Intertemporal Segmentation via Flexible-Duration …individual.utoronto.ca/minghu/download/flexible_group...Intertemporal Segmentation via Flexible-Duration Group Buying Ming Hu, a

MANUFACTURING & SERVICE OPERATIONS MANAGEMENTArticles in Advance, pp. 1–18

http://pubsonline.informs.org/journal/msom ISSN 1523-4614 (print), ISSN 1526-5498 (online)

Intertemporal Segmentation via Flexible-Duration Group BuyingMing Hu,a Jingchen Liu,b Xin Zhaic

aRotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada; b School of Business, Nanjing University,Nanjing 210093, China; cGuanghua School of Management, Peking University, Beijing 100871, ChinaContact: [email protected], https://orcid.org/0000-0003-0900-7631 (MH); [email protected],

https://orcid.org/0000-0002-1219-8873 (JL); [email protected], https://orcid.org/0000-0002-0401-6670 (XZ)

Received: September 13, 2018Revised: June 11, 2019; September 24, 2019;December 3, 2019Accepted: December 4, 2019Published Online in Articles in Advance:April 23, 2020

https://doi.org/10.1287/msom.2020.0869

Copyright: © 2020 INFORMS

Abstract. Problem definition: We study a special form of group buying: the group buyingsucceeds only if the number of sign-ups reaches a preset threshold, with no durationconstraint. Customers with heterogeneous valuations arrive sequentially and decide be-tween signing up for the group buying or purchasing a regular product. To decide whetherto join the group buying, customers need to estimate their expected waiting time, whichvaries depending on the cumulative sign-ups by the time of their arrival. The firm decides onthe prices for the group-buying product and regular product, with the product quality levelsand group-buying size exogenously determined.Academic/practical relevance: This type ofgroup buying is often adopted for a special edition of the product and offered alongside aconstantly available regular product. Methodology: We study the product line design withthe group-buying sign-up behavior of customers characterized by the rational expectationsequilibrium in a random pledging process. Results: We show that group buying withflexible duration can result in intertemporal customer segmentation, as different segmentsmight be admitted at different times in the dynamic sign-up process. Such intertemporalsegmentation is a natural discrimination scheme and has nontrivial implications. First, theefficiency loss due to waiting for enough sign-ups may decrease when a larger batch size isrequired for economic production. Second, as valuation heterogeneity in the market in-creases, the firm may not always benefit from offering group buying along with the regularproduct. Third, group buying can achieve a win-win-win situation for both high-end and low-end customers as well as the firm.Managerial implications: In addition to demonstrating theprofitability of flexible-duration group buying, we show that the firm can strengthen itsprofitability by contingently setting prices or concealing sign-up information in group buying.We also confirm the robustness of our main insights by considering customers’ heterogeneouspatience levels and horizontally differentiated products, among other factors.

Funding: This work was supported by the Natural Sciences and Engineering Research Council ofCanada [Grant RGPIN-2015-06757], the National Natural Science Foundation of China [Grants71772006 and 71825007], and the MOE (Ministry of Education in China) Project of Humanities andSocial Sciences [Grant 20YJC630084].

Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2020.0869.

Keywords: group buying • flexible duration • intertemporal segmentation • price discrimination

1. Introduction1.1. MotivationBeauty companies used to adhere to a strict “one in,one out” policy, inwhich slow-moving productswerediscontinued tomake room for newones (Boncompagni2012). Due to the limited shelf space available, firmscould only offer their bread-and-butter products.However, thanks to social network platforms andonline forums, beauty companies can now offer special-edition products online, such as discontinued hot prod-ucts, through a special program. For example, in Feb-ruary 2012, Bobbi Brown and MAC Cosmetics, twobrands owned by the Estée Lauder Companies, rantwo Facebook campaigns called “Bobbi Brings Back:Lip Color” and “MAC by Request,” respectively,asking their fans to sign up for discontinued lipsticks

(Boncompagni 2012, Gattis 2012). Indeed, firms canonly make profits with reissues when the number ofsign-ups reaches a specific threshold because cos-metics (e.g., lipsticks) are always produced in batchesto benefit from economies of scale (Brumberg 1986).Without these online campaigns, firmswould lose theopportunity to satisfy customers who desperatelybrowse the Internet for their favorite discontinuedcosmetics andmay have to settle for bread-and-butterproducts instead.The cosmetic industry is not alone. First, many

tourist platforms (e.g., Ctrip, the counterpart of Expediain China) offer customized and private tour routes thatdiffer fromstandardones.However, these special routeswill only materialize if the number of sign-ups exceedsa certain threshold, whereas there is no threshold for

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standard routes. Second, as an emerging practice, on-demand transportation (e.g., Bus.com, Uber Central,Call-n-Ride) will be readily available if there are enoughonline requests. For example, Bus.com offers groupbuying of bus services with a customizable experienceor for a cheaper price than current routes. Third, manyplatforms in China provide flexible-duration group-buying opportunities for food, apparel, electronics,and hotel reservations. For example, group buying onPinduoduo.com has no preset deadline (Wong 2018),unlike the oncepopular group-buyingwebsiteGrouponin its heyday of “a deal a day” (Girotra et al. 2013),or the crowdfunding website Kickstarter. In the flexible-duration cases, group buying is only unlockedwhen the number of sign-ups reaches a threshold.Thus, customers who sign up are uncertain abouthow long they are going to wait, whereas they haveimmediate access to the regular products or ser-vices from the same vendor through other online oroffline channels.

Group buying with a deadline is successful if andonly if the number of sign-ups exceeds a predeterminedthreshold before a specific date, that is, the duration isfixed (see, e.g., Hu et al. 2013, Liu and Tunca 2019).Given the relatively short and fixed duration of thecampaign, for example, one day in the case of Grouponand LivingSocial’s “a deal a day,” waiting times tendto be the same for all pledgers. In contrast, groupbuying with flexible duration has a predeterminedgoal, but its duration is uncertain. Customers facedifferent waiting costs depending on when they signup, which cannot be ignored because of the relativelylong and random waiting times. This difference be-tween group buying with and without a deadline issimilar to that between auctions with and without adeadline (Roth and Ockenfels 2002).

Although group buying with flexible duration iscommon, it is still unclear whether such a strategyeffectively enhances the firm’s profitability, because itcan cannibalize the sales of a regular product. Even ifflexible-duration group buying is profitable, it is notclear how it should be designed and how it affectscustomers. In the base model, we consider groupbuying for a premium product. By and large, offeringflexible-duration group buying for a premium special-edition product along with the regular product can bedouble-edged. On the positive side, it exploits customerpreferences and allows for market expansion or bettermarket segmentation. On the negative side, groupbuying with flexible duration inevitably means thatcustomers, who might otherwise purchase the regularproduct, have to wait for the threshold to be met,resulting in efficiency loss. If the special-edition productis in low demand, gathering enough sign-ups can take along time. To shorten thewait, thefirmmaypromote thegroup-buying product to a larger market (beyond the

diehards expected to by the special edition), butmakingthe premium product available to regular customerscan result in a lower profit margin and cannibalizationof the regular market. Thus, it is crucial to understandthe optimal design of group buying with flexible du-ration, which is a nontrivial task due to the interactionsjust mentioned.

1.2. ResultsIn view of these difficulties, we build a stylizedmodelto understand the mechanism behind flexible-durationgroup buying. Two segments of customers with het-erogeneous valuations arrive sequentially following aPoisson process. Upon arrival, customers can see thecumulative number of sign-ups up to their arrival time.Each customer decides between buying the regularproduct immediately and signing up for group buyingof the special-edition product. Depending on whencustomers join, signing up for group buying has dif-ferent waiting costs proportional to waiting times. Forall customers, the time they have to wait for enoughsign-ups is uncertain and factors into their decisionmaking. In anticipation of the rational sign-up behaviorof subsequent arrivals, customers make a rational ex-pectation of their own waiting time. Anticipatingcustomers’ sign-up behavior, the firm determineswhether to offer group buying and how to optimallydesign it in terms of pricing andmarket segmentation.We show that answers to these questions criticallydepend on the interaction of supply and demand, inparticular the batch size needed for economic pro-duction on the supply side and market valuationheterogeneity on the demand side.In flexible-duration group buying, customers may

wait a long time for the threshold to be met, partic-ularly when the batch size for economic production islarge. Hence, the loss of efficiency due to waitingcannot be assumed away and may need to be com-pensated for by the firm in its pricing. Tomitigate thisefficiency loss, the firmmay invite different segmentsof customers to sign up at different times during thedynamic pledging process, which we refer to asintertemporal customer segmentation. As an impor-tant feature of flexible-duration group buying whencustomer waiting cost is considered, this intertempo-ral segmentation has the following implications.First, the loss of efficiency due to waiting for

enough sign-ups may decrease in the group-buyingthreshold that is assumed to be the batch size foreconomic production. This is perhaps surprising asone may expect the opposite. When the batch size issmall, group buying optimally targets only the high-end segment of themarket. However, as the batch sizeincreases, the firm may be forced to also target thelow-end segment by reducing the price, with onlyhigh-value customers signing up at the early stage

Hu, Liu, and Zhai: Intertemporal Segmentation via Flexible-Duration Group Buying2 Manufacturing & Service Operations Management, Articles in Advance, pp. 1–18, © 2020 INFORMS

and both segments admitted at the later stage of thegroup-buying process. Indeed, the pledging processcan be accelerated by the participation of both seg-ments. Therefore, bothwaiting times and efficiency losscan be reduced when the batch size becomes larger.

Second, as the valuation heterogeneity increases,the firm may not always want to offer group buyingin addition to the regular product, though this iscounterintuitive. As the valuation heterogeneity in-creases, common intuition would suggest that thefirm has more incentive to resort to group buying,with the regular product and a premium product forgroup buying targeted at different segments. How-ever, we show that the profitability of group buying ismoderated by the batch size for economic production.Specifically, when the batch size is in an intermediaterange, as valuation heterogeneity increases, the firm’soptimal strategy goes from no group buying, to groupbuying, to no group buying and finally back to groupbuying. This nonmonotonic behavior is driven bythe possible intertemporal segmentation enabled bygroup buying. When both the batch size and valua-tion heterogeneity are in an intermediate range, groupbuying allows the firm to intertemporally segmentcustomers, but as valuation heterogeneity further in-creases, the firm may find it optimal to serve the high-end customers with the regular product (not servinglow-end customers) and eliminate the offering of groupbuying all together. This is because group buying re-quires customer waiting, which needs to be compen-sated for by a lower price, and inviting both segments tojoin at the late pledging process canmake it necessary tolower the price even more. But when the valuationheterogeneity is sufficiently large, group buying canbecome profitable again, as now the group-buyingcampaign targets only the high-end customers.

Third, every stakeholder can benefit from the group-buying offer. In particular, group buying can increasethe firm’s profitability when the inventory holdingcost is high enough. Besides, its introduction alwaysleads to an increase in the total sales volume. Fur-thermore, imagine that the group-buying product isalways offered as the regular product, that is, bothproducts are regularly offered and thus availablewithout any wait. Despite this, customers will stillprefer the flexible-duration group buying alongsidethe regular product, because the high-end segment isalways strictly better off by paying less and obtains alarger surplus, and the low-end segment is alwaysweakly better off, thanks to the intertemporal cus-tomer segmentation achieved. Specifically, group buy-ing enables low-end customers to jump on the band-wagon to buy the premium product (i.e., intertemporalsegmentation), which would not be affordable other-wise.Moreover, theparticipation of the low-end segment

benefits high-end customers by shortening their wait-ing times.We then extend our base model in several directions.

First,we allow thefirm to charge state-dependent pricesfor the group-buying product (referred to as contingentpricing) to different pledgers, with two endogenizedprice points. Perhaps counterintuitively, it can be op-timal for the firm to offer a lower price to people signingup late. This is because when the batch size is belowa certain threshold, group buying can succeed evenwithout an early-bird discount; with a guaranteedsuccess, the end-of-cycle discount becomes more ef-fective than the early-bird discount. Indeed, as cus-tomers who sign up early expect to wait, the accelera-tion of the later pledging process can be anticipated byall of the early arrivals, shortening waiting times andincreasing their willingness to pay. Hence, the firm cancharge those customers who sign up early a higherprice. In contrast, an early-bird discount accelerates theearly pledging process but has no effect on the laterarrivals, as each customer’s waiting time depends onlyon the cumulative number of sign-ups by the time ofthe customer’s arrival. This result contrasts starklywith the literature on traditional group buying with adeadline, which suggests that the early-bird discountis more profitable.Second, we investigate unobservable group buy-

ing. Interestingly, the firm prefers to conceal sign-upinformation if the premium product is of sufficientlyhigh quality. The reason is that the firm must per-suade the first customer to sign up by setting anincentive-compatible price, as this customer bears thehighest waiting cost. When the sign-up information isavailable, the first sign-up customer knows that he orshe will wait the longest; thus the firm must com-pensate the customer by offering a sufficiently lowprice, which applies to everyone else and results inunextracted surpluses for all subsequent sign-ups. Incontrast, with sign-up information concealed, cus-tomers use the average expectedwaiting time tomaketheir sign-up decisions. Hence, the firm can benefit byoffering less compensation to customers than in ob-servable group buying, which further improves theprofitability of unobservable group buying, particu-larly when the quality level of the group-buyingproduct is sufficiently high.We also study several other extensions. For ex-

ample, we incorporate customers’ heterogeneous pa-tience levels, investigate the group-buying of an in-ferior product, and explore the context of horizontallydifferentiated products. In the optimalflexible-durationgroup buying, we find that it is always those customersin the highest-priority class for the group-buyingproductwho sign up first at the early stage. “Highest priority”can refer to either the highest-valuation segment or a

Hu, Liu, and Zhai: Intertemporal Segmentation via Flexible-Duration Group BuyingManufacturing & Service Operations Management, Articles in Advance, pp. 1–18, © 2020 INFORMS 3

lower-valuation but most patient segment (in thecontext of vertically differentiated products) or thesegment of customers who like the group-buyingproduct most (in the context of horizontally differ-entiated products). Meanwhile, the firm may have anincentive to invite customers in the lower-priorityclasses for the group-buying product to sign up ata later stage.

1.3. ContributionsWemake the following contributions. First, to the bestof our knowledge, this work is the first to formallyinvestigate group buying with flexible duration bystudying its optimal design. Our model captures oneof the key features of flexible-duration group buying,assumed away in previous studies of fixed-durationgroupbuying, namely, customers’waiting cost. Hence,our model offers a new operational perspective thatcomplements the existing literature. Second, this studyhighlights the significance of taking into account op-erational considerations in the implementation of in-novative marketing programs. In particular, the firmshould consider customers’ sequential arrivals andtheir dynamic sign-up behavior in designing its group-buying offer. Third, this research recognizes the prof-itability of offering contingent product lines online viaflexible-duration group buying. In general, if theinventory holding cost is high enough or customersare patient enough, offering the contingent productline through flexible-duration group buying is moreprofitable than offering a fixed product line. Finally,our work contributes by proposing a more naturaldiscrimination scheme for firms, that is, intertemporalcustomer segmentation. Unlike most of the literature,in which the firm proactively discriminates betweencustomers by offering time-varying prices, and cus-tomers may wait for lower prices, we show that inflexible-duration group buying, the firm does not needto proactively price-discriminate between different seg-ments, since the price for the group-buying productremains unchanged. Instead, the firm can passively dis-criminate between customers based on their differ-ent expected waiting times (and costs) resulting fromtheir sequential arrivals.Hence, intertemporal customersegmentation can be more natural and acceptable thanthose price discrimination policies.

2. Literature ReviewFrom a variety of perspectives,many papers study theprofitability of group buying, in which the campaignwill be activated if at least a prespecified number ofcustomers sign up. Anand andAron (2003) are amongthe earliest to study group buying as a mechanism ofoffering a contingent quantity discount. They showthat group buying offers a way to better respond todemand uncertainty because the reduced price will

only be offered if the demand is sufficiently high.Chen andZhang (2015) study interpersonal bundling,in which the group discount is effective only if thenumber of sign-ups belongs to a certain interval, witha minimum or maximum group size. Taking intoaccount strategic customers, Marinesi et al. (2018)show that the firm can take advantage of the group-buying activation threshold to reveal the state of themarket and reduce the mismatch between supply anddemand. From a supply chain perspective, Chen andRoma (2011) study the group-buying discount re-ceived by two competing retailers, based on theiraggregated purchasing quantity, in a two-level dis-tribution channel. Focusing on social interaction, Jingand Xie (2011) show that group buying with a dis-counted price and a minimum group size can moti-vate informed customers to work as “sales agents” toacquire less informed customers.In these papers, the customer sign-up process is

often simplified. However, some research, includingours, zooms in on the group-buying process to ex-plore the pledging dynamics. For example, incorpo-rating strategic customer behavior, Surasvadi et al.(2017) propose a contingent markdown mechanismthat resembles group buying, in which the discountprice will be offered to not only the sign-ups but alsoall subsequent buyers if the number of sign-upsreaches a prespecified threshold or at the end of theselling season, whichever comes first. Liu and Tunca(2019) characterize the stochastic dynamic equilib-rium behavior of consumers’ pledging in a group-buying scheme with two threshold levels, using arecursive differential and difference equation system.They empirically estimate consumer arrival rates andutility distributions utilizing data from group-buyingevents hosted by an online retailer, and provideempirical evidence of consumer network effects ingroup buying. They show that for low and highconsumer arrival rates, the retailer sets a small pricediscount, whereas for an intermediate consumer ar-rival rate, the retailer sets a deeper price discount.Three papers study the group-buying design from

an information disclosure perspective.Hu et al. (2013)use a two-period model and show that revealing thecumulative number of sign-ups increases the group-buying success rate. Hu et al. (2020) consider a pos-itive network externality among customers in a gen-eral form, which includes group buying as a specialcase, and show that it may not be optimal for the firmto disclose the number of sign-ups. Subramanian andRao (2016) study consumer observational learningfrom deal sales displayed on Groupon and Living-Social and demonstrate that displaying daily salesvolumes can benefit the high-typemerchant by crediblysignaling its type, thus enabling it to acquire newcustomers at a higher margin. In our context, we show


in an extension that when customer waiting cost isconsidered, information transparency can be detrimen-tal to the firm because it must compensate customers forthe high waiting cost of early sign-ups.

All in all, group buying without a deadline is not aspecial case of group buying with a finite duration,though it may be considered as group buying with aninfinite duration. With the duration changed fromfinite to infinite, the model changes fundamentally inthe following respects. First, the success rate of agroup-buying campaign with a finite duration is lessthan 1, that is, there is a positive probability thatgroup buying may not reach the target within thefixed duration. By contrast, in our theoretical model,an optimally designed group-buying campaign isassured of success, even though the waiting times arerandom and can be long. Second, in the group-buyingliterature, we are not aware of any other paper ex-plicitly taking customers’ waiting costs into account,likely due to these papers’ focus on relatively shortfixed durations. However, waiting costs become acritical factor in customers’ decisionmakingwhen thetime to meet the group-buying threshold becomeslong. As a feature, we incorporate customers’waitingcost in ourmodel and investigate its potential impactson customers’ sign-up behavior and on the firm’soptimal group-buying design. We uncover a noveltype of discrimination scheme enabled by customers’waiting, that is, intertemporal customer segmenta-tion. Third, even though intertemporal customer seg-mentation can exist in fixed-duration group buying(although it has not been explicitly studied in theexisting literature on group buying; see Online Sup-plement A for a detailed comparison), the drivingforce behind customer sign-up behavior differs sig-nificantly from that of our flexible-duration groupbuying. To be specific, in fixed-duration group buy-ing, the high-valuation customers can sign up at anearlier stage than the low-valuation customers due todifferent levels of risk borne by the two segments ofcustomers, as the probability of a successful group-buying deal would be lower at the earlier stage of thecampaign. By contrast, in flexible-duration groupbuying, the risk borne by the two segments of cus-tomers stays the same, as the probability of a suc-cessful group-buying deal is always 1. Thus, thedriving force of the intertemporal customer segmen-tation in this case would be the heterogeneous waitingcosts faced by customers who sign up at different times.Moreover, in fixed-duration group buying, if we extendthe deadline to infinity without considering the cus-tomers’ waiting costs (as in the existing literature ongroup buying), there would be no difference in therisk of signing up, because the success rate is always 1.Under this circumstance, intertemporal customer seg-mentation would not exist, which further confirms that

our flexible-duration group buying is not a special caseof fixed-duration group buying that does not considerwaiting costs.Our research is closely related to the literature on

product line design that involves simultaneouslyoffering products of different qualities. The earlierwork includes Moorthy (1984), who develops a frame-work of market segmentation based on customerself-selection. The follow-ups theoretically model thevariety and quality of products considering duopolycompetition (Moorthy 1988, Desai 2001), time of prod-uct introduction (Moorthy and Png 1992), and com-municating cost (Villas-Boas 2004), among others.In this stream, Netessine and Taylor (2007) take intoaccount the supply side, which is very close to ourwork. Both papers analyze the optimal customersegmentation using two products and studying theinteraction of supply and demand sides. But there aresome distinct differences. Unlike their economic or-der quantity (EOQ) model in which two products aresimultaneously produced in advance and wait forcustomers to purchase them (i.e., made to stock), inour study one product is produced beforehand,whereas the other will not be produced unless thegroup-buying deal succeeds. In other words, we treatgroup buying as a way to offer a contingent productline and customers have to wait for the group-buyingproduct. From the system efficiency perspective, thedecision whether to make to stock or make to group-buying order hinges on which cost is lower: the in-ventory holding cost versus the customers’ waitingcost. Hence, our study can be viewed as a comple-ment to their research. In general, if the inventoryholding cost is high enough or customers are patientenough, offering the product line through group buyingis more profitable.Our work also contributes to the growing body of

literature on intertemporal price discrimination (Conlisket al. 1984, Su 2007, Besbes and Lobel 2015, Garrett2016, Ory 2017, Chen et al. 2019), in which the firmdiscriminates between different customer segmentsby using intertemporal pricing. It is worth noting thatthe intertemporal customer segmentation throughflexible-duration group buying differs from inter-temporal price discrimination. Most critically, in thepapers mentioned previously, the firm proactivelydiscriminates between different segments of customersby offering time-varying prices. By contrast, in ourstudy, the price for the group-buying product remainsunchanged. Instead, the firm passively discriminatesbetween customers based on their different expectedwaiting times (and costs). Furthermore, intertemporalcustomer segmentation via group buying can achieve awin-win-win situation for all stakeholders, which isabsent in intertemporal price discrimination. Last butnot least, in those papers, the firm suffers if more


customers arewilling towait,whereas in our setting, thefirm can even have an incentive to induce more cus-tomers to wait.

In addition to customer cooperation via groupbuying, researchers also study collaboration betweensellers through group buying. Examples include firms’group buying from their upstream supplier to obtaina discount (Chen and Roma 2011), and suppliers’group selling to their downstream firm to counteractthe default risk (Huang et al. 2016) or customers’strategic behavior (He et al. 2016).

Finally, our research is also related to some of themost popular business models driven by crowds (seeChen et al. 2019 for a review), such as crowdfunding(Hu et al. 2015, Chemla and Tinn 2019) and crowd-voting (Marinesi and Girotra 2013), all of which ex-plicitly or implicitly adopt a predetermined deadline.We offer a framework for the optimal design of suchbusiness processes from a flexible-duration perspec-tive. Also allowing for flexible duration, Araman andCaldentey (2016) let the firm decide when to stop acrowdvoting process, depending on the number ofvotes and the updated belief about the customer ar-rival rate. In contrast, the threshold of the group-buying campaign in our setting is exogenously de-termined by the production side and the campaignduration is random—an outcome of random cus-tomer arrivals with random valuations.

3. The Base ModelIn this section, we introduce the setup for the basemodel with a two-point valuation distribution. Wethen focus on a prototypical setting where customers’valuations are continuous and only the group-buyingproduct is offered, to present preliminary results oncustomers’ sign-up behavior.

3.1. Model SetupIn the base model, we consider a monopolistic firmselling one regular product to customers who arriveaccording to a Poisson process with arrival rate λ.Customers are heterogeneous in their valuations ofproduct quality attributes and belong to one of thetwo segments: high-end segment with valuationH, orlow-end segment with valuation L (H > L > 0). Thefractions of high- and low-end customers in thepopulation are γ (0 < γ < 1) and 1 − γ, respectively.Each customer intends to purchase at most one unitof one of the products, and the customer type is pri-vate information.

To better discriminate between high- and low-endcustomers, the firm can choose to offer group buyingfor a specific premium product. We assume that theregular product and the premium product are ver-tically differentiated in quality. (We consider hori-zontally differentiated products in Section 5.5.) The

quality levels of the group-buying product and theregular product are θ (θ > 1) and 1, respectively. (Weconsider θ < 1 in Section 5.4 and consider the case inwhich whether the premium product is a fit forcustomers is uncertain in Online Supplement I.) Al-though we interpret θ as the quality level of thegroup-buying product, it can also represent a com-bination of product characteristics. With the group-buying offer, the firm posts its group-buying cam-paign at the beginning of a sales horizon, which ischaracterized by the price p for the premium productand the minimum number N of customers required,alongside the price r for the regular product.When thenumber of sign-ups for the premium product reachesthe threshold N, the firm immediately produces thepremium product in a batch of size N and then de-livers it to those who have signed up during thecurrent campaign. Another group-buying cycle canstart again. We assume that the threshold N is ex-ogenously determined,whichmay stand for the batchsize required for economic production. (We numer-ically analyze the endogenized batch size N in OnlineSupplement J.) To make the model parsimonious, wedo not explicitly consider different production costsof the regular and the premium product. Instead, weassume different batch sizes in production, which isreasonable because of the following. Generally, theregular and premium products have different setupcosts: K1 and K2, respectively. As the regular productis the bread-and-butter product of the firm, its pro-duction can be in a continuous flow, and thus K1 isrelatively low. In contrast, since the premiumproductis to some extent customized, its specialized devel-opment cost K2 can be quite high. That is, K1 � K2.Without loss of generality, we assume K1 � 0 andK2 � K. Moreover, the setup cost K is equivalent toimposing a batch size N for economic production,implying that at least N units of the product are re-quired to cover the setup cost. Thefirmdetermines theprices r and p, whichwill remain the same throughoutthe selling season, to maximize the long-run averageprofit. (We consider the case in which the firm setsprices for the group-buying product contingently inSection 5.1.) Our model accommodates the situationin which group buying either occurs once or repeatsmultiple times.Customers incur a waiting cost c > 0 per unit time.

(We consider heterogeneous waiting costs in Sec-tion 5.3.) Everything else being equal, the longercustomers wait, the less they want to join the group-buying campaign. Upon arrival, each customer decideswhether to purchase the regular product immediately,or sign up andwait for the premium product (if the firmoffers groupbuying), or buynothing and exit themarket.(We consider stand-alone group buying without any reg-ular product in Section 3.2 and Online Supplement H.)


For simplicity, we assume a zero surplus for the outsideoption.A customerwill signup for thepremiumproductif and only if doing so offers a benefit that is at leastas high as purchasing the regular product. Moreover,customers cannot renege after theirpledge.When joiningthe campaign, customers can see the prices p and r aswell as the additional number of sign-ups needed toreach the target N. In practice, the firm commonlydiscloses to customers the number of sign-ups inreal time. (We will discuss an alternative informa-tion disclosure strategy in Section 5.2.) For ease ofexposition, we denote the state of pledge-to-go byn (1 ⩽ n ⩽ N), which represents the additional numberof sign-ups required to reach the threshold N. In de-ciding whether to sign up, customers consider theirown valuation and belief about the expected waitingtime, denoted by w(n), which depends on the real-time state n of pledge-to-go. Last, all exogenous pa-rameters, including H, L, λ, γ, c, and θ, are com-mon knowledge.

3.2. A General Valuation ModelIn this subsection, we consider a prototypical modelin which only the group-buying product is offered inorder to gain insight into customers’ sign-up be-havior. We assume customers’ valuations follow ageneral distribution F(·), which can be either con-tinuous or discrete with a finite or unbounded range.For simplicity, we normalize θ to 1, since we do notconsider the regular product. All other assumptionsremain the same as in Section 3.1.

Theorem 1 (Sign-up Behavior). For a given N, there existthresholds for customers’ valuations, vn, 1 ⩽ n ⩽ N, suchthat upon arrival at any pledge-to-go state n, customerswhose valuations are no less than vn will be induced tosign up for group buying, and those whose valuations arebelow vn will not. Moreover, (i) vn is increasing in n; and(ii) Δvn ≡ vn+1 − vn is increasing in n if F(·) is continuous.(The monotonicity in this paper is in its weaker sense unlessotherwise stated.)

As Theorem 1 demonstrates, there exist N thresh-olds for customers’ valuations that govern customers’sign-up behavior in equilibrium. More importantly,Theorem 1 also indicates that as the pledge-to-gostate n decreases (i.e., as the time elapses), the ad-mission threshold vn becomes lower. That is, morecustomers would be invited to sign up at the laterstage of the group buying (as the expected waitingtimes are shortened), whichwe refer to as intertemporalcustomer segmentation, since the group-buying cam-paign admits different types of customers during thedynamic pledging process. Besides, Theorem 1(ii)shows that as the time goes, the admission thresholdvn decreases at a slower pace, because it is better forthe firm to admit fewer lower-valuation customers as

the pressure tomeet the threshold of a successful group-buying deal is reduced.In the rest of the paper, for simplicity, we focus on

the setting with a two-point valuation distribution,because we need to optimize the product line design.Our study can be extended to incorporate multiplesegments of customers and the main insights wouldcarry through.

4. Model AnalysisThe base model is a Stackelberg game. In the firststage, the firm determines whether to offer group buy-ing and decides on the price for the regular product andthat for the group-buying product, if any. In the secondstage, customers purchase the regular product, or signup for group buying if it is offered, or exit the market,based on their own valuation and the real-time sign-upinformation upon their arrival. We analyze the gamebackward. In the second stage, we assume customersmake rational expectations of future arrivals and solvecustomers’ equilibrium sign-up behavior, and then goback to the first stage to analyze the firm’s optimaldecisions, in anticipation of customers’ rational be-havior in the second stage. We adopt the concept ofrational expectations equilibrium (REE), in whichagents make choices based on their rational antici-pations and available information, and the expecta-tions are consistent with the realizations in equilib-rium (see, e.g., Muth 1961 and Lucas 1972).

4.1. Equilibrium Market Segmentation withGroup Buying

In this subsection, we assume the group-buying pre-mium product is always offered alongside the regularproduct, and then endogenize the group-buying offerdecision in Section 4.3. We use the superscript G toemphasize the presence of the group-buying offer. Ina group-buying campaign, the firm can target eitherhigh- or low-end customers to sign up for the group-buying product, or both, by manipulating prices pG

and rG. In our hypothesis, all customers who sign upwill eventually get the group-buying product, al-though their expected waiting times differ. Theorem 1characterizes customers’ dynamic sign-up behaviorin the general setting, with Lemma A.1 in OnlineAppendix A customized for the setting with twosegments of customers. Hence, there are five possiblecustomer segmentations in terms of which segmentsigns up for the group buying in a given state n (1 ⩽n ⩽ N): only high-end customers sign up (referred toas scenario {H}); high-end customers sign up first,then both high- and low-end customers sign up (re-ferred to as scenario {H;H + L}); both high- and low-end customers sign up from the beginning (referred toas scenario {H + L}); only low-end customers sign up(referred to as scenario {L}); and finally, low-end


customers sign up first, then both high- and low-endcustomers sign up (referred to as scenario {L;H + L}).However, when θ > 1, only the first three scenarioscan occur in equilibrium, which is summarized in thefollowing proposition. By contrast, when θ < 1, onlythe last three are possible in equilibrium (see Prop-osition E.1 in Online Appendix E).

Proposition 1 (Customer Segmentation with Group Buying).Suppose θ > 1.With group buying, customer segmentation inequilibrium must be one of the following three scenarios: {H},{H;H + L}, or {H + L}.

The three scenarios in Proposition 1 share a com-mon feature, namely, the first sign-up customer is ahigh-end one. Denote by nG the so-called tippingstate. That is, the customer segment(s) signing upfor the group-buying product will change after thepledge-to-go state n drops to nG. More specifically,after the number of N − nG sign-ups has been gath-ered, low-end customers will join the group-buyingcampaign. Take the scenario {H;H + L} as an exam-ple. Those customers who join early at any state n,where nG < n ⩽ N, must be high-end customers,whereasthose who join later at any state n ⩽ nG can be eithertype. Thus, we can simply use the tipping state nG tocharacterize the three scenarios. In particular, nG � 0(never tip), 1 ⩽ nG < N (intertemporal segmentation),and nG � N (always tip) correspond to scenarios {H},{H;H + L}, and {H + L}, respectively.

As the firm cannot observe each customer’s type, itmakes pricing decisions anticipating that each cus-tomer self-selects an incentive-compatible choice. Tothis end, the prices pG and rG should satisfy the in-dividual rationality (IR) and incentive compatibil-ity (IC) constraints for all pledge-to-go states. Byanalyzing the IR and IC constraints, we can viewboth pG and rG, as well as the firm’s long-run averageprofit πG, as functions of tipping state nG. With groupbuying, customer segmentation in REE is character-ized by the following proposition (see Figure 1 foran illustration).

Proposition 2 (REE with Group Buying). With groupbuying, for any given θ > 1 and N, there exist two thresh-olds for the batch size N1 ≡ (θ − 1)(1 − γ)Lλ/c + 1 − γand N2 ≡ (θ − 1)(H − L)γλ/c + 1 − γ, such that the fol-lowing holds:

(i) When H/L ⩽ 1/γ, the firm sets prices such that(i.1) if N ⩽ N1, {H + L} is an REE;(i.2) if N > N1, {H;H + L} is an REE.

(ii) When H/L > 1/γ, the firm sets prices such that(ii.1) if N ⩽ N2, {H} is an REE;(ii.2) if N > N2, {H;H + L} is an REE.

Proposition 2 reveals that the equilibrium is de-termined not only by the supply-side factor, namely,

the batch size N for economic production, but also bythe demand-side factor, namely, H/L, a measure thatcaptures the (dis)similarity of customer segments.A small H/L indicates that customer segments areclose to each other, whereas a large H/L implies theyare far apart. When the batch size N is sufficientlysmall and the valuation heterogeneity H/L is suffi-ciently low, the optimal strategy for the firm is to setprices so that all customers purchase the premiumproduct through group buying (see subcase (i.1) inProposition 2 and the region {H + L} in Figure 1).Indeed, since the premium product is more profitable(as θ > 1), waiting times are short due to the small N,and the difference of valuations between the twosegments is not significant, thefirmprefers to use onlythe premium product to capture the whole market.When the valuation heterogeneity H/L is suffi-

ciently high and the batch size N is not too large, thefirm has an incentive to segment the market perfectlyby completely excluding low-end customers from thegroup buying of the premium product, a strategyreferred to as perfect customer segmentation (seesubcase (ii.1) in Proposition 2 and the region {H} inFigure 1). In this case, the firm uses the premiumproduct to target the high-end segment and theregular product to target the low-end segment. Bycombining subcases (i.1) and (ii.1), we find that whenN is small enough, the market partition is mainlyinfluenced by H/L, which is similar to the situation inNetessine and Taylor (2007, figure 3), where the firmoffers a product line of premanufactured products tocustomers with different valuations, when the pro-duction technology cost is intermediate.When the batch size N is sufficiently large, our

result is in stark contrast with the literature. In-creasing the batch size N could be expected to furtherreinforce the firm’s price discrimination, by allowingonly high-end customers to participate in groupbuying.

Figure 1. (Color online) Customer Segmentation withGroup Buying


The intuition is that with a larger batch size N, waitingtimes would increase, thus only high-end customerswould be willing to wait. Interestingly, when the pric-ing decisions are endogenized, we observe a distinctphenomenon: high-end customers sign up for groupbuying first; then, when there are enough sign-ups toreach the tipping point, both high- and low-end cus-tomers join the group-buying campaign (see subcases(i.2) and (ii.2) in Proposition 2 and the region {H;H + L}in Figure 1). That is, the group buying admits differ-ent customer segments during the dynamic pledg-ing process, which is referred to as intertemporal cus-tomer segmentation (see Figure 2 for an illustration).In other words, intertemporal customer segmenta-tion outperforms perfect customer segmentation whenthe batch size N is sufficiently large, which is some-what counterintuitive. We summarize this observa-tion as follows.

Corollary 1 (Comparison of Two Types of Segmentation).With group buying, there exists a threshold for the batchsize N, above which intertemporal customer segmentationoutperforms perfect customer segmentation, and below whichthe opposite is true.

The underlying reason is as follows. As the batchsize N increases, waiting times will also increase. Tomaintain the attractiveness of group buying, the firmneeds to shorten waiting times. The solution is tolower the group-buying price pG and allow some low-end customers to jump on the bandwagon and join thegroup buying, which only occurs at the later stage ofthe pledging process. In this way, the firm mitigatesefficiency loss due to waiting by sacrificing somebenefits of price discrimination. Moreover, since thelater stage in which both segments sign up for thegroup-buying product can be a relatively short period(especiallywhen the quality level of the group-buyingproduct, the valuation heterogeneity, the proportionof high-end customers, or the arrival rate is high, orthe unit-time waiting cost is low), the impact of nosales for the regular product is somewhat limited.Even if we take into account no sales of the regularproduct for the late sign-up stage by considering the

firm’s holding cost of the regular product, the insightson intertemporal segmentation largely hold, exceptthat the firm has less incentive to admit the low-endcustomers at the later stage of the pledging process.Overall, intertemporal segmentation can benefit

both the firm and the high-end segment. Indeed, high-end customers wait for less time to obtain the group-buying product. Besides, the participation of low-endcustomers admitted only during the late pledgingprocess ensures that the group-buying price pG isneither too low nor too high, leaving some profitablemargin to the firm and also some surpluses to thehigh-end customers. Interestingly, we find that effi-ciency loss may decrease with N, due to the firm’sendogenized pricing decisions.When the batch size issmall, group buying optimally targets only the high-end segment, so the firm can benefit from setting ahigher price for the premium product. However, asthe batch size increases, it is profitable for the firm toencourage the low-end segment to sign up as well bylowering the group-buying price, so that the latepledging process is accelerated, waiting times areshortened, and thus efficiency loss is reduced.

4.2. No-Group-Buying BenchmarksTo validate the effectiveness and evaluate the po-tential profitability of group buying, we compare itwith three widely used benchmark strategies. In thefirst and second benchmarks, the firm sells only theregular product. The first strategy is called the vol-ume strategy, in which the firm always charges thelow price L to attract all customers. The secondstrategy is called the margin strategy, in which thefirm charges the high price H to target only the high-end market. The third strategy is called the product-line strategy, in which the firm simultaneously offersthe regular and premium products. We use the su-perscripts V, M, and P to denote the equilibriumoutcomes when the firm adopts the volume, margin,and product-line strategies, respectively.We assume that the firm incurs some inventory

holding and extra management costs when offeringthe premium product at the beginning of the saleshorizon. We denote by h the inventory holding costper unit time per unit of the premium product. Theinventory holding cost is obviously different for thetwo products. For the ease of comparison, we nor-malize the inventory cost for the regular product tozero. This is reasonable since the regular product isthe bread-and-butter product and usually less costlyto hold than the premium product.In the volume strategy, the firm sets the price rV � L

and the corresponding long-runaverageprofit isπV �Lλ,resulting in zero surpluses for low-end customers andpositive surpluses for high-end customers. Thus, thelong-run average customer surplus is SV � (H−L)γλ.

Figure 2. (Color online) Illustration of a Pledging Processwith Intertemporal Segmentation


In the margin strategy, the firm sets the price rM � Hand the corresponding long-run average profit isπM � Hγλ, leading to zero surpluses for both seg-ments, thus SM � 0. In the product-line strategy, thefirm sets the prices rP � L and pP � (θ − 1)H + L, andthe corresponding long-run average profit is πP �(θ − 1)Hγλ + Lλ − (N + 1)h/2, resulting in zero sur-pluses for low-end customers and positive surplusesfor high-end customers. Thus, the long-run averagecustomer surplus is SP � (H − L)γλ. Notice that pP −rP > pG − rG, implying that with group buying, thefirm prices discriminate between two segments lessaggressively. Among the three strategies, the optimalone is described in Proposition A.1 in Online Ap-pendix A. Put plainly, when the inventory holdingcost is sufficiently low, it is optimal for the firm tooffer both products using the product-line strategy,with the premium and regular products targetinghigh- and low-end customers, respectively; other-wise, only the regular product will be offered. Whenonly the regular product is available, it is not sur-prising that the optimal price and the resultingmarket segmentation are entirely determined byvaluation heterogeneity. The firmmust weigh a highprofit margin with a small market share against alarge market share but a low profit margin. With alow level of valuation heterogeneity, it is moreprofitable for the firm to target both segments, notfully extracting surpluses from high-end customers.With a high level of valuation heterogeneity, thefirm benefits more by targeting only the high-end segment.

4.3. Group Buying or NotNow we compare the performance of group buying,from the perspectives of both the firm and the cus-tomers, against the three benchmarks. First, we usethe firm’s long-run average profit as the criterion toinvestigate the condition under which the firm has anincentive to offer group buying.

Theorem 2 (Profit Comparison). Suppose θ > 1. Thereexists a threshold h for the inventory holding cost and athreshold m for the valuation heterogeneity such that thefollowing hold:

(i) If h ⩽ h, it is optimal for the firm to adopt the product-line strategy.

(ii) If h > h,(ii.1) if H/L ⩽ 1/γ, as N increases, the firm’s optimal

group-buying strategy varies from {G (H + L), R (Ø)} →{G (H;H + L), R (L; Ø)} → {NG, R (H + L)};

(ii.2) if 1/γ < H/L ⩽ m, as N increases, the firm’soptimal group-buying strategy varies from {G (H), R (L)} →{G (H;H + L), R (L; Ø)} → {NG, R (H)}; and

(ii.3) if H/L > m, as N increases, the firm’s optimalgroup-buying strategy varies from {G(H),R(L)}→{NG,R(H)}.

Theorem 2 characterizes the firm’s optimal group-buying strategy and targeted customer segments.When the inventory holding cost h is low, the firmalways prefers to sell both products simultaneouslyusing the product-line strategy: that is, the firm willnot choose group buying as a way to sell the pre-mium product. By contrast, when the inventoryholding cost h is high, the firm will never offer bothproducts make-to-stock, but instead, may resort togroup buying. Since this intuition always holds, forthe remainder of the paper we focus on the caseswhere the inventory holding cost h is high by as-suming the following.

Assumption 1. The inventory holding cost is higher than h,that is, h > h.

As mentioned earlier, in the cosmetic industry, shelfspace is always limited and offering extra products iscostly, which motivates firms to offer a contingent prod-uct online via group buying. If the inventory holdingcost is high enough, or, as an equivalent, customers arepatient enough (since h increases in c), offering thepremium product through group buying is potentiallymore profitable.Figure 3 illustrates the regions in the parameter

space where it is optimal to offer group buying, andthe resulting market segmentation. In that figure, Gand R denote the group-buying product and theregular product, respectively (whereas NG indicatesthat group buying is not offered);H, L,H + L,H;H + L,L; Ø, and Ø denote the customer segments that pur-chase a specific product (whereas Ø means that nosegment purchases the corresponding product). Forinstance, G (H;H + L), R (L; Ø) specifies a region inwhich the firm benefits more from offering groupbuying.More specifically, in the early sign-up processof the group buying, only the high-end segment joinsthe campaign, while the low-end segment purchasesthe regular product. In the late phase, both segmentssign up for the group-buying campaign, while no onepurchases the regular product.As the difference between valuations of the two

segments increases, the firm may not always want tooffer group buying alongside the regular product.This is counterintuitive, as group buying providesthe firm with an additional tool for price discrimi-nation. As the valuation heterogeneityH/L increases, itwould seem likely that the firm had more incentive toresort to group buying as an additional price dis-crimination scheme, with the regular product andgroup buying targeting different segments. However,we show that the profitability of group buying ismoderated by the batch size for economic productionN on the supply side. Besides, it should be noted thatthe quality level of the premium product θ also in-fluences the firm’s decision. For θ > 2 and 1 < θ ⩽ 2,


the optimal group-buying strategies differ when H/Lis high enough, because a small value of θ limits theprofitability of group buying (see Figure 3).

Offering group buying means a trade-off betweenthe benefit of price discrimination and the efficiencyloss due to customer waiting. Therefore, the firm has anincentive to offer group buyingwhen the benefit of pricediscrimination is sufficiently strong compared with theefficiency loss. The profitability of price discriminationincreases with the valuation heterogeneity, whereasthe efficiency loss increases with the batch size.How to strike a balance can be summarized in thefollowing cases.

First, when the batch sizeN is sufficiently small, theefficiency loss is small as well, and thus can be easilydominated by the benefit. Therefore, the firm has anincentive to offer group buying regardless of the levelof valuation heterogeneity. With a low level of val-uation heterogeneity, the firm invites both segmentsto sign up (see the region G (H + L),R (Ø) in Figure 3).However, with a sufficiently high level of valuationheterogeneity, the firm invites only the high-end seg-ment to join the group-buying campaign, leaving thelow-end segment to buy the regular product (see theregion G (H),R (L) in Figure 3). This case is similar tothe classical result on product line design with ver-tical differentiation (see, e.g., Moorthy 1984).

Second, when the batch size N is sufficiently large,the efficiency loss due to customer waiting is signif-icant and can no longer be compensated for by in-viting the low-end segment to participate in groupbuying. In this case, the benefit of price discriminationis dominated by the efficiency loss. Consequently, it isno longer profitable for the firm to offer group buyingand the firm sells only the regular product (see theregions NG,R (H + L) and NG,R (H) in Figure 3).

Last, when the batch size N is in an intermediaterange, as valuation heterogeneity increases from 1,the firm’s optimal strategy can go from no groupbuying, to group buying, to no group buying, andfinally back to group buying (see the following cor-ollary and the shaded region in Figure 3).

Corollary 2 (Nonmonotonic Group-Buying Strategy). WhenN is in an intermediate range, the firm’s group-buyingstrategy is nonmonotonic in H/L. Specifically, as H/Lincreases, the firm’s optimal group-buying strategy can varyfrom NG → G → NG → G.

Corollary 2 suggests that when the batch size ismoderate, there can be two disconnected ranges ofvaluation heterogeneity, in which the firm has anincentive to offer or not to offer group buying. Thisnonmonotonic behavior of offering group buying withrespect to valuation heterogeneity is driven by the pos-sible intertemporal segmentation enabled by groupbuying. In a homogeneous market (i.e., H/L � 1), thereis no need for price discrimination. Thus, the firmprefers the volume strategy. As H/L increases, thefirm can segment the market by offering group buy-ing. In this case, when N is not too low, the efficiencyloss cannot be ignored. Hence, the firm reduces ef-ficiency loss by inviting the low-end segment toparticipate in group buying during the late pledgingprocess. As a result, when both N and H/L are in anintermediate range, group buying allows the firm tointertemporally segment the market (see the changefrom NG, R (H + L) to G (H;H + L),R (L; Ø) in Fig-ure 3). AsH/L further increases, the profit potential ofprice discrimination also increases. However, to offergroup buying in this case, the firm needs to sacrificethe potentially high profit margin from the high-endsegment to attract the low-end segment. Thus, group

Figure 3. (Color online) Optimal Group-Buying Strategy and Customer Segmentation


buying becomes less attractive, and the firm switches tothe margin strategy (see the change from G (H;H + L),R (L; Ø) to NG,R (H) in Figure 3). Finally, as H/Lfurther increases, group buying can once again bemore attractive with a different market composition(recall Corollary 1). Indeed,whenH/L is large enough,by perfectly segmenting the market, the benefit ofprice discrimination via group buying overcomes theloss of efficiency due to customer waiting (see thechange from NG,R (H) to G (H),R (L) in Figure 3).

From the supply side, as N increases, the group-buying strategy changes from G to NG, regardless ofthe level of valuation heterogeneity H/L. However,the corresponding customer segmentation dependson valuation heterogeneity. The optimal group-buyingstrategy has the following market segmentation. Thereexists a threshold forH/L such that if H/L is below thethreshold, both high- and low-end segments partic-ipate in the group-buying campaign; otherwise, onlythe high-end segment joins the group-buying cam-paign. Recall that to offer group buying, the firmneeds to balance the benefit of price discriminationand efficiency loss. As mentioned, when valuationheterogeneity H/L is sufficiently low, the firm has anincentive to reduce expected waiting times by invit-ing both segments to sign up. Specifically, when N issmall enough, both segments are invited to sign up atthe beginning of the group-buying campaign, whereaswith a largerN, the group-buying product targets thehigh-end segment first, then both segments. In con-trast, when the valuation heterogeneity H/L is suffi-ciently high, only the high-end segment is invited tosign up, as the benefit of price discrimination domi-nates the efficiency loss due to customer waiting.Thus, the firm has less incentive to invite the low-endsegment to join and reduce waiting times, and hencecompensate for efficiency loss by sacrificing the highprofit margin.

Corollary 3 (Total Sales Volume Comparison). The totalsales volume with group buying is as high as the best of theother three benchmarks. Specifically, qG � qP � qV > qM.

All the previous analyses use the profit criterion.However, in practice, thefirmmay also consider otherfactors, such as the market share. Corollary 3 showsthat the total sales volume with group buying is ashigh as the best of the other three benchmarks. Fromthe firm’s viewpoint, another merit of offering groupbuying alongside the regular product is that the firmcan achieve a larger total market share. In our ex-ample from the cosmetic industry, where the shelfspace is limited, offering an additional product linerequires extra shelf space and may incur additionalcosts. However, the emerging online group-buyingprogram provides an opportunity to offer additionalproductswithout requiring extra physical shelf space.

In addition, by offering group buying online, the firmdoes not incur inventory holding costs, as the group-buying product is manufactured only when enoughbuyers have been assembled. In sum, offering groupbuying of the premium product alongside the regu-lar product is similar to offering a line of make-to-stock products, but without the disadvantages men-tioned earlier.

4.4. Customer WelfareFrom the customers’ perspective, we measure thelong-run average customer surplus. With the optimalgroup buying, the long-run average customer surplusSG is given by

SG � ∑Nn�1

SGH n( ) · γλ · P n( ) + ∑nGn�1

SGL n( ) · 1 − γ( )

λ · P n( )⏟⏞⏞⏟customer surplus from premium product

+ ∑Nn�nG+1

SGL n( ) · 1 − γ( )

λ · P n( )⏟⏞⏞⏟customer surplus from regular product

,

where the individual surpluses of high- and low-endcustomers at a state n are

SGH n( ) � θH − pG − c · wG n( ),

SGL n( ) � θL − pG − c · wG n( ) if 1 ⩽ n ⩽ nG,

0 if nG < n ⩽ N.

{

Moreover, P(n) represents the probability of staten (1 ⩽ n ⩽ N) in the optimal group-buying campaign,which can also be viewed as the proportion of timewhen state n occurs. Due to the memoryless propertyof the Poisson process, the expected waiting timewG(n) of a customer who arrives at state n is inde-pendent of the customer’s arrival time. Furthermore,we denote by SGH and SGL the long-run average cus-tomer surpluses for high- and low-end segments,respectively, when the optimal group buying is of-fered. We denote by SVH, S

VL , S

MH , S

ML , S

PH, and SPL the

high- and low-end customer surpluses under the vol-ume, margin, and product-line strategies, respectively.

Theorem 3 (Customer Surplus Comparison). The com-parison of customer surpluses under different strategies ischaracterized as follows:(i) Customers as a whole always strictly benefit from

group buying of the premium product alongside the reg-ular one, that is, SG > SP � SV > SM.(ii) Both the high- and low-end segments always

(weakly) benefit from group buying of the premium prod-uct alongside the regular one, that is, SGH > SPH �SVH > SMH ,SGL ⩾ SPL � SVL � SMH .

Theorem 3 illustrates that customers always benefitfrom the group-buying offer. Additionally, both high-and low-end customers always (weakly) benefit from


the group-buying offer. The underlying rationale is asfollows. For high-end customers, even the first to signup has a surplus gain from group buying (beyondindividual surpluses obtained in the other three bench-marks), because thefirmencourageshigh-end customersto sign up for the group-buying product rather than topurchase the regular product immediately. It is note-worthy that the individual surpluses for all of the sub-sequent high-end arrivals are even higher than that ofthe first sign-up, because they wait for less time. Con-sequently, the customer surplus for the high-end seg-ment in group buying (which is strictly higher thanH − L) is always strictly higher than the surplus in theother three benchmarks (i.e., H − L or 0). By contrast,in the other three benchmarks, the individual sur-pluses for the low-end customers are always zero, asthey either purchase the regular product at price L orare priced out of the market. However, in groupbuying, some (or even all) low-end customers canobtain positive individual surpluses by jumping onthe bandwagon to buy the (otherwise unaffordable)premium product. Similarly, the later a low-end cus-tomer arrives, themore individual surplus the customerobtains. Hence, the customer surplus for the low-endsegment in group buying is always (weakly) higherthan in the other three benchmarks. Moreover, theparticipation of the low-end segment can benefit high-end customers by reducing their waiting times, whichmanifests an intertemporal cooperation between thetwo segments. To summarize, every stakeholder cansimultaneously benefit from the group-buying offer,leading to a win-win-win situation.

Corollary 4. As the arrival rate λ increases, the followingresults hold:

(i) The region in which intertemporal customer seg-mentation is optimal shrinks.

In the region where the intertemporal segmentation isoptimal, as the arrival rate λ increases,

(ii) low-end customers join the group-buying campaignat a later time;

(iii) the firm charges a higher price for the premiumproduct, and enjoys a higher profit; and

(iv) the individual surpluses for both high- and low-endcustomers decrease.

Corollary 4 summarizes the impact of the customerarrival rate on intertemporal segmentation. With ahigher arrival rate, the intertemporal segmentationis less likely to be adopted by the firm as an inter-mediate solution. Moreover, in the optimal inter-temporal segmentation, low-end customers tend tojoin the group-buying campaign later. With a higherarrival rate, it takes a shorter amount of time to as-semble enough high-end customers, which effec-tively alleviates the waiting costs, as the exogenouslydetermined threshold size N remains unchanged.

Hence, the firm has less incentive to admit low-endcustomers into group buying and can charge a higherprice, leading to a higher profit. For customers, whiletheir waiting times are shortened, both segmentssuffer from an individual surplus loss, because thehigh-end customers and those low-end customerswho join the group buying have to pay more, andfurthermore, a larger number of low-end customersare excluded from enjoying positive surpluses in thegroup buying.

5. ExtensionsWe use a simplified base model to derive our mainfindings. It is necessary to verify that these findingsare robust when certain assumptions are relaxed. Inthis section, we investigate a set of extensions. Thedetails are relegated to the online supplements.

5.1. Contingent PricingIn the base model, we focus on uniform pricing, inwhich the same price is charged for the group-buyingproduct, regardless of when customers join the cam-paign. Nevertheless, as pledgers face different waitingtimes for the success of the group-buying campaign, it isnatural to see whether contingent pricing, that is, of-fering the group-buying product at different prices todifferent pledgers based on their sign-up time, wouldbe more profitable. Now we investigate the situationwhere the firm sets prices based on the pledge-to-gostate n, with the superscript C denoting the equilib-rium outcome. For simplicity, we first assume that thefirm can only adopt two endogenized price points pC1and pC2 , and only change prices once at a so-calledtipping state, denoted by nC, where 0 ⩽ nC ⩽ N (seeOnline Appendix B and Online Supplement C formore details).One main observation is that customer segmenta-

tion in equilibrium is largely consistent with the basemodel, which confirms the robustness of our mainfindings (see Proposition 2 and Proposition B.1 inOnline Appendix B). Nevertheless, there are somedifferences. Figure 4 illustrates the change of the op-timal customer segmentation when the firm switchesfrom uniform pricing to contingent pricing. Nota-bly, under contingent pricing, the intertemporal seg-mentation {H;H + L} is more likely to sustain inequilibrium (see shaded regions (II) and (III) in Fig-ure 4). Specifically, under uniform pricing, the firmcannot discriminate between high- and low-endcustomers in region (II), due to the low level of valu-ation heterogeneity. However, under contingent pric-ing, intertemporal price discrimination is viable. Con-versely, in region (III), under uniform pricing, it isoptimal for the firm to implement perfect segmenta-tion due to the high level of valuation heterogeneity,


but it needs to endure significant efficiency loss causedby long waiting times (as only the high-end segmentparticipates in the group-buying campaign). However,under contingent pricing, the firm can invite low-endcustomers to join the group-buying campaign at thelater stage of the pledging process by charging a lowerprice, effectively shortening waiting times withoutlosing the high profit margin at the early stage.

Proposition 3 (Early-Bird vs. End-of-Cycle Discount).Under contingent pricing, for any H/L, there exists athreshold for the batch size N below which the firm offersthe end-of-cycle discount, that is, pC1 > pG > pC2 ; otherwise, itoffers the early-bird discount, that is, pC1 < pG < pC2 .

Asmentioned, in the context of group buyingwith adeadline (see, e.g., Hu et al. 2013, Liu and Tunca 2019),the firm may have more incentive to offer the early-bird discount to boost early sign-ups,which generatesa cascade effect among the later arrivals, because onemore early sign-up will increase the success rate of acampaign and boost the confidence of every subse-quent arrival. Perhaps surprisingly, in the case ofgroup buying with flexible duration, Proposition 3says that the optimal price path can be decreasing.Contrary to conventional wisdom, it is optimal for thefirm to offer a discount to customers who sign up late(i.e., pC1 > pC2 )when the batch sizeN is not too high (seeregions (I), (II), and (III) in Figure 4). In addition, forthese cases, the optimal price for early (resp., late)sign-ups pC1 (resp., pC2 ) is higher (resp., lower) thanthe optimal price pG under uniform pricing, that is,pC1 > pG > pC2 . The reason is that the firm can encour-age customers to sign up either by lowering pC1 toprompt early sign-ups or by lowering pC2 to promptlate sign-ups. When the batch size N is sufficientlylarge, the firm must offer an early-bird discount tojump-start the sign-up process (see the region abovethe dashed line in Figure 4); otherwise, no one wouldwant to be the first to sign up due to the significantlyhigh waiting cost, and the group-buying campaign

would fail. In this case, to join the group-buyingcampaign, low-end customers arriving late pay morethan high-end customers arriving early. Nevertheless,when the batch size N is not large, group buying cansucceed even without the early-bird discount, as thewaiting cost borne by the first customer is not sig-nificantly high. With a guaranteed success, the end-of-cycle discount is more effective than the early-birddiscount. The acceleration of the late pledging pro-cess can be anticipated by all of the early arrivals inREE, reducing waiting times and increasing theirwillingness to pay. Thus, the firm can charge a higherprice for early sign-ups. In contrast, when the firmoffers the early-bird discount, the acceleration of theearly pledging process has no effect on the late ar-rivals, as waiting times only depend on the currentstate of pledge-to-go.

Proposition 4 (No Incentive to Behave Strategically).Suppose the firm adopts the optimal price path inProposition 3 as if customers are myopic. Even whencustomers are forward-looking, in a pure-strategy equilib-rium they would have no incentive to wait and act as if theywere myopic.

In our study, we assume that customers need todecide whether to purchase the regular product now,sign up for the group-buying product now, or leaveimmediately without purchasing anything. In otherwords, we assume that customers are not forward-looking. However, if they were forward-looking, onemight wonder whether they had an incentive to wait.Suppose the firm adopts the optimal price path inProposition 3 as if customers are myopic. Proposi-tion 4 says that even if customers were forward-looking, they would behave myopically in a pure-strategy equilibrium. The argument goes as follows.Although the regular product price does not changeover time, theremay exist an incentive to wait when thegroup-buying product has a decreasing price path, thatis, pC1 > pC2 . Whether to buy now or wait until later is avalid question only to high- and low-end customerswho arrive early at a state n > nC because they observethe higher price pC1 . For any high-end customer ar-riving at state n > nC, if the customer delayed thepurchase, so would all high-end customers who ar-rive later, because their utilities of delaying the pur-chase would be even higher. Consequently, groupbuying would not succeed and everyone would earnzero surplus. In anticipation of this situation, it is adominant strategy for high-end customers arrivingearly to sign up immediately without waiting. Anylow-end customer arriving at state n > nC who delayedthe purchase would earn a negative utility, becausethe lower price pC2 the customer hoped to wait forexactly extracts all the surplus of a low-end customer

Figure 4. (Color online) Change of Customer Segmentationfrom Uniform Pricing to Contingent Pricing


arriving later at state n � nC. Hence, any low-endcustomer arriving early at state n > nC has no incentiveto wait either. Moreover, in a mixed-strategy equilib-rium, high-end customers may have a positive prob-ability of waiting. But by the same logic mentionedearlier, there will be a non-zero probability of theirimmediate sign-up, which implies that our main in-sight into intertemporal customer segmentation wouldstill hold to some extent.

In Online Appendix B, Proposition B.2 highlightsthe economic value of contingent pricing for the firmwhen offering group buying with flexible duration(see also Theorem B.1 in Online Appendix B andFigure C.1 in Online Supplement C for the optimalgroup-buying strategy under contingent pricing).Recall that under uniform pricing, the firm inter-temporally discriminates between high- and low-endcustomers, either directly via different products(i.e., perfect segmentation) or indirectly via differentsign-up times (i.e., intertemporal segmentation). Nev-ertheless, contingent pricing further allows the firm todiscriminate by charging different prices over time evento customers in the same segment (i.e., intertemporalprice discrimination). Contingent pricing cannot onlyenable intertemporal price discrimination, but can alsounleash the full potential of intertemporal segmenta-tion, which are two sides of the same coin. On the onehand, the firm can extract more surplus by chargingdifferent prices over time dependent on the state of thegroup-buying campaign. This corresponds to a simpleutility transfer from a customer to the firm, without anynew surplus generated for the total welfare. On theother hand, by encouraging more customers to sign upat the later stage, the entire sign-up process is shortened(see region (III) {H} → {H;H + L} in Figure 4). As aresult, contingent pricing reduces the total waitingtime and generates additional welfare by reducingthe efficiency loss. Taken together, contingent pricingenhances the profitability of group buying with flexibleduration and provides the firmwith a stronger incentiveto offer this kind of group buying.

In the previous analyses, we consider a special caseof contingent pricing with only two price points forthe group-buying product. More generally, the firmcan charge an entirely different price pCn at any state n.Two possible price paths are illustrated in Figure 5. Inboth paths, the price monotonically increases fromstateN to nC + 1, for which only the high-end segmentsigns up, and from state nC to 1, for which bothsegments sign up. It is worth noting that Figure 5, (a)and (b), correspond to the end-of-cycle discount andthe early-bird discount in Proposition 3, respectively(see the dashed lines in Figure 5). Moreover, when thefirm can freely charge contingent prices, the entirecustomer surplus can be extracted by the firm (see the

shaded regions in Figure 5, corresponding to thecustomer surplus left on the table when only twoprice points are allowed).

5.2. Unobservable Sign-up InformationIn addition to the pricing policy, the firm may ma-nipulate the information structure to better designgroup buying. In Online Appendix C and OnlineSupplement D, we explore the effect of concealingsign-up information in flexible-duration group buy-ing, referred to as unobservable group buying, forwhich we use the superscript U to denote the equi-librium outcome. By contrast, the group buying wherethe firm reveals the pledge-to-go state n to customersis called observable group buying.Figure 6 illustrates the change of the optimal cus-

tomer segmentation from observable to unobservablegroup buying. One main observation is that thecustomer segmentation here differs significantly fromthat in the base model (see Proposition 2 and Prop-osition C.1 in Online Appendix C). Notice thatintertemporal segmentation depends on an observ-able pledge-to-go state.Hence, in unobservable groupbuying, intertemporal segmentation does not exist(see shaded regions (I) and (II) in Figure 6). Althoughwe have verified the profitability of intertemporalsegmentation with observable sign-up information,the firm may arguably benefit even more from itsabsence. Indeed, the firm can actually charge a higherprice for the group-buying product, that is, pU > pG,because there is no need to compensate for a highwaiting cost to encourage the first sign-up. (Note thatwe assume that once customers sign up, they can-not renege; otherwise, this claim does not hold.) Weconfirm this observation in Proposition C.2 in OnlineAppendix C (see also Theorem C.1 in Online Ap-pendix C and Figure D.1 in Online Supplement Dfor the optimal unobservable group-buying strategy).Notice that in group buyingwith a deadline, observablegroup buying may be favored by firms (see, e.g., Huet al. 2013). Now in group buying with flexible du-ration, unobservable group buying is more profitablewhen θ is sufficiently large (see Proposition C.2). Asmentioned earlier, without knowing the pledge-to-gostate n, no matter when a customer joins the cam-paign, the customer’s expected waiting time is thesame even if the actual waiting time differs. The firmcan take advantage of this information uniformity bycharging a higher price for the group-buying productcompared with that in observable group buying,because it only needs to compensate for customers’waiting cost at an average level, which can increasethe firm’s total revenue, especially when the group-buying product is attractive enough (with a highvalue of θ).


5.3. Heterogeneous Waiting CostsThroughout the paper,we assume customers have thesame waiting cost per unit time. However, customerscan be heterogeneous along two dimensions, that is,valuation and patience (e.g., Su 2007). In OnlineAppendix D and Online Supplement E, we assumethat high- and low-end customers have waiting costsper unit time cH and cL, respectively.We show that ourqualitative findings are preserved (see Lemma E.1 inOnline Supplement E and Propositions D.1 andD.2 inOnline Appendix D). Specifically, first, when cH ⩽ cL,which means the high-end customers are more pa-tient than the low-end customers, we find that theequilibrium outcomes remain qualitatively unchanged.Moreover, in this case, intertemporal customer seg-mentation {H;H + L} becomes less attractive to thefirm compared with perfect segmentation {H} thanthat in the base model (see Corollary D.1 in OnlineAppendix D). Second, when cL < cH ⩽ cH , indicatingthat the high-end customers have higher waitingcosts than the low-end customers, but not signifi-cantly higher, we observe that the equilibrium out-comes still remain qualitatively unchanged. Moreimportant, in this case, intertemporal customer seg-mentation {H;H + L} becomes evenmore attractive tothe firm compared with perfect segmentation {H}than that in the base model (see Corollary D.1). Third,when cH > cH, which implies that the high-end cus-tomers are very impatient compared with the low-end customers, the firm still has an incentive to adoptintertemporal customer segmentation, but in a dif-ferent way. That is, it is now optimal for the firm toinvite low-end customers to sign up first and adoptthe intertemporal segmentation {L; L +H} becauselow-end customers are much more patient.

5.4. Inferior Group-Buying ProductIn the model, we assume that the premium group-buying product is of high quality. In Online Appen-dix E and Online Supplement F, we consider a group-buying product that is inferior to the regular product,

that is, θ < 1. In the base model, the premium group-buying product targets the high-end segment, whereasthe regular product targets the low-end segment. How-ever, with the inferior group-buying product, the seg-ment targets have changed with the group-buyingproduct targeting the low-end segment and the reg-ular product targeting the high-end segment (see Prop-ositions E.1 and E.2 in Online Appendix E). More-over, as in the base model, intertemporal customersegmentation still exists. As the segments targeted bythe product line are reversed, the roles of differentsegments in managerial insights will be reversed aswell. For example, when θ < 1 (resp., θ > 1), thosehigh-end (resp., low-end) customers who join late inthe group buying are the free-riders of the inferior(resp., premium) group-buying product, while thelow-end (resp., high-end) customers who join earlybenefit from shorter waiting times. In addition, groupbuying of an inferior product becomes less profitablethan that of a premium product. Compared with thevolume and margin strategies, offering group buyingof an inferior product benefits the firm only when theprobability of the high-end segment γ is sufficiently

Figure 5. (Color online) Price Path and Sample Path Under General Contingent Pricing

Figure 6. (Color online) Change of Customer Segmentationfrom Observable to Unobservable Group Buying


high and the batch size N is in an intermediate range(see Theorem E.1 in Online Appendix E).

5.5. Horizontally Differentiated ProductsIn the base model, we focus on vertically differenti-ated products. Nonetheless, ourmodel can be appliedto horizontally differentiated products. In OnlineAppendix F and Online Supplement G, we considertwo segments of customers, with one preferring thegroup-buying product (denoted by type-G) and theother preferring the regular product (denoted bytype-R). We assume that the two products are locatedat the two ends of a Hotelling line, that is, positions 0and vm � H + L, respectively. Type-G and type-R cus-tomers are located at locations L and H, respec-tively. Customers have a base valuation u > vm andthe unit traveling cost is normalized to 1. Hence,type-G (resp., type-R) customers’ valuations for thegroup-buying and regular products are u − L and u −H(resp., u −H and u − L), respectively. We confirm thatthe main insights regarding intertemporal customersegmentation are qualitatively preserved (see Prop-osition F.1 andTheoremF.1 inOnlineAppendix F). Thatis, no matter what products the firm sells, either hori-zontally or vertically differentiated, the fundamentaltrade-off in offering flexible-duration group buyingis the same. Because of customers’ sequential arrivaland the resulting different expected waiting times(and costs) in group buying, it is optimal for the firmto invite the customers who have the higher valua-tion or preference for the group-buying product, ormore patience, to sign up first at the early stage of thepledging process.

6. ConclusionIn this paper, we build a stylizedmodel to understandthe mechanism behind offering group buying of aspecial-edition product without a predetermined dead-line, alongwith offering the regular product.We explorethe interaction between customers’ sign-up dynamicsand the firm’s optimal product design, includingpricing and market segmentation. The current liter-ature on traditional group buying with a predeter-mined deadline does not take into account customers’waiting cost, and only focuses on the group-buyingproduct itself. In contrast, we consider customers’waiting cost as a unique operational feature in groupbuying. We investigate how to better design theproduct line by treating the product offered throughgroup buying as a contingent product. We find thatflexible-duration group buying can create an inter-temporal cooperation among customers throughtheir self-interested behavior. This kind of inter-temporal customer segmentation occurs when high-and low-end customers are invited to participate in

the group-buying campaign at different times duringthe pledging process.Our study has the following practical implications.

First, we show why flexible-duration group buyingcan be a profitable add-on alongside the regularproduct. Generally, if the inventory holding cost ishigh enough or customers are patient enough, of-fering a contingent product line through flexible-duration group buying is more profitable than of-fering a product line in the normal way, because thefirm can trade the high holding cost with the lowcustomer waiting cost. Second, we identify flexible-duration group buying as a more natural and fairerdiscrimination scheme. This is because the firm canpassively discriminate between different segments byoffering a constant price, which can be more ac-ceptable and deemed fairer than intertemporal pricediscrimination. Third, through customers’ intertemporalcooperation, the firm can obtain a higher profit withouthurting customers, that is, achieve a win-win-win sit-uation. Finally, to better design flexible-duration groupbuying, thefirm can adopt contingent pricing or concealthe sign-up information.Thanks to the internet and social network plat-

forms, the traditional retail industry has been revo-lutionized. Firms can now offer contingent productlines online via flexible-duration group buying.Whetherto adopt this contingent product scheme and how todesign it optimally depend heavily on both the supply-and demand-side characteristics of a firm. For example,beauty companies usually face limited shelf space (im-plying a high inventory holding cost), and hence, it isbetter for them to offer special-edition products throughonline group buying rather than a product line of make-to-stock products. Moreover, several group-buyingplatforms in the retail industry (e.g., Pinduoduo)have also resorted to flexible-duration group buying,since their inventory holding and offline managementcosts tend to be high. In addition, as the demand forfairness has risen in recent years, firms may wantto avoid proactive price discrimination in order tonurture sustainable customer relationships. To thisend, flexible-duration group buying can be a goodoption, because not only does it enable intertemporalcustomer segmentation through a one-price-for-allscheme, but also the price difference between the twoproducts is reduced. Last, depending on the demand-side characteristics, firms could further optimize thedesign of flexible-duration group buying in terms ofproduct offering, pricing, and information disclosure.For instance, tourist platforms could adopt contingentpricing to some extent as people are more likely totolerate differentiated pricing in the travel industry.Future research directions may include the fol-

lowing. First, one might consider alternative infor-mation structures adopted by the firm, such as


contingent information disclosure depending on thereal-time pledge-to-go state. Second, group-buyingcampaigns for multiple products might also be worthstudying, along with the question of how manycampaigns the firm wants to launch simultaneously.Third, it would be interesting to examine the be-havioral aspects of customers’ pledging decisions,such as risk aversion and bounded rationality. Fi-nally, a model in which both the price and batch sizeare endogenously determined, or one with an alter-native customer arrival pattern such as high-endcustomers arriving first followed by low-end, couldbe a fruitful future direction.

AcknowledgmentsThe first and second authors contributed equally to this pa-per. The second and third authors serve as the correspondingauthors of this paper. The authors gratefully acknowledgeHau Lee (the department editor), the associate editor, andtwo anonymous referees for their valuable comments, whichhelped significantly improve this paper.

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https://www.nytimes.com/2012/05/03/fashion/social-media-breathes-new-life-into-discontinued-beauty-products.html



https://doi.org/10.1287/mnsc.2018.3278

https://doi.org/10.1287/mnsc.2018.3278


https://www.popsugar.com/beauty/Bobbi-Brown-Makeup-Discontinued-Shades-Come-Back-21553978



https://hbr.org/2013/12/can-groupon-save-its-business-model

https://hbr.org/2013/12/can-groupon-save-its-business-model

https://www.wsj.com/articles/chinas-groupon-is-on-offerat-full-price-1531913943

https://www.wsj.com/articles/chinas-groupon-is-on-offerat-full-price-1531913943

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