Uninformative Advertising as an Invitation to Search

Dina Mayzlin and Jiwoong Shin�

Yale University

October 2009

�The authors contributed equally, and their names are listed in alphabetical order. We thank Kyle Bag-

well, Dirk Bergemann, Dmitri Kuksov, David Miller, K. Sudhir, Duncan Simester, Joel Watson, Birger Wern-

erfelt, and seminar participants at QME conference, SICS conference at Berkeley, JDCL Festschrift confer-

ence, NEMC conference at MIT, Yale Economics Theory Lunch, marketing seminars at Erasmus University,

Korea University, University of Maryland, Tilburg University, and Yale University for their helpful comments.

Correspondence: 135 Prospect St, P.O. Box 208200, New Haven, CT 06520, email:dina.mayzlin@yale.edu,

jiwoong.shin@yale.edu

Uninformative Advertising as an Invitation to Search

Abstract

The choice of content in an advertising message is a critical managerial decision. In this paper, we

investigate under what circumstances the �rm prefers to include a product attribute-based appeal in

its ad (i.e.: "No Hassle Rewards") versus an appeal with no direct information on product attributes

(i.e.: "My Life, My Card, American Express.") Since attribute-based messages are meant to inform

consumers of the product�s high value, here we focus on how the content decision is impacted by

the product�s quality. One intuitive hypothesis is that the high-quality product would choose to

emphasize its attributes. However, the limited bandwidth of advertising media implies that a �rm

can only communicate about a limited number of attributes in its message. Hence, an attribute

message may not di¤erentiate a truly excellent product from an average one. We show that there

can exist an equilibrium where a high-quality �rm chooses to produce messages devoid of any

information on product attributes in order to encourage the consumer to engage in search, which

is likely to uncover positive information. Hence, an uninformative message can serve as a signal

of con�dence on the part of the �rm. An average �rm that imitates this strategy risks to lose its

customer in cases when she uncovers negative information as part of the search. Therefore, an

average �rm may choose to engage in an attribute-based appeal, despite the fact that this perfectly

reveals its type. While most of the previous literature has focused on the decision to advertise as a

signal of quality, here we show that message content, coupled with consumer search, can also serve

as a credible signal of quality.

Keywords: Advertising, advertising content, uninformative advertising, quality signal, con-

sumer search.

1 Introduction

For the past forty years, economists and marketers have studied how advertising can help consumers

learn about products. The information that advertising provides can be direct, such as the existence

of the product or its price (for example, see Grossman and Shapiro 1984). The information can also

be indirect, where the mere fact that the �rm advertises signals an experience good�s high quality

(see Nelson 1974 and Milgrom and Roberts 1986). The latter is known as the "money-burning"

theory of advertising.

One of the important and surprising take-aways of the money-burning theory is that it is the

level of spending that signals the quality of the product, and not the content of the message.

That is, content is irrelevant for conveying information on product quality. However, a quick

look at trade publications such as Ad Age and Ad Week con�rms our intuition as consumers that

content is an important driver behind advertising persuasiveness, and one to which �rms pay close

attention. In this paper, we revisit the result that advertising is irrelevant for signaling quality

and investigate whether and how advertising content can convey information on product quality in

a rational framework.

Speci�cally, we ask when a �rm would choose to mention speci�c product attributes as opposed

to making vague claims in its advertising. We will refer to a campaign that emphasizes product

attributes as "attribute-based" advertising. By de�nition, this type of advertisement contains

"hard" information (Tirole 1986) about product bene�ts and, hence, the claims are credible and

veri�able. In contrast, following Bagwell and Ramey (1994), we will refer to a campaign that

does not emphasize any particular product attributes as "uninformative." Of course, the term

"uninformative" may be somewhat confusing since even vague claims may contain information to

the consumer. For example, a message with no speci�c claims may simply make a consumer

aware of the product or reinforce the product�s image. Here we focus on the signaling value in

the �rm�s decision not to include attribute information in its communication. Hence, the term

1

"uninformative" emphasizes the apparent lack of attribute information.1

As an example of attribute-based advertising, consider the credit card issuer Capital One�s

"What�s in Your Wallet?" campaign. One ad featuring the comedian David Spade focused on

the di¢ culty involved in claiming rewards from the competing cards as opposed to the Capital

One�s "No Hassle Rewards" card. The ad ended with the statement, "No annual fee! There

are no blackout dates on any airline at any time." In contrast, consider ads by the credit card

issuers American Express and the First Premier Bank. The 2004 American Express "My Life.

My Card." campaign did not directly mention any of the bene�ts of owning an American Express

card, such as the card�s excellent rewards program. For example, one ad featured Robert De Niro

reciting a "love letter" to New York City. The brand was mentioned only in the closing line,

"My life happens here. My card is American Express." Similarly, a recent TV ad for the First

Premier Bank did not mention any speci�c product attribute. Moreover, the practice of avoiding

mentioning product attributes is fairly widespread: Abernethy and Butler (1992) �nd that 37.5%

of U.S. TV advertising has no product attribute cues. We will refer to these types of messages as

uninformative advertising.2

How will these di¤erent types of advertising campaigns a¤ect consumers�inference about prod-

uct quality? What is the relationship between product quality and the �rm�s decision to make

attribute-based claims? One intuitive hypothesis is that the high-quality product would choose to

emphasize its product bene�ts which are, by de�nition, strong. However, the limited bandwidth

of communication inherent in any form of advertising implies that a �rm can talk about only a

1 In advertising literature, the authors di¤erentiate between various non-attribute based appeals, such as image or

humor-based communication. In this paper, we do not di¤erentiate them and group all non-attribute-based forms

of advertisements into the "uninformative" rubric.2 In practice, the discrete classi�cation of all ads into attribute-based v. uninformative is di¢ cult since even the

most uninformative ad often contains some basic information about the product. For example, a consumer who views

the American Express ad can learn that it is a credit card. Hence, the simple classi�cation of "attribute-based" or

"uninformative" is an approximation of what is really a continuum.

2

small subset of its product�s attributes. It is impossible for the �rm to accurately communicate

all of the features associated with its product in a 30-second commercial or a print ad (Shapiro

2006, Bhardwaj et al. 2008). Hence, if a �rm claims to be good on a few selected attributes, its

advertising will be indistinguishable from the advertising of the �rm that is only good at those

attributes. If, on the other hand, the �rm makes no attribute-based claims and engages in unin-

formative advertising, its advertising will be indistinguishable from the advertising of a �rm that

cannot deliver high quality on any attributes.

For example, consider the digital camera Sony Cybershot DSCW300 which was ranked number

one by Consumer Reports in 2009 in the subcompact digital camera category. This camera is

high-quality on a large number of attributes; the Sony web site lists over 30 product features for

this product. Clearly, Sony Cybershot cannot emphasize all of its superior attributes in a 30-

second commercial. On the other hand, if Sony decides to focus on one of its attributes, such as

high image quality, it cannot distinguish itself from a camera such as Panasonic Lumix DMC-FS15,

which happens to have high image quality but is dominated by Sony on the versatility dimension.

If Sony instead chooses to emphasize the versatility dimension, then it cannot distinguish itself

from Nikon Coolpix S230, which is equally versatile but is dominated by Sony on image quality.3

The argument above highlights the point that the �rm may not be able to entirely resolve the

uncertainty about its product through advertising alone under limited bandwidth in advertising

communication. However, a consumer who is uncertain about the product�s features following

exposure to advertising may take actions to resolve this uncertainty: she can conduct her own

search to discover the product�s quality prior to purchase by engaging in activities such as reading

online product reviews or talking to her friends. Therefore, the high quality �rm may actually

prefer to encourage the consumer to search since it is con�dent that the information uncovered will

be positive. We show that there exists an equilibrium where uninformative advertising serves as

an invitation to search. In contrast, an average �rm that imitates this strategy risks losing its

3See http://www.consumerreports.org.

3

customer in cases when she uncovers negative information as part of her search. Hence, an average

�rm may choose to engage in an attribute-based appeal, despite the fact that this perfectly reveals

its type. Therefore, in a situation with limited communication bandwidth and active consumers,

advertising with no information on features may serve as an invitation for the consumer to search.

In this paper, we formalize the above argument and develop a framework to analyze simulta-

neously the choice of advertising content (whether to emphasize attributes or not) and the pricing

decisions of a monopolist. By taking into account the fact that consumers may choose to search,

which serves as an additional source of noisy information about product quality, a �rm can signal

its product quality through its advertising content.

The paper is organized in the following manner. In Section 2, we relate our paper to the existing

literature in economics and marketing. Section 3 presents the model set-up. We discuss the model

results in Section 4 and conclude in Section 5.

2 Literature Review

In this Section, we review the literature that applies to the primary issue in this paper: the role of

advertising content in signaling product quality. Most models that consider the quality-signaling

role of advertising do not �nd that advertising content can credibly signal quality (Nelson 1974,

Kihlstrom and Riordan 1984, Milgrom and Roberts 1986, Bagwell and Ramey 1994, also see Bagwell

2007 for a comprehensive review). In these models, the high-type �rm can credibly signal quality

only through conspicuous money burning. In contrast, we show that content may play a role in

signaling quality above and beyond public money burning.

Several previous papers have focused directly on advertising content. For example, Butters

(1977) and Grossman and Shapiro (1984) allow the �rm to announce the existence of the product

or its price through advertising. Simester (1995) and Shin (2005) examine the credibility of price

claims in advertising. However, neither of these papers considers content other than prices as a

potential signal on quality. Two recent papers consider the role of content (other than prices)

4

in signaling quality. Anderson and Renault (2006) look at the possibility of the �rm informing

consumers about product attributes through advertising content in a context where consumers are

imperfectly informed about product characteristics.4 Although consumers always learn their true

match value before buying, the possibility of a hold-up problem by the �rm implies that advertising

that provides either match or price information alone is optimal in di¤erent cases. Anand and

Shachar (2007) show that advertising content can enable quality signaling by in�uencing beliefs on

the o¤-equilibrium path.

In addition, the �rm can signal its unobservable quality through actions other than advertising.

Moorthy and Srinivasan (1995) show that warranties such as money-back guarantees can signal

the �rm�s unobservable quality, and Wernerfelt (1988) shows that umbrella branding can signal

the quality of a new product. Our model closely relates to Bhardwaj et al.(2008). In the latter,

the high-quality �rm prefers to allow the consumers to choose what features they want to inquire

about (a "buyer-initiated" selling format) since it is con�dent about the high quality of all of its

features. On the other hand, the low-quality �rm prefers a "seller-initiated" selling format, where

the �rm chooses which features to highlight as part of its selling process. Hence, the buyer-initiated

format can serve as a signal of quality. Although our paper explores a very similar problem in

the advertising context, our work di¤ers from Bhardwaj et al. (2008) along several important

dimensions. First, in our model the (costly) search is a decision variable on the part of the

consumer, while in Bhardwaj et al. (2008) the search is costless and always occurs. Second, in

Bhardwaj et al. (2008) a counter-signaling equilibrium (the highest and the lowest types choose

the same action) is ruled out since their model only has two types of �rms.

Formally, the model we present here is most closely related to the literature on countersignaling

4Sun (2009) also investigates the monopolistic seller�s incentive to disclose the horizontal matching attributes of

a product. Kuksov (2007) studies the incentives of consumers to reveal or conceal information about themselves to

others through brand choices in the consumer matching context. Yoganarasimhan (2009) �nds that �rms sometimes

prefer to conceal information to increase the social value of its product.

5

(Teoh and Hwang 1991, Feltovich et al. 2002, Araujo et al. 2008, Harbaugh and To 2008).5

In contrast to the standard signaling models where high types send a costly signal to separate

themselves from the low types, in countersignaling models the high type chooses not to undertake

a costly signaling action. People of average abilities, for example, get more education than bright

people in labor markets (Hvide 2003). Mediocre �rms reveal their favorable earning information

while both high quality and low quality �rms tend to conceal their earning information in �nancial

market (Teoh and Hwang 1991). Feltovich et al. (2002) formalize this intuition and show that in

the presence of an external signal, the high type may pool with the low type while the medium type

prefers to separate. Their motivating example is one of a job seeker, who has not seen his letters of

recommendations, deciding whether or not to reveal his high school grades during an interview.

While the model we present is a countersignaling model in that the high and low types pool

on the same actions, the advertising context makes it necessary for us to de�ne a model that is

di¤erent from extant counter-signaling models. First and most importantly, while in the previous

countersignaling models (for example, Feltovich et al. 2002, Harbaugh and To 2008), the player is

assumed to always receive the second signal, in our model the consumer only receives this additional

information if she chooses to search after observing the price and content of the advertising message;

that is, we endogenize the presence of a second signal, which plays a critical role in enabling the

countersignaling equilibrium. Second, we also allow price to be a potential signal, which was not

an issue in the earlier models. The decision to search is of course also impacted by the price that

the �rm charges.

Although we have focused on rational explanations for uninformative advertising, there are a

number of behavioral-based explanations for this phenomenon (see Carpenter et al. 1994, Holbrook

and O�Shaughnessy 1984, Kardes 2005, and Scott 1994). These models emphasize the importance

5A similar phenomenon is known in the sociology literature as the middle-status conformity theory: the high and

low-status players may deviate from conventional behavior, while the middle-status players conform to social norms

(Phillips and Zuckerman 2001). These models, however, do not involve a signaling story.

6

of both the cognitive and the emotional response to advertising. Since we predict that �rms may

choose to engage in uninformative advertising even in the absence of these psychological forces, our

work complements these explanations.

3 Model

The game consists of one �rm and one consumer. There is an informational asymmetry about the

quality of the monopolist�s product: the �rm knows its product�s quality while the consumer must

infer the product�s quality from signals that she receives from the �rm as well as information that

she may obtain on her own. To model quality, we use the concept of a discrete match between the

product and consumer (Wernerfelt 1994, Bhardwaj et al 2008). That is, we equate quality with the

product�s ability to frequently meet the customer�s needs, regardless of the exact circumstances.

In particular, suppose that the product consists of two attributes: � 2 fA; ag; � 2 fB; bg, where

the capital letter stands for higher quality on that dimension. There are two possible states of

the world, � 2 f1; 2g, where either state is equally likely a priori. If � = 1, only attribute �

impacts the customer�s experience. Similarly, if � = 2, only attribute � matters. Neither the

customer nor the �rm can predict the future state of the world. For example, suppose that Bob

is considering buying a jogging stroller for his newborn daughter. If he ends up using the stroller

mostly for running in his neighborhood, then it would be important for him that the stroller has

good shock absorption. However, if he also ends up often driving with his child to the mall, it is

important that the stroller be able to fold compactly in order to �t in the trunk of his Jetta. Since

this is Bob�s �rst child, he cannot accurately predict which mode will be more likely. Similarly,

when consumers purchase a personal computer, they do not know whether the CPU speed or the

memory is the more important attribute.

The product utilities in the two states of the world are

V�=1 =

8><>:V if � = A

� otherwise

9>=>; ; V�=2 =8><>:V if � = B

� otherwise

9>=>;7

We normalize � = 0 for simplicity. We also assume that an attribute is equally likely to be high

or low quality, and that there may be correlation between levels of the two attributes: P (� = A) =

P (� = B) = 12 , and P (� = Bj� = A) = P (� = Aj� = B) = P (� = bj� = a) = P (� = aj� = b) = �;

where 0 < � < 1. Hence, there are three possible types (�) of products based on the quality

levels of the attributes: � 2 fH;M;Lg = ffA;Bg; fA; bg or fa;Bg; fa; bgg, with the a priori

probabilities of (�2 ,1 � �,�2) respectively.

6 A priori, the H-type product delivers utility V to a

customer with probability 1, the M -type product delivers utility V with probability 12 and utility

of 0 with probability 12 , and L always delivers 0 utility. Note that while the exact utility levels are

not important to our results (for example, we can re-normalize � > 0 to better capture the reality

that even inferior products yield some utility to the consumer), the rank-ordering of products from

the consumer�s perspective is important. Hence, all else equal, a consumer would prefer H to

M , and M to L, which in turn implies that L type wants to imitate H and M ; M type wants to

separate itself from L and imitate H, and H wants to separate itself from M and L.

The �rm can communicate to the consumer through advertising. We assume that the cost of

advertising is zero.7 We also assume that the �rm must advertise in order to inform the consumer

of its product�s existence. These two assumptions imply that the �rm always chooses to advertise.

This allows us to focus on the role of content in advertising above and beyond the well-known e¤ect

of money burning where the �rm can signal that it is high type by engaging in excessive advertising

activity. Moreover, while our model primarily deals with the quality-signaling role of advertising,

this assumption acknowledges the importance of the awareness role of advertising.

The �rm�s action space consists of two possible advertising choices. First, the �rm can choose

an ad that centers on the product�s attributes, an "attribute-based" advertising. Here, we impose

a truth-telling assumption: the �rm cannot claim to be high quality on an attribute on which it

6Note that if � = 1 (perfect positive correlation), only fA;Bg and fa; bg products exist, and if � = 2=3, all products

are equally likely.7The results of the model are not qualitatively a¤ected by the presence of an advertising cost, as long as it is not

too large.

8

is in fact low quality. While we acknowledge that advertisers often exaggerate their claims, the

Federal Trade Commission does require that "advertising be truthful and non-deceptive" and that

all claims must have a "reasonable basis."8

To capture the reality of the limited bandwidth inherent in a communication medium such as

TV, we allow the �rm to transmit information about only one attribute �either � or �: a = aj ,

where j 2 (�; �g. In practice, a product contains a large number of features. However, given

the constraints on the time available for communication as well as the limited cognitive resources

available to the consumer for processing advertisement information (Shapiro 2006), the �rm is only

able to communicate about a small subset of these features (Bhardwaj et al 2008). We can extend

this two-attribute model to a more general multi-attribute setting. If the �rm chooses to emphasize

more than one attribute in its ads, one can think of the set of advertised features as �, and the set

of the unadvertised features as �; for example.

In contrast to attribute-based advertising, a �rm can choose not to emphasize any particular

attribute: a = a0. We refer to this as "uninformative" advertising. In Table 1 we summarize the

possible types and the actions available to them.

Table 1: All Types and Possible Actions

Product Type Attribute � Attribute � Expected Utility Possible Ads Price

L a b 0 a0 p � 0

M A (or a) b (or B) V2 a0; aj p � 0

H A B V a0; aj p � 0

Following Meurer and Stahl (1994), we assume that the consumer can costlessly obtain infor-

mation on the �rm price, p, after observing an ad. Otherwise, a hold-up problem can occur (see

Wernerfelt 1994). After the consumer receives the advertising message and observes the price,

she can choose to invest a cost c in order to discover the quality of the product. After incurring

8http://www.ftc.gov/bcp/conline/pubs/buspubs/ad-faqs.shtm

9

this cost of search, the consumer obtains extra noisy information about the product quality. This

may involve searching for online reviews (Chevalier and Mayzlin 2006), observing word-of-mouth

(Chen and Xie 2008, Godes and Mayzlin 2004), reading Consumer Reports, or doing other types of

search activities. We assume that consumer search yields a binary signal on the product quality,

s 2 fs; sg, where s denotes positive news and s denotes negative news. The search outcome is

related to the product�s quality level, � 2 fL;M;Hg, according to the following probabilities:

Pr(sj�) = �; where � 2 fL;M;Hg (1)

L < M < H :

The �rm knows that the consumer can obtain this extra information with the above probabilities,

but does not observe whether the consumer actually chooses to search for this extra signal, let alone

what signal the consumer ultimately receives if she chooses to do so. The signal space of each

type has the same support so that no signal is perfectly informative. Also, Equation (1) implies

that the higher quality �rm is more likely to generate favorable information. This amounts to a

MLRP (Monotone Likelihood Ratio Property) assumption over the signal space across types. In

other words, positive news (s) is really "good news" regarding the �rm�s quality (Milgrom 1981).

For example, suppose that after viewing an ad for Sony Cybershot camera, Bob posts an inquiry

about this camera on a digital photography forum. Since this camera is excellent, Bob is likely

to receive a positive recommendation. Bob is less likely to receive a positive review for Nikon

Coolpix, which is more likely to disappoint a random consumer. This example illustrates several

important points. First, the information the consumer receives through search is potentially richer

than the information she can obtain after viewing an ad. The binary signal above can be viewed

as a summary of all the product attributes. Second, even an excellent product may generate a

negative signal: there is noise in the signal due to factors such as individual taste idiosyncrasies

or promotional chat generated by �rms, for example. However, a better product is more likely to

yield a positive signal (Mayzlin 2006). Hence, the additional signal is informative but noisy.

10

After the consumer receives information regarding the product (through either advertising,

prices, or own research), she forms a belief on the quality of the product. Here, we signify by

the consumer�s information set, and by �() the consumer�s belief. In particular, �() =

(�L(); �M (); �H()), where �L() = P (Lj), �M () = P (M j), �H() = P (Hj). The con-

sumer�s information set () includes the observation of advertising (a), price (p), and consumer�s

own search (s) if that takes place. That is, if the consumer performs own search, then = faj ; p; sg

for a �rm that advertises an attribute, and = fao; p; sg for a �rm that employs uninformative

advertising. If, on the other hand, no consumer search takes place, then = faj ; pg for a �rm

that advertises an attribute, and = fao; pg for a �rm with an uninformative advertising.

The consumer then decides whether to purchase the product at its posted price based on the

posterior belief on its quality: �(a; p; s) in the case of consumer research, and �(a; p) in the case of

no search. We assume that a consumer who is indi¤erent between purchasing and not purchasing

the product chooses to purchase it. The timing of the model can be summarized as follows:

Figure 1: Timing of the Game

4 Perfect Bayesian Equilibrium

We start with the consumer�s problem �the consumer observes advertising and price, (a; p), and

decides whether to search for additional information before making a �nal purchase decision �and

then turn to the �rm�s strategy. If the consumer is uncertain about the �rm�s type even after

11

observing the price and advertising, she can either (1) forego search for additional information and

make a purchase decision based on her belief, �(a; p), which we abbreviate to �, or (2) search for

additional information s at a cost c. In the absence of additional search, the consumer buys the

product if and only if E(V j�)� p � 0: That is, she buys the product if the prior belief is relatively

favorable or the price is relatively low. The consumer will search for additional information if

EU(search) � EU(no search) � max(0; E(V j�)� p) (2)

Note that the consumer undertakes a costly search only if her decision to purchase di¤ers de-

pending on the outcome of the signal (i.e., there must be value in the information received). In

other words, when the consumer chooses to search, she buys only if the signal is high (s = s). The

conditions for when the consumer chooses to search are speci�ed in the following Lemma:

Lemma 1 (Consumer search)

1. If E(V j�)� p � 0, the consumer will search for additional information i¤

c � Pr(sj�)[p� E(V j�; s)], E(V j�; s) + c

Pr(sj�) � p (3)

2. If E(V j�)� p < 0, the consumer will search for additional information i¤

c � Pr(sj�)[E(V j�; s)� p], p � E(V j�; s)� c

Pr(sj�) (4)

Moreover, when p = E(V j�); Pr(sj�)[p� E(V j�; s)] = Pr(sj�)[E(V j�; s)� p]:

Proof. See Appendix

Equations (3) and (4) compare the marginal cost and the marginal bene�t of search. The

marginal cost of search (the left hand side of Equations (3) and (4)) is c. The marginal bene�t

is represented by the right hand side of these equations and di¤ers depending on the price. If

E(V j�) � p � 0, the consumer would choose to buy the product based on the prior alone in the

absence of an additional signal. Hence, the marginal bene�t of search is in preventing purchase

in the case when the signal is negative (s = s). On the other hand, when E(V j�) � p < 0, the

12

consumer would not purchase a product in the absence of an additional signal. Therefore, the

marginal bene�t of search is in enabling the consumer to purchase the product in the case when

the signal is positive (s = s). Note that if the conditions in either Equation (3) or Equation (4)

hold, then Equation (2) holds �the consumer chooses to search before purchase.

One implication of Lemma 1 is that given a belief, the consumer chooses to search for additional

information only if the product�s price is within a certain range (see Lemma 2 in the Appendix for

more details). Hence, we can identify the range of prices and beliefs that ensures the existence

of consumer search. For example, Figure 2 illustrates the consumer�s decision to search for extra

information when the consumer is not certain whether the �rm is type H or type M . This can

occur if a consumer observes an attribute-based ad, which implies that the product is not L-type,

but could be either H-type or M -type. In the Figure, the prior belief �H (the probability that the

product is H-type prior to engaging in search) is graphed on the x -axis (where 0 � �H � 1).

Figure 2: Consumer Beliefs and Optimal Response Behaviors

13

For a given belief (�H), if the price is low enough (p < p(�H)), the consumer prefers to buy the

product without further search (see point D in Figure 2). As we mentioned in our discussion of

Lemma 1, at relatively low levels of p, i.e., p � E(V j�), the value of additional search is in preventing

purchase when the outcome of search is negative, which in this case is captured by p� E(V j�; s).

Hence, when p is low, the marginal bene�t of search is not high enough to justify its marginal cost.

At any point on the convex curve p = p(�H), the consumer is indi¤erent between buying without

search or engaging in further search. At a higher price (p < p(�H) < p), the consumer prefers to

search (see points B and C). That is, here the consumer incurs a cost c to obtain an additional signal

and purchases if and only if the outcome is positive, s = s, since E(V j�; s) > p and E(V j�; s) < p.

On the other hand, at any point on the concave curve p = p(�H), the consumer is indi¤erent

between no purchase and engaging in further search, and at p > p(�H) the price is so high that the

consumer surplus obtained in the case when the outcome of search is positive (E(V j�; s)�p) is not

high enough to justify the cost of search (see point A). As we can see from the Figure, given �H ,

the consumer chooses to search for additional information only if p 2 [p(�H); p(�H)]. Moreover,

if the belief is extreme (�H < �Hor �H > �H), the consumer does not engage in search at any

price. However, at the intermediate level of uncertainty, �H 2 [�H ; �H ], there exists a price range

at which search occurs. Note that the cut-o¤ beliefs, �H; �H , are a function of the search cost c:

As c increases, the range [�H; �H ] decreases and becomes empty when c >

V ( H� M )8 V (see the

Lemma 2 in the Appendix). That is, search will not occur under any belief if the search cost is

su¢ ciently high.

What is the potential role of search in our model? As we can see from the Figure above, given

the prior belief �H , the possibility of consumer search allows the �rm to charge a higher price (see

point B, for example), as compared to a situation where no consumer search is possible, in which

case the maximum the �rm can charge is p = E(V j�). That is, the fact that the consumer can

undertake an action to resolve the uncertainty surrounding the �rm�s quality enables the �rm to

charge a higher price. In this sense, the �rm may want to invite the consumer to search. We

14

can think of this as the bene�t of search to the �rm. However, while the possibility of search

increases the upside of a transaction through higher price, it also introduces the possibility that

no transaction occurs in the case when the consumer receives a negative signal, which may happen

even for the highest type since the signal is noisy. We can think of the no transaction outcome as

the cost of search (or alternatively as the risk inherent in search) to the �rm. Since the probability

of a negative signal di¤ers across di¤erent types, search is di¤erentially costly to di¤erent quality

types. Therefore, a �rm that "invites" the consumer to search through an advertising action may

be able to signal its quality by credibly demonstrating its con�dence in the outcome of the search.

Since we want to model an active consumer who can choose to engage in her own search, we focus

on the region of the parameter space where the cost c is low enough such that search is a feasible

option to the consumer.9

Assumption: Search cost is low enough such that c � V ( H� M )8 V .

We next consider the �rm�s strategy in more detail. We focus on pure strategies only. Hence,

each type chooses an advertising and price combination � (a�; p�), where � 2 fL;M;Hg. There

are a number of equilibria that are possible, ranging from full separation to pooling (see Table 2).

For example, in HM equilibrium, the H and M types send out the same advertising message and

post the same price, while L-type di¤ers in at least one of these actions: (aH ; pH) = (aM ; pM ) �

(aHM ; pHM ) 6= (aL; pL). This in turn implies that if the consumer observes (aL; pL), she infers that

the product is L-type. On the other hand, if she observes (aHM ; pHM ), she is uncertain whether

the �rm is H-type or M -type. Her decision to search for extra information depends on her prior

belief as well as the price p. While the advertising action choice is discrete (an advertising action

can be either attribute-based or uninformative), the price variable is continuous, which implies that

a continuum of prices is possible for each type of equilibrium.

We can quickly rule out two potential equilibria: fully-separating equilibrium (FS) and a semi-

9This low search cost assumption guarantees that there always exists a consumer belief under which search is the

best response for the consumer if she observes either a0 or aj . See Lemma 2 in the Appendix for more details.

15

Table 2: All Possible Equilibria

Equilibrium Type Description Notation

Fully Separating H;M;L separate FS

Semi-Separating H;M pool HM

Semi-Separating H;L pool HL

Semi-Separating M;L pool ML

Semi-Separating H;M;L pool HML

separating equilibrium where M and L pool (ML). Note that full separation implies that the

consumer can simply infer the product�s type by examining the prices and the advertising campaign.

That is, (aL; pL) 6= (aM ; pM ) 6= (aH ; pH). From our model assumptions, L-type can only send an

uninformative ad: aL = a0. Since search is costly and the product�s type can be perfectly observed,

the consumer does not search in this equilibrium. Also, note that if pH > pM , the M -type will

deviate to the H-type�s strategy, and if pH < pM , the H-type will deviate to theM -type�s strategy.

This implies that pH = pM = ep. This in turn implies that aH 6= aM . Hence, either H or M must

engage in uninformative advertising in FS equilibrium. Suppose that aH = a0 and let ep < pL.

This of course implies that H-type will mimic L�s strategy. If, on the other hand, ep > pL, L-typewill mimic H�s strategy. Hence, ep = pL or (aL; pL) = (aM ; pM ) = (a0; ep). This is a contradiction;a fully separating equilibrium does not exist in our model.

Proposition 1 A fully separating equilibrium does not exist.

The result above illustrates the importance of search in enabling signaling in our model. Con-

sumer search cannot occur in a fully-separating equilibrium since the consumer has no uncertainty

about the �rm type after observing price and advertising. The assumption that there are more

types (3 types) than possible advertising actions (2 possible actions: attribute vs. uninformative

ad) results in at least some pooling between di¤erent types in advertising. The remaining question

is then whether price can di¤erentiate between types in the absence of search by the consumer. As

16

is illustrated from the proof above, price alone cannot signal quality since our model does not have

any of the elements that would ordinarily enable price to be a signal of quality, such as di¤erential

costs or demand. Instead, as we show below, it is consumer search (coupled with price) that

enables signaling in our model.10

Similarly, we can show that a semi-separating equilibrium, ML, where M and L types pool

cannot exist. In ML, it must be the case that pL = pM � pML, aL = aM = a0. Note that

pML <V2 since even with search the consumer cannot be absolutely certain that the product is not

L-type. However, if M -type deviates to aj , j 2 (�; �g, it can charge at least V2 since an attribute

message credibly signals that it is not type L. Intuitively, since M is able to perfectly separate

itself from all lower-type players (which in this case is L only) through advertising, it prefers to do

so. Hence, an equilibrium where M and L pool does not exist.

Proposition 2 ML equilibrium does not exist.

The remaining three equilibria candidates (HML, HM , and HL) can be categorized into two

types: one in which H separates from M (HL), and one in which H pools with M (HML, and

HM).

As is the case for any signaling model, we have to deal with the technical issue of specifying

the out-of-equilibrium beliefs. There are two main approaches to dealing with this. The �rst is

to assume a particular set of beliefs following a deviation (see, for example, McAfee and Schwartz

1994). While this method is often used, it is vulnerable to the criticism that any speci�c set of

chosen beliefs is, by de�nition, arbitrary. The second approach is to start with an unconstrained

set of out-of-equilibrium beliefs, but then narrow it using an existing re�nement. The strength

of this approach is that it imposes some structure on the out-of-equilibrium beliefs �a belief that

10A signaling result requires that the single-crossing property be imposed across types. In existing models, single-

crossing property is exogenously given through di¤erential costs, demands or pro�ts from repeat purchases (Milgrom

and Roberts 1986, Bagwell and Ramey 1994). In our model, the single-crossing property arises from the consumer�s

endogenous search.

17

is consistent with a re�nement is more "reasonable." A number of signaling models employ the

Intuitive Criterion (Cho and Kreps 1987) to re�ne the beliefs (for example, Simester 1995, Desai and

Srinivasan 1995). The idea behind this criterion is as follows. Suppose that a consumer observes

the deviation A1 = (a; p). If type � makes lower pro�t in deviation than in equilibrium under all

possible consumer beliefs, the consumer does not believe that the product could be type �. That

is, if L-type would not bene�t from the deviation even under the most optimistic belief, �H = 1,

the consumer does not think that the deviating �rm could be type L. In our model, however, no

search occurs under extreme beliefs, such as �H = 1, since the consumer would rationally choose

not to search under certainty. Of course, if search does not occur, and as was illustrated in our

discussion following Proposition 1, all types equally bene�t (or are hurt) by a deviation. Hence, the

Intuitive Criterion does not narrow the beliefs in our model; in other words, any out-of-equilibrium

belief in our model can survive the Intuitive Criterion.

Instead, and following other counter-signaling papers (for example, Feltovich et al. 2002, Har-

baugh and To 2008), we use a stronger re�nement, the D1 criterion (Fudenberg and Tirole 1991),

to eliminate unreasonable out-of-equilibrium beliefs. The idea behind this re�nement is roughly

as follows. Consider a set of best responses associated with a particular out-of-equilibrium belief.

Suppose that H-type bene�ts from the deviation under a bigger set of best responses than L-type.

Moreover, this is the case for all possible beliefs. D1 then requires that the consumer does not

believe that the deviating type is L. More generally, suppose that in deviation A1 = (a; p), type

�0 makes higher pro�t than in equilibrium under a strictly bigger set of best responses from the

consumer than type � does. D1 then requires that the consumer does not believe that the product

could be type �.

Note that unlike the Intuitive Criterion, D1 does not require that L-type must not bene�t

from the deviation under any possible belief. Instead, it requires that the set of consumer�s best

responses, which are based on the consumer�s beliefs, should be strictly smaller than that of H-type.

We show that our equilibrium is supported by out-of-equilibrium beliefs that not only survive the

18

Intuitive Criterion, but also even the stronger D1 re�nement. We discuss the D1 criterion and its

application in the Appendix.

4.1 Uninformative Advertising Can Signal High Quality

We �rst consider the equilibrium that is the core of this paper: HL equilibrium. In this equilibrium,

H and L types pool on uninformative advertising and price (aH = aL = a0; pH = pL � p�HL),

whereas M type engages in attribute-based advertising and, therefore, perfectly reveals own type

to the consumer (aM = aj ; pM = V2 ). HL is a countersignaling equilibrium in that the high and

low types pool together on the same action (Feltovich et al. 2002). Surprisingly, in this equilibrium

the type with the most to say (H-type) chooses a message devoid of any information on product

attributes.

Proposition 3 A semi-separating HL equilibrium where the consumer chooses to search after

observing (a0, p�HL), exists if:

(1� H)V + 2c2� H � L

� p�HL < HV � 2c H + L

(5)

Mp�HL <

V

2< Hp

�HL (6)

Here, ��(H) = Hp�HL > �

�(M) = V2 > �

�(L) = Lp�HL.

Proof. See the Appendix

Under the assumption that search is feasible for the consumer (c � V ( H� M )8 V ), the consumer

chooses to search for additional information in HL equilibrium as long as the equilibrium price is

not too low or too high: (1� H)V+2c2� H� L� p�HL <

HV�2c H+ L

. (If p�HL <(1� H)V+2c2� H� L

, the consumer�s best

response is to buy without search, and if p�HL > HV�2c H+ L

, the consumer�s best response is not to

purchase). Under consumer search, the �rm can charge a quality premium based on the reduced

consumer uncertainty. That is, in the case when the consumer receives good news (s = s), she

is willing to pay a higher price compared to the price she is willing to pay for M -type. Hence,

19

H-type may prefer to extend an invitation to search to the consumer by pooling with L-type on

uninformative advertising.

In equilibrium, all types prefer their equilibrium strategies to the optimal deviation. Of course,

the optimal deviation depends on the out-of-equilibrium beliefs. To show existence, we assume the

following out-of-equilibrium beliefs: �L = 1 for all (a0; p 6= p�HL) and �H = 0 for all (aj ; p 6= V2 ).

Below we show that this belief is indeed reasonable. Given this, the �rm�s non-deviation conditions

are the following:

��(a0; p�HLjq = H) = Hp

�HL > MaxA1�(A1jq = H) =

V

2; (7)

��(aj ; pM jq = M) =V

2> MaxA1�(A1jq =M) = Mp�HL;

��(a0; p�HLjq = L) = Lp

�HL > MaxA1�(A1jq = L) = 0:

The belief we assumed above is maximally pessimistic in the sense that if a deviation is observed,

the consumer assumes that it comes from the lowest type capable of that action. However, it is

easy to show that more optimistic beliefs would yield the same outcome.11

The Proposition above demonstrates the existence of the HL equilibrium with consumer search.

We next show that this equilibrium can survive the D1 re�nement (and the Intuitive Criterion as

well).

Proposition 4 A semi-separating HL equilibrium where the consumer chooses to search after

observing (a0, p�HL), exists and survives D1 if:

( H � M ) pj + V2 (1� H)

H(1� M )� p�HL < min

� HV � 2c H + L

;V

2 M

�; (8)

where pj = 34V +

qV2

4( H� M )2�2V c( H� M )

2( H� M ).

11For example, suppose that, as before, �L = 1 for all (a0; p 6= p�HL) and �H = 0 for all (aj ; p � p�HL), but �H = "(c)

for all (aj ; p > p�HL). It is easy to see that for "(c) small enough, the consumer would not purchase the product if

she observes the deviation (aj ; p > p�HL) since p�HL >

V2. Hence, the �rm�s non-deviation conditions would remain

the same.

20

Proof. See the Appendix

Here, we only consider those beliefs that are consistent with D1. In Lemma 3 in the Appendix,

we show that the belief we assumed above, �L = 1 for all (a0; p 6= p�HL) and �H = 0 all (aj ; p 6=

V2 ), satis�es the properties imposed by D1. Note that in addition to the conditions we had in

Proposition 3, Equation 8 also includes a lower limit on price which is necessary in order for the

equilibrium to survive D1.12 Since not all of the conditions are binding, the constraints reduce to

the ones given in Proposition 4.

To summarize, we have shown in Proposition 3 that a counter-signaling equilibrium where the

best and the worst types pool on uninformative advertising can exist. In other words, advertising

content can signal quality. In Proposition 4 we show that this equilibrium survives the D1 re�ne-

ment. This demonstrates the robustness of HL equilibrium since D1 eliminates equilibria that are

supported by unreasonable out-of-equilibrium beliefs.

Based on the results of these two Propositions, when do we expect to see this equilibrium?

From Equation (7), we can see that in order for HL with consumer search to exist, it must be

the case that H is su¢ ciently large and M is su¢ ciently small. Here H-type prefers to pool

with L-type on uninformative advertising rather than pursue an attribute-based strategy which

perfectly signals that the �rm is not L-type. Since the additional signal associated with each type

is noisy, after an uninformative ad and own search, the consumer may mistake a H-type �rm for

a L-type. Therefore, the risk H bears by pooling with L must be relatively small ( H is large)

such that H-type prefers this to the certain outcome of pretending to be M -type by engaging in

an attribute-based ad. Moreover, when H is large relative to L, the consumer is willing to pay

a higher price following an uninformative ad and good news (s = s) since she is con�dent that

the product is H-type and not L-type. Hence, when H is large, not only is the probability of

a transaction high, but the price charged can increase. This is the source of H�s con�dence in

12We �nd that if p�HL is low enough, then there exists a deviation A1 = (aj ; pdev > p�HL) such that D1 imposes

�H(A1) = 1. This of course would destroy HL. Hence, in order to rule this out, we need the additional constraint

that p�HL �( H� M )pj+

V2(1� H )

H (1� M ). See the Appendix for more details.

21

extending the invitation to search to the consumer. On the other hand,M -type prefers to separate

itself from L-type rather than pool with it. This can happen only if the additional signal cannot

e¤ectively separate between M and L types (in other words, M is small). Hence, M lacks H�s

con�dence and prefers not to mimic H-type because the probability that it may be misjudged as

L-type is too high. That is, while H-type is willing to relinquish control in its communication

strategy (by engaging in uninformative advertising with an uncertain outcome following consumer

search), the M -type prefers the lower risk attribute-based strategy.

Finally note that in this HL equilibrium, all types make a positive pro�t. In particular, L-type

is able to extract rents that arise due to the consumer�s mistakes as a result of search. However,

L�s pro�t is strictly lower than those of H and M -types: ��(H) = Hp�HL > �

�(M) = V2 > �

�(L)

= Lp�HL > 0: In particular, as the noise associated with L�s signal decreases ( L decreases), L�s

pro�t decreases.

As we see from the discussion above, consumer search is the core mechanism which enables

signaling in equilibrium. In fact, we can formally show that this equilibrium does not exist without

consumer search:

Proposition 5 A semi-separating HL equilibrium without consumer search does not exist.

Proof. See Appendix

Without consumer search, the �rm is constrained to charge a relatively low price due to con-

sumer�s uncertainty about product quality. The maximum price that the H and L-type can charge

in equilibrium such that the consumer chooses not to search is strictly less than V2 when the search

cost is su¢ ciently low. Hence, H-type would prefer to deviate in order to signal that it is not type

L, which of course destroys this potential equilibrium.

4.2 Other Equilibria

In the preceding Section, we show that H-type can signal its quality by extending an invitation to

search (through uninformative advertising) to the consumer. Can there be other equilibria where

22

M as well extends this invitation? As we show below, there indeed can be equilibria where M ,

as well as H, extends an invitation to search. In the HML full pooling equilibrium, all types

engage in uninformative advertising and post the same price, and the consumer chooses to search

in equilibrium. Note that while an uninformative advertising is an invitation to search in HML, it

is not a signal of higher quality. In contrast, in the HM semi-separating equilibrium, an attribute

ad can serve as an invitation to search, while an uninformative ad reveals that the �rm is L-type.

We show that these other equilibria exist only if M is high enough �the mediocre product is

willing to extend an invitation to search only if it is fairly certain that the outcome of search will

be positive. In other words, if M is low or the mediocre product is not con�dent in the outcome

of the search process, only the HL countersignaling equilibrium exists.

We �rst turn to the full pooling equilibrium, HML, where all types engage in the same type

of advertising and post the same price (a� = a�HML and p� = p�HML, where � 2 fL;M;Hg). Of

course, since L-type can only engage in uninformative advertising, a�HML = a0. The consumer, in

turn, may either choose to purchase the product without search based on the prior information only

or may search for extra information. As we show in Proposition 6 below, given our assumption that

search is feasible for the consumer (c � V ( H� M )8 V ), there does not exist an HML equilibrium

without consumer search, but there does exist a full pooling equilibrium where consumer searches

if M is high enough.13

Proposition 6

1. There does not exist a full pooling equilibrium (HML) without consumer search.

2. A full pooling equilibrium HML where the consumer chooses to search exists if M is high

enough. Here, ��(H) > ��(M) > ��(L). Moreover, this equilibrium survives D1.

Proof. See the Technical Appendix.13Please see the Technical Appendix for the exact statement of the existence conditions, such as the conditions on

the M and the price bounds.

23

The �rst result is very similar to the result we obtain in Proposition 5. If the higher types pool

with the lowest type, and no search occurs, the price that is charged in a potential equilibrium is too

low to prevent a deviation. On the other hand, the �rm may be able to charge a high enough price

such that the consumer would choose to search after observing uninformative advertising. The

mediocre �rm would choose this strategy only if it is fairly con�dent about the positive outcome of

search �i.e., M is high enough. In this equilibrium, search still allows the �rm to charge a high

price due to the decreased uncertainty. However, since M is high, the possibility of search is not

a credible threat to the M type and, hence, M prefers to pool with H (and L) as opposed to reveal

its quality. All types extend an invitation to search through uninformative advertising, but this

invitation to search does not signal quality.

The �nal remaining equilibrium is the semi-separating HM equilibrium. In this equilibrium, H

and M types pool on attribute advertising and price: a� = aj , where � 2 fM;Hg, p� = p�HM . The

fact that the higher types engage in an attribute-based communication allows them to separate

themselves from the L-type: aL = a0.14 The consumer, of course, can choose to search following

(aj ; p�HM ) in order to further di¤erentiate whether the �rm is H-type or M -type. In this semi-

separating equilibrium, and in contrast to HL, both H and M types choose to emphasize their

strong attribute: the �rm which has anything positive to say about its product chooses to do so.

In this sense, this equilibrium is a very intuitive one.

Proposition 7 Suppose that search cost is low enough such that c � V2 �(1� �)( H � M ):

1. A semi-separating HM equilibrium without consumer does not survive D1.

2. A semi-separating HM equilibrium, where the consumer chooses to search after observing

(aj, p�HM ), exists if M is su¢ ciently high. Here, ��(H) > ��(M) > ��(L). Moreover, this

equilibrium survives D1.14Since L�s advertising perfectly reveals its type, L makes zero pro�t in equilibrium. Again, this zero pro�t result

is driven from our simplifying assumption that � = 0: The results would not change qualitatively if we allow that

L-type product yields small but non-zero utility to the consumer.

24

Proof. See the Technical Appendix.

The �rst result in Proposition 7 mirrors our earlier results. An equilibrium without consumer

search does not survive D1 if cost of search is low enough. This is again due to the fact that

without search, the �rm is constrained to charge a relatively low price.15

On the other hand, HM equilibrium where the consumer chooses to search can exist. As was

the case for HML, here M is willing to extend an invitation to the consumer to search. However,

search follows an attribute-based ad as opposed to an uninformative ad in HML. The consumer

searches in order to di¤erentiate between the H and M types. Note that while both of these types

deliver relatively high value to the consumer, the pooling price in equilibrium is high enough so that

the consumer prefers to undertake the costly search in order to further resolve the uncertainty.16

Hence, the condition of low search cost, c � V2 �(1 � �)( H � M ); ensures that the consumer

searches for additional information in equilibrium.

As we can see from the condition on the search cost above, here � plays a role in the decision to

search. Recall that � is the correlation between attributes, which in this equilibrium translates to

a prior belief about the product�s type following aj since P (Hjaj) = P (� = Bj� = A) = �. The

consumer chooses to search only if the search cost is low enough relative to the bene�t that can

be obtained through seeking additional information; i.e., resolving the uncertainty. Therefore, if

� is either close to 1 or to 0, there is little remaining uncertainty on whether the �rm is H-type or

M -type following aj , which in turn implies that search would not arise in equilibrium unless the

search cost is also close to zero. Hence, depending on the magnitude of the search cost c and the

15We show that there exists a deviation A1 = (aj ; pdev > p�HM ), such that following this deviation the consumer

believes (based on D1) that the �rm must be type H. Therefore, under this re�ned belief, the consumer chooses

to purchase without search. This, in turn, destroys the HM equilibrium without search since both types prefer to

deviate to (aj ; pdev) rather than play the equilibrium strategy.16Note that while the exact expressions for the conditions on the search cost as well as the price bounds di¤er

across HM and HML since they pool on di¤erent actions, the basic conditions remain the same: (1) the cost search

is small compared to H � M , (2) the price is in a certain range which ensures that the consumer searches, and (3)

M is high enough.

25

correlation �, HM equilibrium with search may or may not exist.

In summary, for the HML and HM to exist, M must be high enough. In the equilibria where

H and M types pool, the probability that M receives a positive signal following search must be

high enough so that M is willing to pool with H in price and advertising. By pooling with a

higher type and charging a high price, as is the case for HM and HML, M -type loses control over

the consumer�s �nal inference since in both of these equilibria the consumer chooses to search for

additional information. On the other hand, in the HL equilibrium, by revealing its type, M faces

lower risk since the consumer has no uncertainty. This decrease in uncertainty, however, comes

with a lower upside potential since in this caseM cannot charge more than V2 . The amount of risk

that M faces �summarized by M , where a higher M entails a lower risk �determines whether a

pooling equilibrium with H and M exists.

Finally, we show that when H is large and M is low, HL is the only equilibrium that survives

the D1 re�nement.

Proposition 8 Under D1, HL equilibrium is unique when H is su¢ ciently large and M is

su¢ ciently small such that,

1. The conditions for HL hold (see Proposition 4),

2. c < V2 �(1� �)( H � M ) and M < V

2pHM.

Moreover, this region is non-empty.

Proof. See the Appendix:

4.3 Discussion

When would we expect to observe high H and low M , the prerequisites for the existence (and

uniqueness) of HL? Note that this parameters represents the probability of positive news for

product following search by the consumer. One factor that may moderate the relative size of M

is the propensity to discuss negative experiences with others. For example, Godes and Wojnicki

(2009) show that experts may be less likely to share their negative experiences since it sends a

26

negative signal about their ability to choose a high-quality product. Hence, we would expect that

in a category with a higher proportion of experts, word of mouth about a mediocre product may be

skewed to be more positive (higher M ), while a category with fewer experts would be less biased

(lower M ). Similarly, the average price level of the category may impact the level of M . That is,

a bad experience with a luxury car may prompt an instant posting on a blog, whereas a negative

experience with a toothpaste may not inspire as much outrage. Again, this would imply that a

higher average category price would lead to a lower M . Finally, in a category where consumers

have high expectations about product quality, a product which is extremely high-quality on some

attributes but not others (M type) is more likely to have a lower M .

Another moderating factor on the H and M parameters is the relative quality of H-type and

M -type products. That is, in reality, a product is composed of multiple attributes. Though in

our model we assume only two attributes for simplicity, we can think of � as the set of attributes

that the �rm emphasizes in an ad, and � as the remaining set of attributes. Moreover, suppose

that there are n attributes in a product, and H-type is high quality on h attributes (n > h), while

M -type is high quality on m attributes (n > h > m). In this set-up, when the �rm emphasizes

its k high quality attributes in an ad, the consumer is still uncertain about the quality of n � k

attributes which are not advertised. Here we would expect H to be increasing in h, and M to

be increasing in m. That is, depending on the size of n; h; and m, H and M should vary.

In summary, we show that in the case of limited bandwidth, two types of equilibria are possible:

one in which H andM types pool (HML;HM), and another one in which H and L types separate

(HL). In the latter, the superior �rm (H) extends an invitation to search by pooling with the

terrible product (L) in its communication strategy in order to distinguish itself from the mediocre

product (M). The mediocre product, on the other hand, prefers to perfectly separate itself from

the terrible product rather than risk being confused with it. Hence, the invitation to search through

uninformative advertising can be a signal of quality �advertising content can signal quality. Our

�ndings emphasize the importance of modeling the decision to search (with its costs and bene�ts)

27

since search is crucial in enabling this separation across neighboring types. A superior �rm chooses

uninformative advertising as an invitation to search since it is con�dent that consumers will realize

its high quality on their own. When the �rm is not con�dent about its quality, which is the case

for the mediocre �rm, it prefers to make a product claim in order to separate itself from the terrible

�rm.

5 Conclusion

We show that advertising content �whether the advertisement is uninformative or attribute-based

� can be a credible quality signal under the realistic assumptions of (1) limited bandwidth of

communication, and (2) the possibility of consumer search following the consumer�s exposure to

the advertisement. We show that this desire to signal one�s quality may result in the surprising

phenomenon that a �rm with the most to say may choose not to make any "hard" claims at

all. This withholding strategy may be rational in that vague claims can be made by either the

superior or the terrible products, which necessitates search for further information on the part of

the consumer. In our opening example, American Express Card is con�dent that a consumer

who engages in own search will �nd out about its superior service17. This con�dence allows it to

engage in uninformative advertising in favor of making any hard claims. Capital One, on the other

hand, which is weaker on some attributes, is not con�dent that search will distinguish it from a

truly terrible product and does not want to undertake the risk of search. Instead, it chooses to

emphasize one of its attributes in order to separate itself from a truly terrible product. Finally,

the First Premier Bank Credit Card, which engaged in uninformative advertising, can be seen as

an example of a low quality product: in 2008 Consumer Reports listed it as one of three cards from

172008 Credit Card Satisfaction Study (J.D.Power, http://www.jdpower.com/�nance/articles/2008-Credit-Card-

Satisfaction-Study) shows that Amex is ranked at number 1 while Capital One is ranked number 12 in the customer

satisfaction index.

28

which its readers should stay away.18

In conclusion, the combination of advertising content and consumer search enables the �rm

to signal its quality even in the absence of a money-burning e¤ect. When there exists limited

bandwidth in advertising communication, the high quality �rm can signal its quality by extending

an invitation to search through uninformative advertising to the consumer. The consumer search

(which is determined endogenously in the model) is crucial in enabling this type of equilibrium.

While most of the previous literature has focused on the decision to advertise (the mere fact that

the �rm is willing to burn its money) as a signal of quality, we show that message content, coupled

with consumer search, can also serve as a credible signal of quality.

There can be, of course, a lot of di¤erent explanations for the existence and e¤ectiveness of

uninformative advertising (in particular, image advertising), and we do not wish to claim that

our explanation is the only possible theory for this phenomenon. Nevertheless, we o¤er a novel

explanation for uninformative advertising, one that to our knowledge is the �rst one that assumes

consumer rationality.

18http://www.consumerreports.org/cro/money/credit-loan/credit-cards/credit-cards/stay-away-from-these-

cards/credit-cards-stay-away-from-these.htm, "Stay away from these cards."

29

Appendix 1

Proof of Lemma 1

The consumer will search if and only if EU(search) = Pr(sj�)[E(V j�; s) � p] � c � EU(no

search) = max(0; E(V j�)� p). Therefore,

1) If E(V j�)� p � 0, then EU(search) � EU(no search) i¤

Pr(sj�)[E(V j�; s)� p]� c � E(V j�)� p (9)

, Pr(sj�)E(V j�; s)� Pr(sj�)p� c � Pr(sj�)E(V j�; s) + Pr(sj�)E(V j�; s)� p

, c � Pr(sj�)[p� E(V j�; s)] � g

2) If E(V j�)� p < 0, then EU(search) � EU(no search) if

Pr(sj�)[E(V j�; s)� p]� c � 0, c � Pr(sj�)[E(V j�; s)� p] � f (10)

Next we show that f = g at p = E(V j�)

f � g = Pr(sj�)[E(V j�; s)� p]� Pr(s)[p� E(V j�; s)] (11)

= Pr(sj�)E(V j�; s)� Pr(sj�)p� Pr(sj�)p+ Pr(sj�)E(V j�; s)

= Pr(sj�)E(V j�; s) + Pr(sj�)E(V j�; s)� p = E(V j�)� p = 0

This completes the proof. Q.E.D.

D1 Re�nement

We apply D1 (Fudenberg and Tirole 1991) to eliminate unreasonable out of equilibrium beliefs.

Following Fudenberg and Tirole (1991, p 452), we de�ne ��(�) to be the equilibrium pro�t of

type �. We also de�ne the set of mixed strategy best responses of the consumer, �2 (�2 =

f�21; �22; �23g = fPr(purchase without search); Pr(no purchase); Pr(search)g) to a deviation by

the �rm, A1 = (a; p), such that type � strictly prefers A1 to the equilibrium strategy:

D(�;A1) = (12)

f�2 2MBR(�(A1); A1) s.t. ��(�) < �(A1; �2; �)j �H(A1) + �M�(A1) + �M�

(A1) + �L(A1) = 1g

30

Note that the consumer�s best response depends on her belief, �(A1) = (�H(A1); �M�(A1); �M�

(A1); �L(A1)).

Similarly, we de�ne a set of consumer�s best responses such that the �rm is indi¤erent between

deviating and playing the equilibrium strategy.

D0(�;A1) = (13)

f�2 2MBR(�(A1); A1) s.t. ��(�) = �(A1; �2; �)j �H(A1) + �M�(A1) + �M�

(A1) + �L(A1) = 1g

The criterion D1 puts zero probability on type � if there exists another type �0 such that

D(�;A1) [D0(�;A1) � D(�0; A1): (14)

Using Lemma 1, below we derive the set of consumer�s mixed best responses, MBR(�(A1); A1):

1. If E(V j�(A1))� p > 0,

(a) Consumer will search: �2 = f0; 0; 1g; if c < Pr(sj�(A1))[p� E(V j�(A1); s)]

(b) Consumer will purchase without search: �2 = f1; 0; 0g, if c > Pr(sj�(A1))[p�E(V j�(A1); s)]

(c) Consumer mixes between search and purchase without search: �2 = f�21; 0; 1� �21g, if

c = Pr(sj�(A1))[p� E(V j�(A1); s)]

2. If E(V j�(A1))� p < 0,

(a) Consumer will search: �2 = f0; 0; 1g, if c < Pr(sj�(A1))[E(V j�(A1); s)� p]

(b) Consumer will not purchase: �2 = f0; 1; 0g; if c > Pr(sj�(A1))[E(V j�(A1); s)� p]

(c) Consumer mixes between search and no purchase: �2 = f0; �22; 1��22g, if c = Pr(sj�(A1))�

[E(V j�(A1); s)� p]

3. If E(V j�(A1))� p = 0 and c = Pr(sj�(A1))[E(V j�(A1))�E(V j�(A1); s)], consumer chooses

either �2 = f0; �22; 1� �22g or �2 = f�21; 0; 1� �21g.

Note that �2 = f�21; 1 � �21; 0g =2 MBR(�(A1); A1) since we assume that if the consumer is

indi¤erent between purchasing the product and no purchase, she chooses to purchase it.

31

Bounds on prices and beliefs for consumer search

Next, using the results above, we derive explicit bounds on prices and beliefs such that the consumer

searches as a best response to A1.

Lemma 2 1. Consider the case where the �rm engages in attribute-based advertising, A1 = (aj ;

p) and the consumer�s belief is �j = (0; �jM ; �jH): There exists a consumer belief under

which search is a best response for the consumer if c � V ( H� M )8 and p 2 [pj ; pj ], where

pj = 34V �

qV2

4( H� M )2�2V c( H� M )

2( H� M )� V

2 ; pj = 3

4V +

qV2

4( H� M )2�2V c( H� M )

2( H� M )� V :

Moreover, for a given �jH ; consumer chooses to search i¤ pj(�jH) =

�jH(1� H)V+(1��jH)(1� M )

V2+c

�jH(1� H)+(1��jH)(1� M )

� p � �jH HV+(1��jH) M

V2�c

�jH H+(1��jH) M

= pj(�jH):

2. Consider the case where the �rm engages in uninformative advertising, A1 = (a0; p) and the

consumer�s belief is �0 = (�0L; �0M ; �

0H), where �

0L � c�L = 1

2(1 +q1� 4c

V ( H� L)). There

exists a consumer belief (�0) under which search is a best response for the consumer if c �V ( H� L)

4 and p 2 [p0; p0]; where p0 � min0��0L�b�L p0(�0L) � pj ; p0 � max0��0L�b�L p0(�0L) �pj :

Moreover, for a given �0; consumer chooses to search i¤ p0(�0) =�0H(1� H)V+�0M (1� M )

V2+c

�0H(1� H)+�0M (1� M )+�0L(1� L)

� p � �0H HV+�0M M

V2�c

�0H H+�0M M+�

0L L

= p0(�0):

Proof. See the Technical Appendix.

We can easily show that V ( H� M )8 < V ( H� L)4 since L < H and L < M . This of course

implies that if c � V ( H� M )8 , there exists a belief under which the consumer chooses to search after

observing aj and a0.

HL Equilibrium

Proof of Proposition 3

Here we show that HL equilibrium with consumer search exists if c < V ( H� M )8 , (1� H)V+2c2� H� L

�

p�HL < HV�2c H+ L

and Hp�HL >

V2 > Mp

�HL.

32

We �rst turn to the consumer�s problem. As we can see from Lemma 2, in order for the consumer

to search in equilibrium, it must be the case that c � V ( H� M )8 and pHL 2 [p0(�L); p0(�L)]; where

p0(�L) =�0H HV+�

0M M

V2�c

�0H H+�0M M+�

0L L

and p0(�L) =�0H(1� H)V+�0M (1� M )

V2+c

�0H(1� H)+�0M (1� M )+�0L(1� L). In addition, on the

equilibrium path, the probabilities that the �rm is H-type and L-type following (a0; p�HL) are12

and 12 . Hence, p0(12) =

HV�2c H+ L

> 12V and p0(12) =

(1� H)V+2c2� H� L

< V2 since c � V ( H� M )

8 :

Hence, in order for the consumer to search in equilibrium, the price must be in the appropriate

range: p�HL 2 [(1� H)V+2c2� H� L

; HV�2c H+ L]:

Next, we need to ensure that all types prefer their equilibrium strategy to an optimal deviation.

To show existence, and as we discuss in the body of the paper, we impose the following out-of-

equilibrium belief: �L = 1 for all (a0; p 6= p�HL) and �H = 0 for all (aj ; p 6= V2 ). Given the

assumed out-of-equilibrium beliefs, the non-deviation conditions for H-type and M -type reduce to

the following:

��(a0; p�HLjq = H) = Hp

�HL > MaxA1�(A1jq = H) =

V

2(15)

��(aj ; pM jq = M) =V

2> MaxA1�(A1jq =M) = Mp�HL

Finally, the L-type by de�nition cannot deviate on advertising. A deviation on price only yields a

maximum pro�t of 0 under the o¤-equilibrium beliefs. Hence, ��(a0; pHLjq = L) = Lp�HL > 0;

which is trivially satis�ed. Q.E.D.

Proof of Proposition 4

We examine the restrictions on the out-of-equilibrium beliefs that are imposed by D1. First,

we assume that p�HL <V2 M

. We will return to this assumption below and con�rm that it is indeed

the case in equilibrium.

Lemma 3 Suppose that p�HL <V2 M

. D1 imposes the following constraints on out-of-equilibrium

beliefs:

1. Let bp � ( H� M )pj+V2(1� H)

H(1� M ). If the consumer observes A1 =

�aj ; p

dev�,

(a) when V2 < p

dev < min( Hp�HL; p

j), �H(A1) = 0,

33

(b) if bp � p�HL; when pj � pdev � pj = min(bp; pj), �H(A1) = 0,(c) if bp > p�HL, when max(pj ; bp) < pdev � pj, �H(A1) = 1:

2. If the consumer observes the deviation A1 =�a0; p

dev�,

(a) when Lp�HL < p

dev < min( Hp�HL; p

0), �H(A1) = 0;

(b) when Mp�HL <

V2 ,and max(p

0; Lp�HL) < p

dev < min(p�HL; p0), �L(A1) = 1;

(c) when Mp�HL <

V2 ,and p

�HL < p

dev < p0, �M (A1) = 0:

Proof. Let us �rst de�ne the sets for � = fL;M;Hg

D0(H;A1) [D(H;A1) =dXH [ cYH =�(0; �22; 1� �22) j �22 �

pdev � p�HLpdev

�[((�21; 0; 1� �21) j�21 �

H�p�HL � pdev

�(1� H)pdev

)D0(M;A1) [D(M;A1) = dXM [dYM =(

(0; �22; 1� �22) j �22 � Mp

dev � V2

Mpdev

)[((�21; 0; 1� �21) j�21 �

V2 � Mp

dev

(1� M )pdev

)

D0(L;A1) [D(L;A1) = cXL [cYL =�(0; �22; 1� �22) j �22 �

pdev � p�HLpdev

�[((�21; 0; 1� �21) j�21 �

L�p�HL � pdev

�(1� L)pdev

)

1. Consider a deviation to a price such that the consumer chooses not to purchase at any o¤-

equilibrium belief: A1 =�aj ; p

dev�where pdev > pj or A1 =

�a0; p

dev�where pdev > p0; i.e.,

�22 = 1: Here, D1 does not apply.

2. Next, consider a deviation to a price such that the consumer chooses to purchase without

search at any o¤-equilibrium belief: A1 =�aj ; p

dev�where pdev < pj or A1 =

�a0; p

dev�where

pdev < p0; i.e., �21 = 1. Therefore, D1 imposes that �H(A1) = 0 if A1 =�aj ; p

dev�, for all

V2 � p

dev < min( Hp�HL; p

j). Similarly, if A1 =�a0; p

dev�, for all Lp

�HL � pdev < min( Hp�HL; p0),

�H(A1) = 0:

3. Consider A1 =�aj ; p

dev�; and pj � pdev � pj .

First, we assume that( H� M )pj+V

2(1� H)

H(1� M )� p�HL , pj �

H(1� M )p�HL�V2(1� H)

H� M. If pdev <

H(1� M )p�HL�V2(1� H)

H� M, we can show, using simple calculus, that

H(p�HL�pdev)(1� H)pdev

> Mp

dev�V2

(1� M )pdev; which

34

implies that cYH � YM . Also, we can see that H(1� M )p�HL�V2(1� H)

H� M< p�HL as long as p

�HL <

V2 M

:

Hence, we have pdev < H(1� M )p�HL�

V2(1� H)

H� M< p�HL here. This in turn implies that XM =

dXH = ?. Therefore, for pj < pdev < min( H(1� M )p�HL�

V2(1� H)

H� M; pj), D1 constrains the belief to

be �H = 0 following A1: Of course, since pj � H(1� M )p�HL�

V2(1� H)

H� M, for pj < pdev < pj , �H = 0

following A1.

Second, consider( H� M )pj+V

2(1� H)

H(1� M )> p�HL , pj >

H(1� M )p�HL�V2(1� H)

H� M: Then, there exists

an interval such that H(1� M )p�HL�

V2(1� H)

H� M� pdev < min(pj ; p�HL). Using the same argument

as in (a) above, we can show that here dYM � YH , and XH = dXM = ?. Hence, as long as

max(pj ; H(1� M )p�HL�

V2(1� H)

H� M) < pdev < min(pj ; p�HL), D1 constrains the belief to be �H = 1

following A1: Next, consider pdev � p�HL. We can see that when p�HL < V2 M

, Mp

dev�V2

Mpdev <

pdev�p�HLpdev

< 1, which implies that dXM � XH : Also, we know that in this regiondYM � YH . Hence,

D1 implies that �H = 1 following pdev, where max(p�HL; p

j) < pdev < pj . In summary, D1 implies

that for max(pj ; H(1� M )p�HL�

V2(1� H)

H� M) < pdev � pj , �H = 1.

4. Consider A1 = (a0; pdev 6= p�HL) and p0 � pdev � p0.

First, consider the case pdev < p�HL, which implies that XH = XM = XL = ?: Also,

L(p�HL�pdev)(1� L)pdev

< H(p�HL�pdev)(1� H)pdev

, L(p�HL�pdev)(1� L)pdev

< 1 if pdev > Lp�HL, and

L(p�HL�pdev)(1� L)pdev

<V2� Mpdev

(1� M )pdevif

pdev <V2(1� L)� L(1� M )p�HL

M� L. Moreover, we can see that when Mp

�HL <

V2 , p

�HL <

V2(1� L)� L(1� M )p�HL

M� L.

Hence, when Mp�HL <

V2 ;cYH � YL anddYM � YL if max(p0; Lp�HL) < pdev < min(p�HL; p0), which

implies that D1 constrains the belief to be �L = 1 following A1 = (a0; pdev):

Second, consider the case pdev > p�HL, which implies thatdXH = cXL 6= ? and YH = YL = f8�21 2[0; 1]g: Also, if Mp�HL < V

2 ; Mp

dev�V2

(1� M )pdev<

pdev�p�HLpdev

; which implies that dXM � XL and dXM � XH :

Hence, D0(M;A1) [D(M;A1) � D(L;A1) and D0(M;A1) [D(M;A1) � D(H;A1); which implies

that D1 constraints the belief to be �M = 0 following A1 = (a0; pdev):

Given the out-of-equilibrium beliefs which are consistent with D1, if p�HL <( H� M )pj+V

2(1� H)

H(1� M ),

there always exists a pro�table deviation under D1. To show this, consider A1 =�aj ; p

dev�

where H(1� M )p�HL�

V2(1� H)

H� M< pdev � pj . Based on Lemma 3 1-(c), �H = 1: consumer buys the

35

product without search. Both H andM types prefer to deviate to A1, which, in turn, destroys this

equilibrium. Hence, for the HL equilibrium to exist, it must be the case that( H� M )pj+V

2(1� H)

H(1� M )�

p�HL. When( H� M )pj+V

2(1� H)

H(1� M )< p�HL <

V2 M

, one example of an o¤-equilibrium belief which is

consistent with the properties described above is �L = 1 for all (a0; p 6= p�HL) and �H = 0 for all

(aj ; p 6= V2 ). This is the belief that we assume to demonstrate existence below.

From the equation (??) in the proof of Proposition 3 above and the search condition that

p�HL 2 [ (1� H)V+2c2� H� L; HV�2c H+ L

] as well as the condition from D1,( H� M )pj+V

2(1� H)

H(1� M )� p�HL, we

can see that the equilibrium price must be max�

V2 H

; (1� H)V+2c2� H� L;( H� M )pj+V

2(1� H)

H(1� M )

�� p�HL <

minn HV�2c H+ L

; V2 M

o. Also note that (1� H)V+2c2� H� L

< V2 <

V2 H

. Moreover, we can see that pj � V2

implies that V2 H

� ( H� M )pj+V2(1� H)

H(1� M ). This reduces the price condition for the existence of

the HL equilibrium under D1 to following:( H� M )pj+V

2(1� H)

H(1� M )� p�HL < min

n HV�2c H+ L

; V2 M

o:

Q.E.D.

Proof of Proposition 5

We show this result by contradiction. Suppose that there exists an HL equilibrium without

consumer search: (aH = aL = a0; pH = pL � pnsHL; aM = aj ; pM = V2 ). Note that in equilibrium,

given a prior beliefs, the belief following (a0; pHL) must be �0H = 12 , �

0L =

12 . Hence, applying

Lemma 2, we know that pnsHL � p0 =12(1� H)V+c

12(1� H)+ 1

2(1� L)

. Note that p0 < V2 as long as c <

V ( H� L)4 .

Hence, this implies that if c < V ( H� L)4 , pnsHL <

V2 and H-type prefers to deviate to M�s strategy,

which would destroy the proposed equilibrium. Finally, note that V ( H� L)4 > V ( H� M )8 . Hence,

for c < V ( H� M )8 , this equilibrium similarly does not exist. Q.E.D.

Proof of Proposition 8

The �rst condition ensures that HL exists (see Proposition 4). The remaining equilibria that

survive the D1 re�nement are HM with search and HML with search (see Proposition 6 and

Proposition 7).

We �rst turn to HM . Note that in order for the consumer to search in equilibrium, p�HM �

36

pHM when c < V2 �(1 � �)( H � M ) , where pHM = H�V+ M (1��)V�c

H�+ M (1��)� pj(�) (see the proof of

Proposition 7 in the Technical Appendix). Suppose that MpHM < V2 , which of course implies

that Mp�HM < V

2 : Consider a deviation by M to A1 =�aj ; p

dev = V2

�. The consumer is willing

to purchase the product with no additional search (see Lemma 2). Hence, this implies that M

prefers to deviate, which destroys this equilibrium. Hence, we demonstrated that HM does not

exist if MpHM < V2 .

Next, in order for the consumer to search in HML equilibrium, p�HML � p0HML, where p0HML =

p0(�) = � HV+(1��) MV�2c�( H+ L)+2(1��) M

(see the proof of Proposition 6 in the Technical Appendix). Similarly,

we can show that HML does not exist if Mp0HML <

V2 . Therefore, HM and HML do not exist

if M � max�p0HML; pHM

�< V

2 . Finally, using algebra, we can show that pHM > p0HML, which

reduces the su¢ cient "non-existence" condition to M �pHM < V2 . To demonstrate that this region

is non-empty, consider the following example: H = 0:9; M = 0:5; L = 0:1; V = 100; c = 5; � =23 ;

and p�HL = [77:491; 80]. Here HL is the only equilibrium that survives D1.

37

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