Advance Demand Information, Price Discrimination, and Preorder Strategies

MANUFACTURING & SERVICE

OPERATIONS MANAGEMENT

Vol. 15, No. 1, Winter 2013, pp. 57–71

ISSN 1523-4614 (print)  ISSN 1526-5498 (online)

http://dx.doi.org/10.1287/msom.1120.0398

Advance Demand Information, Price Discrimination,

and Preorder Strategies

Cuihong Li

School of Business, University of Connecticut, Storrs, Connecticut 06269, [email protected]

Fuqiang Zhang

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

his paper studies the preorder strategy that a seller may use to sell a perishable product in an uncertain

market 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 may

improve 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 preorder

season. This cautions the seller about a potential conﬂict between the beneﬁts of advance demand information

and price discrimination when facing strategic consumers. A common practice to contain consumers’ strategic

waiting is to offer price guarantees that compensate preorder consumers in case of a later price cut. Under

price 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 can

no longer beneﬁt from a high demand in the regular season. Therefore, under price guarantees, more accurate

advance 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 be

offered and whether it should be coupled with price guarantees) and ﬁnd that the answer depends on the

relative 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 Advance

September 4, 2012.

1. Introduction

Preorder refers to the practice of a seller accepting

customer orders before a product is released. Such a

practice has become commonplace for a wide vari-

ety of products in recent years. Consumer electronic

products 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-troubled

company (Wall Street Journal 2002). When launching

the new iPhone 3G S, the third generation of the

smart phone, Apple allowed customers to preorder

the product to secure the delivery on the release

date (Keizer 2009). In early September 2009, Nokia

announced that its ﬁrst Linux-based smart phone, the

N900, was available through preorders in the U.S.

market (Goldstein 2009). Amazon offered the pre-

order option to consumers when unveiling the second

version of its e-book reader, Kindle 2 (Carnoy 2009).

Game consoles, such as Nintendo’s Wii and Sony’s

Playstation 3, had been put on preorder before they

were formally released (Martin 2006, Macarthy 2007).

The preorder option is clearly beneﬁcial to con-

sumers because it guarantees prompt delivery on

release. This is especially valuable when the product

is a big hit and will be hard to ﬁnd in stores due

to its popularity. It is not uncommon for extremely

popular gadgets to run out of stock immediately after

release. Consumers may have to wait for weeks or

even months to get the product. For instance, retail-

ers warned customers in mid-2006 that no Wii units

would be available without a preorder until 2007

(Martin 2006). Apple sold out its preorder inventory

for iPad before the release of the product (Berndtson

2010). Preorders are often placed by enthusiastic con-

sumers who are eager to be the ﬁrst to get their hands

on a new product.

The preorder strategy may bring signiﬁcant bene-

ﬁts to the seller as well. First, the seller can gauge

how much demand there will be for his product from

the preorder sales. For new products with relatively

short life cycles, the demand is usually hard to pre-

dict, yet matching supply with demand is important.

Thus, the advance demand information obtained from

preorder sales will be very useful in procurement,

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

production, and inventory planning. The use of pre-

orders has been further promoted by the advent of

the Internet and other information technologies that

have greatly reduced the costs associated with data

collection and processing. It has been reported that

by accepting preorders for iPhone 3G S, Apple did

not experience the same kind of stockout problems

that occurred with its iPhone 3G due to a mismatch

between supply and demand (Keizer 2009).

Second, the preorder strategy provides leverage for

the 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 is

willing to pay a premium price for guaranteed early

delivery. These consumers are either new technol-

ogy lovers or simply loyal fans of the brand. They

are often referred to as “early adopters,” and the

extra price they pay is called an “early adopter tax.”

In fact, recently the early adopter tax has received

many discussions in various industries (see Nair 2007

for video games; Jack 2007 for Apple’s iPhone; and

Falcon 2009 for Sony’s latest gaming gadget, PSP

Go). These discussions are corroborated by the obser-

vation that many products on preorder exhibit pat-

terns of price cutting. For example, Nokia started

accepting preorders for its N900 smart phone at $649

and then slashed the price to $589 when it was

close to release (Goldstein 2009, King 2009). Walmart

dropped the preorder price of myTouch 3G Slide

from $199.99 to $129.99 shortly before the release

(Tenerowicz 2010). Amazon charged a preorder price

of $359 for its Kindle 2 and then dropped the price

to $299 after the release (Carnoy 2009). Not surpris-

ingly, consumers and market analysts may anticipate

such price reductions and make purchasing decisions

accordingly. See Coursey (2010) and Tofel (2010) for

market conjectures about the iPad’s price drop even

before it is released.

With the preorder option, a forward-looking cus-

tomer will choose the timing of purchase: Placing a

preorder 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 is

released) sounds quite attractive, but meanwhile the

consumer has to face the risk of stockout. How much

a consumer is willing to pay for a preorder depends

on 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 the

prevalence of the preorder practice, there has been

surprisingly little research that analyzes the seller’s

optimal 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 that

incorporates all the important elements mentioned

above: 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? From

the operations point of view, a major beneﬁt of accept-

ing preorders is that the seller can obtain advance

demand information. This information helps improve

the seller’s decision on initial production runs to sat-

isfy demand, and its effectiveness has been frequently

lauded in the literature. However, a better match

between supply and demand implies that availability

of the product becomes less of a concern, which may

affect consumers’ willingness to pay for a preorder.

Thus, it would be interesting to study when advance

demand information is valuable to the seller in the

presence of strategic consumer behavior.

What is the impact of price guarantees? Consumers

may be reluctant to place preorders if they expect a

possible price cut in the future. To encourage early

purchases, the seller may offer a price guarantee along

with the preorder option. That is, a customer would

receive a refund if the price declines over time. Price

guarantee has become a common industry practice

during the past decade (Lai et al. 2010). This raises

the question of how price guarantees affect the value

of advance demand information.

When and how should a seller use the preorder strategy?

A seller may choose to use or not to use the preorder

strategy. For example, Apple adopted the preorder

strategy for its iMac computers and iPhone 3G S, but

not for its iPhone 3G. Furthermore, when a preorder

strategy is used, the seller may choose to offer or not

to offer the price guarantee. When and how to use

the preorder strategy is an important question for the

seller.

The rest of this paper is organized as follows.

Section 2 reviews the related literature. Section 3

introduces the model setting. Section 4 presents the

analysis of the preorder strategy. Section 5 studies

the impact of price guarantees. Section 6 compares

the preorder strategy and the no-preorder strategy.

Sections 7 discusses several extensions of the basic

model. Section 8 concludes the paper. All proofs are

given in Online Appendix A (provided in the elec-

tronic companion; http://dx.doi.org/10.1287/msom

.1120.0398).

2. Literature Review

This paper is related to the literature on inventory

planning with advance demand information. Fisher

and Raman (1996) propose a quick-response strategy

under which a retailer utilizes early sales for estimat-

ing demand distribution. Eppen and Iyer (1997) study

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

a fashion-buying problem for retailers who can divert

inventory to outlet stores using updated demand

information. Gallego and Özer (2001, 2003), Özer

(2003), and Özer and Wei (2004) study inventory man-

agement with advance demand information obtained

from customer orders that are placed in advance of

their needs. In these papers, the advance demand

information 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) and

McCardle et al. (2004) study the beneﬁts of an

advance booking discount program by which a

retailer offers a price discount to consumers who

make early order commitments prior to the selling

season. 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 based

on an aggregate demand function. Similar to these

papers, we also consider the dependence between

advance demand information and pricing. However,

we differ in that we model consumers’ strategic

purchasing decisions explicitly. Because of strategic

waiting of consumers, we show that more accurate

advance demand information does not necessarily

beneﬁt the seller.

Existing papers that study advance selling with

strategic consumers typically consider the situations

where consumers have uncertain value (or demand)

about the product or service (e.g., sport event tickets,

books, videos, computer games, etc.) when making

advance purchases. In these papers, value uncertainty

causes 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 the

capacity is relatively small). This line of research often

assumes that the product quantity (service capacity) is

ﬁxed, and models advance selling as a tool to increase

market participation (e.g., Xie and Shugan 2001, Yu

et al. 2007, Alexandrov and Lariviere 2012) or segment

the 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 selling

to obtain advance demand information. Differently

from the above studies, we focus on the situations in

which consumers face relatively certain product value

but uncertain product availability. This is plausible

for consumer electronic goods, for which there is usu-

ally sufﬁcient information for consumers to evaluate

the product before its release, but short product life

cycles and unpredictable market make it difﬁcult to

match supply with demand. In this case, consumers

are willing to pay a premium preorder price to secure

product availability. In our model, preorder is driven

by both beneﬁts of premium proﬁts and advance

demand information, and we study the interplay

between these two forces.

There has been a growing interest in studying the

impact of strategic consumer behavior on a seller’s

inventory decision (e.g., Su and Zhang 2008, 2009).

Cachon and Swinney (2009) and Swinney (2011)

examine the quick-response strategy that allows the

seller to replenish inventory after the selling season

starts. They focus on the value of a late ordering

opportunity (after demand is realized), whereas we

investigate the value of an early selling opportunity

(before inventory is ordered). Cachon and Swinney

(2009) ﬁnd that early demand information is more

valuable under strategic consumer behavior, which is

in contrast with our ﬁndings. There is a key difference

between these two papers: In Cachon and Swinney

(2009), consumers may wait for a clearance sale, the

probability of which is lower if the seller can better

match supply with demand using advance demand

information; in our model, consumers may wait for

a price cut in the regular season after preorder sales,

and the product availability in regular selling is higher

when more advance demand information is obtained

from preorder sales. Swinney (2011) shows that quick

response may hurt a seller’s proﬁt when consumers

face uncertain product valuations. We establish a par-

allel result that advance demand information may

be detrimental to a seller’s proﬁt, which does not

depend on value uncertainty of the product. Huang

and Van Mieghem (2009) study the value of online

click tracking, which allows a seller to collect advance

demand information for pricing and inventory plan-

ning. In their model, because clicking is separated

from purchasing, advance demand information from

click 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 the

impact 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 ﬁxed

inventory to two types of consumers. The size of the

total consumer pool is ﬁxed, but the relative sizes

of 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 information

by allowing general correlation between demand seg-

ments. Lai et al. (2010) examine the value of using

price guarantees for a newsvendor seller who has

the opportunity to mark down the product at the

end of the selling season. In their problem, the seller

determines the inventory before accepting consumer

orders; therefore, they do not include the element of

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

advance demand information. Levin et al. (2007) ana-

lyze a dynamic pricing problem with ﬁxed capac-

ity and price guarantees. They focus on determining

the optimal dynamic price and guarantee policies by

assuming myopic consumers.

Finally, dynamic pricing problems have been

widely studied in the revenue management litera-

ture. The objective of these studies is to ﬁnd the opti-

mal pricing and capacity (inventory) allocation rules

to maximize a seller’s revenue/proﬁt. Elmaghraby

and 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’ strategic

response 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 of

our paper is to consider the capacity decision along

with demand updating in a dynamic pricing problem,

which, to the best of our knowledge, has not yet been

addressed.

3. Model

A seller sells a perishable product in a two-period

time horizon. The product is released at the beginning

of 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 valuation

and the low type has a valuation v

for the prod-

uct, where v

> v

. For instance, the high type may

refer to technology-savvy consumers. The difference

between these two valuations may represent the high-

type consumers’ stronger preference over the product

technology; 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 that

there is sufﬁcient information for consumers to eval-

uate the product before its release. This is typically

the case for consumer electronic products. Many ﬁrms

nowadays use exhibitions, advertising, and their web-

sites to offer demonstration and detailed product

information to consumers, and comprehensive prod-

uct reviews can often be found in professional media

columns before the release. Consumers are inﬁnites-

imal, as widely assumed in the literature. Usually,

the technology-savvy consumers are early adopters

who follow the market trend closely. Therefore, we

assume all the high-type consumers arrive in the ﬁrst

period whereas all the low-type consumers arrive in

the second period (see Moe and Fader 2002 for a

similar assumption). In §7 we relax this assumption

and examine the robustness of our results. Because

early adopters value being among the ﬁrst to own

the product, we assume that the valuation v

will

be discounted by a factor  ≤ 1 if a high-type con-

sumer chooses to wait and purchase the product in

the second period; that is, a high-type consumer’s val-

uation becomes v

in the second period. We assume

v

> v

. All players are risk neutral and forward

looking, i.e., the seller aims to optimize his total

expected proﬁt, and the consumers maximize their

expected net utility.

Market demand is uncertain in both periods. Let

denote the demand of type i (i = H1L), where

follows a normal distribution ê

(density 

) with

mean 

and standard deviation 

. Let 

= 

/

be the ratio between the mean and standard devi-

ation of X

(i.e., the reciprocal of the coefﬁcient of

variation). Bivariate normal distribution has been

commonly used in the literature, especially when

modeling demand information updating (see, e.g.,

Fisher and Raman 1996, Tang et al. 2004). Let  ∈

4−11 15 be the correlation coefﬁcient between X

and

. A positive correlation corresponds to situations

where the primary uncertainty is on the total size of

the 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 relatively

certain, but the relative sizes of the two demand types

are uncertain. For ease of exposition, we will focus on

 ≥ 0 in this paper; the analysis of the case  < 0 is

similar and will be discussed in §7.1. We may view

 as an indicator of the accuracy of advance demand

information. That is, a larger  means less uncertainty

in the second-period demand with the observation

of the ﬁrst-period demand. Deﬁne X ≡ 4X

− 

5/

which follows the standard normal distribution; let

ê () denote the distribution (density) function for

the standard normal distribution. We will work with

X instead of X

due to their one-to-one relation-

ship. For a given realization x of X, the updated

low-type demand

4x5 follows a normal distribution

with mean ˜

4x5 = 

+ 

x and standard deviation

˜

= 

1 − 

We ﬁrst describe the seller’s problem. The seller

sets a preorder price p

in the ﬁrst period. Given this

price, the high-type consumers make their preorder

decisions. After the number of preorders q is received,

the seller decides the second-period price p

and the

total production/order quantity q + Q, where Q is the

quantity used to satisfy the second-period demand.

There is a constant unit cost c (c < v

) for the product.

Unsold products at the end of the second period have

negligible salvage value, and there is no penalty for

unsatisﬁed demand. Thus, in the second period the

seller essentially faces a newsvendor problem with

pricing. Note that the seller observes the preorder

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

quantity and may use this information to update his

belief about the second-period demand when making

the quantity decision.

Next we describe the consumers’ problem. The

problem for a low-type consumer is trivial: As she

arrives in the second period, she buys the product if

and only if p

≤ v

. A high-type consumer, arriving in

the ﬁrst period, needs to decide whether she should

place a preorder or delay the purchasing to the next

period. If she places a preorder, then she pays the

price p

and will deﬁnitely receive the product; oth-

erwise, she may purchase the product at a possibly

lower price p

in the regular season, but under the risk

that the product is no longer available. Whether a con-

sumer is willing to preorder depends on her belief of

the rationing risk, i.e., the chance the product will be

available in the second period. We model such a belief

using a parameter  ∈ 401 15: A consumer believes

that 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 believes

that she will be the ﬁrst in the waiting line; on the

other extreme,  = 1 means that the consumer is pes-

simistic and thinks she will be the last in the waiting

line. Cachon and Swinney (2009) provide a detailed

discussion of this modeling approach and focus on

speciﬁc  values for tractability. For ease of exposi-

tion, we assume  = 1/2 in this paper. The qualitative

insights will remain if this assumption is relaxed (see

Lemma 6 in Online Appendix A for the analysis of

general ). 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 the

extension in §7.3.

4. Preorder Strategy

In this section we analyze the seller’s preorder strat-

egy. In the analysis, we start with the seller’s price

and 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 analyze

the seller’s ﬁrst-period price decision, which induces

the high-type consumers to preorder under a rational

expectations equilibrium.

In the second period, with the number of pre-

orders q received in the ﬁrst period, the seller must

determine the price p

and the order quantity Q to sat-

isfy the second-period demand (besides the quantity

q to be ordered for the preorder demand). Because all

high-type consumers are assumed to choose preorder,

the number of preorders is equal to the high-type

demand, q = x

, and only the low-type consumers are

present in the second period. Thus, it is optimal for

the seller to set p

= v

. The seller’s order quantity

Q depends on the high-type demand realization x

Deﬁne z

≡ ê

−1

44v

− c5/v

5, where ê4z

5 is the criti-

cal fractile for the low-type demand. Then the optimal

order quantity for the second period is given by

Q4 x5 = ˜

4x5 + z

˜

1 (1)

where ˜

4x5 = 

+ 

x and ˜

= 

1 − 

are the

mean and standard deviation of the updated low-type

demand

4x5 for x ≡ 4x

− 

5/

. The resulting

proﬁt for the second period is

4x5 = 4v

− c54

+ 

x5 − v

4z

5

1 − 

0 (2)

Note that the expected second-period proﬁt is

Ɛ6ç

4X57 = ç

405 because Ɛ6X7 = 0. Throughout the

paper we use Ɛ to denote the expectation operation.

In the ﬁrst period, a high-type consumer will

choose between preorder and wait. We consider sym-

metric strategies for the high-type consumers because

they 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 v

− r;

if she waits, then her expected utility is 4v

− p

5,

where  is the consumer’s belief of the availability of

the product in the second period. By deﬁnition we

know that v

−r = 4v

−p

5 or r = v

−4v

−p

5.

Here we assume a consumer always preorders if there

is a tie, because the seller can always reduce the price

by 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 

about the con-

sumers’ reservation price r. Given the belief 

, it is

clear that the seller’s optimal price to induce preorder

is p

= 

We focus on the rational expectations (RE) equi-

librium of the above game. This equilibrium con-

cept has been recently applied to various settings in

the marketing and operations literatures (see Su and

Zhang 2009 and the references therein). In any RE

equilibrium, the players’ beliefs must be consistent

with the actual outcome, and the players have no

unilateral incentives to deviate. Speciﬁcally, the equi-

librium requires the following conditions: (i) p

= 

;

(ii) p

= v

; (iii) the seller orders the quantity accord-

ing to (1) for the second period; (iv) 

= r; and (iv) the

consumer’s belief of product availability in the second

period satisﬁes

 = Ɛ





4X5

< Q4X5



= Ɛ







+ X

1 − 

+ 2z



1 (3)

where the second equality is by plugging

4x5 and

Q4 x5 into the ﬁrst expression. Among these condi-

tions, (i), (ii), and (iii) state that the seller chooses the

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

proﬁt-maximizing decisions, whereas (iv) and (v) are

the consistency conditions (players’ beliefs are consis-

tent with the actual outcome). The above discussion

leads to the following proposition that characterizes

the equilibrium outcome of the game.

Proposition 1. There is a unique RE equilibrium

under the preorder strategy. In the equilibrium, the seller

sets p

= v

− 4v

− p

5 and p

= v

, where  is given

in (3), and all consumers will preorder in the ﬁrst period.

For notational convenience, deﬁne ã = v

− v

From Proposition 1, the seller’s total expected proﬁt

is (we use superscript p for preorder strategy):

= 4v

− ã − c5

+ ç

4051 (4)

where 4v

−ã −c5

is the seller’s ﬁrst-period proﬁt,

and ç

405 is the second-period proﬁt.

4.1. Impact of Demand Correlation 45

What is the value of advance demand information in

the preorder strategy? The accuracy of the advance

information 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 after

updating). In this subsection, we investigate how the

seller’s proﬁt depends on .

Based on Equation (4), the derivative of ç

with

respect to  can be written as

dç

d

= −ã

d

d

4050 (5)

The demand correlation  affects both the ﬁrst-period

proﬁt (through its inﬂuence on , the equilibrium

belief of product availability in the second period)

and the second-period proﬁt ç

405. It is clear that

4d/d5ç

405 = v

4z

5

4/

1 − 

5 is positive—more

accurate advance demand information helps the seller

better match supply with demand, thus improving

the second-period proﬁt. The effect of  on the ﬁrst-

period proﬁt depends on its impact on , which is

characterized in Lemma 1.

Lemma 1. (i) For c < v

< 2c (i.e., z

< 0),  is

increasing in .

(ii) For v

≥ 2c (i.e., z

≥ 0),  is decreasing in .

Lemma 1 suggests that the availability probability 

may either increase or decrease in the demand corre-

lation , depending on z

When v

< 2c, then z

< 0,

and the order quantity decreases in the updated

demand variance ˜

based on Equation (1). Because

a greater  reduces the variance of the updated

demand, both the order quantity Q and its associated

product availability  increase in . If v

≥ 2c, then

≥ 0, and the seller will order more when facing

Lemma 6 in Online Appendix A studies general  ∈ 40115 and

identiﬁes a similar threshold structure based on the value of z

greater demand uncertainty ˜

. This causes the prod-

uct availability  to decrease in . Because the ﬁrst-

period price hinges upon the product availability, the

result in Lemma 1 implies that depending on the

problem parameters, advance demand information

may 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 the

low-type demand in the second period, which helps

improve the second-period proﬁt. However, more

accurate 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 charging

a high preorder price (see Proposition 1). Therefore,

the seller’s total proﬁt may not necessarily increase

with . Deﬁne the following threshold value

˜45 ≡ −

4z

5

2ãz

42z

1 − 

+ 

(6)

with the following property:

Lemma 2. (i) For z

∈ 4−

/21 05, ˜45 increases

in .

(ii) For z

≤ −

/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  as

shown in the following proposition.

Proposition 2. (i) If c < v

< 2c (i.e., z

< 0), then

increases in  when 

< ˜4 5, and decreases in 

when 

≥ ˜45. In particular, there exists an 

> 0 such

that ç

always decreases in  if v

< c + 

(ii) If v

≥ 2c (i.e., z

≥ 0), then ç

always increases

in .

Proposition 2 suggests that the seller’s proﬁt

increases in  only when the low-type valuation is

sufﬁciently large (v

≥ 2c) or the high-type demand

is relatively small (

< ˜45). The intuition is as

follows: When v

is large, a greater  improves

the second-period proﬁt and also the preorder price.

When v

is small, increasing  has a negative effect

on the preorder price. This negative effect, however, is

dominated by the positive effect on the second-period

proﬁt if 

is low. Therefore, more accurate advance

information beneﬁts the seller either when v

is large

or when 

is small.

Figure 1 illustrates the situations in which the proﬁt

may decrease in . It draws ç

as a function of 

for different 

and v

values. If v

is less than 2c

but not too small (−

/2 < z

< 0), ˜45 is increasing

(Lemma 2(i)). Thus, ç

decreases in  when  is rela-

tively low. This case is shown in the plot on the left.

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

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

0.09

0.08

0.07

0.06

0.05

0.01

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



= 0.11



= 0.004

0.003

0.002

0.001



= 1.02 

= 1.001



Note. 

= 5, 

= 3, 

= 405, v

= 2, c = 1, and  = 1.

When v

is very small (z

≤ −

/2), ˜45 is quasi-

convex (Lemma 2(ii)). Thus, ç

decreases in  when

 is intermediate. This case is shown in the plot on

the right.

The above analysis delivers a message that more

accurate advance demand information (higher ) does

not necessarily improve a seller’s proﬁtability. This

is in contrast with the traditional wisdom that early

sales information (e.g., test sales, preorders) helps

a ﬁrm better forecast demand and hence increase

proﬁt (e.g., Fisher and Raman 1996). The new driv-

ing force underlying our model is the counteract-

ing effects of advance demand information and price

discrimination: Because of strategic consumer behav-

ior, a better ability to match supply with demand may

actually prevent the ﬁrm from charging premium

prices to extract consumer surplus. The negative effect

of  can be substantial in some situations: In the

extreme case where  is close to 1 with a large , the

seller has to charge a preorder price almost equal to

the regular-season price v

, losing the opportunity to

price-discriminate different customer segments. This

can lead to substantial proﬁt loss of the seller if the

product value is highly diverse between the two cus-

tomer segments (large ã) or the high-type customer

segment is large (high 

). Practically speaking, our

results imply that the preorder strategy could be less

attractive when preorders are highly predictive of the

regular-season demand.

5. Preorder with Price Guarantee

Under a price guarantee, a consumer will be com-

pensated if the product price declines over time. For

example, Apple promises to refund the difference if

price is dropped within 14 days of purchase.

A pur-

pose of price guarantee is to eliminate consumers’

incentives to wait for markdowns so the seller can

enjoy quicker sales at a relatively high price. Gener-

ally, there should be some technological requirements

for implementing a price guarantee, and it might be

costly to satisfy these requirements (e.g., the seller

has to invest in hardware and manpower to monitor

transactions and manage the refunding process). For

simplicity, we assume that all necessary technologies

are already in place and there is a zero implementa-

tion cost. Under this assumption, we study the impact

of 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 guarantee

along with the preorder option? Second, how does the

introduction of the price guarantee affect the value of

advance demand information?

5.1. Value of Price Guarantee

With a price guarantee, the seller needs to determine

not only the prices p

and p

in the two periods, but

also the refund  paid to each preorder consumer if

< p

. An intuitive special case is  = p

− p

, which

we call a full-price guarantee. Most of the existing

literature focuses on this special case (see, e.g., Png

1991, Lai et al. 2010). Here we consider the general

case without imposing any restriction on .

Similar

http:// store.apple.com/Catalog/US/Images/salespolicies.html (last

accessed August 8, 2012).

We have also analyzed the full-price guarantee and obtain

similar qualitative results. In particular, the full-price guarantee

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

to the preorder mechanism without price guarantee,

we ﬁrst analyze the seller’s decisions in the second

period, assuming that all high-type consumers have

chosen 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 is

not necessarily p

= v

because the seller may choose

to maintain a high price to avoid refunding the ear-

lier buyers. At the beginning of the second period, the

seller’s price decision depends on the realization of

the high-type demand in the ﬁrst period, x

, or equiv-

alently, x = 4x

− 

5/

. Speciﬁcally, the price will

be reduced if and only if the proﬁt from the low-type

consumers, ç

4x5, is greater than the total refund,

4

+ 

x5, where ç

4x5 is given in (2). Deﬁne the

breakeven level of x to be

x45 ≡

405 − 



− 4v

− c5

0 (7)

Negative demand realizations from a normal dis-

tribution may cause impractical price reduction deci-

sions. For instance, the seller may reduce the price

when the high-type demand is negative, because in

this case the refund becomes essentially a net trans-

fer to the seller; or, the seller may not reduce the

price simply because the size of the low-type segment

could be negative. To avoid these unrealistic scenar-

ios, we follow the literature (e.g., Fisher and Raman

1996) to assume hereafter the probability of negative

demand is negligible; that is, we treat Pr4X

≤ 05 and

Pr4X

≤ 0  X

5 as zero as an approximation. It can be

shown that such an approximation is accurate in the

asymptotic situation where the probability of nega-

tive demand approaches zero (see Online Appendix A

for more explanation). In addition, numerical exper-

iments indicate that the qualitative insights derived

under this approximation will hold when the coefﬁ-

cient of variation is reasonably small (

reasonably

large).

Lemma 3 reveals how the price reduction

decision depends on the refund  and high-type

demand realization x.

Lemma 3. (i) If  ≤ 4v

− c54

/

5, then price

reduction will always happen.

(ii) If  > 4v

− c54

/

5, then price reduction hap-

pens when x <

x45, and

x45 decreases in .

For  < 4v

− c54

/

5, the seller will always

reduce the price regardless of x to beneﬁt from

serving the low-type consumers. This case essentially

performs very close to optimal. More details can be found

in Online Appendix B (available in the electronic companion;

http://dx.doi.org/10.1287/msom.1120.0398).

For example, with 

= 3 and 

= 4, the probability of a negative

is only 000014 and the conditional probability of a negative X

at most 00004. The main insights hold in this example, even without

the approximation.

reduces to our original preorder strategy with an

effective preorder price p

− . Hence, without los-

ing generality, we restrict our attention to  ≥ 4v

− c5

4

/

5. In this case, price reduction occurs only

when the preorder demand is relatively small (x <

x);

otherwise, the seller will keep the price at p

to avoid

refunding the large group of preorder consumers. Our

original preorder strategy can be considered as one

with a price guarantee in which the refund is so low

that the price will always be dropped, i.e.,

x ≥ 

Next we analyze the seller’s ﬁrst-period decision

on the preorder price p

and refund . Note that the

price reduction threshold,

x45, depends on  but not

on p

. If a high-type consumer preorders, her expected

utility is u

1 5 = v

−p

+ê4

x455; if she waits till

the second period, her expected utility is u

1 5 =

4

x455, where

4

x5 ≡ Ɛ





4X5

< Q4X51 X <



= Ɛ







+ X

1 − 

+ 2z





X ≤



ê4

x5 (8)

is the probability that the product is available at the

low price (p

= v

) in the second period. By comparing

Equations (8) and (3), we know

4

x5 ≤ .

Given , the optimal p

must satisfy u

1 5 =

1 5 so that the high-type consumers will pre-

order. This gives

45 = v

+ ê4

x455 − ã

4

x4550 (9)

Because there is a one-to-one relationship between

x and , we will work with the decision variable

x instead of , which is more convenient. For any

given

x, we have 4

x5 = ç

x5/4

+ 

x5 and p

given by Equation (9). Thus, the seller’s proﬁt can

be written as (we use the superscript g for price

guarantee):

x5 = 4p

x5 − c5

+ Ɛ6ç

4X5 − 4

x54

+ 

X5  X <

x7ê4

= 4v

− ã

4

x5 − c5

+ Ɛ6ç

4X5 − 4

x5

X  X <

x7ê4

x50 (10)

When should the seller provide a price guaran-

tee? We may compare the seller’s proﬁts under the

preorder strategy with and without price guarantee.

From (10), the proﬁt margin from the high-type con-

sumers in the price guarantee mechanism is v

−

4

x5 − c, which is greater than the one without a

price guarantee, v

− ã − c. This is true because a

price guarantee enables the seller to charge a higher

preorder price by discouraging consumers from wait-

ing. Such an observation suggests that offering a price

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

guarantee will be more effective if the size of the

high-type consumers is larger. Indeed, Proposition 3

conﬁrms this intuition. We use ç

= max



45 to

denote the seller’s optimal proﬁt in the price guaran-

tee mechanism.

Proposition 3. Suppose 

is ﬁxed. Then there exists

a ˆ

such that ç

> ç

(i.e., the seller should offer a price

guarantee in the preorder strategy) if and only if 

> ˆ

Proposition 3 suggests that a price guarantee is ben-

eﬁcial to the seller only when 

is above a thresh-

old value, ˆ

(a closed-form expression of ˆ

can be

found in the proof). In other words, the size of the

high-type consumer segment must be large enough

to warrant the use of price guarantees; otherwise, the

seller should not offer a price guarantee. Two points

are worth mentioning about this threshold result:

First, ﬁxing 

implies that the standard deviation

of the high-type demand changes proportionally with

the mean. We ﬁnd from numerical analysis that a sim-

ilar result holds when 

, rather than 

, is ﬁxed.

That is, the result can be extended to settings with

a ﬁxed standard deviation. Second, the threshold ˆ

depends on the relative sizes of the two consumer

segments. Analogously, it can be shown that for a

ﬁxed 

, there is a threshold ˆ

such that the price

guarantee is preferred if and only if 

< ˆ

. This

is the counterpart of Proposition 3 and is therefore

omitted.

5.2. Impact of  Under Price Guarantee

We have shown in §4.1 that a higher  may decrease

the seller’s proﬁt in the preorder strategy because of

the strategic waiting behavior. The underlying reason

is that when z

< 0, a higher  improves the product

availability in the second period, and thus the seller

has to charge a lower preorder price. How does this

result change when price guarantees are used? Here

we investigate the impact of  under price guarantees.

As an intermediate result, Lemma 4 reveals the effect

of  on the probability that the product is available at

the low price in the second period,

.

Lemma 4. (i) For c < v

< 2c (i.e., z

< 0) and a given

x, d

/d ≤ 0 at  = 0, and there exists 



> 0 such that

/d ≥ 0 for  ≥ 1 − 



(ii) For v

≥ 2c (i.e., z

≥ 0) and a given

4

x5 = ê4

is independent of .

Recall from Lemma 3 that a price reduction occurs

only when the high-type demand is relatively low

(x <

x), which indicates a weak low-type demand as

well. Therefore, in case of a price reduction, a higher

 implies both smaller mean and variance for the

updated low-type demand. Whereas the effect on the

variance drives the second-period product availabil-

ity to increase in  with z

< 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 result

without a price guarantee that  is always increasing

in  for z

< 0. When z

≥ 0, under the assumption

that 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 z

≥ 0, as

shown 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, as

suggested by Lemma 4(i). However, in the meantime

the price guarantee prevents the seller from serving a

large low-type segment, because the price is reduced

to target the low-type segment only when the seg-

ment is relatively small. This implies that the price

guarantee introduces an adverse effect of  on the

second-period proﬁt. To better understand the impact

of  on the seller’s total proﬁt, we focus on two spe-

cial cases: the case when v

is small (close to c) and

the case when v

is large (greater than 2c). When v

very small, the second-period proﬁt is negligible, and

the effect of  focuses on the price and proﬁt in the

preorder period. When v

≥ 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-period

proﬁt.

Proposition 4. (i) There exists 1 

1

1 

2

> 0 such

that, if v

− c < , then dç

/d > 0 for  = 0 and

dç

/d < 0 for  > 1 − 

1

, with d ˆ

/d < 0 for  = 0

and d ˆ

/d > 0 for  > 1 − 

2

(ii) When v

≥ 2c (i.e., z

≥ 0), ç

is quasi-convex

( ﬁrst decreasing and then increasing) in ; in addition, ˆ

is increasing in .

When v

is very small, we know from Proposi-

tion 2(i) that the seller’s proﬁt without price guarantee

always decreases in . With a price guarantee, how-

ever, Proposition 4(i) shows that the seller’s proﬁt is

increasing in  for  close to 0, and decreasing in 

for  close to 1. Through numerical experiments, we

observe that ç

is quasi-concave over  ∈ 601 15. This

difference results from the fact that the price guaran-

tee mitigates and may even reverse the negative effect

of  on the preorder price, especially when  is small.

Proposition 4(ii) also indicates that ˆ

decreases in

 when  is close to 0, and increases in  when  is

close to 1. Again, we observe from numerical exper-

iments that ˆ

is quasi-convex over  ∈ 601 15. Thus,

when v

is small, price guarantees are favored only

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

for intermediate ; when  is either high or low, the

preorder strategy without price guarantee is better.

When v

≥ 2c, recall from Proposition 2(ii) that

the seller’s proﬁt without price guarantee is always

increasing in . Interestingly, Proposition 4(ii) shows

that, with the optimal price guarantee, the seller’s

proﬁt may be decreasing in  for sufﬁciently small .

That is, more accurate advance demand information

may hurt the seller’s proﬁt under price guarantees

even when it would only beneﬁt the seller without

a price guarantee. This result is due to the negative

effect of  on the second-period proﬁt introduced by

the price guarantee. In comparison, note that without

price guarantee, the negative effect of  is realized

only on the ﬁrst-period proﬁt.

From Proposition 3, the seller prefers to use a price

guarantee when 

> ˆ

. Proposition 4(ii) suggests

that, for v

≥ 2c, the seller is less likely to use a

price guarantee as  increases. This is again due to

the adverse effect of a higher  on the second-period

proﬁt. Such an effect is substantial for large v

, mak-

ing price guarantees less attractive as  increases.

6. No-Preorder Strategy

When should the seller offer the preorder option? In

this section, we compare the preorder strategy with

the no-preorder strategy. With no preorder, the prod-

uct is sold only in the regular selling season (i.e., after

the product is released). As a result, the seller does not

have advance demand information when deciding the

order quantity. In this case, the seller may charge a

high price to target the high-type consumers ﬁrst, and

then drop the price to satisfy the low-type consumers

if there is still inventory left. For ease of exposition,

we divide the regular season into two stages, and

let p

and p

≥ p

) denote the prices in the two

stages (we use “stage” to distinguish from the notion

of “period” used in the previous sections). Below we

study the game under no preorder and then compare

the three strategies we have examined so far. Again,

we analyze the equilibrium in which all high-type

consumers purchase in the ﬁrst stage; in this equilib-

rium, the second-stage price p

is set to v

to target

the 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 v

for

the loss of early-adopter advantages.

Let the seller’s order quantity be Q. If a high-type

consumer delays purchasing to the second stage, she

faces the availability probability



4Q 5 = Pr4X

+ X

< Q5 = ê



Q − 





1 (11)

where 

= 

+ 

and 



+ 



+ 2



are the mean and standard deviation of X

+X

. The

superscript n stands for no preorder. In the RE equi-

librium, for a given Q, the ﬁrst-stage price satisﬁes

4Q 5 = v

− ã

4Q 50 (12)

Given Q and p

, the seller’s total proﬁt is

1 Q5 = 4p

− v

5 Ɛ6min4Q1 X

+ v

Ɛ6min4Q1 X

+ X

57 − cQ0

The seller’s optimal order quantity Q

is given by

the ﬁrst-order condition 4¡/¡Q5ç

1 Q5 = 0 for p

deﬁned in (12). The seller’s total proﬁt in equilibrium

can be written as

= ã41 − 

55 Ɛ6min4Q

1 X

+ v

Ɛ6min4Q

1 X

+ X

57 − cQ

1 (13)

where ã41 − 

55 represents the premium margin

from 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 

is ﬁxed. There exists a ˆ

such that ç

> ç

(i.e., the seller prefers the preorder strat-

egy over the no-preorder strategy) if and only if 

< ˆ

Proposition 5 states that the preorder strategy

should be used if and only if the size of the high-type

demand is less than a threshold value, ˆ

. Through

numerical experiments we ﬁnd that a similar thresh-

old value exists when 

, rather than 

, is ﬁxed.

Thus, we conclude that the preorder strategy out-

performs the no-preorder strategy when the relative

size of the high-type customers is smaller than a

certain threshold. The intuition can be explained as

follows. Without advance demand information, the

future product availability tends to be lower, thus

raising a high-type consumer’s willingness to pay at

the beginning. With a greater proﬁt margin from the

high-type consumers, the no-preorder strategy bene-

ﬁts more from the expansion of the high-type demand

segment than the preorder strategy. It can be shown

that both ç

and ç

are linearly increasing in 

(for

ﬁxed 

). Thus, the search of ˆ

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 5

may help the seller make pairwise comparisons of

the strategies. However, ranking all three strategy

choices is difﬁcult. Hence, we rely on an extensive

numerical study to obtain some insights. We report

two main observations from the numerical analysis.

First, as 

increases, the seller’s optimal strategy

shifts from preorder to no preorder and then to pre-

order with price guarantee. Second, the range for the

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

Figure 2 Comparison of ç

, ç

, and ç

for Different 

and v

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





= 1.01



= 1.05

0.04 0.05 0.06 0.05 0.10 0.15 0.20 0.25 0.30

Note. 

= 5, 

= 405, 

= 3, v

= 2, c = 1, and  = 1.

no-preorder strategy to stand out may degenerate to

zero, especially when v

is large. Figure 2 shows a

representative example, where the left plot illustrates

the 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 

is relatively small (

< ˆ

). From Proposition 3,

we know the price guarantee strategy outperforms

the preorder strategy when 

is relatively large

(

> ˆ

). Therefore, the preorder strategy is opti-

mal among the three when 

is sufﬁciently small

(

< min4 ˆ

1 ˆ

5). Now we focus on the compari-

son between the no-preorder strategy and the price

guarantee strategy. In the no-preorder strategy, the

proﬁt margin from the high-type consumers is inde-

pendent of 

. In the price guarantee strategy, by con-

trast, the proﬁt margin from the high-type consumers

is increasing in 

: Because of the refund liability, the

seller is less likely to reduce the price when facing a

larger 

; 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 margin

from the high-type consumers will be higher than that

in the no-preorder strategy when 

is sufﬁciently

large. This suggests that the price guarantee strat-

egy dominates the no-preorder strategy for large 

Thus, the no-preorder strategy can only stand out

for intermediate 

. However, such a range may

degenerate to zero when v

is large for the following

reason. With a large v

, the advance demand infor-

mation obtained from the preorder sales will be more

valuable because selling to the low-type consumers is

highly proﬁtable. Therefore, for large enough v

, the

seller should always accept preorders, either with or

without a price guarantee.

7. Extensions

The basic model studied in the previous sections is

built on some assumptions that help maintain ana-

lytical tractability and reveal the key driving forces

underlying the results. This section relaxes some of

the assumptions and discusses their implications to

the analysis and results.

7.1. Negative Demand Correlation 4 < 05

So far we have focused on  ≥ 0 in the analysis. This

is appropriate when modeling new product introduc-

tions, of which the total market size is variable and

each consumer segment expands with the total mar-

ket. There may be situations where the total market

size is relatively certain, but the portion of each con-

sumer segment is variable. These situations can be

captured by a negative demand correlation (see, for

example, 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 preorder

strategy without price guarantee in §4. By replacing

 with −, it can be readily shown that all results in

§4 apply to  ∈ 4−11 07 as well. Next we discuss the

preorder strategy with price guarantee.

Under a price guarantee, the seller will lower the

price in the second period if and only if the realized

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

high-type demand is less than a threshold. In contrast

to the case of positive , now  < 0 means that price

reduction occurs when the low-type demand is rela-

tively high. That is, as  increases, the variance of

the low-type demand under price reduction becomes

smaller, whereas the mean becomes stochastically

larger. Therefore, under a negative demand correla-

tion, the negative effect of advance information intro-

duced by price guarantees on the second-period proﬁt

does not exist anymore.

Although  < 0 removes the negative impact of

increasing  on the second-period proﬁt, interest-

ingly, it aggravates the negative effect on the ﬁrst-

period proﬁt. This is because, with a higher , the

low-type demand in case of price reduction tends to

be larger, which motivates the seller to order more to

satisfy demand in the regular season. This improves

the product availability in the regular season and

leads to a lower preorder price. Thus, for  < 0, a

higher  will have a stronger adverse impact on the

preorder price under a price guarantee; as a result,

the seller’s optimal preorder price always decreases

in .

To summarize, with negative , all results about

the preorder strategy without price guarantee remain.

Under a price guarantee and  < 0, a larger  hurts

the 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 that

more accurate advance demand information may hurt

a seller’s proﬁt under a price guarantee, although this

result is solely caused by the conﬂict between advance

demand information and price discrimination.

7.2. Mixed Arrivals

It has been assumed in the basic model that the

high-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 always

and lower than the preorder price. In this subsec-

tion we extend the basic model to consider a mixed

arrival model where the high-type customers arrive

in both periods. For simplicity, we still assume that all

the low-type consumers show up in the regular sell-

ing season.

Let  ( ≤ 1) be the fraction of high-type

A more general model is to allow some low-type consumers in the

preorder season as well. However, this will not change the anal-

ysis as long as the preorder sales target the high-type customers

only. In this case, the low-type consumers will wait to purchase

the product in the regular season. For fashion and innovative prod-

ucts, the high-type consumers usually dominate in the preorder

season whereas the low-type consumers dominate in the regular

season, and they differ substantially in their willingness to pay. It

is unlikely the seller sets a low price to satisfy both types of con-

sumers in the preorder season. Therefore, we focus on the situation

where the preorder sales target the high-type consumers only.

consumers to arrive in the preorder season (1 −  is

the fraction in the regular season). We use X

X

and X

= 41 − 5X

to denote the high-type

demand in the preorder and regular seasons, respec-

tively. Let the correlation coefﬁcient between X

and

be . Thus, the seller can update his belief about

both the low-type demand and second-period high-

type demand after observing X

: Given a realization

= 

+ 

x, the updated distribution of

will

have a mean ˜

4x5 = 

+ 

x and standard devia-

tion ˜

= 

1 − 

, and the high-type demand in the

regular season will be

4x5 = 41/ − 15x

. We fur-

ther assume  = 1 in this extension. The rest of the

model setting is the same as before. Our basic model

represents a special case with  = 1. The purpose of

this subsection is to examine whether the key insight

carries over from the basic model with  = 1 to gen-

eral  < 1. The detailed analysis is provided in Online

Appendix 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 p

to satisfy

the high-type customers. Then, after observing the

preorder demand X

, she updates her belief about

future demand (X

and X

) and determines the order

quantity Q; meanwhile, she also sets a price p

> v

to induce the high-type customers to purchase in

the regular season. Finally, if there is still leftover

inventory, the seller lowers the price to p

= v

clear the inventory. In fact, we may view this as

a three-stage model where p

denotes the price in

stage i (i = 11 21 3). The customers in each stage decide

whether they want to purchase immediately or wait

until the next stage. Again we focus on the rational

expectations equilibrium under symmetric strategies

for the high-type consumers. In the equilibrium, all

the high-type customers in stage 1 will preorder at

price p

, and all the high-type customers in stage 2

will purchase at price p

Note that p

depends on the realization of the pre-

order demand X

, or X = 4X

− 

5/

. It can be

shown that p

= Ɛ6p

4X57; thus, depending on the real-

ization of X, both p

> p

and p

< p

may happen: If

the realization of X is low, then the product availabil-

ity in stage 3 will be low, and this allows the seller

to charge a high price p

in stage 2; the opposite is

true when the realization of X is high. Therefore, for

the more general setting, we may observe a preorder

price that is either higher (i.e., a premium preorder

price) or lower (i.e., a discount preorder price) than

the regular price. In the advance selling (preorder) lit-

erature, a discount advance selling price is attributed

to the uncertainty in product valuation, whereas we

have shown that a discount preorder price is possible

even without valuation uncertainty. Despite the more

complex pricing patterns, our result about the impact

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

of  remains unchanged as shown in the next propo-

sition. That is, the adverse effect of advance demand

information on the seller’s proﬁt does not rely on a

premium preorder price. Instead, it only hinges upon

the possibility that the product may be available at

a future low price, no matter when the price will be

dropped (it can be after the product release).

Proposition 6. Consider the mixed arrival model. If

< 0, there exists a ˜ such that ç

increases in  if and

only if 

≤ ˜. If z

≥ 0, then ç

always increases in .

Next we consider the case with price guarantee.

The analysis for mixed arrivals is more involved

because the seller needs to set multiple prices and

refunds. To simplify analysis, we assume that for any

customer, the refund is based on the purchasing price

and the ﬁnal price of the product. There are two pos-

sible ﬁnal prices in stage 3: v

if the seller lowers the

price to satisfy the low-type customers, or v

if the

seller does not serve the low-type customers at all.

The seller needs to determine two refunds 

and 

in stages 1 and 2, respectively, where 

is the refund

to the preorder customers in stage 1 and 

is the

refund to the high-type customers in stage 2, if the

ﬁnal price is reduced to v

Again, we ﬁnd that even under price guarantees,

the seller’s total proﬁt may decrease with  in certain

circumstances. In particular, the price guarantee miti-

gates the negative effect of  on the margin from the

high-type customers, but it introduces a new negative

effect of  on the proﬁt from the low-type customers.

Together with Proposition 6, this ﬁnding conﬁrms the

robustness 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 use

of price guarantees.

7.3. Proportional Rationing Rule

In this extension, we examine the robustness of our

key results under the proportioning rationing rule.

To facilitate discussion, we deﬁne the probability

of product availability in the second period, contin-

gent on the preorder demand 

+ 

x, to be (the

superscript pr stands for proportional rationing):



4x5 = Ɛ



min4Q4x51

4x55

4x5



1 (14)

where

4x5 is the updated low-type demand.

Lemma 5. 

4x5 is increasing in  if and only if

x ≥ −

In the preorder strategy (without price guaran-

tee), a high-type customer’s belief of product avail-

ability is given by Ɛ6

4X57. Lemma 5 shows that



4x5 is increasing in  when the realization of high-

type demand is large. Through extensive numerical

experiments, we ﬁnd that its expectation Ɛ6

4X57 is

always increasing in . This implies that under the

proportional rationing, again, more advance demand

information leads to a lower preorder price in the pre-

order strategy.

In the price guarantee mechanism, for a given price

reduction threshold

x < 0, the probability that the

product is available at the low price (p

= v

) in the

second period is



x5 = Ɛ6

4x5  x ≤

x7ê4

x5. From

Lemma 5,



x5 is decreasing in  if  < −

x/

; this

suggests that the negative effect of advance demand

information on the preorder price may be reversed

with a price guarantee when  is small.

The above results indicate that advance demand

information has a similar effect on the seller’s ﬁrst-

period proﬁt with or without price guarantee as

under the -rationing rule. Note that the choice of

the rationing rule does not affect the seller’s second-

period proﬁt. Therefore, the main results about the

effect of  on the seller’s overall proﬁt continue to

hold under the proportional rationing rule.

8. Conclusion

This paper studies the prevailing preorder practice

in which a seller accepts consumer orders before

the release of a product. Consumers who are eager

to obtain the product will beneﬁt from preorder

because it guarantees immediate product availabil-

ity on release. Preorder is also beneﬁcial to the seller

because it allows the seller to gauge market demand

from preorder sales, and to charge distinct prices

to different consumer segments. In this paper, we

develop a modeling framework to analyze the pre-

order strategy a seller may use to sell a perishable

product in a short selling season. The market con-

sists of two consumer segments, those who arrive in

the preorder season with valuation v

and those in

the regular selling season with valuation v

, respec-

tively. There is a correlation between these two ran-

dom demand segments, which we use to measure

the accuracy of advance demand information. To the

best of our knowledge, this modeling framework is

the ﬁrst to simultaneously incorporate the following

three important elements: seller’s inventory and pric-

ing decisions, consumers’ forward-looking behavior,

and advance demand information.

The value of advance demand information has

been widely studied in the operations literature. Most

studies emphasize the beneﬁt of advance demand

information, 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 decrease

with the accuracy of advance demand informa-

tion obtained from the preorder sales. Speciﬁcally,

the seller will beneﬁt from more accurate advance

Li and Zhang: Advance Demand Information, Price Discrimination, and Preorder Strategies

demand information only if the low-type valuation

is 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 price

discrimination: Accurate demand information may

increase product availability in the regular selling

period, which hinders the seller from charging a high

price to the high-type customers in the preorder season.

An effective way of resolving such a conﬂict

between advance demand information and price dis-

crimination is to offer a price guarantee: the seller

promises to compensate early purchasers in case the

price is lowered later. Interestingly, we ﬁnd that the

seller’s proﬁt may still decrease in the accuracy of

advance demand information, even when the seller

would beneﬁt from more advance demand informa-

tion if the price guarantee were not offered. The expla-

nation of this result is as follows. Although price

guarantees can mitigate (and in some situations may

even reverse) the effect of the above conﬂict, they

introduce another adverse effect of advance demand

information: With price guarantees, a seller will lower

the price to proﬁt from low-type consumers only

when the preorder demand is relatively low, but low

preorder demand implies weak low-type demand as

well (when the two demand segments are positively

correlated). As a result, the use of price guaran-

tees excludes situations where the seller can enjoy a

great proﬁt in the regular season from low-type con-

sumers, and such an adverse effect is stronger when

the advance demand information is more accurate.

Therefore, contrary to conventional wisdom, we

have demonstrated that advance demand informa-

tion can be detrimental to ﬁrms when facing forward-

looking consumers: (1) It may hurt the seller’s proﬁt

in the preorder season through its negative effect

on the preorder price. (2) In the presence of price

guarantees, it can also hurt the seller’s proﬁt in

the regular season through its negative effect on

the regular-season demand. Because of such nega-

tive effects of advance demand information, the seller

needs to carefully decide whether to accept pre-

orders and whether to provide price guarantees with

preorders. We ﬁnd that the seller’s strategy choice

depends critically on the relative market sizes of the

two types of consumers. To be speciﬁc, the preorder

option should be used without a price guarantee if

the high-type segment is relatively small, but with a

price guarantee if the high-type segment is relatively

large, and no preorder may be optimal for the cases

in between.

This research can be extended in a couple of direc-

tions. First, a more sophisticated consumer valuation

model can be introduced. For instance, consumers

may update their uncertain valuations based on pre-

order sales (e.g., a highly sought-after product during

the preorder season provides a positive signal about

the product value). Incorporating information updat-

ing for the consumers in addition to demand updat-

ing for the seller is an interesting direction for future

research. Second, this paper focuses on a monopolist’s

selling strategy. A natural extension is to consider the

preorder strategy in a duopoly setting. It would be

interesting to study how competition affects the ﬁrms’

strategy choice and the associated pricing and inven-

tory decisions.

Electronic Companion

An electronic companion to this paper is available as part

of the online version at http://dx.doi.org/10.1287/msom

.1120.0398.

Acknowledgments

The authors thank Laurens Debo, Stephen Gilbert, Guoming

Lai, Martin Lariviere, Özalp Özer, Kathryn Stecke, and

Xuying Zhao, as well as participants at the 2009 MSOM

Conference in Boston, Massachusetts; the 2009 INFORMS

Annual Meeting in San Diego, California; and the 2010

MSOM Supply Chain Management SIG Conference in

Haifa, Israel, for helpful comments and discussions. The

authors acknowledge the ﬁnancial support from the Boeing

Center for Technology and Informational Management and

the Connecticut Information Technology Institute.

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