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MANUFACTURING & SERVICEOPERATIONS MANAGEMENT

Vol. 15, No. 1, Winter 2013, pp. 57–71ISSN 1523-4614 (print) � ISSN 1526-5498 (online) http://dx.doi.org/10.1287/msom.1120.0398

© 2013 INFORMS

Advance Demand Information, Price Discrimination,and Preorder Strategies

Cuihong LiSchool of Business, University of Connecticut, Storrs, Connecticut 06269, [email protected]

Fuqiang ZhangOlin Business School, Washington University in St. Louis, St. Louis, Missouri 63130, [email protected]

This paper studies the preorder strategy that a seller may use to sell a perishable product in an uncertainmarket with heterogeneous consumers. By accepting preorders, the seller is able to obtain advance demand

information for inventory planning and price discriminate the consumers. Given the preorder option, the con-sumers react strategically by optimizing the timing of purchase. We find that accurate demand information mayimprove the availability of the product, which undermines the seller’s ability to charge a high preorder price.As a result, advance demand information may hurt the seller’s profit due to its negative impact for the preorderseason. This cautions the seller about a potential conflict between the benefits of advance demand informationand price discrimination when facing strategic consumers. A common practice to contain consumers’ strategicwaiting is to offer price guarantees that compensate preorder consumers in case of a later price cut. Underprice guarantees, the seller will reduce price in the regular season only if the preorder demand is low; however,such advance information implies weak demand in the regular season as well. This means that the seller canno longer benefit from a high demand in the regular season. Therefore, under price guarantees, more accurateadvance demand information may still hurt the seller’s profit due to its adverse impact for the regular season.We also investigate the seller’s strategy choice in such a setting (i.e., whether the preorder option should beoffered and whether it should be coupled with price guarantees) and find that the answer depends on therelative sizes of the heterogeneous consumer segments.

Key words : preorder; advance demand information; price discrimination; strategic consumer behavior;price guarantee

History : Received: September 10, 2010; accepted: March 22, 2012. Published online in Articles in AdvanceSeptember 4, 2012.

1. IntroductionPreorder refers to the practice of a seller acceptingcustomer orders before a product is released. Such apractice has become commonplace for a wide vari-ety of products in recent years. Consumer electronicproducts are among the categories for which pre-orders are often used. To name a few examples:In 2002, Apple reported the successful use of pre-orders for both the original and new iMac comput-ers, which revived the fortunes of the then-troubledcompany (Wall Street Journal 2002). When launchingthe new iPhone 3G S, the third generation of thesmart phone, Apple allowed customers to preorderthe product to secure the delivery on the releasedate (Keizer 2009). In early September 2009, Nokiaannounced that its first Linux-based smart phone, theN900, was available through preorders in the U.S.market (Goldstein 2009). Amazon offered the pre-order option to consumers when unveiling the secondversion of its e-book reader, Kindle 2 (Carnoy 2009).Game consoles, such as Nintendo’s Wii and Sony’sPlaystation 3, had been put on preorder before theywere formally released (Martin 2006, Macarthy 2007).

The preorder option is clearly beneficial to con-sumers because it guarantees prompt delivery onrelease. This is especially valuable when the productis a big hit and will be hard to find in stores dueto its popularity. It is not uncommon for extremelypopular gadgets to run out of stock immediately afterrelease. Consumers may have to wait for weeks oreven months to get the product. For instance, retail-ers warned customers in mid-2006 that no Wii unitswould be available without a preorder until 2007(Martin 2006). Apple sold out its preorder inventoryfor iPad before the release of the product (Berndtson2010). Preorders are often placed by enthusiastic con-sumers who are eager to be the first to get their handson a new product.

The preorder strategy may bring significant bene-fits to the seller as well. First, the seller can gaugehow much demand there will be for his product fromthe preorder sales. For new products with relativelyshort life cycles, the demand is usually hard to pre-dict, yet matching supply with demand is important.Thus, the advance demand information obtained frompreorder sales will be very useful in procurement,

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Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies58 Manufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS

production, and inventory planning. The use of pre-orders has been further promoted by the advent ofthe Internet and other information technologies thathave greatly reduced the costs associated with datacollection and processing. It has been reported thatby accepting preorders for iPhone 3G S, Apple didnot experience the same kind of stockout problemsthat occurred with its iPhone 3G due to a mismatchbetween supply and demand (Keizer 2009).

Second, the preorder strategy provides leverage forthe seller to charge different prices based on the tim-ing of a customer’s purchase. By accepting preorders,the seller can identify the consumer segment that iswilling to pay a premium price for guaranteed earlydelivery. These consumers are either new technol-ogy lovers or simply loyal fans of the brand. Theyare often referred to as “early adopters,” and theextra price they pay is called an “early adopter tax.”In fact, recently the early adopter tax has receivedmany discussions in various industries (see Nair 2007for video games; Jack 2007 for Apple’s iPhone; andFalcon 2009 for Sony’s latest gaming gadget, PSPGo). These discussions are corroborated by the obser-vation that many products on preorder exhibit pat-terns of price cutting. For example, Nokia startedaccepting preorders for its N900 smart phone at $649and then slashed the price to $589 when it wasclose to release (Goldstein 2009, King 2009). Walmartdropped the preorder price of myTouch 3G Slidefrom $199.99 to $129.99 shortly before the release(Tenerowicz 2010). Amazon charged a preorder priceof $359 for its Kindle 2 and then dropped the priceto $299 after the release (Carnoy 2009). Not surpris-ingly, consumers and market analysts may anticipatesuch price reductions and make purchasing decisionsaccordingly. See Coursey (2010) and Tofel (2010) formarket conjectures about the iPad’s price drop evenbefore it is released.

With the preorder option, a forward-looking cus-tomer will choose the timing of purchase: Placing apreorder guarantees the availability of the product,but this is probably at the expense of a higher price;waiting for a lowered price (e.g., after the product isreleased) sounds quite attractive, but meanwhile theconsumer has to face the risk of stockout. How mucha consumer is willing to pay for a preorder dependson her valuation of the product and the expecta-tion of future price and availability of the product.The seller needs to base inventory and pricing deci-sions on the presence of advance demand informa-tion and consumers’ strategic behavior. Despite theprevalence of the preorder practice, there has beensurprisingly little research that analyzes the seller’soptimal decisions while taking both demand informa-tion updating and forward-looking consumers explic-itly into account. In this paper, we study the preorder

strategy by developing a modeling framework thatincorporates all the important elements mentionedabove: the seller’s inventory and pricing decisions,advance demand information, and consumers’ strate-gic response. Specifically, we aim to address the fol-lowing research questions:

What is the value of advance demand information? Fromthe operations point of view, a major benefit of accept-ing preorders is that the seller can obtain advancedemand information. This information helps improvethe seller’s decision on initial production runs to sat-isfy demand, and its effectiveness has been frequentlylauded in the literature. However, a better matchbetween supply and demand implies that availabilityof the product becomes less of a concern, which mayaffect consumers’ willingness to pay for a preorder.Thus, it would be interesting to study when advancedemand information is valuable to the seller in thepresence of strategic consumer behavior.

What is the impact of price guarantees? Consumersmay be reluctant to place preorders if they expect apossible price cut in the future. To encourage earlypurchases, the seller may offer a price guarantee alongwith the preorder option. That is, a customer wouldreceive a refund if the price declines over time. Priceguarantee has become a common industry practiceduring the past decade (Lai et al. 2010). This raisesthe question of how price guarantees affect the valueof advance demand information.

When and how should a seller use the preorder strategy?A seller may choose to use or not to use the preorderstrategy. For example, Apple adopted the preorderstrategy for its iMac computers and iPhone 3G S, butnot for its iPhone 3G. Furthermore, when a preorderstrategy is used, the seller may choose to offer or notto offer the price guarantee. When and how to usethe preorder strategy is an important question for theseller.

The rest of this paper is organized as follows.Section 2 reviews the related literature. Section 3introduces the model setting. Section 4 presents theanalysis of the preorder strategy. Section 5 studiesthe impact of price guarantees. Section 6 comparesthe preorder strategy and the no-preorder strategy.Sections 7 discusses several extensions of the basicmodel. Section 8 concludes the paper. All proofs aregiven in Online Appendix A (provided in the elec-tronic companion; http://dx.doi.org/10.1287/msom.1120.0398).

2. Literature ReviewThis paper is related to the literature on inventoryplanning with advance demand information. Fisherand Raman (1996) propose a quick-response strategyunder which a retailer utilizes early sales for estimat-ing demand distribution. Eppen and Iyer (1997) study

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Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder StrategiesManufacturing & Service Operations Management 15(1), pp. 57–71, © 2013 INFORMS 59

a fashion-buying problem for retailers who can divertinventory to outlet stores using updated demandinformation. Gallego and Özer (2001, 2003), Özer(2003), and Özer and Wei (2004) study inventory man-agement with advance demand information obtainedfrom customer orders that are placed in advance oftheir needs. In these papers, the advance demandinformation is free and exogenously available.

When the seller faces price-sensitive customers,advance demand information becomes an endoge-nous outcome of pricing. Tang et al. (2004) andMcCardle et al. (2004) study the benefits of anadvance booking discount program by which aretailer offers a price discount to consumers whomake early order commitments prior to the sellingseason. Boyacı and Özer (2010) investigate the capac-ity planning strategy for a seller who collects pur-chasing commitments of price-sensitive customers.In these papers, the advance demand is realized basedon an aggregate demand function. Similar to thesepapers, we also consider the dependence betweenadvance demand information and pricing. However,we differ in that we model consumers’ strategicpurchasing decisions explicitly. Because of strategicwaiting of consumers, we show that more accurateadvance demand information does not necessarilybenefit the seller.

Existing papers that study advance selling withstrategic consumers typically consider the situationswhere consumers have uncertain value (or demand)about the product or service (e.g., sport event tickets,books, videos, computer games, etc.) when makingadvance purchases. In these papers, value uncertaintycauses price discounts for advance selling (an excep-tion is Xie and Shugan 2001, who show that a pre-mium advance-selling price may be possible when thecapacity is relatively small). This line of research oftenassumes that the product quantity (service capacity) isfixed, and models advance selling as a tool to increasemarket participation (e.g., Xie and Shugan 2001, Yuet al. 2007, Alexandrov and Lariviere 2012) or segmentthe market (e.g., Dana 1998, Chu and Zhang 2011).Zhao and Stecke (2010) and Prasad et al. (2011) con-sider a newsvendor retailer who uses advance sellingto obtain advance demand information. Differentlyfrom the above studies, we focus on the situations inwhich consumers face relatively certain product valuebut uncertain product availability. This is plausiblefor consumer electronic goods, for which there is usu-ally sufficient information for consumers to evaluatethe product before its release, but short product lifecycles and unpredictable market make it difficult tomatch supply with demand. In this case, consumersare willing to pay a premium preorder price to secureproduct availability. In our model, preorder is drivenby both benefits of premium profits and advance

demand information, and we study the interplaybetween these two forces.

There has been a growing interest in studying theimpact of strategic consumer behavior on a seller’sinventory decision (e.g., Su and Zhang 2008, 2009).Cachon and Swinney (2009) and Swinney (2011)examine the quick-response strategy that allows theseller to replenish inventory after the selling seasonstarts. They focus on the value of a late orderingopportunity (after demand is realized), whereas weinvestigate the value of an early selling opportunity(before inventory is ordered). Cachon and Swinney(2009) find that early demand information is morevaluable under strategic consumer behavior, which isin contrast with our findings. There is a key differencebetween these two papers: In Cachon and Swinney(2009), consumers may wait for a clearance sale, theprobability of which is lower if the seller can bettermatch supply with demand using advance demandinformation; in our model, consumers may wait fora price cut in the regular season after preorder sales,and the product availability in regular selling is higherwhen more advance demand information is obtainedfrom preorder sales. Swinney (2011) shows that quickresponse may hurt a seller’s profit when consumersface uncertain product valuations. We establish a par-allel result that advance demand information maybe detrimental to a seller’s profit, which does notdepend on value uncertainty of the product. Huangand Van Mieghem (2009) study the value of onlineclick tracking, which allows a seller to collect advancedemand information for pricing and inventory plan-ning. In their model, because clicking is separatedfrom purchasing, advance demand information fromclick tracking always benefits the seller.

This paper is related to the literature that stud-ies the use of price guarantees in intertemporal pric-ing. Png (1991) is one of the first to study theimpact of offering most-favored-customer protection(i.e., price guarantee) in a two-period pricing prob-lem. In Png’s model, a seller wishes to sell a fixedinventory to two types of consumers. The size of thetotal consumer pool is fixed, but the relative sizesof the two types are uncertain (so there is a per-fect negative correlation between the demand seg-ments). We differ from Png (1991) in important ways:First, we endogenize the seller’s inventory decision,which takes the preorder sales as an input. Second,we study the effect of advance demand informationby allowing general correlation between demand seg-ments. Lai et al. (2010) examine the value of usingprice guarantees for a newsvendor seller who hasthe opportunity to mark down the product at theend of the selling season. In their problem, the sellerdetermines the inventory before accepting consumerorders; therefore, they do not include the element of

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advance demand information. Levin et al. (2007) ana-lyze a dynamic pricing problem with fixed capac-ity and price guarantees. They focus on determiningthe optimal dynamic price and guarantee policies byassuming myopic consumers.

Finally, dynamic pricing problems have beenwidely studied in the revenue management litera-ture. The objective of these studies is to find the opti-mal pricing and capacity (inventory) allocation rulesto maximize a seller’s revenue/profit. Elmaghrabyand Keskinocak (2003) and Talluri and van Ryzin(2004) provide comprehensive reviews of these stud-ies. Recently, there have been an increasing num-ber of papers that incorporate consumers’ strategicresponse to a seller’s pricing or capacity decisions;see, for example, Su (2007), Aviv and Pazgal (2008),Elmaghraby et al. (2008), Liu and van Ryzin (2008),Yin et al. (2009), Levin et al. (2009), Jerath et al. (2009),and Mersereau and Zhang (2012). The contribution ofour paper is to consider the capacity decision alongwith demand updating in a dynamic pricing problem,which, to the best of our knowledge, has not yet beenaddressed.

3. ModelA seller sells a perishable product in a two-periodtime horizon. The product is released at the beginningof the second period (i.e., the regular selling season),but the seller may accept preorders in the first period(i.e., the preorder season). There are two types of con-sumers in the market: The high type has a valuationvH and the low type has a valuation vL for the prod-uct, where vH > vL. For instance, the high type mayrefer to technology-savvy consumers. The differencebetween these two valuations may represent the high-type consumers’ stronger preference over the producttechnology; or, it may be interpreted as the addi-tional psychological value a technology-savvy con-sumer obtains from owning the product (Darlin 2010).Product valuation is deterministic, which means thatthere is sufficient information for consumers to eval-uate the product before its release. This is typicallythe case for consumer electronic products. Many firmsnowadays use exhibitions, advertising, and their web-sites to offer demonstration and detailed productinformation to consumers, and comprehensive prod-uct reviews can often be found in professional mediacolumns before the release. Consumers are infinites-imal, as widely assumed in the literature. Usually,the technology-savvy consumers are early adopterswho follow the market trend closely. Therefore, weassume all the high-type consumers arrive in the firstperiod whereas all the low-type consumers arrive inthe second period (see Moe and Fader 2002 for asimilar assumption). In §7 we relax this assumption

and examine the robustness of our results. Becauseearly adopters value being among the first to ownthe product, we assume that the valuation vH willbe discounted by a factor � ≤ 1 if a high-type con-sumer chooses to wait and purchase the product inthe second period; that is, a high-type consumer’s val-uation becomes �vH in the second period. We assume�vH >vL. All players are risk neutral and forwardlooking, i.e., the seller aims to optimize his totalexpected profit, and the consumers maximize theirexpected net utility.

Market demand is uncertain in both periods. LetXi denote the demand of type i (i = H1L), whereXi follows a normal distribution êi (density �i) withmean �i and standard deviation �i. Let �i = �i/�i

be the ratio between the mean and standard devi-ation of Xi (i.e., the reciprocal of the coefficient ofvariation). Bivariate normal distribution has beencommonly used in the literature, especially whenmodeling demand information updating (see, e.g.,Fisher and Raman 1996, Tang et al. 2004). Let � ∈

4−1115 be the correlation coefficient between XH andXL. A positive correlation corresponds to situationswhere the primary uncertainty is on the total size ofthe market but not on the portion of each market seg-ment, whereas a negative correlation relates to situa-tions where the total size of the market is relativelycertain, but the relative sizes of the two demand typesare uncertain. For ease of exposition, we will focus on� ≥ 0 in this paper; the analysis of the case � < 0 issimilar and will be discussed in §7.1. We may view� as an indicator of the accuracy of advance demandinformation. That is, a larger � means less uncertaintyin the second-period demand with the observationof the first-period demand. Define X ≡ 4XH −�H 5/�H ,which follows the standard normal distribution; letê (�) denote the distribution (density) function forthe standard normal distribution. We will work withX instead of XH due to their one-to-one relation-ship. For a given realization x of X, the updatedlow-type demand X̃L4x5 follows a normal distributionwith mean �̃L4x5=�L + ��Lx and standard deviation�̃L = �L

√

1 −�2.We first describe the seller’s problem. The seller

sets a preorder price p1 in the first period. Given thisprice, the high-type consumers make their preorderdecisions. After the number of preorders q is received,the seller decides the second-period price p2 and thetotal production/order quantity q+Q, where Q is thequantity used to satisfy the second-period demand.There is a constant unit cost c (c < vL) for the product.Unsold products at the end of the second period havenegligible salvage value, and there is no penalty forunsatisfied demand. Thus, in the second period theseller essentially faces a newsvendor problem withpricing. Note that the seller observes the preorder

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quantity and may use this information to update hisbelief about the second-period demand when makingthe quantity decision.

Next we describe the consumers’ problem. Theproblem for a low-type consumer is trivial: As shearrives in the second period, she buys the product ifand only if p2 ≤ vL. A high-type consumer, arriving inthe first period, needs to decide whether she shouldplace a preorder or delay the purchasing to the nextperiod. If she places a preorder, then she pays theprice p1 and will definitely receive the product; oth-erwise, she may purchase the product at a possiblylower price p2 in the regular season, but under the riskthat the product is no longer available. Whether a con-sumer is willing to preorder depends on her belief ofthe rationing risk, i.e., the chance the product will beavailable in the second period. We model such a beliefusing a parameter � ∈ 40115: A consumer believesthat a � portion of consumers remaining in the mar-ket will get the product before her. On one extreme,� = 0 means a consumer is optimistic and believesthat she will be the first in the waiting line; on theother extreme, � = 1 means that the consumer is pes-simistic and thinks she will be the last in the waitingline. Cachon and Swinney (2009) provide a detaileddiscussion of this modeling approach and focus onspecific � values for tractability. For ease of exposi-tion, we assume � = 1/2 in this paper. The qualitativeinsights will remain if this assumption is relaxed (seeLemma 6 in Online Appendix A for the analysis ofgeneral �). An alternative approach is to use the pro-portional rationing rule (see, e.g., Png 1991). Again,this will not change the main results as shown by theextension in §7.3.

4. Preorder StrategyIn this section we analyze the seller’s preorder strat-egy. In the analysis, we start with the seller’s priceand quantity decisions in the second period, assum-ing that all high-type consumers have chosen to pre-order given the first-period price. Then we analyzethe seller’s first-period price decision, which inducesthe high-type consumers to preorder under a rationalexpectations equilibrium.

In the second period, with the number of pre-orders q received in the first period, the seller mustdetermine the price p2 and the order quantity Q to sat-isfy the second-period demand (besides the quantityq to be ordered for the preorder demand). Because allhigh-type consumers are assumed to choose preorder,the number of preorders is equal to the high-typedemand, q = xH , and only the low-type consumers arepresent in the second period. Thus, it is optimal forthe seller to set p2 = vL. The seller’s order quantityQ depends on the high-type demand realization xH .

Define zL ≡ ê−144vL − c5/vL5, where ê4zL5 is the criti-cal fractile for the low-type demand. Then the optimalorder quantity for the second period is given by

Q4x5= �̃L4x5+ zL�̃L1 (1)

where �̃L4x5 = �L + ��Lx and �̃L = �L

√

1 −�2 are themean and standard deviation of the updated low-typedemand X̃L4x5 for x ≡ 4xH − �H 5/�H . The resultingprofit for the second period is

çL4x5= 4vL − c54�L +��Lx5− vL�4zL5�L

√

1 −�20 (2)

Note that the expected second-period profit isƐ6çL4X57 = çL405 because Ɛ6X7 = 0. Throughout thepaper we use Ɛ to denote the expectation operation.

In the first period, a high-type consumer willchoose between preorder and wait. We consider sym-metric strategies for the high-type consumers becausethey are homogeneous. Let r denote the consumers’reservation preorder price, at which they are indiffer-ent between preorder and wait. If a consumer pre-orders at price r , then she receives a net utility vH − r ;if she waits, then her expected utility is 4�vH − p25�,where � is the consumer’s belief of the availability ofthe product in the second period. By definition weknow that vH − r = 4�vH −p25� or r = vH − 4�vH −p25�.Here we assume a consumer always preorders if thereis a tie, because the seller can always reduce the priceby an infinitely small amount to break the tie; see Png(1991) and Xie and Shugan (2001) for similar assump-tions. The seller must form a belief �r about the con-sumers’ reservation price r . Given the belief �r , it isclear that the seller’s optimal price to induce preorderis p1 = �r .

We focus on the rational expectations (RE) equi-librium of the above game. This equilibrium con-cept has been recently applied to various settings inthe marketing and operations literatures (see Su andZhang 2009 and the references therein). In any REequilibrium, the players’ beliefs must be consistentwith the actual outcome, and the players have nounilateral incentives to deviate. Specifically, the equi-librium requires the following conditions: (i) p1 = �r ;(ii) p2 = vL; (iii) the seller orders the quantity accord-ing to (1) for the second period; (iv) �r = r ; and (iv) theconsumer’s belief of product availability in the secondperiod satisfies

� = Ɛ

[

Pr(

X̃L4X5

2<Q4X5

)]

= Ɛ

[

ê

(

�L +�X√

1 −�2+ 2zL

)]

1 (3)

where the second equality is by plugging X̃L4x5 andQ4x5 into the first expression. Among these condi-tions, (i), (ii), and (iii) state that the seller chooses the

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profit-maximizing decisions, whereas (iv) and (v) arethe consistency conditions (players’ beliefs are consis-tent with the actual outcome). The above discussionleads to the following proposition that characterizesthe equilibrium outcome of the game.

Proposition 1. There is a unique RE equilibriumunder the preorder strategy. In the equilibrium, the sellersets p1 = vH − 4�vH − p25� and p2 = vL, where � is givenin (3), and all consumers will preorder in the first period.

For notational convenience, define ã = �vH − vL.From Proposition 1, the seller’s total expected profitis (we use superscript p for preorder strategy):

çp= 4vH −ã� − c5�H +çL4051 (4)

where 4vH −ã�−c5�H is the seller’s first-period profit,and çL405 is the second-period profit.

4.1. Impact of Demand Correlation 4�5What is the value of advance demand information inthe preorder strategy? The accuracy of the advanceinformation can be measured by the demand corre-lation, �. For the positive domain, a higher � cor-responds to more accurate advance information (i.e.,the uncertainty of the low-type demand is lower afterupdating). In this subsection, we investigate how theseller’s profit depends on �.

Based on Equation (4), the derivative of çp withrespect to � can be written as

dçp

d�= −ã�H

d�d�

+d

d�çL4050 (5)

The demand correlation � affects both the first-periodprofit (through its influence on �, the equilibriumbelief of product availability in the second period)and the second-period profit çL405. It is clear that4d/d�5çL405= vL�4zL5�L4�/

√

1 −�25 is positive—moreaccurate advance demand information helps the sellerbetter match supply with demand, thus improvingthe second-period profit. The effect of � on the first-period profit depends on its impact on �, which ischaracterized in Lemma 1.

Lemma 1. (i) For c < vL < 2c (i.e., zL < 0), � isincreasing in �.

(ii) For vL ≥ 2c (i.e., zL ≥ 0), � is decreasing in �.

Lemma 1 suggests that the availability probability �may either increase or decrease in the demand corre-lation �, depending on zL.1 When vL < 2c, then zL < 0,and the order quantity decreases in the updateddemand variance �̃L based on Equation (1). Becausea greater � reduces the variance of the updateddemand, both the order quantity Q and its associatedproduct availability � increase in �. If vL ≥ 2c, thenzL ≥ 0, and the seller will order more when facing

1 Lemma 6 in Online Appendix A studies general � ∈ 40115 andidentifies a similar threshold structure based on the value of zL.

greater demand uncertainty �̃L. This causes the prod-uct availability � to decrease in �. Because the first-period price hinges upon the product availability, theresult in Lemma 1 implies that depending on theproblem parameters, advance demand informationmay or may not help price discrimination in a pre-order setting.

Now we are ready to analyze the influence of� on the seller’s total profit in the preorder strat-egy. A higher � means lower uncertainty about thelow-type demand in the second period, which helpsimprove the second-period profit. However, moreaccurate demand information may reduce the first-period profit at the same time: Based on Lemma 1(i),a higher � may lead to greater availability in the sec-ond period, which prevents the seller from charginga high preorder price (see Proposition 1). Therefore,the seller’s total profit may not necessarily increasewith �. Define the following threshold value

�̃4�5≡ −vL�4zL5�L

2ãzL�42zL√

1 −�2 +�L5(6)

with the following property:

Lemma 2. (i) For zL ∈ 4−�L/2105, �̃4�5 increasesin �.

(ii) For zL ≤ −�L/2, �̃4�5 is quasi-convex in �.

The threshold �̃4�5 plays a critical role in the rela-tionship between the seller’s total profit and � asshown in the following proposition.

Proposition 2. (i) If c < vL < 2c (i.e., zL < 0), thençp increases in � when �H < �̃4�5, and decreases in �when �H ≥ �̃4�5. In particular, there exists an �v > 0 suchthat çp always decreases in � if vL < c+ �v.

(ii) If vL ≥ 2c (i.e., zL ≥ 0), then çp always increasesin �.

Proposition 2 suggests that the seller’s profitincreases in � only when the low-type valuation issufficiently large (vL ≥ 2c) or the high-type demandis relatively small (�H < �̃4�5). The intuition is asfollows: When vL is large, a greater � improvesthe second-period profit and also the preorder price.When vL is small, increasing � has a negative effecton the preorder price. This negative effect, however, isdominated by the positive effect on the second-periodprofit if �H is low. Therefore, more accurate advanceinformation benefits the seller either when vL is largeor when �H is small.

Figure 1 illustrates the situations in which the profitmay decrease in �. It draws çp as a function of �for different �H and vL values. If vL is less than 2cbut not too small (−�L/2 < zL < 0), �̃4�5 is increasing(Lemma 2(i)). Thus, çp decreases in � when � is rela-tively low. This case is shown in the plot on the left.

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Figure 1 Impact of � on the Seller’s Profit in the Preorder Strategy

0.09

0.08

0.07

0.06

0.050.01

0.05

0.08

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

�H = 0.11

�H = 0.004

0.003

0.002

0.001

�L = 1.02 �L = 1.001

� �

Note. �L = 5, �H = 3, �L = 405, vH = 2, c = 1, and �= 1.

When vL is very small (zL ≤ −�L/2), �̃4�5 is quasi-convex (Lemma 2(ii)). Thus, çp decreases in � when� is intermediate. This case is shown in the plot onthe right.

The above analysis delivers a message that moreaccurate advance demand information (higher �) doesnot necessarily improve a seller’s profitability. Thisis in contrast with the traditional wisdom that earlysales information (e.g., test sales, preorders) helpsa firm better forecast demand and hence increaseprofit (e.g., Fisher and Raman 1996). The new driv-ing force underlying our model is the counteract-ing effects of advance demand information and pricediscrimination: Because of strategic consumer behav-ior, a better ability to match supply with demand mayactually prevent the firm from charging premiumprices to extract consumer surplus. The negative effectof � can be substantial in some situations: In theextreme case where � is close to 1 with a large �, theseller has to charge a preorder price almost equal tothe regular-season price vL, losing the opportunity toprice-discriminate different customer segments. Thiscan lead to substantial profit loss of the seller if theproduct value is highly diverse between the two cus-tomer segments (large ã) or the high-type customersegment is large (high �H ). Practically speaking, ourresults imply that the preorder strategy could be lessattractive when preorders are highly predictive of theregular-season demand.

5. Preorder with Price GuaranteeUnder a price guarantee, a consumer will be com-pensated if the product price declines over time. For

example, Apple promises to refund the difference ifprice is dropped within 14 days of purchase.2 A pur-pose of price guarantee is to eliminate consumers’incentives to wait for markdowns so the seller canenjoy quicker sales at a relatively high price. Gener-ally, there should be some technological requirementsfor implementing a price guarantee, and it might becostly to satisfy these requirements (e.g., the sellerhas to invest in hardware and manpower to monitortransactions and manage the refunding process). Forsimplicity, we assume that all necessary technologiesare already in place and there is a zero implementa-tion cost. Under this assumption, we study the impactof the price guarantee on the seller’s preorder strat-egy. We aim to answer the following two questions:First, when should a seller offer a price guaranteealong with the preorder option? Second, how does theintroduction of the price guarantee affect the value ofadvance demand information?

5.1. Value of Price GuaranteeWith a price guarantee, the seller needs to determinenot only the prices p1 and p2 in the two periods, butalso the refund � paid to each preorder consumer ifp2 < p1. An intuitive special case is � = p1 − p2, whichwe call a full-price guarantee. Most of the existingliterature focuses on this special case (see, e.g., Png1991, Lai et al. 2010). Here we consider the generalcase without imposing any restriction on �.3 Similar

2 http:// store.apple.com/Catalog/US/Images/salespolicies.html (lastaccessed August 8, 2012).3 We have also analyzed the full-price guarantee and obtainsimilar qualitative results. In particular, the full-price guarantee

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to the preorder mechanism without price guarantee,we first analyze the seller’s decisions in the secondperiod, assuming that all high-type consumers havechosen to preorder. Then we analyze the seller’s deci-sions in the first period that induce consumers to pre-order under a rational expectations equilibrium.

Under a price guarantee, the second-period price isnot necessarily p2 = vL because the seller may chooseto maintain a high price to avoid refunding the ear-lier buyers. At the beginning of the second period, theseller’s price decision depends on the realization ofthe high-type demand in the first period, xH , or equiv-alently, x = 4xH −�H 5/�H . Specifically, the price willbe reduced if and only if the profit from the low-typeconsumers, çL4x5, is greater than the total refund,�4�H + �Hx5, where çL4x5 is given in (2). Define thebreakeven level of x to be

x̂4�5≡çL405−��H

��H − 4vL − c5��L

0 (7)

Negative demand realizations from a normal dis-tribution may cause impractical price reduction deci-sions. For instance, the seller may reduce the pricewhen the high-type demand is negative, because inthis case the refund becomes essentially a net trans-fer to the seller; or, the seller may not reduce theprice simply because the size of the low-type segmentcould be negative. To avoid these unrealistic scenar-ios, we follow the literature (e.g., Fisher and Raman1996) to assume hereafter the probability of negativedemand is negligible; that is, we treat Pr4XH ≤ 05 andPr4XL ≤ 0 �XH 5 as zero as an approximation. It can beshown that such an approximation is accurate in theasymptotic situation where the probability of nega-tive demand approaches zero (see Online Appendix Afor more explanation). In addition, numerical exper-iments indicate that the qualitative insights derivedunder this approximation will hold when the coeffi-cient of variation is reasonably small (�i reasonablylarge).4 Lemma 3 reveals how the price reductiondecision depends on the refund � and high-typedemand realization x.

Lemma 3. (i) If � ≤ 4vL − c5�4�L/�H 5, then pricereduction will always happen.

(ii) If � > 4vL − c5�4�L/�H 5, then price reduction hap-pens when x < x̂4�5, and x̂4�5 decreases in �.

For � < 4vL − c5�4�L/�H 5, the seller will alwaysreduce the price regardless of x to benefit fromserving the low-type consumers. This case essentially

performs very close to optimal. More details can be foundin Online Appendix B (available in the electronic companion;http://dx.doi.org/10.1287/msom.1120.0398).4 For example, with �H = 3 and �L = 4, the probability of a negativeXH is only 000014 and the conditional probability of a negative XL isat most 00004. The main insights hold in this example, even withoutthe approximation.

reduces to our original preorder strategy with aneffective preorder price p1 − �. Hence, without los-ing generality, we restrict our attention to � ≥ 4vL − c5�4�L/�H 5. In this case, price reduction occurs onlywhen the preorder demand is relatively small (x < x̂);otherwise, the seller will keep the price at p1 to avoidrefunding the large group of preorder consumers. Ouroriginal preorder strategy can be considered as onewith a price guarantee in which the refund is so lowthat the price will always be dropped, i.e., x̂ ≥ �H .

Next we analyze the seller’s first-period decisionon the preorder price p1 and refund �. Note that theprice reduction threshold, x̂4�5, depends on � but noton p1. If a high-type consumer preorders, her expectedutility is u14p11�5= vH −p1 +�ê4x̂4�55; if she waits tillthe second period, her expected utility is u24p11�5 =

ã�̂4x̂4�55, where

�̂4x̂5 ≡ Ɛ

[

Pr(

X̃L4X5

2<Q4X51X < x̂

)]

= Ɛ

[

ê

(

�L +�X√

1 −�2+ 2zL

)

∣

∣

∣

∣

X ≤ x̂

]

ê4x̂5 (8)

is the probability that the product is available at thelow price (p2 = vL) in the second period. By comparingEquations (8) and (3), we know �̂4x̂5≤ �.

Given �, the optimal p1 must satisfy u14p11�5 =

u24p11�5 so that the high-type consumers will pre-order. This gives

p14�5= vH +�ê4x̂4�55−ã�̂4x̂4�550 (9)

Because there is a one-to-one relationship betweenx̂ and �, we will work with the decision variablex̂ instead of �, which is more convenient. For anygiven x̂, we have �4x̂5 = çL4x̂5/4�H + �H x̂5 and p1given by Equation (9). Thus, the seller’s profit canbe written as (we use the superscript g for priceguarantee):

çg4x̂5 = 4p14x̂5− c5�H

+ Ɛ6çL4X5−�4x̂54�H +�HX5 �X < x̂7ê4x̂5

= 4vH −ã�̂4x̂5− c5�H

+ Ɛ6çL4X5−�4x̂5�HX �X < x̂7ê4x̂50 (10)

When should the seller provide a price guaran-tee? We may compare the seller’s profits under thepreorder strategy with and without price guarantee.From (10), the profit margin from the high-type con-sumers in the price guarantee mechanism is vH −

ã�̂4x̂5 − c, which is greater than the one without aprice guarantee, vH − ã� − c. This is true because aprice guarantee enables the seller to charge a higherpreorder price by discouraging consumers from wait-ing. Such an observation suggests that offering a price

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guarantee will be more effective if the size of thehigh-type consumers is larger. Indeed, Proposition 3confirms this intuition. We use çg = max�ç

g4�5 todenote the seller’s optimal profit in the price guaran-tee mechanism.

Proposition 3. Suppose �H is fixed. Then there existsa �̂

gH such that çg >çp (i.e., the seller should offer a price

guarantee in the preorder strategy) if and only if �H > �̂gH .

Proposition 3 suggests that a price guarantee is ben-eficial to the seller only when �H is above a thresh-old value, �̂g

H (a closed-form expression of �̂gH can be

found in the proof). In other words, the size of thehigh-type consumer segment must be large enoughto warrant the use of price guarantees; otherwise, theseller should not offer a price guarantee. Two pointsare worth mentioning about this threshold result:First, fixing �H implies that the standard deviationof the high-type demand changes proportionally withthe mean. We find from numerical analysis that a sim-ilar result holds when �H , rather than �H , is fixed.That is, the result can be extended to settings witha fixed standard deviation. Second, the threshold �̂

gH

depends on the relative sizes of the two consumersegments. Analogously, it can be shown that for afixed �L, there is a threshold �̂

gL such that the price

guarantee is preferred if and only if �L < �̂gL. This

is the counterpart of Proposition 3 and is thereforeomitted.

5.2. Impact of � Under Price GuaranteeWe have shown in §4.1 that a higher � may decreasethe seller’s profit in the preorder strategy because ofthe strategic waiting behavior. The underlying reasonis that when zL < 0, a higher � improves the productavailability in the second period, and thus the sellerhas to charge a lower preorder price. How does thisresult change when price guarantees are used? Herewe investigate the impact of � under price guarantees.As an intermediate result, Lemma 4 reveals the effectof � on the probability that the product is available atthe low price in the second period, �̂.

Lemma 4. (i) For c < vL < 2c (i.e., zL < 0) and a givenx̂, d�̂/d� ≤ 0 at � = 0, and there exists �� > 0 such thatd�̂/d�≥ 0 for �≥ 1 − ��.

(ii) For vL ≥ 2c (i.e., zL ≥ 0) and a given x̂, �̂4x̂5=ê4x̂5is independent of �.

Recall from Lemma 3 that a price reduction occursonly when the high-type demand is relatively low(x < x̂), which indicates a weak low-type demand aswell. Therefore, in case of a price reduction, a higher� implies both smaller mean and variance for theupdated low-type demand. Whereas the effect on thevariance drives the second-period product availabil-ity to increase in � with zL < 0, the effect on the mean

does the opposite. Therefore, as shown in Lemma 4(i),�̂ may decrease (thus the preorder price may increase)in � when � is small. This is in contrast to the resultwithout a price guarantee that � is always increasingin � for zL < 0. When zL ≥ 0, under the assumptionthat the probability of negative demand is negligible,it can be shown that the second-period product avail-ability upon price reduction is one, independent of �.Thus, �̂ (and �) is independent of � for zL ≥ 0, asshown in Lemma 4(ii).

Because the influence of � on the product avail-ability applies only when there is a price reduction,a price guarantee will mitigate the negative effect of� on the preorder price. Furthermore, the price guar-antee may even reverse the effect when � is small, assuggested by Lemma 4(i). However, in the meantimethe price guarantee prevents the seller from serving alarge low-type segment, because the price is reducedto target the low-type segment only when the seg-ment is relatively small. This implies that the priceguarantee introduces an adverse effect of � on thesecond-period profit. To better understand the impactof � on the seller’s total profit, we focus on two spe-cial cases: the case when vL is small (close to c) andthe case when vL is large (greater than 2c). When vL isvery small, the second-period profit is negligible, andthe effect of � focuses on the price and profit in thepreorder period. When vL ≥ 2c, the product availabil-ity in the second period (conditional on a price reduc-tion) is independent of � according to Lemma 4(ii);thus, the effect of � is primarily on the second-periodprofit.

Proposition 4. (i) There exists �1��11��2 > 0 suchthat, if vL − c < �, then dçg/d� > 0 for � = 0 anddçg/d� < 0 for � > 1 − ��1, with d�̂g

H/d� < 0 for � = 0and d�̂g

H/d�> 0 for �> 1 − ��2.(ii) When vL ≥ 2c (i.e., zL ≥ 0), çg is quasi-convex

( first decreasing and then increasing) in �; in addition, �̂gH

is increasing in �.

When vL is very small, we know from Proposi-tion 2(i) that the seller’s profit without price guaranteealways decreases in �. With a price guarantee, how-ever, Proposition 4(i) shows that the seller’s profit isincreasing in � for � close to 0, and decreasing in �for � close to 1. Through numerical experiments, weobserve that çg is quasi-concave over � ∈ 60115. Thisdifference results from the fact that the price guaran-tee mitigates and may even reverse the negative effectof � on the preorder price, especially when � is small.

Proposition 4(ii) also indicates that �̂gH decreases in

� when � is close to 0, and increases in � when � isclose to 1. Again, we observe from numerical exper-iments that �̂

gH is quasi-convex over � ∈ 60115. Thus,

when vL is small, price guarantees are favored only

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for intermediate �; when � is either high or low, thepreorder strategy without price guarantee is better.

When vL ≥ 2c, recall from Proposition 2(ii) thatthe seller’s profit without price guarantee is alwaysincreasing in �. Interestingly, Proposition 4(ii) showsthat, with the optimal price guarantee, the seller’sprofit may be decreasing in � for sufficiently small �.That is, more accurate advance demand informationmay hurt the seller’s profit under price guaranteeseven when it would only benefit the seller withouta price guarantee. This result is due to the negativeeffect of � on the second-period profit introduced bythe price guarantee. In comparison, note that withoutprice guarantee, the negative effect of � is realizedonly on the first-period profit.

From Proposition 3, the seller prefers to use a priceguarantee when �H > �̂

gH . Proposition 4(ii) suggests

that, for vL ≥ 2c, the seller is less likely to use aprice guarantee as � increases. This is again due tothe adverse effect of a higher � on the second-periodprofit. Such an effect is substantial for large vL, mak-ing price guarantees less attractive as � increases.

6. No-Preorder StrategyWhen should the seller offer the preorder option? Inthis section, we compare the preorder strategy withthe no-preorder strategy. With no preorder, the prod-uct is sold only in the regular selling season (i.e., afterthe product is released). As a result, the seller does nothave advance demand information when deciding theorder quantity. In this case, the seller may charge ahigh price to target the high-type consumers first, andthen drop the price to satisfy the low-type consumersif there is still inventory left. For ease of exposition,we divide the regular season into two stages, andlet p1 and p2 (p1 ≥ p2) denote the prices in the twostages (we use “stage” to distinguish from the notionof “period” used in the previous sections). Below westudy the game under no preorder and then comparethe three strategies we have examined so far. Again,we analyze the equilibrium in which all high-typeconsumers purchase in the first stage; in this equilib-rium, the second-stage price p2 is set to vL to targetthe low-type consumers. As in the previous models,if a high-type consumer waits to purchase in the sec-ond stage, the product value is discounted to �vH forthe loss of early-adopter advantages.

Let the seller’s order quantity be Q. If a high-typeconsumer delays purchasing to the second stage, shefaces the availability probability

�n4Q5= Pr4XH + �XL <Q5=ê

(

Q−�a

�a

)

1 (11)

where �a =�H + ��L and �a =√

�2H + �2�2

L + 2��L�H

are the mean and standard deviation of XH +�XL. The

superscript n stands for no preorder. In the RE equi-librium, for a given Q, the first-stage price satisfies

p14Q5= vH −ã�n4Q50 (12)

Given Q and p1, the seller’s total profit is

çn4p11Q5 = 4p1 − vL5Ɛ6min4Q1XH 57

+ vL Ɛ6min4Q1XH +XL57− cQ0

The seller’s optimal order quantity Qn is given bythe first-order condition 4¡/¡Q5çn4p11Q5 = 0 for p1defined in (12). The seller’s total profit in equilibriumcan be written as

çn= ã41 − �n4Qn55Ɛ6min4Qn1XH 57

+ vL Ɛ6min4Qn1XH +XL57− cQn1 (13)

where ã41 − �n4Qn55 represents the premium marginfrom the high-type consumers.

We may compare the seller’s profit in Equation (13)to that under the preorder strategy in Equation (4),which leads to the following result.

Proposition 5. Suppose �H is fixed. There exists a �̂nH

such that çp >çn (i.e., the seller prefers the preorder strat-egy over the no-preorder strategy) if and only if �H < �̂n

H .

Proposition 5 states that the preorder strategyshould be used if and only if the size of the high-typedemand is less than a threshold value, �̂n

H . Throughnumerical experiments we find that a similar thresh-old value exists when �H , rather than �H , is fixed.Thus, we conclude that the preorder strategy out-performs the no-preorder strategy when the relativesize of the high-type customers is smaller than acertain threshold. The intuition can be explained asfollows. Without advance demand information, thefuture product availability tends to be lower, thusraising a high-type consumer’s willingness to pay atthe beginning. With a greater profit margin from thehigh-type consumers, the no-preorder strategy bene-fits more from the expansion of the high-type demandsegment than the preorder strategy. It can be shownthat both çp and çn are linearly increasing in �H (forfixed �H ). Thus, the search of �̂n

H is straightforward,as shown in the proof of the proposition.

Thus far we have studied three different strategies:no preorder, preorder, and preorder with price guar-antee. The threshold values in Propositions 3 and 5may help the seller make pairwise comparisons ofthe strategies. However, ranking all three strategychoices is difficult. Hence, we rely on an extensivenumerical study to obtain some insights. We reporttwo main observations from the numerical analysis.First, as �H increases, the seller’s optimal strategyshifts from preorder to no preorder and then to pre-order with price guarantee. Second, the range for the

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Figure 2 Comparison of çp, çg, and çn for Different �H and vL Values

0.06

0.05

0.04

0.03

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.01 0.02 0.03

�H�H

�L = 1.01 �L = 1.05

0.04 0.05 0.06 0.05 0.10 0.15 0.20 0.25 0.30

Πp

Πg

Πn

Note. �L = 5, �L = 405, �H = 3, vH = 2, c = 1, and �= 1.

no-preorder strategy to stand out may degenerate tozero, especially when vL is large. Figure 2 shows arepresentative example, where the left plot illustratesthe first observation and the right plot shows the sec-ond observation.

Here is the intuition behind these observations:Based on Proposition 5, we know the preorder strat-egy dominates the no-preorder strategy when �H

is relatively small (�H < �̂nH ). From Proposition 3,

we know the price guarantee strategy outperformsthe preorder strategy when �H is relatively large(�H > �̂

gH ). Therefore, the preorder strategy is opti-

mal among the three when �H is sufficiently small(�H < min4�̂n

H1 �̂gH 5). Now we focus on the compari-

son between the no-preorder strategy and the priceguarantee strategy. In the no-preorder strategy, theprofit margin from the high-type consumers is inde-pendent of �H . In the price guarantee strategy, by con-trast, the profit margin from the high-type consumersis increasing in �H : Because of the refund liability, theseller is less likely to reduce the price when facing alarger �H ; this reduces a high-type consumer’s incen-tive to wait, leading to a higher preorder price. Hence,under the price guarantee strategy, the profit marginfrom the high-type consumers will be higher than thatin the no-preorder strategy when �H is sufficientlylarge. This suggests that the price guarantee strat-egy dominates the no-preorder strategy for large �H .Thus, the no-preorder strategy can only stand outfor intermediate �H . However, such a range maydegenerate to zero when vL is large for the followingreason. With a large vL, the advance demand infor-mation obtained from the preorder sales will be morevaluable because selling to the low-type consumers is

highly profitable. Therefore, for large enough vL, theseller should always accept preorders, either with orwithout a price guarantee.

7. ExtensionsThe basic model studied in the previous sections isbuilt on some assumptions that help maintain ana-lytical tractability and reveal the key driving forcesunderlying the results. This section relaxes some ofthe assumptions and discusses their implications tothe analysis and results.

7.1. Negative Demand Correlation 4� < 05So far we have focused on �≥ 0 in the analysis. Thisis appropriate when modeling new product introduc-tions, of which the total market size is variable andeach consumer segment expands with the total mar-ket. There may be situations where the total marketsize is relatively certain, but the portion of each con-sumer segment is variable. These situations can becaptured by a negative demand correlation (see, forexample, a model with �= −1 in Png 1991). For com-pleteness, here we provide a brief discussion of neg-ative demand correlation.

With a negative �, a small � (thus a large ��)means more accurate advance information. A nega-tive � does not change the analysis of the preorderstrategy without price guarantee in §4. By replacing� with −�, it can be readily shown that all results in§4 apply to � ∈ 4−1107 as well. Next we discuss thepreorder strategy with price guarantee.

Under a price guarantee, the seller will lower theprice in the second period if and only if the realized

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high-type demand is less than a threshold. In contrastto the case of positive �, now � < 0 means that pricereduction occurs when the low-type demand is rela-tively high. That is, as �� increases, the variance ofthe low-type demand under price reduction becomessmaller, whereas the mean becomes stochasticallylarger. Therefore, under a negative demand correla-tion, the negative effect of advance information intro-duced by price guarantees on the second-period profitdoes not exist anymore.

Although � < 0 removes the negative impact ofincreasing �� on the second-period profit, interest-ingly, it aggravates the negative effect on the first-period profit. This is because, with a higher ��, thelow-type demand in case of price reduction tends tobe larger, which motivates the seller to order more tosatisfy demand in the regular season. This improvesthe product availability in the regular season andleads to a lower preorder price. Thus, for � < 0, ahigher �� will have a stronger adverse impact on thepreorder price under a price guarantee; as a result,the seller’s optimal preorder price always decreasesin ��.

To summarize, with negative �, all results aboutthe preorder strategy without price guarantee remain.Under a price guarantee and � < 0, a larger �� hurtsthe first-period profit (in a stronger way compared to�≥ 0), but always improves the second-period profit.Therefore, with � < 0, we still have the result thatmore accurate advance demand information may hurta seller’s profit under a price guarantee, although thisresult is solely caused by the conflict between advancedemand information and price discrimination.

7.2. Mixed ArrivalsIt has been assumed in the basic model that thehigh-type consumers arrive in the preorder season,whereas the low-type consumers appear in the reg-ular season. As a result, the regular price is alwaysvL and lower than the preorder price. In this subsec-tion we extend the basic model to consider a mixedarrival model where the high-type customers arrivein both periods. For simplicity, we still assume that allthe low-type consumers show up in the regular sell-ing season.5 Let � (�≤ 1) be the fraction of high-type

5 A more general model is to allow some low-type consumers in thepreorder season as well. However, this will not change the anal-ysis as long as the preorder sales target the high-type customersonly. In this case, the low-type consumers will wait to purchasethe product in the regular season. For fashion and innovative prod-ucts, the high-type consumers usually dominate in the preorderseason whereas the low-type consumers dominate in the regularseason, and they differ substantially in their willingness to pay. Itis unlikely the seller sets a low price to satisfy both types of con-sumers in the preorder season. Therefore, we focus on the situationwhere the preorder sales target the high-type consumers only.

consumers to arrive in the preorder season (1 −� isthe fraction in the regular season). We use X1H =

�XH and X2H = 41 − �5XH to denote the high-typedemand in the preorder and regular seasons, respec-tively. Let the correlation coefficient between X1H andXL be �. Thus, the seller can update his belief aboutboth the low-type demand and second-period high-type demand after observing X1H : Given a realizationx1H = �1H +�1Hx, the updated distribution of ˜XL willhave a mean �̃L4x5 = �L + ��Lx and standard devia-tion �̃L = �L

√

1 −�2, and the high-type demand in theregular season will be x̃2H 4x5= 41/�− 15x1H . We fur-ther assume � = 1 in this extension. The rest of themodel setting is the same as before. Our basic modelrepresents a special case with � = 1. The purpose ofthis subsection is to examine whether the key insightcarries over from the basic model with � = 1 to gen-eral �< 1. The detailed analysis is provided in OnlineAppendix A. Here we highlight the key findings.

First we describe the case without price guaran-tee. The seller’s decisions are as follows: In the pre-order season, the seller sets a price p1 to satisfythe high-type customers. Then, after observing thepreorder demand X1H , she updates her belief aboutfuture demand (X2H and XL) and determines the orderquantity Q; meanwhile, she also sets a price p2 >vL

to induce the high-type customers to purchase inthe regular season. Finally, if there is still leftoverinventory, the seller lowers the price to p3 = vL toclear the inventory. In fact, we may view this asa three-stage model where pi denotes the price instage i (i = 11213). The customers in each stage decidewhether they want to purchase immediately or waituntil the next stage. Again we focus on the rationalexpectations equilibrium under symmetric strategiesfor the high-type consumers. In the equilibrium, allthe high-type customers in stage 1 will preorder atprice p1, and all the high-type customers in stage 2will purchase at price p2.

Note that p2 depends on the realization of the pre-order demand X1H , or X = 4X1H −�1H 5/�1H . It can beshown that p1 = Ɛ6p24X57; thus, depending on the real-ization of X, both p1 > p2 and p1 < p2 may happen: Ifthe realization of X is low, then the product availabil-ity in stage 3 will be low, and this allows the sellerto charge a high price p2 in stage 2; the opposite istrue when the realization of X is high. Therefore, forthe more general setting, we may observe a preorderprice that is either higher (i.e., a premium preorderprice) or lower (i.e., a discount preorder price) thanthe regular price. In the advance selling (preorder) lit-erature, a discount advance selling price is attributedto the uncertainty in product valuation, whereas wehave shown that a discount preorder price is possibleeven without valuation uncertainty. Despite the morecomplex pricing patterns, our result about the impact

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of � remains unchanged as shown in the next propo-sition. That is, the adverse effect of advance demandinformation on the seller’s profit does not rely on apremium preorder price. Instead, it only hinges uponthe possibility that the product may be available ata future low price, no matter when the price will bedropped (it can be after the product release).

Proposition 6. Consider the mixed arrival model. IfzL < 0, there exists a �̃ such that çp increases in � if andonly if �1H ≤ �̃. If zL ≥ 0, then çp always increases in �.

Next we consider the case with price guarantee.The analysis for mixed arrivals is more involvedbecause the seller needs to set multiple prices andrefunds. To simplify analysis, we assume that for anycustomer, the refund is based on the purchasing priceand the final price of the product. There are two pos-sible final prices in stage 3: vL if the seller lowers theprice to satisfy the low-type customers, or vH if theseller does not serve the low-type customers at all.The seller needs to determine two refunds �1 and �2in stages 1 and 2, respectively, where �1 is the refundto the preorder customers in stage 1 and �2 is therefund to the high-type customers in stage 2, if thefinal price is reduced to vL.

Again, we find that even under price guarantees,the seller’s total profit may decrease with � in certaincircumstances. In particular, the price guarantee miti-gates the negative effect of � on the margin from thehigh-type customers, but it introduces a new negativeeffect of � on the profit from the low-type customers.Together with Proposition 6, this finding confirms therobustness of the key insight from the basic model:In the preorder strategy, more accurate demand infor-mation may hurt a seller’s profit regardless of the useof price guarantees.

7.3. Proportional Rationing RuleIn this extension, we examine the robustness of ourkey results under the proportioning rationing rule.To facilitate discussion, we define the probabilityof product availability in the second period, contin-gent on the preorder demand �H + �Hx, to be (thesuperscript pr stands for proportional rationing):

�pr 4x5= Ɛ

[

min4Q4x51 X̃L4x55

X̃L4x5

]

1 (14)

where X̃L4x5 is the updated low-type demand.

Lemma 5. �pr 4x5 is increasing in � if and only ifx ≥ −��L.

In the preorder strategy (without price guaran-tee), a high-type customer’s belief of product avail-ability is given by Ɛ6�pr 4X57. Lemma 5 shows that�pr 4x5 is increasing in � when the realization of high-type demand is large. Through extensive numerical

experiments, we find that its expectation Ɛ6�pr 4X57 isalways increasing in �. This implies that under theproportional rationing, again, more advance demandinformation leads to a lower preorder price in the pre-order strategy.

In the price guarantee mechanism, for a given pricereduction threshold x̂ < 0, the probability that theproduct is available at the low price (p2 = vL) in thesecond period is �̂pr 4x̂5 = Ɛ6�pr 4x5 � x ≤ x̂7ê4x̂5. FromLemma 5, �̂pr 4x̂5 is decreasing in � if � < −x̂/�L; thissuggests that the negative effect of advance demandinformation on the preorder price may be reversedwith a price guarantee when � is small.

The above results indicate that advance demandinformation has a similar effect on the seller’s first-period profit with or without price guarantee asunder the �-rationing rule. Note that the choice ofthe rationing rule does not affect the seller’s second-period profit. Therefore, the main results about theeffect of � on the seller’s overall profit continue tohold under the proportional rationing rule.

8. ConclusionThis paper studies the prevailing preorder practicein which a seller accepts consumer orders beforethe release of a product. Consumers who are eagerto obtain the product will benefit from preorderbecause it guarantees immediate product availabil-ity on release. Preorder is also beneficial to the sellerbecause it allows the seller to gauge market demandfrom preorder sales, and to charge distinct pricesto different consumer segments. In this paper, wedevelop a modeling framework to analyze the pre-order strategy a seller may use to sell a perishableproduct in a short selling season. The market con-sists of two consumer segments, those who arrive inthe preorder season with valuation vH and those inthe regular selling season with valuation vL, respec-tively. There is a correlation between these two ran-dom demand segments, which we use to measurethe accuracy of advance demand information. To thebest of our knowledge, this modeling framework isthe first to simultaneously incorporate the followingthree important elements: seller’s inventory and pric-ing decisions, consumers’ forward-looking behavior,and advance demand information.

The value of advance demand information hasbeen widely studied in the operations literature. Moststudies emphasize the benefit of advance demandinformation, i.e., it helps improve a firm’s inven-tory decision when facing uncertain market demand.However, we find that the seller’s profit may decreasewith the accuracy of advance demand informa-tion obtained from the preorder sales. Specifically,the seller will benefit from more accurate advance

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demand information only if the low-type valuationis sufficiently large or the high-type demand is rel-atively small. This result is due to a possible con-flict between advance demand information and pricediscrimination: Accurate demand information mayincrease product availability in the regular sellingperiod, which hinders the seller from charging a highprice to the high-type customers in the preorder season.

An effective way of resolving such a conflictbetween advance demand information and price dis-crimination is to offer a price guarantee: the sellerpromises to compensate early purchasers in case theprice is lowered later. Interestingly, we find that theseller’s profit may still decrease in the accuracy ofadvance demand information, even when the sellerwould benefit from more advance demand informa-tion if the price guarantee were not offered. The expla-nation of this result is as follows. Although priceguarantees can mitigate (and in some situations mayeven reverse) the effect of the above conflict, theyintroduce another adverse effect of advance demandinformation: With price guarantees, a seller will lowerthe price to profit from low-type consumers onlywhen the preorder demand is relatively low, but lowpreorder demand implies weak low-type demand aswell (when the two demand segments are positivelycorrelated). As a result, the use of price guaran-tees excludes situations where the seller can enjoy agreat profit in the regular season from low-type con-sumers, and such an adverse effect is stronger whenthe advance demand information is more accurate.

Therefore, contrary to conventional wisdom, wehave demonstrated that advance demand informa-tion can be detrimental to firms when facing forward-looking consumers: (1) It may hurt the seller’s profitin the preorder season through its negative effecton the preorder price. (2) In the presence of priceguarantees, it can also hurt the seller’s profit inthe regular season through its negative effect onthe regular-season demand. Because of such nega-tive effects of advance demand information, the sellerneeds to carefully decide whether to accept pre-orders and whether to provide price guarantees withpreorders. We find that the seller’s strategy choicedepends critically on the relative market sizes of thetwo types of consumers. To be specific, the preorderoption should be used without a price guarantee ifthe high-type segment is relatively small, but with aprice guarantee if the high-type segment is relativelylarge, and no preorder may be optimal for the casesin between.

This research can be extended in a couple of direc-tions. First, a more sophisticated consumer valuationmodel can be introduced. For instance, consumersmay update their uncertain valuations based on pre-order sales (e.g., a highly sought-after product during

the preorder season provides a positive signal aboutthe product value). Incorporating information updat-ing for the consumers in addition to demand updat-ing for the seller is an interesting direction for futureresearch. Second, this paper focuses on a monopolist’sselling strategy. A natural extension is to consider thepreorder strategy in a duopoly setting. It would beinteresting to study how competition affects the firms’strategy choice and the associated pricing and inven-tory decisions.

Electronic CompanionAn electronic companion to this paper is available as partof the online version at http://dx.doi.org/10.1287/msom.1120.0398.

AcknowledgmentsThe authors thank Laurens Debo, Stephen Gilbert, GuomingLai, Martin Lariviere, Özalp Özer, Kathryn Stecke, andXuying Zhao, as well as participants at the 2009 MSOMConference in Boston, Massachusetts; the 2009 INFORMSAnnual Meeting in San Diego, California; and the 2010MSOM Supply Chain Management SIG Conference inHaifa, Israel, for helpful comments and discussions. Theauthors acknowledge the financial support from the BoeingCenter for Technology and Informational Management andthe Connecticut Information Technology Institute.

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