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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:[email protected],
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.
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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
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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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