welfare with the parameter 𝛼 and 𝛿 are shown inFigures 2–5.


Table 2: The intervals of parameters.

Parameter Variation range𝛼 [0.1, 0.2, 0.3, 0.4]𝛿 0∼1

𝛿

0 0.2 0.4 0.6 0.8 10.12

0.125

0.13

0.135

0.14

0.145

𝛼 = 0.1

𝛼 = 0.2

𝛼 = 0.3

𝛼 = 0.4

𝜋PM(𝛼 = 0.1)

𝜋PM(𝛼 = 0.2)

𝜋PM(𝛼 = 0.3)

𝜋PM(𝛼 = 0.4)

𝜋EM

𝜋NM

Figure 2: 𝜋𝑀in different supply chain structures.

Figure 2 depicts the change of themanufacture’s profit𝜋𝑀

according to the coefficient of electronic channel perception𝛿 and platform commission ratio 𝛼 in different supply chainstructures. It shows that the manufacturer earns more moneyin 𝐸 Structure than single channel structure only when theparameter 𝛿 is sufficiently high. In 𝑃 Structure, the profits ofthe manufacturer decrease with the increasing of 𝛼. And themanufacturer only benefits in the condition of the platformcommission ratio 𝛼 within a certain scope of the function of𝛿. At the same time, we find out that when the parameter 𝛿 ishigh, the manufacturer gets better profits in 𝐸 Structure thanin 𝑃 Structure.

Figure 3 depicts the change of the traditional retailer’sprofit 𝜋TR according to the coefficient of electronic channelperception 𝛿 and the platform commission ratio 𝛼 in differ-ent supply chain structures. Figure 3 shows that traditionalretailer earns more money in 𝐸 Structure than that in singlechannel structure if the electronic channel perception 𝛿 is nothigh enough. But if the electronic channel is competitive suf-ficiently, 𝐸 Structure will reduce the profits of the traditionalretailer. However, 𝑃 Structure always hurts the profits of thetraditional retailer. Finally, we can indicate that the profit oftraditional retailer in 𝑃 Structure is always higher than thatin 𝐸 Structure with the same parameter 𝛿.

Combining Figure 2 with Figure 3, we can find that, in 𝐸Structure, when the parameter 𝛿 is within a certain scope, a“win-win” situation for the manufacturer and the traditionalretailer can be formed. On the contrary, in 𝑃 Structure this“win-win” situation cannot be formed. Nevertheless, oncethe parameter 𝛿 is beyond the scope, both of dual-channelsupply chain structures damage the interests of the traditionalretailers.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.010.020.030.040.050.060.070.080.09

0.1

𝛿

𝛼 = 0.1𝛼 = 0.2

𝛼 = 0.3𝛼 = 0.4

𝜋PTR(𝛼 = 0.1)

𝜋PTR(𝛼 = 0.2)

𝜋PTR(𝛼 = 0.3)

𝜋PTR(𝛼 = 0.1)

𝜋NTR

𝜋ETR

Figure 3: 𝜋TR in different supply chain structures.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

𝛿

𝛼 = 0.1𝛼 = 0.2

𝛼 = 0.3𝛼 = 0.4

CSP(𝛼 = 0.1)

CSP(𝛼 = 0.2)

CSP(𝛼 = 0.3)

CSP(𝛼 = 0.4)

CSN

CSE

Figure 4: Consumer surplus in different supply chain structures.

Figures 4 and 5 depict the change of the consumersurplus and the social welfare according to the coefficient ofelectronic channel perception𝛿 and the platform commissionratio 𝛼 in different supply chain structures. As the figuresshow, the consumer surplus and the social welfare in anydual-channel structure are always bigger than those in thesingle channel structure. We also find out that when theparameter 𝛿 is low, the consumer surplus and the socialwelfare in 𝐸 Structure are bigger than those in 𝑃 Structure.When the parameter 𝛿 is big, consumer surplus and socialwelfare in 𝑃 Structure are higher than those in 𝐸 Structureand increase with the growth of the parameter 𝛼. That isbecause the price in both channels would decrease withincreasing of𝛼 in𝑃 Structure.Themeaning is that the surplusvalue of the products increases for consumers.

7. Conclusions

Most companies in China are small and medium enter-prises. In this scenario, themajority ofmanufacturers develop


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2

0.220.240.260.28

0.30.320.340.360.38

𝛿

𝛼 = 0.1𝛼 = 0.2

𝛼 = 0.3𝛼 = 0.4

SWP(𝛼 = 0.1)

SWP(𝛼 = 0.2)

SWP(𝛼 = 0.3)

SWP(𝛼 = 0.1)

SWN

SWE

Figure 5: Social welfare in different supply chain structures.

the electronic channel via third-party e-commerce platforms.However, the platform owner can act either as an e-taileror as an intermediary agency that forms two supply chainstructures. Utilizing the game theory approach, we comparethe two different structures in the paper and summarize somesignificant conclusions.

The wholesale price and the retail price in both channelsof two different structures are always lower than those inthe single channel structure. The wholesale price and theretail price in the traditional channel in which dual-channelstructure is higher depended on the value of the commissionrate 𝛼. Otherwise, the retail price of the electronic channel in𝐸 Structure is always higher than the one in 𝑃 Structure. Itmeans that the competition is more vehement in 𝐸 Structure.The important finding is that the manufacturer and thetraditional retailer can achieve a “win-win” situation in𝐸 Structure if the consumer perception of the electronicchannel is modest. In contrast, the dual-channel strategyalways damages the interests of the traditional retailers if themanufacturer adopts 𝑃 Structure. However, the requirementof 𝛿 is higher in 𝐸 Structure, which means that when theconsumer perception of the electronic channel 𝛿 is not highenough, the platform enterprise has no intention to saleproducts by 𝐸 Structure and the manufacturer only has thechoice of 𝑃 Structure if the commission rate 𝛼 is withinthe ideal range. In the last step we use the method of thenumerical analysis to study the change of the consumersurplus and the social welfare in different supply chainstructures. The comparison of the results indicates that dual-channel structures are always better for both the consumersurplus and the social welfare than single channel structure,and 𝐸 Structure is better for the consumer surplus andthe social welfare than 𝑃 Structure when the consumerperception of the electronic channel is low. Oppositely, 𝑃Structure is better for the consumer surplus and the socialwelfare than 𝐸 Structure when the consumer perception ofelectronic channel is high.

From this research,we canfind that the traditional retailerprefers 𝐸 Structure when the supply chain develops theelectronic channel. And themanufacturer prefers𝑃 Structureif the commission rate 𝛼 is within the ideal range. However,when the consumer perception of the electronic channel 𝛿 issufficiently high, which means the consumers’ acceptabilityof the electronic channel is also sufficiently high, any dual-channel structure decreases the interest of the traditionalretailer. Thus, the traditional retailers should adopt measuressuch as good service to improve the consumer perception ofthe traditional channel.

Appendix

All of the equilibrium results in different supply chain struc-tures used in proofs are gotten in Section 4, and parameterssatisfy the conditions 0 < 𝛿 < 1 and 0 < 𝛼 < 1.

Proof of Proposition 1. Comparing the equilibrium wholesaleprice and sale price in different dual-channel supply chainstructures with that in the single channel,

𝑤𝐸− 𝑤𝑁=𝛿 (3 − 𝛿)

4−1

2= −(1 − 𝛿) (2 − 𝛿)

4< 0,

𝑤𝑃− 𝑤𝑁=8 − 4𝛿 + 𝛿

2− 2𝛿𝛼

2 (8 − 3𝛿 + 𝛿𝛼)−1

2

= −𝛿 (1 + 3𝛼 − 𝛿)

2 (8 − 3𝛿 + 𝛿𝛼)< 0,

𝑝𝐸

𝑅− 𝑝𝑁

𝑅=

(8 + 5𝛿 − 6𝛿2+ 𝛿3)

4 (4 − 𝛿)−3

4

=𝛿 (2 − 𝛿)

4−1

(4 − 𝛿)<𝛿 (2 − 𝛿)

4−1

4

= −(𝛿 − 1)

2

4< 0,

𝑝𝑃

𝑅− 𝑝𝑁

𝑅=(2 − 𝛿) (6 − 𝛿)

2 (8 − 3𝛿 + 𝛿𝛼)−3

4= −𝛿 (7 − 2𝛿 + 3𝛼)

4 (8 − 3𝛿 + 𝛿𝛼)

< 0.

(A.1)

Proof of Proposition 2. Comparing the equilibrium wholesaleprice in 𝐸 Structure with that in 𝑃 Structure,

𝑤𝐸− 𝑤𝑃=𝛿 (3 − 𝛿)

4−8 − 4𝛿 + 𝛿

2− 2𝛿𝛼

2 (8 − 3𝛿 + 𝛿𝛼)

= −

(4 − 𝛿) (4 + 3𝛿2− 7𝛿 − 𝛿 (1 + 𝛿) 𝛼)

4 (8 − 3𝛿 + 𝛿𝛼).

(A.2)

So we obtain a threshold value

��1≡3𝛿2− 7𝛿 + 4

𝛿 (𝛿 + 1). (A.3)


Proof of Proposition 3. (1) Comparing the equilibrium retailprice of the traditional channel in 𝐸 Structure with thatin 𝑃 Structure,

𝑝𝐸

𝑅− 𝑝𝑃

𝑅= −

(32 − 104𝛿 + 84𝛿2− 28𝛿

3+ 3𝛿4− (8𝛿 + 5𝛿

2− 6𝛿3+ 𝛿4) 𝛼)

4 (4 − 𝛿) (8 − 3𝛿 + 𝛿𝛼). (A.4)

We obtain a threshold value

��2≡3𝛿4− 28𝛿

3+ 87𝛿

2− 104𝛿 + 32

𝛿 (8 + 𝛿3 − 6𝛿2 + 5𝛿). (A.5)

(2) Comparing the equilibrium retail price of the electronicchannel in 𝐸 Structure with in 𝑃 Structure,

𝑝𝐸

𝐷− 𝑝𝑃

𝐷=𝛿 (5 − 𝛿)

2 (4 − 𝛿)−𝛿 (6 − 𝛿)

2 (8 − 3𝛿 + 𝛿𝛼)

=

𝛿 (16 − 13𝛿 + 5𝛿𝛼 + 𝛿2(2 − 𝛼))

2 (4 − 𝛿) (8 − 3𝛿 + 𝛿𝛼)> 0.

(A.6)

Proof of Proposition 4. Comparing the equilibrium sales vol-ume of the traditional channel and the electronic channel in𝐸 Structure with that in 𝑃 Structure,

𝑄𝐸

𝑅− 𝑄𝑃

𝑅

=

(32 − 40𝛿 + 21𝛿2− 3𝛿3− (8𝛿 + 3𝛿

2− 𝛿3) 𝛼)

4 (4 − 𝛿) (8 − 3𝛿 + 𝛿𝛼)

>

32 − 40𝛿 + 21𝛿2− 3𝛿3− (8𝛿 + 3𝛿

2− 𝛿3)

4 (4 − 𝛿) (8 − 3𝛿 + 𝛿𝛼).

(A.7)

Denote a function as

𝑔1 (𝛿) = 32 − 40𝛿 + 21𝛿

2− 3𝛿3− (8𝛿 + 3𝛿

2− 𝛿3) . (A.8)

Because 𝜕𝑔1(𝛿)/𝜕𝛿 = −6𝛿

2+ 36𝛿 − 48 < 0, 𝜕2𝑔

1(𝛿)/𝜕𝛿

2=

−12𝛿 + 36 > 0.We can obtain𝑔(𝛿) > 𝑔(1) = 1 > 0, and then𝑄𝐸

𝑅−𝑄𝑃

𝑅> 0:

𝑄𝐸

𝐷− 𝑄𝑃

𝐷=

(5𝛿 − 𝛿2− 2)

4 (4 − 𝛿)−6 − 𝛿

2 (8 − 3𝛿 + 𝛿𝛼)

<

(5𝛿 − 𝛿2− 2)

4 (4 − 𝛿)−6 − 𝛿

2 (8 − 3𝛿 + 𝛿)

= −

(8 − 6𝛿 + 𝛿2)

4 (4 − 𝛿)< 0.

(A.9)

Proof of Proposition 5. Comparing the equilibrium profits ofthe traditional retailer and the manufacturer in 𝐸 Structurewith that in 𝑃 Structure,

𝜋𝐸

TR − 𝜋𝑃

TR =(32 − 40𝛿 + 21𝛿

2− 3𝛿3− (8𝛿 + 3𝛿

2− 𝛿3) 𝛼) (96 − 120𝛿 + 37𝛿

2− 3𝛿3+ (24𝛿 − 11𝛿

2+ 𝛿3) 𝛼)

16 (4 − 𝛿)2(8 − 3𝛿 + 𝛿𝛼)

2. (A.10)

We get (32−40𝛿+21𝛿2 −3𝛿3 − (8𝛿+3𝛿2 −𝛿3)𝛼) > 0 in proofof Proposition 4.

It is obvious that (96 − 120𝛿 + 37𝛿2 − 3𝛿3 + (24𝛿 − 11𝛿2 +𝛿3)𝛼) > 96 − 120𝛿 + 37𝛿

2− 3𝛿3.

Denote a function as

𝑔2 (𝛿) = 96 − 120𝛿 + 37𝛿

2− 3𝛿3. (A.11)

Because 𝜕𝑔2(𝛿)/𝜕𝛿 = −120 + 74𝛿 − 9𝛿

2< 0, 𝜕2𝑔

2(𝛿)/𝜕𝛿

2=

−18𝛿 + 74 > 0.We can obtain 𝑔

2(𝛿) > 𝑔

2(1) > 0, and then 𝜋𝐸TR−𝜋

𝑃

TR > 0.

𝜋𝐸

𝑀− 𝜋𝑃

𝑀= −

(32 − 80𝛿 + 83𝛿2− 28𝛿

3+ 3𝛿4− (32𝛿 + 𝛿

2− 6𝛿3+ 𝛿4) 𝛼)

8 (4 − 𝛿) (8 − 3𝛿 + 𝛿𝛼). (A.12)


We obtain the threshold value

��3≡32 − 80𝛿 + 83𝛿

2− 28𝛿

3+ 3𝛿4

𝛿 (32 + 𝛿 − 6𝛿2 + 𝛿3). (A.13)

Proof of Proposition 6. (1) Comparing the profits of themanufacturer and the traditional retailer in 𝐸 Structure withthat in the single channel structure,

𝜋𝐸

𝑀− 𝜋𝑁

𝑀=𝛿 (3 − 𝛿)

2

8 (4 − 𝛿)−1

8

=

(2 − 𝛿) ((𝛿 − 2)2− 2)

8 (4 − 𝛿),

𝜋𝐸

TR − 𝜋𝑁

TR =(𝛿2− 7𝛿 + 8)

2

16 (4 − 𝛿)2−1

16

=

(2 − 𝛿) (6 − 𝛿) ((𝛿 − 3)2− 5)

16 (4 − 𝛿)2

.

(A.14)

In summary, we obtain 𝜋𝐸𝑀> 𝜋𝑁

𝑀and 𝜋𝐸TR > 𝜋

𝑁

TR, when 2 −√2 < 𝛿 < 3 − √5; 𝜋𝐸

𝑀> 𝜋𝑁

𝑀and 𝜋𝐸TR < 𝜋

𝑁

TR, when 3 − √5 <𝛿 < 1; 𝜋𝐸

𝑀< 𝜋𝑁

𝑀and 𝜋𝐸TR > 𝜋

𝑁

TR, when 0 < 𝛿 < 2 − √2.(2) Comparing the profit of the manufacturer and the

traditional retailer in 𝑃 Structure with that in the singlechannel structure,

𝜋𝑝

𝑀− 𝜋𝑁

𝑀=4 + 𝛿2− 4𝛿𝛼

4 (8 − 3𝛿 + 𝛿𝛼)−1

8

=𝛿 (3 + 2𝛿 − 9𝛼)

8 (8 − 3𝛿 + 𝛿𝛼),

𝜋𝑃

TR − 𝜋𝑁

TR =(2 − 2𝛿 + 𝛿𝛼)

2

(8 − 3𝛿 + 𝛿𝛼)2−1

16

= −𝛿 (5 − 3𝛼) (16 − 11𝛿 + 5𝛿𝛼)

16 (8 − 3𝛿 + 𝛿𝛼)2> 0.

(A.15)

In summary, we obtain 𝜋𝑝𝑀> 𝜋𝑁

𝑀and 𝜋𝑃TR > 𝜋

𝑁

TR, when 0 <𝛼 < (3 + 2𝛿)/9; 𝜋𝑝

𝑀< 𝜋𝑁

𝑀and 𝜋𝑃TR > 𝜋

𝑁

TR, when (3 + 2𝛿)/9 <𝛼 < 1.

Competing Interests

The authors declare that they have no competing interests.

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