paperdownload.me · web viewaccepted manuscript. joint quality and pricing decisions for service...
TRANSCRIPT
Accepted Manuscript
Joint quality and pricing decisions for service online group-buying
strategy Yifan Wu, Ling Zhu
PII:DOI:Reference:
S1567-4223(17)30053-4
http://dx.doi.org/10.1016/j.elerap.2017.07.003
ELERAP 719
To appear in: Electronic Commerce Research and Applications
Received Date:
Revised Date:Accepted Date:
1 July 201612 July 201712 July 2017
Please cite this article as: Y. Wu, L. Zhu, Joint quality and pricing decisions for service online group-buying strategy,
Electronic Commerce Research and Applications (2017), doi: http://dx.doi.org/10.1016/j.elerap.2017.07.003
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we
are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of
the resulting proof before it is published in its final form. Please note that during the production process errors may be
discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Joint quality and pricing decisions for service online group-buying
strategyYifan Wu, Ling Zhu
School of Business, East China University of Science and Technology, Shanghai 200237, China
Abstract: In this paper, we study the popular group-buying model in which a seller
offers a discount on group-buying websites to attract new customers coming to
experience his/her service. We analyze the conditions under which a seller could benefit
from the group-buying strategy, in addition to discussing the optimal decisions
concerning service quality and online price. We find that only when the website scale is
sufficiently large will the seller benefit from adopting the group-buying strategy. We
also consider the customers’ substitution effect, that is, the existing offline customers
turn to an online channel when the seller offers a discount on the group-buying website.
When the website scale is relatively small and the substitution rate is high, the seller
cannot benefit from group-buying. The seller should set a service quality higher than the
base service quality when he/she cooperates with large group-buying websites.
Moreover, compared to purely offline businesses, the seller will set a higher quality
level if adopting a group-buying strategy.
Key Words: Group-buying, Service quality, Pricing, Substitution effect
1
1. IntroductionWith the rapid development of e-commerce, online group-buying has become a
common and important sales channel for service providers. Since the birth of Groupon in 2008, group-buying websites have sprung up across the world. In 2014 in China, trading volume for group-buying deals reached 74.75 billion RMB and increased by 108.3% compared to the 2013 turnover (Chinese group-buying statistical report). However, not all the sellers who join a group-buying website benefit from this channel. Dholakia (2011) surveyed 324 sellers who have sold products or services through group-buying websites such as Groupon, LivingSocial, Open Table, Travelzoo and Buywithme. The results show that 55.5% of the sellers joining the group-buying website benefited from this channel, while 26.6% lost money and 17.9% broke even. Hence, it is critical to understand how a seller can benefit from adopting a group-buying strategy (GS).
Even with its overall benefits, group-buying comes with some problems. As Groupon
CEO Andrew Mason said on his official blog, “It has always been Groupon policy to
allow merchants to cap deals. If a merchant sells too many Groupons, they’ll have a bad
experience, the customer will have a bad experience, and therefore, Groupon loses.”
Some sellers join group-buying websites without adjusting their service quality, which
leads to diminished service quality, such as group-buying customers being treated
differently than other customers; these problems cause customers to feel unsatisfied
with the seller. According to the Chinese Online Group-Buying Survey Report (Chinese
E-Commerce Research Center 2010) released by the Internet Data Center, the group-
buying product’s service quality is the main factor affecting customers’ decisions to buy
on a group-buying website. Service quality has been a strategic measure for maintaining
competitive strength in the market. If the seller’s service quality level is high, it can
attract relatively more customers coming to experience its service in the next period, but
doing so requires the seller bearing higher service costs. On the other hand, if the
seller’s service quality level is low, the service cost will be low, but there will be fewer
customers who are willing to experience the service in the next period due to poor
reputation. Thus, it is crucial to coordinate service quality with the seller’s GS to
guarantee its success.
Selling on group-buying websites also introduces the substitution effect (i.e., an existing offline customer takes advantage of the online discount). Based on survey data gathered from 641 small- and medium-sized businesses, Dholakia (2012) found that these businesses attract close to 80% new customers (i.e., customer substitution
2
rate of approximately 20%). We find that a high substitution rate will weaken the marketing power of a GS.
In this paper, we consider two scenarios. In the first scenario, a seller runs purely
offline and decides the selling price and service quality to maximize his/her profit over
two periods: the current and future period. In the second scenario, the seller can join the
group-buying website and set the new service quality and online price to maximize
profits for both the offline and online businesses. The optimal profits in the two
scenarios are then compared to decide whether the GS benefits the seller. We
investigate how the seller should adjust his/her service quality to align with the online
group-buying channel. Furthermore, we examine the substitution rate’s impact on the
seller’s group-buying decision. We also study the seller’s group-buying decision under
an endogenous substitution rate that depends on the offline and online prices.
The remainder of the paper is organized as follows: In Section 2, we present the relevant literature; Section 3 introduces the base model; Section 4 develops the group-buying model that is compared to the base model to investigate various parameters’ impact on the seller’s best strategy; in Section 5, we conduct a numerical analysis with the aim of revealing more managerial implications; finally, we conclude our research in Section 6.
2. Literature reviewThe group-buying mechanism is a special type of online distribution channel that
has been widely studied in literature (Khouja and Wang 2010, Geng et al. 2016, Tan et al. 2016, Kannan and Li 2017, Tan and Carrillo 2017). Thus far, it has undergone three stages: traditional dynamic group-buying, deal-of-the-day group-buying, and today’s group-buying. Traditional group-buying adopts a dynamic pricing strategy, whereas the deal-of-the-day mechanism adopts a fixed-pricing strategy. There are minimum deal sizes in both mechanisms. Today’s group-buying adopts the same fixed-pricing strategy as the deal-of-the-day mechanism but without the minimum deal size.
Traditional group-buying announces the price-quantity schedules at the beginning of
a given selling period. Customers pay the relative price depending on the total quantity
at the end of the selling period (Ni et al. 2015). Traditional group-buying has been
extensively studied in the literature. Kagel and Levin (2001) regarded the online group-
buying auction as a kind of homogeneous multi-unit auction whose price curve steps
down from one price-quantity schedule to the next. Chen et al. (2002)
3
recognized that this traditional group-buying mechanism is global and encourages all buyers who want to purchase a particular product or service to join a group-buying website to accomplish the desired purchase within a given time frame. Van Horn and Gustafsson (2002) showed that online group-buying enables individual buyers to obtain the same discount as retailers who buy in large volumes. Kauffman and Wang (2002) collected data on Mobshop-listed products over various periods of time and found three effects are important for customers’ buying decision. Anand and Aron (2003) revealed that the dynamic group-buying pricing mechanism outperforms fixed-pricing mechanisms when the seller faces an uncertain market. Chen et al. (2009) analyzed a bidder cooperation’s effect on group-buying, and they found that cooperation can improve profits for both sellers and bidders, which differs from traditional auctions.
The dynamic group-buying mechanism gradually became obsolete due to its three main drawbacks, as outlined by Kauffman and Wang (2001): (1) the business model is too complex for common consumers; (2) the group-buying auction cycle is too long and hinders impulse buying; and (3) the transaction volume is too low. Groupon was established in 2008, and it launched deal-of-the-day group-buying by offering certain products each day to help small businesses attract customers. Deal-of-the-day group-buying announces only one price-quantity pair for a given selling period. The transactions are valid only until the number of cumulative customers reaches a given minimum deal size. Groupon broke even after running for seven months and garnered $50 million in net income within its first year. Since then, many researchers have studied this new group-buying model. Dholakia and Tsabar (2011) conducted an in-depth descriptive analysis of the Gourmet Prep Meals experience and found that group-buying has a significant impact on sellers’ future profits. Jiang and Deng (2014) put forward the concepts of advertisement with a limited availability and market spill-over effects, and they studied how to set the optimal group-buying price and maximum deal size for service providers. Jing and Xie (2011) investigated the group-buying discount’s effect on motivating informed customers to work as sales agents.
In 2012, Groupon began to eliminate the minimum deal size. The seller just needed to
set the group-buying price and the selling time frame. Now, most group-buying
websites have begun to adopt this business model, but few academic studies have been
conducted on it because of its novelty. Ni et al. (2015) studied the package deal group-
buying model, which is one form of this new group-buying model; they
4
formulated the basic model as a Stackelberg game where the website is the leader and the seller is the follower. They found that group-buying is more efficient when the customers’ search and communication cost factors are low. The UGS model (seller has his/her own group-buying website) is more profitable for the seller than the basic model. However, the model only includes the online business, not the offline business. Gao and Chen (2015) considered customers’ preference uncertainty and consumption state uncertainty. By taking a comprehensive perspective, they found that a no-show of voucher buyers might not be a good thing for the merchant, especially for large or start-up businesses. They also found that websites sharing total revenues with sellers and providing full refunds to customers are able to maximize social welfare. Zhang et al. (2016) studied the impact of a group-buying network’s positive and negative effects on the group-buying business model’s performance. They compared three different scenarios in which the seller runs a group-buying business, an offline business, and both businesses. Zhao et al. (2014) considered a start-up service provider that decides whether to advertise its service product by offering a temporary daily deal promotion. They showed that both the commission rate charged by the daily deal website and the discount level offered by the service provider play important roles in signaling the service provider’s initially unobservable quality level. Ni et al. (2015) investigated the seller’s GS for both collectivist customers and individualistic customers.
However, with the increasing number of sellers joining group-buying websites, many
service-quality-related problems have been exposed. Many group-buying sellers receive
complaints about bad service quality and customers being treated unfairly. In San
Francisco, a bakery’s Groupon orders exceeded 72,000, which forced the bakery seller
to increase its daily production capacity from 800 up to 1,700, but this still failed to
guarantee the customers’ service experience quality (Galante 2010). According to the
Internet Data Center’s Chinese Online Group-Buying Survey Report (Chinese E-
Commerce Research Center 2010), service quality is one of the primary factors
affecting customers’ online group-buying website shopping decisions. Thus, it is crucial
for the sellers to adjust their service quality when starting an online group-buying
business. The service quality’s impact on the service industries and individual providers
has been systematically studied. Levitt (1972) stated that service quality refers to the
measuring of whether the service result can meet the established service standards.
Gronroos (1984) believed that service quality depends on a comparison between the
customer’s expectations and the actual service quality level.
5
Oh and Parks (1997) recognized that customer satisfaction and service quality are quite important in service industries. Yen et al. (2004) supported the proposition that customers’ participation in service failures influence how customers attribute the service failure’s cause. Zhang et al. (2015) suggested that e-retailers within the Chinese culture context should pay more attention to process quality and service recovery. Liu and Lee (2016) found service quality to be related to the service’s increased price perception, which can increase word-of-mouth and revisit intentions. However, service quality’s impact on the group-buying business model remains poorly understood in the literature.
To date, the most popular group-buying mechanism, which primarily focuses on the traditional dynamic group-buying and deal-of-the-day models with minimum deal sizes, has not been thoroughly studied in the extant literature. This paper examines the seller’s joint decision making regarding service quality and product price, which is considered vital for the group-buying adoption’s success. First, this paper looks at a situation where the seller runs only an offline business before having the option to join the group-buying website. When considering the seller’s revenue management, we consider both the online and offline profits and the future profit, which is extremely meaningful for the seller’s decision. We find that when the website scale is relatively large, choosing a GS will bring the seller more profit. Otherwise, the seller can benefit from this strategy only when the trading commission is relatively low. If the seller chooses to join the group-buying website, it is optimal for the seller to improve service quality. The seller will set a lower service quality and higher group-buying price with a higher substitution rate. Moreover, if the website scale is small and the substitution rate exceeds the critical value, it is not advisable for the seller to adopt a group-buying strategy.
3. The base modelIn this study, we consider a monopolist business that is using an offline strategy
(OS) to provide services over two periods: the current and future period. The seller
decides the price and service quality, which can be described as the environment,
service attitude, or waiting time. A comfortable environment, friendly service attitude,
and short waiting time represents high service quality, which can attract more customers
in the future period, but this implies a higher cost. In this paper, we assume that the
customers are homogenous in their service-quality expectations, which is defined as the
base service-quality level. If the seller’s actual service quality is higher
6
than the base service quality, there will be higher potential demand in the future period due to the word-of-mouth or online social learning. Otherwise, the potential future demand will drop because of a compromised reputation. The base service quality depends on the service industry’s standards and the customers’ expectations. We start from the base model using the following notations:
regular service pricebase service quality
service quality when the seller runs an offline business onlyλ seller’s demand in the current periodΛ seller’s potential demand in the future period
λ seller’s demand in the future periodβ customer’s quality sensitivityη service quality cost coefficient
Π seller’s total profit
We assume that the seller’s initial potential demand is 1. Each potential customer needs at most one unit of service in each period. When the seller runs his/her offline business, he/she will charge a regular price for the service. The offline demand can be described as λ = 1 − . The customers will form their own base service quality level before they experience the service. Consistent with the economic literature’s examination of experience goods (Nelson 1970), quality level is observed or experienced after purchasing and can only impact future customers’ purchase behavior. Therefore, after experiencing the service, customers will realize the seller’s real service quality, which will influence the future period’s market potential. Specifically, if the service quality is higher than the base service quality, the customers will be satisfied, and the market potential will increase. If the service quality is lower than the base service quality, some customers will be disappointed, and the market potential will decrease. Therefore, we define the future potential demand as Λ = 1 + λs − s. We include the term “λ” in the expression to capture the fact that the market potential change is proportional to the current customer population. If s > s, the additional potential demand comes from new customers who are referred to the service by the current period’s highly satisfied customers. Otherwise, the fraction of the current customers who are not satisfied will not return for the service. In the future period, the seller will stop his/her
7
group-buying activity and offer only offline business at price , and there will beλ =
Λ − = 1 + s − s1 − customers coming for the service in the
future period. To the seller, higher service quality will attract more potential demand in the future period, but it could also demand more cost. In line with Tsay and Agrawal (2000), we assume that the cost to the service-quality level s is given by s. Then, the seller’s profit maximization problem can be described as follows:
Maximize: Π, s = λ + λ − s
= 2 + s − s1 − − s (1)Subject to: 0 < < 1, (2)
0 < ≤ 1 (3)
Constraint (2) ensures a nonnegative demand. Similar to Chiang et al. (2013), weassume 0 < ≤ 1, which is constraint (3). We have the following Hessian matrix of
Π:
In the appendix, we prove that the Hessian matrix is semi-definite when 4 > . The optimal regular price and service quality can be obtained by solving the first-order conditions. The main results are summarized in Proposition 1.
Proposition 1: The seller’s optimal price and service
quality are ∗ = % and
s∗ = '(&, respectively. The corresponding seller’s optimal profit is Π∗ = % + *+(&) −
&,+.
By analyzing the optimal service quality and profit, we note that when customers’ service-quality sensitivity is high, the seller is more likely to provide a higher service quality than base service quality; this provides Theorem 1.
Theorem 1: When > - = 8( ≤ -), the seller’s provided service quality s∗ will be
higher (lower) than the base service quality ,and the seller’s optimal profit Π∗ will
increase (decrease) with the customers’ quality sensitivity β.The relationships between the optimal service quality, the seller’s optimal profit,
and the customers’ quality sensitivity can be clearly seen in Fig. 1. When the
8
= !−22 + s − s1 − 2"1 − 2 −2
customers care more about the quality ( > 0.24), the seller will set his/her service
quality higher than the base service quality. Moreover, the seller’s profit will
increase with when > 0.24.
1s*
o
ΔΠ*
0.8
o
0.5
0.6 0.495
s* o
0.4 0.49
0.2 0.485
0 0.48
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
β
Notes: The setting is = 0.6and = 0.05.
Fig. 1. Parametric analysis of ∗ and Π5∗ with respect to β
4. The group-buying model
In this model, we focus on an offline seller who has the option to partner with group-buying websites. The seller runs the online group-buying business and offline regular business simultaneously in the current period and runs only the offline business in the future period, which can be defined as the GS.
We assume that the seller does not change the regular offline price, meaning that this price is the same as the optimal regular price in the base model. This assumption is consistent with the findings of Bhardwaj and Sajeesh (2016), who argued that the Groupon website states that the online website’s advertised list price must be consistent with the price available on the local business’s price list, and the local business may be asked to provide written proof of the pricing. The seller must choose the online price and service quality depending on the group-buying website’s trading commission.
The advantage of a GS is that the group-buying website can help the seller attract uninformed customers who were not aware of the existence of the seller. The potential demand might increase in the future period for two reasons. The first is that the online group-buying channel brings uninformed customers who could be turned into informed
customers, so the potential customer population increases. The second reason is similar to what was in in the base model: potential demand increases due to
9
the word-of-mouth effect when service quality is set high. Potential demand plays a key role in our model when it comes to capturing the market dynamics influenced by service quality and the group-buying strategy.
The disadvantage of a GS is that some existing offline customers (informed customers) may resort to a group-buying website because of the discounted price after browsing online information (substitution effect). According to our analysis, this
behavior can affect the seller’s profit, as well as his/her group-buying decisions.
4.1 The group-buying model with substitution effect
In reality, the substitution effect is pervasive. There are many offline customers who could, for instance, resort to an online channel because of a discounted price. We introduce the following new notations that will be used in the following model:
6 online price of the service
s6 service quality when the seller joins the group-buying website7 substitution rate
Λ6 group buying potential service demand in the current period86 nominal group buying service demand in the current period89 actual offline demand86
9 actual group buying demand
Λ seller’s total potential demand in the future period
λ seller’s total demand in the future periodρ trading commission charged by the website
Π6 seller’s profit when he/she chooses to join the group-buying website
ΔΠ profit gap between the GS and OS
The substitution effect is illustrated in Fig. 2. The shaded area represents the substituted offline customers, which can be divided into two parts. The first part is the realized informed customers under regular selling price = 1/2 who switch to the online channel. The second part is the informed customers who would not buy under price = 1/2 but who will now purchase at the lower group-buying price 6. We neglect the deal-seeking behavior of unrealized informed customers, that is, the second part of the substituted customers in our mathematical model. It makes the following analysis more tractable without sacrificing any general managerial findings because this additional demand would not structurally alter the seller’s optimal
10
strategy. The substitution rate is the ratio of the substituted customer population to the entire informed customer population.
With the existence of the substitution effect, the offline demand and group-buying
demand can be described as 8 9 = 1 − 7λ = %=> and 869 = Λ6 − 6 + > . The
potential and actual demand in the future period will be Λ = 1 + Λ6 + ?s6 − s@?λ + λA
and λB=ΛB−5=12+ΛA+sA−s12+ΛA−A, respectively. The seller’s profitmaximization problem can be expressed as follows:
Maximize: Π6?6, A@ = 89 + ?6 − C@869 + 8 − A
1 2 − 7 1 7
= ! + Λ6 + ?A − s@ D + Λ6 − 6E" + ?6 − C@ FΛ6 − 6 + G − A (4)2 2 2 2
Subject to: 0 < 6 < 7HI J%
, Λ6K, (5)
0 < C <%
, (6)
0 <6 ≤ 1 (7)
Constraint (5) means that the online group-buying price is lower than the regular price, so the group-buying demand is positive. Constraint (6) ensures that the trading commission will be lower than the regular price. We can prove that Π6 is concave with both 6 and 6, thus giving Proposition 2, which describes the seller’s optimal decisions regarding online price and service quality.
869
Offline customer 89Group-buying customer
Realized informed customer λRealized uninformed
Unrealized informed
λ6customer customer 1 − λ
Fig. 2. Illustration of the substitution effect
Proposition 2: When a substitution effect exists, the seller’s optimal group-buying
price and service quality are 6∗
='LM>N?OPNQ@R=&)?%NOP@N'L&S
%*L=&)
andA∗ =
βM2−7+2?ΛA−C@−βR
, respectively. Correspondingly, the seller’s optimal profit is16η−2
)
) ) ) ) ) )
=>NUP %*(?UP=Q@
ΠT∗ = + +
=%*(&SN&N%*>(=>& ?UP=Q@N+(& S='=>(&SN+>(N%=>&
,+ +%*(=&) +%*(=&)
11
=&)UP=&VS
WX
N
and the profit gap between these two strategies is ΔΠ = ΠT∗ − Π∗ =
YZ[
++%*(=&)
) ) ) ) ) )
+(& S %*(?UP=Q@ N=%*(&SN&N%*>(=>& ?UP=Q@N'>(&SN+>(=%*>(N\(UP
+ .+%*(=&) +%*(=&)
According to the profit gap (ΔΠ) analysis, the seller’s optimal group-buying
strategies in different scenarios depend on the scale of the group-buying website and
the trading commission charged. The optimal strategies are summarized in Table 1.
Detailed derivations are provided in the Appendix.
From Table 1, we generate Theorem 2.
Table 1
The seller’s optimal strategy
C 0 < C ≤ C C_< C <1
0, 7ef 0, ΛT
2Λ6 b – OS7ef 0, Λ6 , Λ6
GS –/OSb
Λ6, +iGS GS
) ) ) ) )
=%*>(&S =`∆
Notes: ^^^^
%*>(N>& => & \(UP=%*(&SN&N%*>(=>&
,
= \( C_ = \( ,b
]6
) ) ) ) )
,
]6 =='>(N'(&SN>&=%*(Nc=> & N%*(N& =%*>(&SN\>(=%*(&S%*(=&
d = ?−47 − 647 −%*(128]A+647+87216−2
Theorem 2: When the group-buying website is relatively large (]6 > ^^^^]6), it is
optimal for the seller to choose a GS because it can always bring more profit. But
when7ef?0, ]gA@ ≤ ΛA ≤ ^]^^A, the seller will not choose a GS unless the website’scharged trading commission is relatively low C < \(UP=%*(&SN&)N%*>(=>&)=`∆.
\(
When Λ6 < 7ef?0, ]hA@, the seller will choose an OS.
Only when the website is relatively large can the seller be ensured of gaining more
profit by adopting a GS. If the group-buying website scale is small and the trading
commission charged is high, choosing an OS is more profitable for the seller. So when
choosing to join a group-buying website, the seller should try to collaborate with a more
mature website. If the website is new and has a small size of subscribers, the seller
should negotiate with the website for a lower trading commission.
12
]6 ββ <
=> β
Corollary 1: ^^^^ decreases with when '(S and increases with otherwise.From corollary 1, the threshold website scale decreases with the customers’ service
quality sensitivity when this value is relatively low. The seller could benefit from group-buying even when working with a small website. Moreover, as shown in Fig. 3,
when the substitution rate is relatively large (7 > 2 − 8 ]6
), ^^^^ will always decrease
with β.
We can obtain Theorem 3 by analyzing the seller’s optimal service quality.
Λ6 ≥
Q=N>&N%*(S
Theorem 3: If choosing a GS is a better strategy, then when , the&
seller will set his/her service quality higher than the base service quality; when
0 < Λ6 <
Q=N>&N%*(S
the seller will set his/her service quality lower than the base,&service quality.
Theorem 3 indicates that the seller will set the service quality higher than the base service quality when partnering with a large group-buying website. The reason is that larger group-buying websites can help the seller attract more uninformed customers and more potential customers in the future period. The total profit will be higher, even though the higher service quality will incur a higher cost.
Notes: The parameter setting is = 0.4and = 0. 3Fig. 3. Parametric analysis of ^]^^^6 to β
In the following example, let β = 0.6, 7 = 0.5, = conclusions can be drawn using other parameters that
0.8and = 0.1. Similar
Fig. 4
13
describes the seller’s optimal decision given the trading commission and website scale. The dash area is where the seller can enhance profits by choosing a GS. If the website scale Λ6 > 0.214, it is always optimal to join the group-buying website. However, if
0.17 < Λ6 ≤ 0.214 , only when the trading commission satisfies
) )
\(UP=%*(&SN&N%*>(=>& =`∆
C < C_ = \( will the seller join the group-buying website.Moreover, the dash area above the red line is where the seller chooses to set the service quality lower than the base service quality, which is defined as the low service-quality group-buying strategy (LGS). The dash area below the red line is where the seller chooses the high service-quality group-buying strategy (HGS).
Fig. 4. Seller’s optimal group-buying decision
The base service quality’s impact on the seller’s group-buying decision is summarized in Theorem 4.
]6 C_Theorem 4: ^^^^ decreases with the base service quality .decreases with when
'>(N>& ) ='> ) (=%*(U P
0 < ≤ '>(& and increases with otherwise.
The above theorem is explained in Fig. 5, where β = 0.6, 7 = 0.5, and = 0.1. As
shown in Fig. 5 (a),^]^^^6 decreases with the base service quality, meaning that it iseasier for the seller to adopt a GS when the base service quality increases. Fig. 5 (b) zooms in on the left bottom part of Fig. 5 (a), where C ≤ 0.16 and 0.15 < ]A ≤ 0.22.According to Fig. 5 (b), when the website’s scale is relatively large, C_will initially
increase with the base service quality. Thus, choosing a GS will be easier as the base
service quality increases because the seller can benefit from a GS even if the website
charges a higher commission. However, with the website scale decreasing to
14
0 < ]6 ≤
'>(N>& ) ='> ) (='>(&S
C_decreases with the base service quality. Thus, it is%*( ,
more unlikely for the seller to choose a GS because the base quality increases while
the base service quality is relatively low. This is because when the base service
quality increases, the seller will enhance his/her online price and decrease the
service quality, which will save on service cost, and the threshold website market
scale ^]^^^6 decreases. However, when the base service quality is relatively small
with the base service quality increasing, the customer loss effect will dominate the
service cost saving effect, which leads C_to decrease.
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.16
0.14
0.12
0.1
ρ0.08
0.06
0.04
0.02
0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32
0
0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22
Λg Λ g
(a) (b)— = 0.,4— = 0.,3— = 0.2
C_
Fig. 5. A comparison analysis of
]6
and^^^^ as changes
Theorem 5: If a GS is a better strategy for the seller, then the following occurs:
(a) The seller will improve the service quality compared to choosing an OS, that is, 6∗ > s ∗, while the service quality 6∗ decreases with the optimal online price
6∗;
(b) The seller’s service quality 6∗ decreases with substitution rate 7 and the trading commission C , but his/her online price 6∗ increases with the substitution rate 7 and the trading commission C. Moreover, 6∗ and 6∗ both increase with the website scale Λ6;(c) The seller’s maximum profit ΠT
∗ and the profit gap between the two mechanisms 7 and the trading commission C
butΔΠbothdecreasewiththesubstitutionrate
increase with the website scale Λ6.
From Theorem 5, the seller will improve his/her service quality if the seller adopts a GS because it can help the seller attract more customers in the future. However, if more offline existing customers go to the online group-buying channel, the seller’s
15
offline channel profit in the current period will drop. Thus, the seller will choose to decrease the service quality, which saves on costs to make up for the revenue loss. If the group-buying website charges a higher trading commission, the seller will increase his/her online price and decrease service quality because this helps to earn more profit from the group-buying channel, even though there will be fewer group-buying customers. Furthermore, in this circumstance, decreasing the service quality can save more cost and is more profitable for the seller than raising the service quality to attract more future customers. The seller’s total profit decreases with the trading commission because the seller will improve his/her online price, leading to fewer current and future customers.
4.2 Critical substitution rate value for the seller’s group-buying decision
In reality, the existing customers’ substitution effect is regarded as harmful to the GS because it will reduce the seller’s profit margin. According to the analysis in the above section, the major factors affecting the seller’s optimal decisions, ]6 and C, are both related to the substitution rate m. This section will focus on the impact of the value of m on the seller’s best strategy.
By analyzing the profit gap between these two strategies as a function of m, we establish Theorem 6.
Theorem 6:(a) Regardless of the substitution rate, choosing a GS is always a better strategy if
4 − \ ++
+ 8 − 12 + ℒ?]6@ ≥ 0 (8)16
holds, where ℒ?]6@ = 16?]6 − C@ + −16 + 16?]6 − C@ + 32 + 2]6.4 − + + 8 − 12 + ℒ?]@ < 0
(b) If \ &X 6 , t he sell er wi ll adopt a GS i f and
%*(
) q
0 ≤ 7 ≤ 7o =
=M'(=& ?UP=Q@N'(&S=%*(R=`p
9 = 16 − M4?]6 −only if , wherein'(
C−2]A+2C+8−8−32]A−16+16+2.
Note that function ℒ?]6@ is increasing in ]6 (see the Appendix). Inequality (8) is
more likely to hold with a higher ]6, which means that a larger group-buying websitecan guarantee that the seller gains more profits from the GS, even though the substitution rate is relatively high. Going with a GS is still a better choice when the substitution rate is lower than a critical value (7o), meaning that even condition (8) does not hold. As seen in Fig. 6, the shaded area is where the GS is better. If the
16
website scale is relatively large, adopting a GS is always a better choice, no matter the substitution rate. However, if condition (8) does not hold, the seller will benefit from a GS only when 7 < 7o. Thus, when the group-buying website is not mature and there are too many existing customers resorting to the online channel, it is not suitable for the seller to choose a GS. This result partly explains why some sellers lost money after joining the group-buying website.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
00 0.1 0.2 0.3 0.4 0. 5 0.6
Λg
Notes: The parameter setting is β = 0.5, = 0.5, = 0.1, andC = 0. 1
Fig. 6. Critical substitution rate value for the seller’s group-buying decision
4.3 Endogenous substitution rateIn the previous study, we regard the substitution rate as an exogenous variable.
However, the substitution effect depends heavily on customer choice, which is affected
by the regular and group-buying prices. Thus, in this section, we consider the
substitution rate to be a function of the online and offline price, that is, 7 = 1 − rrPs.
With a fixed regular price , the substitution rate will decrease with the group-buying price. The offline demand and group-buying demand can be described
as89 = 26λ = 6 and 869 = Λ6 − 6 + ?1 − 26@λ =
%
+ Λ6 − 26 .
Correspondingly, the seller’s future demand will be λ = Λ − = 1 + Λ6 +?s6 − s@ F% + Λ6 − 6G − % = % + Λ6 + ?s6 − s@ F% + Λ6 − 6G . The seller’s profit
maximization problem can be expressed as follows:
Maximize:Π6?6, 6@ = 8 9 + ?6 − C@869 + 8 − 6
=1
M1 + ?s6 − s@ + 2?6 − C@R D1
+ Λ6 − 6E + 6?1 − 6 + C@ − 6 (9)2 2
17
Subject to: 0 < 6 < 7HI J%
, Λ6K, (10)
0 < C <%
, (11)
0 <6 ≤ 1 (12)
We can prove that Π6 is jointly concave in 6 and 6 and establish the seller’soptimal group-buying decisions, which are stated in Proposition 3.
Proposition 3: When 7 = 1 −rP
, the seller’s optimal group-buying price and servicers
6∗
=
%*L?OPNQN%@=&)?%NOP@N'&,(
6∗
=
&M?\OP=QN%@=&,R
quality are and ,\(=&)
\(=&)
respectively. Correspondingly, the seller’s optimal profit is
Π6∗ =
+&)OP
)=+&
)QOPN+&
),)(=&
)Q=&
)=+'&,(OPN\&,Q(=%*&,(N%*(OP
)=*+Q(OPNt*(OPN*+Q
)(N+'( +\(=&
)
, and these two strategies’ profit gap is
ΔΠ =&
X=%*&
V,(N*+&
),)()N*+&
)(OP
)=*+&
)Q(OP=\&
)Q(=%*&
)(=u*'&,(
)OP
+*+(\(=&)
'&,Q()N+&,(
)N+(
)OP
)=%*Q(
)OPN+(
)OPN%*Q
)()=+(
)
(\(=&) .
According to the profit gap (ΔΠ) analysis, we can also obtain the seller’s optimal
group-buying strategies in different scenarios regarding the group-buying website’s
scale and trading commission charged. The main results are summarized in Table 2.
Table 2
The seller’s optimal strategy with endogenous substitution rate
C 0 < C ≤ C Cx< C <1
0, 7ef 0, ]A
2Λ6 b – OS7ef 0,]A ,ΛA
GS –/OSbΛA, +i
GS GS
vvvv ^
Notes:
Λ6 =*+&,(=+&)=%t(Nc∆^ ,
∆= 4 − 64s + 192 −3 + 32s − 32,
'&) − 16
\(OPN&)OPN&)=%*&,(=c py
, y = −32 − ?4Λ6 + 4Λ6 − 3 − 64sΛ6 + 32s + 192Λ6 −Cx = *+(
18
,b
=
+'&,()=t*()Nc \(=&)(&X=%*&V,(N*+&),)()Nz&)(=\z&,()N\z()
'(+(N&)32@ ]6
From Table 2, a GS is preferred when the website is relatively large (]6 > Λ6
vvvv).
When
7ef F0, ]6G ≤ Λ6 ≤ Λ6
the seller will not choose a GS unlessb vvvv ,
) )
cy
=%*&,(= p
ρ <\(OPN& OPN&
. The seller will always prefer to choose an OS when the*+(
website scale
Λ6 < 7ef F0, ]6G
b .
Theorem 7: If a GS is the better strategy, the seller will set his/her service quality
higher than the base service quality when Λ6 ≥%*(,N&Q=%
. Otherwise, the seller will\&set his/her service quality lower than the base service quality.
Theorem 7 is similar to Theorem 3, which indicates that the seller will set the service quality higher than the base service quality when cooperating with a large group-buying website.
According to Table 2 and Theorem 7, we obtain Fig. 7, which describes the seller’s optimal decisions given the trading commission and website scale. The dash area is where the seller can enhance profits by choosing a GS. When the website scaleΛ6 > 0.17, it is always profitable for the seller to choose a GS. When
0.17, a GS is preferred only if C < Cx =\(OPN&)OPN&)=%*&,(=cpy. The dash area below
*+(
the red line is where the seller will set his/her service quality higher than the base service quality (HGS). The dash area above the red line is where the seller prefers to set his/her service quality lower than the base service quality (LGS).
19
Notes: The parameter setting is β = 0.8, = 0.35, and = 0.23
Fig. 7. Seller’s optimal group-buying decision
Λ6 CxWe also further study the parametric analysis of vvvv and to the base service
β = 0.8and = 0.16 Λ6
quality . As shown in Fig. 8, where , vvvv decreases with thebase service quality, and Cxincreases with the base service quality, meaning that it
is easier for the seller to adopt a GS when the base service quality increases. This
conclusion only holds when the base service quality is relatively large and the
substitution rate is exogenous.
0.25
0.2
0.15
0.1
0.05
0
0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24
Λ g
— = 0.,2— = 0.15,— = 0.1
CxΛ6
andFig. 8. A comparison analysis of vvvv as
Moreover, when the seller chooses a GS, the seller will also improve service quality compared to choosing an OS. The optimal service quality decreases with the trading
20
commission and increases with the website’s scale. But the optimal online price increases with both these two parameters, which is the same as the situation where the customers’ substitution rate is exogenous, as shown in Theorem 5.
5. Numerical analysisIn this section, we conduct a numerical analysis and highlight the applications of
our findings. Our numerical analysis explains the relationships among the service quality, online price, and sellers’ optimal profit. Additionally, the comparison between the OS and GS enhances our understanding of the optimal decision, which could aid the service sellers’ decision making.
]6 C
In Theorem 4, we obtain the relationship among ^^^^, , and . According to ournumerical study (see Fig. 9), we find that a more interesting result comes from the
]6 C_ βand
7From Fig. 9(a), whenthe website scale isrelationship among ^^^^, , .
7ef?0, ]h@ ≤ Λ6 ≤ ]6 C_relatively small ( A ^^^^), first increases with , then decreases with
, and finally increases with as increases. From Fig. 9(b),]6
increases with the^^^^substitution rate, but C_decreases with the substitution rate. This means that if there are
a larger number of customers moving to the online channel, a GS is only a better option
when the website is more mature or the trading commission is lower. Thus, when many
offline customers buy through the group-buying website, the seller should try to
cooperate with a relatively mature website or negotiate with the website for a low
trading commission. Otherwise, it is better for the seller to choose an OS.
(a)7 = 0.6 (b)β = 0.4
Notes: The setting is = 0.13, 6Λ = 0.2, and = 0.15Fig. 9. Parametric analysis of ^]^^^6 and C_to β, 7 and α
As Theorem 5 states, if a GS is preferred, the seller will improve his/her service quality compared to adopting an OS. In Fig. 10, where = 0.1and = 0.,1 the
21
optimal online price 6∗, service quality A∗, optimal group-buying profit ΠT∗, and
profit gap ΔΠ have similar trends with 7 and ρ. The online price increases with the
substitution rate and trading commission. However, the service quality and group-
buying profits have the opposite trend with the online price. This is because if the
group-buying website increases its trading commission or there are more existing
offline customers resorting to the online website, the seller will increase the online
price and decrease the service quality for a higher online profit, thus saving more
service costs. However, a higher online price and lower service quality will decrease
the number of current and future customers. Therefore, the total group-buying profit
decreases with these two parameters. If we fix all factors other than Λ6, service
quality A∗ and online price 6∗ will both increase with it, which is shown in Fig.
10(c). Although the higher service quality will cost the seller more, its effect of
attracting more customers can offset the service costs, which leads to higher total
group-buying profit for the seller. From Fig. 10(d), where the parameters can
guarantee our constraints (0 < 6 < 7HI J% , Λ6K , 0 < 6 ≤ 1), the seller’s online price
will increase with when is relatively small and will decrease with when is relatively large. However, the optimal service quality always increases with , and the seller’s profit has the opposite trend with online price. Thus, when the customers care more about the service quality, the seller should improve his/her service quality; however, his/her profit will only increase when the customers’ quality sensitivity is sufficiently high.
0.4 0.6
0.3 0.5
p*
g
s*
g0.2 0.4
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5m
Πg
*
0.82
0.81
0.8
0.79
0.78
0.77
0.76
0.75
0.740
0.31
Πg*
0.3
ΔΠ
0.29
0.28
*g
0.27 Π
0.26
0.25
0.24
0.23
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5m
aβ = 0.3, C = 0.1andΛ6 = 0.5
22
0. 5 0.55
0.8 0.3
0.78 0.28
0. 4 0.5
0.76 0.26p
s
* g *g
Π Π
* g
*g
0.74 0.24
0. 3 0.45
0.72 0.22
pg*
*
sg*
Πg
0.7
Π
0. 2 0.4 0.2
0. 05 0.1 0.15 0.2 0.25 0.3 0.05 0.1 0.15 0.2 0.25 0.3
ρ ρ
|β = 0.3, 7 = 0.3andΛ6 = 0.5
0.5 0.65
0.45 0.6
0.4 0.55
0.35 0.5
0.3 0.45
0.25 0.4
0.2 0.35
0.15 pg* 0.3
s*
g
0.1 0.25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Λg
g
1.5 1
1 0.5
*g
*g
Π
Δ Π
0.5 0
Π g*
Π
0 -0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Λg
}β = 0.3, 7 = 0.3andρ = 0.1
0.4 1 0.35 0.5
p*
gs*
g
0.3 0
0
0.05
0.1
0.
15
0.2
0.25
0.3
0.35
β
g
s*
0.78
0.264
0.775
0.262
0.77
0.26
0.765
0.258
*g *g
Π Π
0.76 0.256
0.755 0.254
0.75 0.252
Πg*
0.745
ΔΠ
0.25
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35β
23
d7 = 0.3, ρ = 0.1andΛ6 = 0.5
Fig.10. Parametric analysis of A∗, 6∗, ΠT
∗, and ΔΠ to 7, ρ, Λ6, α, and β
From the above numerical analysis, the seller’s optimal decision and profit change with the parameters. In addition, when customers care more about the quality, the seller should improve his/her service quality, but his/her profits will
only increase when the customers’ quality sensitivity is sufficiently high.
6. ConclusionIn this paper, we study the seller’s joint service quality and pricing decision when
adopting a GS, which has recently been trending in the service industry. In the base model, we assume that the seller runs an offline business only, and we obtain the seller’s optimal regular price and service quality. In the group-buying model, we consider the seller having two optional strategies: a group-buying strategy (GS) and offline strategy (OS). We find that only when the website scale is sufficiently large can the seller be ensured to gain more profits after choosing a GS. If the group-buying website’s scale is relatively small or if the trading commission is sufficiently large, an OS is a better choice for the seller. A GS will bring in more profit because the base service quality increases when the base service quality is sufficiently large.
We also consider the substitution effect of the seller’s existing customers and find that when the website’s scale is relatively small and the substitution rate is sufficiently high, a GS can fail to bring in more profit compared to an OS. This explains why a sizable percentage of sellers (44.5%, according to Dolakia 2011) failed to benefit from a GS. Then, we extend the study to examine the endogenous substitution rate, depending on both regular and group-buying prices. We find similar conclusions to Section 4.1, except that it will be easier for the seller to adopt a GS when the base service quality increases. If a GS is the preferred strategy, the seller will set the service quality higher than the base service quality when cooperating with a large group-buying website. Moreover, compared to an OS, the seller will always improve his/her service quality when choosing a GS. As the trading commission charged by the website increases, the seller will also decrease service quality and increase online price.
In this study, to simplify the analysis, we use some restrictive assumptions. For instance, we assume that consumers are homogeneous in their base service quality. Although this is a rather common assumption in many other studies, cases where this
24
value is heterogeneous are worth further studying. Also, we treat the customer population as an aggregate demand and do not consider heterogeneous customers’ willingness to pay. It might also be interesting to check whether group-buying is a good competition strategy by including two competing sellers in a similar model. To capture the interactions between different agents, a dynamic game among sellers and the website is required, which deserves a separate study that we leave for future
research.
Acknowledgement
The authors thank the anonymous reviewers, the associate editor and the Editor in Chief for their helpful comments, which greatly improved this paper. This work was supported in part by the National Natural Science Foundation of China (71471062, 71101051, 71431004), the Shanghai Pujiang Program (17PJC023), the Shanghai Educational Development Foundation (11CG33) and the Fundamental Research Funds for the Central Universities.
25
References
Anand, K., Aron, R. 2003. Group-buying on the web: a comparison of price discovery mechanisms. Management Science, 49(11), 1546-1562.
Bhardwaj P, Sajeesh S. 2016. Strategic Revenue Sharing with Daily Deal Sites: A Competitive Analysis. Decision Sciences, Forthcoming.
Chiang, W. C., Cai, G., Xu, X., Chen, X. 2013. Service guarantee and optimal payout models. International Journal of Production Economics, 141(2), 519-528.
Chen, J., Chen, X., Song, X. 2002. Bidder’s strategy under Group-buying auction on the Internet. IEEE Transactions on Systems, Man and Cybernetics, Part A, 32(6), 680-690.
Chen, J., Chen, X., Kauffman, R. J., Song, X. 2009. Should we collude? Analyzing the benefits of bidder cooperation in online Group-buying auctions. Electronic Commerce Research and Applications, 8, 191-202.
Chinese e-commerce research center. 2010. Chinese network group-buying survey
in 2010. http://wenku.baidu.com/view/04fe0bfcfab069dc50220193.html.
Dholakia, U. 2012. How businesses fare with daily deals as they gain experience: A multi-time period study of daily deal performance. Working Paper. Rice University, Houston, USA.
Dholakia, U. 2011. How Businesses Fare with Daily Deals: A Multi-Site analysis of Groupon, Livingsocial, Opentable, Travelzoo, and Buywithme promotions. Working Paper. Rice University, Houston, USA.
Dholakia, U., Tsabar, G. 2011. A startup’s experience with running a Groupon promotion. Working Paper. Rice University, Houston, USA.
Galante, J. Sometimes Groupon coupons work too well. Bloomberg Businessweek, 2010, 33–34.
Gao, F., Chen, J. 2015. The Role of Discount Vouchers in Market with Customer Valuation Uncertainty. Production and Operation Management, 24(4), 665-679.
Geng, X., Tan, Y., Wei, L. 2016. How Add-on Pricing Interacts with Distribution Contracts. Available at SSRN: https://ssrn.com/abstract=2880474
Grönroos C. 1984. A service quality model and its marketing implications. European Journal of marketing, 18(4), 36-44.
Jiang, X., Deng, S. 2014. Optimal Srategy for selling on Group-buying Website.
Journal of Industrial Engineering and Management, 7(4), 770-784.Jing X, Xie J. 2011. Group buying: a new mechanism for selling through social
interactions. Management Science, 57(8), 1354-1372.26
Kagel, J., Levin, D. 2001. Behavior in multi-unit demand auctions: experiments with uniform price and dynamic Vickrey auctions. Econometrica, 69(2), 413-454.
Kannan, P. K., Li, H. 2017. Digital marketing: A framework, review and research agenda. International Journal of Research in Marketing, 34, 22-45.
Kauffman, R. J., Wang, B. 2002. Bid together, buy together: on the efficacy of group-buying business models in Internet-based selling. In P.B. Lowry, J.O. Cherrington, and R.R. Watson (eds.), Handbook of Electronic Commerce in Business and Society, CRC Press, Boca Raton, FL. 99-137.
Kauffman, R. J., Wang, B. 2001. New buyers’ arrival under dynamic pricing market
microstructure: the case of Group-buying discounts on the Internet. Journal of Management Information Systems, 18(2), 157-188.
Khouja, M., Wang, Y. 2010. The impact of digital channel distribution on the experience goods industry. European Journal of Operational Research, 207, 481-491.
Levitt, T. 1972. Production-line approach to service. Harvard business review, 50(5), 41-52.
Liu, C. H. S., Lee, T. 2016. Service quality and price perception of service: influence on word-of-mouth and revisit intention. Journal of Air Transport Management, 52, 42-54.
Nelson, P. 1970. Information and customer behavior. Journal of Political Economy, 78(2), 311-329.
Ni, G., Luo, L., Xu, Y., Xu, J., Dong, Y. 2015. Optimal decisions on group buying option with a posted retail price and heterogeneous demand. Electronic Commerce Research and Applications, 14(1), 23-33.
Oh, H., S.C. Parks. 1997. Customer Satisfaction and Service Quality: A Critical Review of the Literature and Research Implications for the Hospitality Industry. Hospitality Research Journal, 20(3), 35-64.
Tan, Y., Carrillo, J. E. 2017. Strategic analysis of the agency model for digital goods.
Production and Operations Management, 26(4), 724-741.Tan, Y., Carrillo, J. E., Cheng, H. K. 2016. The agency model for digital goods.
Decision Sciences, 47(4), 628-660.
Tsay, A.A., Agrawal, N., 2000. Channel dynamics under price and service competition.
Manufacturing and Service Operation Management, 2(4), 372-391.
Tuan 800. 2015. Chinese group-buying statistical report in 2014.http://zixun.tuan800.com/a/tuangoushujubaogao/20150122/50434.html.
27
Van Horn, T., Gustafsson, N. 2002. Demand aggregation through online buying groups.U.S. Patent 6047266, United States Patent Office, Washington, DC.
Yen, H.R., Gwinner, K.P., Su, W., 2004. The impact of customer participation and service expectation on locus attributions following service failure. International Journal of Service Industry Management, 15(1), 7-26.
Zhang, M., Huang, L., & Wang, Z. H. A. G. 2015. E-service quality perceptions: an empirical analysis of the chinese e-retailing industry. Total Quality Management & Business Excellence, 26(12), 1357-1372.
Zhang G, Shang J, Yildirim P. 2016. Optimal pricing for group buying with network effects. Omega, 63, 69-82.
Zhao M, Wang Y, Gan X. 2014. Signalling effect of daily deal promotion for a start-up service provider. Journal of the Operational Research Society, 23(7), 25-39.
28
Appendix:
1. Proof of Proposition 1.
−22 + s − s 1 − 2The Hessian Matrix ofΠ
is= ! "
. As we1 − 2 −2
mentioned, λ = 1 + s − s1 − ≥ 0, so1 + s − s ≥ 0 and 2 + s − s ≥ 1,then the first order derivative −22 + s − s < 0.
so 42 + s − s −Since 42 + s − s ≥ 4 and 1 − 2 ≤ ,
1 − 2 ≥ 4 − . If 4 > , then 42 + s − s − 1 − 2 > 0 , which
means that the Hessian Matrix is semi-definite. Then, solving the first-order
conditions, we can get: ∗ = %,s∗ = '(&,Π5∗ = % + *+(
&) − &,+.
2. Proof of Theorem 1.
When s ∗ = '(& > s,we can get > 8s. Moreover, solving the first order of
optimal profit, we can get~•s∗
=&
−,
. When~•s∗
> 0 , > 8s . This~& \( + ~&
establishes that when > 8s, the service quality s ∗ will be higher than the base
service qualityΠ
∗ will increase with the customers’, and the seller’s optimal profit
sensitivity to quality .3. Proof of Proposition 2.
Solving the first order conditions of Π6 , we can get 6 =?OPNQ@=&OP?SP=,@ ，+
&M%N?OP=rP@R
6 = . Then, substituting 6 into 6, we can get the optimal group-buying'(
price and service quality, 6 ∗
='LM>N?OPNQ@R=&)?%NOP@N'L&S
%*L=&)
and 6∗ =
M=>N?OP=Q@=SR
, respectively. Then we can get the optimal profit%*L=&)
)
) ) ) ) ) )
=>NUP %*(?UP=Q@
ΠT∗ = + +
=%*(&SN&N%*>(=>& ?UP=Q@N+(& S='=>(&SN+>(N%=>&
.+ +%*(=&) +%*(=&)
Correspondingly, the profit gap between these two strategies is ΔΠ = ΠT∗ − Π∗ =
=&)UP=&VSWX
N ) )
YZ[ +(& S
+ ++%*(=&) +%*(=&)
) ) ) )
%*(?UP=Q@ N=%*(&SN&N%*>(=>& ?UP=Q@N'>(&SN+>(=%*>(N\(UP
.+%*(=&)
4. Proof of Theorem 2.
When ∆Π > 0,16?Λ6 − C@ + −16s + 2 + 167 − 27?Λ6 − C@ + 4s + 87s + 47 −
29
167 + 32Λ6 − 2Λ6 − \s + %*(&X > 0.
Then, assume that Λ6 − C = f, f ∈ FΛ6 − % , Λ6G.
∆Π = 16f2 + −16s+ 22 + 167 − 272f + 42s2+ 87s+ 472 − 167 + 32ΛA − 22ΛA
− 3s+ 4
16
∆= −16s + 2 + 167 − 27
− 64 •4s + 87s + 47 − 167 + 32Λ6 − 2Λ6 − \s + 16+‚
= ?−47 − 647s − 128Λ6 + 647 + 87@16η −
When ∆< 0, −47 − 647s − 128Λ6 + 647 + 87 < 0.
When Λ6 >%*>(N>&)=>)&)=%*>(&,
，∆Π > 0. Therefore, joining the group-buying\(
website can make more profit for the seller. When Λ6 ≤%*>(N>&)=>)&)=%*>(&,
,∆≥ 0.\(
Solving ∆Πf = 0, we can get two solutions:
f = 16s − 2 − 167 + 27 − ` ∆ %32
f = 16s − 2 − 167 + 27 + ` ∆
32
The symmetry axis of ∆Πfis%*(&,=&)=%*>(N>&)
.\(
~ƥ ='(M>N?OP=Q@R=%=>&)N'(&S
= = −89 < 0, which means that ∆Π increases with f.~Q %*L=&)
Therefore,116s − 2 − 167 + 27
< Λ6 −32 2
− 1616s − 2 − 167 + 27<
32Λ6
32 32
32Λ6 − 16 − 16s + 2 + 167 − 27> 0
32
32Λ6 > 0− 16 − 16s + 2 + 167 − 27
32Λ6 − 16s + 2 + 167 − 27> 0
Then we can get f <%*(&,=&)=%*>(N>&)N` ∆
, which means that when\(
\(OP=%*(&,N&)N%*>(=>&)=`
ρ >∆
, it is not optimal for the seller to join the\(
\(OP=%*(&,N&)N%*>(=>&)=`
group-buying website. However, when ρ ≤∆
, joining the\(
group-buying website can bring more profit for the seller.In the following, we assume
30
%*>(N>&)=>)&)=%*>(&, ^^^^，\( = Λ6
32Λ6 − 16s + 2 + 167 − 27 − `= C_
∆
32%
1ƒC_ 32 − M?−47 − 647s − 128Λ6 + 647 + 87@16η − R= 16η − −128
= 2 32ƒΛ6 %
=32 + 6416η − M?−47 − 647s − 128Λ6 + 647 + 87@16η − R=
> 032
%*>(N>&)=>)&)=%*>(&,
Therefore, we can get that C_increases with Λ6 when Λ6 ∈0, .\(
%
Solving C_ = 0and C_ = , we can get
b−87 + 8s+ 72 − 16 + c
=
−722 + 16 + 2 − 167s+ 327 − 16s16 − 2
]6 16
b9= −8 + 8s− 87 + 72 + c −72
2 − 16s+ 327 − 167s+ 216 − 2
]6 ]6 < ]6 16
and b b9.However, we still can’t determine the magnitude relationship among ]b6,]hA
′, 0 and ^]^^^6.
Then, the problem can be divided into these three scenarios:
1) b b9 ^^^^
]6 < ]6 ≤ ]6
b 9 ^^^^when b0 < ]6 < ]6 ≤ ]6
Λ6 … < † ≤
‡ˆ‰Š‹ − Œ•‰Ž•+ ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ ‡ˆ‰Š‹− Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ Œ
< † < ˆ‡ˆ‰ ‡ˆ‰
ΛT
–[0,b) OS
ΛT, ΛT
b b9GS OS
ΛT , Λ6
GS –b9
Λ6 , +i GS GS
when b b9 ^^^^]6 ≤ 0 < ]6 ≤ ]6
Λ6
‡ˆ‰Š‹ − Œ•‰Ž•+ ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ ‡ˆ‰Š‹ − Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ Œ
… < † ≤ < † < ˆ‡ˆ‰ ‡ˆ‰
ΛT
[0,b 9) GS OS
ΛT , Λ6
GS –b9
Λ6 , +i GS GS
when b b 9 ^^^^]6 < ]6 ≤ 0 ≤ ]6
Λ6
‡ˆ‰Š‹ − Œ•‰Ž•+ ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ ‡ˆ‰Š‹ − Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ Œ
… < † ≤ < † < ˆ‡ˆ‰ ‡ˆ‰
[0, Λ6 ] GS –
Λ6 , +i GS GS
2) A ^^^^ A′
]h ≤ Λ6 < ]h
b9when b ^^^^
0 < ]6 ≤ Λ6 < ]631
Λ6
‡ˆ‰Š‹ − Œ•‰Ž• + ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ ‡ˆ‰Š‹− Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ Œ
… < † ≤ ‡ˆ‰ ‡ˆ‰ < † < ˆ
ΛT
[0, b) – OS
ΛT ,Λ6
GS OSb
Λ6 , +i GS GS
when b ^^^^ b9
]6< 0 ≤ ]6 < ]6
Λ6
‡ˆ‰Š‹ − Œ•‰Ž•+ ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ ‡ˆ‰Š‹ − Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ Œ
… < † ≤ < † < ˆ‡ˆ‰ ‡ˆ‰
[0, Λ6 GS OS
Λ6 , +i GS GS
3) ^^^^ b b9
]6 < ]6 < ]6
Λ6 … < † ≤
‡ˆ‰Š‹ − Œ•‰Ž•+ ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ ‡ˆ‰Š‹ − Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘ Œ
< † < ˆ‡ˆ‰ ‡ˆ‰
[0,Λ6 – OS
Λ6 , +i GS GS
Summarizing these three scenarios, we can get
Λ6
… < † ≤ ‡ˆ‰Š‹ − Œ•‰Ž•+ ˆŽ ˆ + Œ••‰ − ˆ•Ž ˆ − ‘ ‡ˆ‰Š‹ − Œ•‰Ž• +ˆŽˆ + Œ••‰ − ˆ•Žˆ − ‘
< † <
Œ
‡ˆ‰ ‡ˆ‰ ˆ
7ef 0, ΛT
[0, b – OS
7ef 0, ΛT, Λ6
GS –/OSb
Λ6 , +i GS GS
5. Proof of Corollary 1.^^^^
)
~UP
=
+>&=> &=%*>(S
.~“^^^^
\(
When
~UP
< 0, we can get~“
^^^^
'(S=>≥ 1, which allows us to get
~UP
≥ 0.~“
6. Proof of Theorem 3.
When6
∗=
&M=>N?OP=Q@=&SR
, we can get&M=>N?OP=Q@R
. When%*L=&) ≥ ≤ %*(
6 ∗ = &M=>N?OP=Q@=&SR , we can get &M=>N?OP=Q@R .Since the optimal service
%*L=&) < > %*(
quality 0 < 6∗ ≤ 1 , so M2 − 7 + 2?Λ6 − C@R < 16η , then&M=>N?OP=Q@R
< 1 . Since%*(
Λ6 > 0, then we can get&M=>N?OP=Q@R
>&=>=Q
> 0.Thus, we can know 0 <%*( %*(&M=>N?O P =Q@R
%*(Q=N>&N%*(S &M=>N?O P =Q@R
< 1 . Also, we can get Λ6 ≥ if ≤ %*( .&
Therefore, when Λ6 ≥
Q=N>&N%*(S
, the seller will set his/her service quality higher&
than the base service quality; when 0 < ΛA <2C−2+7+16
, the seller’s service2
32
quality will be lower than the base service quality.
7. Proof of Theorem 4.%*>(N>&)=>)&)=%*>(&,
^^^^, so obviously, we can get that ^^^^ decreases withs
.
\( = Λ6 Λ6
1
%
ƒC_ −16 − M?−47 − 647s − 128Λ6 + 647 + 87@16η − R= 16η − −647
= 2 32ƒs
%
−16 + 32716η − M?−47
=
− 647s − 128Λ6 + 647 + 87@16η − R=
32
When ~Q~,
o > 0, we can get
−16 + 32716η − M?−47 − 647s − 128Λ6 + 647 + 87@16η − R=% > 0
%
> 1632716η − M?−47 − 647s − 128Λ6 + 647 + 87@16η − R=
s >*+>(N'>&
)=*+>
)(=%'(OP
='>(N>&
)='>
)(=%*(OP
.*+>(& '>(&
'>(N>& ) ='> ) (=%*(U P ~Qo
Therefore, we can get that when > '>(& , > 0, C_increases~,
with s. When s ≤'>(N>&)='>)(=%*(UP
,
~Qo
≤ 0，C_decreases with s.'>(& ~,
8. Proof of Theorem 5.As mentioned before, we can get:
s = M1 + 2?Λ 6 − 6 @R > ∗ =
68”8s ∗ = M2 − 7 + 2?Λ 6 − C@ − R
616η −
6∗
=8ηM7 + 2?Λ6 + C@R − ?1 + 2Λ6@ + 8η
216η −)
) ) ) ) ) )
=>NUP %*(?UP=Q@
ΠT∗ = + +
=%*(&SN&N%*>(=>& ?UP=Q@N+(& S='=>(&SN+>(N%=>&
+ +%*(=&) +%*(=&)
ΔΠ =W
X
=&)UP=&VS N ) )
YZ[ +(& S
+ ++%*(=&) +%*(=&)
) ) ) )%*(?UP=Q@ N=%*(&SN&N%*>(=>& ?UP=Q@N'>(&SN+>(=%*>(N\(UP .
+%*(=&)
Therefore, solving the first-order conditions~,P∗
==&
< 0， ~rP ∗
='L
> 0.~> %*L=&
)
~>)
%*L=&
~,P∗
==&
< 0,~rP∗
=%*L
> 0
~Q
)
~Q
)
%*L=& %*L=&
33
~,P∗
=&
> 0,~rP∗
=%*L=&)
> 0~OP %*L=&
)
~OP
)
∗ 1
%*L=&
1ƒΠT ƒ∆Π 1 1
= = − + ?6∗ − C@ = D6 − C − E < 0ƒ7 ƒ7 4 2 2 2
ƒΠT ∗ ƒ∆Π 7
= = − FΛ6 − 6∗ + G < 0ƒC∗
ƒ7 2ƒΠT ƒ∆Π 1 32?]6 − C@ −16 + 2+ 167 − 27
= = + +ƒΛ6 ƒΛ6 2 416 − 416 −32 − 2 + 32?]6 − C@ − 16 + 2+ 167 − 27
= 416 −
=32 + 32?]6 − C@ − 16 + 167 − 27
416 −
1
=
161 − + 32 F]6 + 2 − CG + 2716 −
> 0416 −
9. Proof of Theorem 6.
As Theorem 4 mentioned,~••
∗
< 0, which means that ΠT∗ decreases with 7.~>
Therefore, we can get that ∆Π decreases with 7.
\ +
−2 ]6 − +
16 4
ΔΠ 7 = 1 = +416 − 416 −16?]6 − C@ + 8 + 4 − 16 + 32]
+6
416 −?]6 − C@−16 + 2+ 16 − 2
+ 416 −
ΔΠ7 = 1 ≥ 0&
X
+ 8 − 12 + 16?]6 − C@ + −16 +4 − +
When , \
%*(
16]A−C+32+22]A≥0. Assuming ℒ]A=16]A−”2+−16+16]A−C+32+22]A,&X
+ 8 − 12 + ?ℒ]6@ ≥ 0 ΔΠ7 = 1 ≥ 04 − +
we can get that if \
%*(
, , which
means that joining the group-buying website can always bring more profit for the seller. However, if ΔΠ7 = 1 < 0, then solving ΔΠ7 = 0, we can get the answer
) q
7o = =M'(=& ?UP=Q@N'(&S=%*(R=`p
, where9 = 16 − M4?]6 − C@?−]6 + C +'(
8−8−32]A−16+16”+2. Thus, when 0≤7≤7, ΔΠ≥0, the seller should join the group-buying
website; when 7o < 7 ≤ 1,ΔΠ < 0, the seller should not join the group-buying website.
ƒℒ?]6@
ƒ]6 = 32?]6 − C@ − 16 + 16 + 32 + 2
34
= 32]6 + 16 − 32C + 16 − 16 + 16 + 2
= 32]6 + 161 − 2C + 161 − + 16 + 2 > 0 ℒ?]6@ increases with ]6.So,wecangetthat
10. Proof of Proposition 3.
Solving the first order conditions of Π6 , we can get 6 =?UPNQ@N&?S=SP@N
,'
6 =&M%N?OP=rP@R
. Then, substituting 6 into 6, we can get the optimal group-buying'(
price and service quality, 6∗
=
%*L?OPNQN%@=&)?%NOP@N'&,(
and 6∗
=
M2?3ΛA−2C+1@−sR
,\(=&) 32−2
respectively. Then, we can get the optimal profit
Π6∗ =
+&)OP)=+&)QOPN+&),)(=&)Q=&)=+'&,(OPN\&,Q(=%*&,(N%*(OP
)=*+Q(OPNt*(OPN*+Q)(N+'(
.+\(=&)
Correspondingly, the profit gap between these two strategies is ΔΠ = ΠT∗ − Π∗ =
&X
=%*&V
,(N*+&),)()N*+&
)(OP
)=*+&
)Q(OP=\&
)Q(=%*&
)(=u*'&,(
)OP
+*+(\(=&)
'&,Q()N+&,(
)N+(
)OP
)=%*Q(
)OPN+(
)OPN%*Q
)()=+(
)
(\(=&) .
11. Proof of Table 2.When ∆Π > 0, we can get10242C2 + ?512s2 − 642ΛA − 322 − 10242ΛA@C +
+ − 16\s + 64s + 64Λ6 − 16 − 768sΛ6 + 256s + 256Λ6 + 1536 Λ6 − 256 > 0.
Then, assuming+ + − 16\s +
thatFρ = 1024C + ?512s − 64Λ6 − 32 − 1024Λ6@C64s + 64Λ6 − 16 − 768sΛ6 + 256s + 256 Λ6 + 1536 Λ6 − 256 ,
we can get y = −32 − ?4Λ6 + 4Λ6− 3 − 64sΛ6 + 32s + 192Λ6 −
y vvvv ^
32@. If , which means that
Λ6 ≥ Λ6 =*+&,(=+&)=%t(Nc∆^ and
∆= 4 − 64s +< 0 '&)
192 − 16−3 + 32s − 32 , Fρ > 0 and the seller can always enhance
0 < ΛA vvv
his/her profit by choosing a GS. However, when< Λ
A , we can get two
) )
cy
) )
cy
OPN& =%*&,(= p =%*&,(N p
solutions after solving Fρ = 0:\(OPN&
,\(OPN& OPN&
. Since*+(
) )
*+(
cy
~p• =%*&,(= p= −86 9 < 0, we can get that, when ρ ≤ Cv =\(OPN& OPN& joining the,
~Q *+(group-buying website can bring more profit for the seller. When
) )
cy
=%*&,(= p
ρ > Cv =
\(OPN& OPN&
it is not optimal for the seller to join the,*+(
35
1
group-buying website. Solving Cx = 0 and Cx = , we can get
2
2 2 2 4 3 2 2 2 2 2 2
G
g =
48s −96 +—32− F −16 s+64 s +20−320s +320
g =84+
]yA and ]yA ′2
2 2 2 2 4 3 2 2 2 2 2
G2+48s −64 +—32− F −16 s+64 s −256s +128
where ]yA ]yA ′ . After some,2
84+ g < garithmetical operations like the proof of Proposition 2, we can get the following table:
C 0 < C ≤ C Cx< C <1
0, 7ef 0, ]A
2Λ6 b – OS7ef 0,]A ,ΛA
GS –/OSbΛA, +i
GS GS.
M1 + 2?Λ6 − 6@R
6 = > ∗ =8 8~rP
∗\( ~rP
∗ %*L=&)
= > 0; = > 0~Q \(=&)~OP \(=&)
~SP∗
=
=+&
< 0;
~SP∗
=
*&
~Q \(=&)~OP \(=&)
Therefore, when the seller chooses a GS, the seller will also improve service quality compared to choosing an OS. In addition, the optimal service quality decreases with the trading commission and increases with the website scale. However, the optimal online price increases with both of these two parameters.
12. Proof of Theorem 7:
Let 6∗ =
&M?\OP=QN%@=&,R
≥ s, we have Λ6 ≥
%*(,N&Q=%
. Thus, the seller will\(=&)
\&set his/her service quality higher than the base service quality when the website scale is relatively large. Otherwise, the seller will set his/her service quality lower than the base service quality.
36
Highlights
The objective of this research is to examine the role of quality in a service seller’s group-buying strategy, i.e. how the seller should manipulate its service quality to align with its channel strategy.
The study compares two strategies, offline strategy and group-buying strategy, to investigate the impact of substitution effect and other critical parameters on the optimal decisions.
We show that the service quality should be enhanced to cooperate with the online group buying strategy for its success.
The website scale and trading commission charged by the website are shown to be two major issues to determine whether group-buying will be a better option.
37