deal by committing in its ad to price below 1/2. Indeed, Anderson and Renault (2006)
establish that the firm cannot improve upon a disclosure strategy that consists of a simple
binary signal that tells the consumer whether her match is above or below a threshold ^r
with no further information. The intuition is as follows. Given the threshold match strat-
egy, it is optimal for the firm to price so as to make the consumer just indifferent between
visiting and not visiting when she learns her match exceeds the threshold. By providing
more information, the firm can only improve the expected surplus of some consumer
types with a match well in excess of the threshold, which does not increase sales because
these types are visiting anyway and then buying with threshold information. However,
because of Bayesian updating, this improved expectation for a high-match consumer
necessarily implies that those consumer types who are close to the threshold learn that
their match is not so good. As a result, the firm would need to lower its price to keep
those consumer types onboard. By contrast with the analogous result for an experience
good, this disclosure strategy does not allow the firm to achieve the full discrimination
profit unless the visit cost is very large.
Anderson and Renault (2006) show that as the visit cost γ increases, the firm’s adver-
tising strategy goes from no advertising to threshold match-only advertising and then to
threshold match and price advertising. In any case, a firm ideally prefers to provide only
partial information to consumers. This result is to be contrasted with the prediction in
Lewis and Sappington (1994) that the optimal information provision should be full if
the firm wishes to inform at all. This result also does not provide much support for
the prediction in
Nelson (1974) that ads for search goods should contain a lot of infor-
mation. Further note that price is never advertised alone. This is true, however, only if
the firm can parse the information it provides sufficiently finely. If product information
must be fully informative, then the firm chooses to advertise price alone for intermediate
visit costs.
Thus far, I have treated γ primarily as a visit cost required to make a purchase that
automatically warrants full access to product information for the consumer. If a product
is elaborate enough, obtaining all relevant information may require some additional cost
and the consumer might choose to purchase while uninformed so as to save on these
costs. To illustrate this possibility, suppose that γ is merely a cost of acquiring full product
information whereas the consumer may now purchase the product with no visit cost if
she only bases her decision on advertised information. Assume γ is low and the firm’s ad
only informs the consumer whether she is willing to purchase the product at monopoly
price 1/2 or not. If the consumer is charged 1/2, she buys without acquiring any further
information. It is possible, however, for the firm to charge a price p > 1=2 such that the
consumer learning that her match is at least 1/2 would still choose to buy without acquir-
ing any further information: this price should satisfy
Ð
p
1=2
p rðÞ2dr γ, where the left-
hand side is what the consumer would save by not purchasing the product when her
match is below p if she was perfectly informed. This allows the firm to sell the monopoly
153Advertising in Markets
quantity at a price above monopoly price. By contrast, if it provides no information as in
the
Anderson and Renault (2006) setting, the consumer is informed if γ is small and the
firm earns the monopoly profit. Hence, the firm chooses to provide partial product infor-
mation in order to reduce the consumer’s incentive to search and become perfectly
informed. This possibility is explored in
Wang (2014)).
30
The analysis of disclosure used in this subsection is suitable for match information but
is not well adapted for quality information. I now turn to a setting that is also relevant for
the disclosure of some quality dimension.
31
4.3.4 Advertising of Product Attributes
The literature on match revelation in Section 4.3.3 assumes a unique ex ante firm type.
When the firm makes more or less information available to the consumer, it does not
know whether it will make its product more or less attractive. The firm’s incentives
to reveal information do not depend on any private information it might hold and
the consumer does not infer anything about such private information. Although this
is a convenient way of thinking of the disclosure of match information, it does not seem
appropriate for investigating the disclosure of quality information. Disclosing such infor-
mation may be more or less desirable, depending on whether the firm’s product quality is
high or low. More generally, some horizontal match attributes may appeal more broadly
to consumers than others.
In order to account for this heterogeneity of firm types, following
Koessler and
Renault (2012)
, I enrich the monopoly model of Section 4.3.3 by assuming that the
willingness to pay r is now written as r(s, t). The first component s 2S is the firm’s type
summarizing the firm’s private information (typically the characteristics of its product)
while t 2T is the consumer’s type or private information (typically her tastes over prod-
uct characteristics). The distribution of r is now derived from the joint distribution of
(s, t ). An ad for the firm now consists of revealing a subset of types in S and misleading
ads are ruled out by requiring that the announced subset contains the firm’s true type.
Throughout I assume that the product is an experience good so the consumer may
30
He actually uses the information transmission technology of Johnson and Myatt (2006) and finds that par-
tial information (α 2 0, 1ðÞ) is optimal when search costs are low.
Bar-Isaac et al. (2010) consider the firm’s
choice to make information more or less costly to acquire for the consumer. They find that an interme-
diate search cost is a price discrimination tool, where only some consumers acquire the information (see
also the recent literature on obfuscation, e.g.,
Ellison and Wolitzky, 2012; Wilson, 2010). Another angle
considered by
Mayzlin and Shin (2011) is to consider the strategic choice of which information to convey
if the firm can only transmit a subset of the relevant information. They show that not revealing horizontal
match information may be a way for a high-quality product to signal that it is high quality.
31
Anderson and Renault (2013) extend Anderson and Renault (2006) by also considering the disclosure of
quality attributes. They find that quality attributes are always revealed in equilibrium if the visit cost is large
enough and that low-quality firms show more match and/or price information. Their analysis of quality
disclosure borrows arguments from the persuasion game literature below.
154
Handbook of Media Economics
not acquire any information other than that revealed by the firm. I also assume that a type
s firm can always credibly reveal that its type is s. For the sake of expositional clarity, I will
take three firm types S ¼ s
1
, s
2
, s
3
fg
and assume a marginal cost independent of the firm’s
type (normalized to zero unless specified otherwise).
4.3.4.1 Unraveling of Quality Information
Milgrom (1981) considered a simple example he called “the persuasion game” to analyze
the disclosure of certified quality information by a monopoly firm.
32
The equilibrium
analysis yields a very crisp and strong result.
In the above framework, products that only differ in quality may be introduced as
follows. Assume that for all t 2T, rs
1
, tðÞ> rs
2
, tðÞ> rs
3
, tðÞ. Then, all consumer types
agree that s
1
is higher quality than s
2
, which in turn is higher quality than s
3
. Further,
assume there is a finite number of consumer types. Consider a candidate equilibrium
where firm type s
1
does not fully reveal that it is selling the highest quality product.
Let p be the price it charges. Let t be, among consumer types who are willing to buy
at that price on the basis of the information provided, a type with the lowest willingness
to pay for s
1
. Because the type t consumer is not sure that the quality is the highest pos-
sible, her expected willingness to pay is strictly less than r(s
1
, t). Then, if it reveals its type is
s
1
, the firm could increase its price still selling to type t. From the definition of t, it would
also be selling to all other consumer types who were willing to buy at price p with imper-
fect information. Hence it cannot be the case that quality s
1
is not fully revealed in equi-
librium. Now given that it is fully revealed, the same argument shows that type s
2
necessarily fully reveals its quality in equilibrium. This in turn implies that in equilibrium,
type s
3
cannot hide it is the lowest quality.
It is rather straightforward to show, using similar arguments, that for any set of possible
product qualities, quality information is fully revealed to the consumer in equilibrium. If
it was not, then a higher quality firm would always find it profitable to reveal it is higher
quality. It is also easy to see that such a fully revealing equilibrium can be sustained by
assuming that, if a firm does not fully disclose, then the consumer believes with proba-
bility 1 that it is of the lowest quality, consistent with the information it has provided.
As I discuss in
Section 4.5.1, an obvious reason why the unraveling result might not
hold is that disclosure of quality information is costly. Another reason (see
Shin, 1994 for
the argument in a related context) is that the consumer might not know whether the
seller is actually able to provide the relevant certified quality information. To illustrate,
suppose all three firm types are equally likely and there is only one consumer type t with
rs
1
, tðÞ¼5, rs
2
, tðÞ¼1, and rs
3
, tðÞ¼0. Assume now that the firm is able to certify its
quality only with probability ρ 2 0, 1ðÞ. Now consider an equilibrium where, in the
event that quality can be certified, only type s
1
reveals its quality. When observing no
32
Other formulations of this problem can also be found in Grossman and Hart (1980) and Grossman (1981).
155
Advertising in Markets
information the consumer believes that, with probability ρ, the product is either s
2
or s
3
with corresponding expected match 1/2 and with probability 1 ρ, the firm is merely
unable to reveal so the expected match is then 2. Hence when no information is revealed
the firm can charge 2 3=2
ðÞ
ρ. For ρ small enough, this is more than 1, which is the price
type s
2
could charge by proving to the consumer it is not s
3
, whenever possible. This
partially revealing equilibrium can therefore be sustained.
The unraveling result suggests that, as long as the firm is able to certify its quality at a
low enough cost, we should expect that quality information will be widely dispersed.
This, however, assumes that this is the only relevant information. I next discuss the
revelation of product attributes in a broader context.
4.3.4.2 Disclosure of Horizontal Match Attributes
My discussion of horizontal match information disclosure in
Section 4.3.3 suggests that a
firm would like to include only a limited amount of such information in ads. This is in sharp
contrast with the unraveling result for quality information. I now reconsider this question in
the context of the persuasion game of this subsection. A major difference with the previous
analysis is that now the consumer may make some inference about the firm’s type from the
content of the ad. To see how this radically changes the analysis of information disclosure,
consider the following result due to
Koessler and Renault (2012). They show that as long as
the firm’s type and the consumer’s type are independently distributed, there exists an equi-
librium in which product information is fully revealed to the consumer. The main argument
underpinning the result can be easily understood from my three-firm-type example above.
Suppose type s
1
deviates from the fully revealing equilibrium by only disclosing that its type
is either s
1
or s
2
and announcing some price p. Now given the price p, it is possible to com-
pute the demand addressed to the firm (probability of a sale) depending on whether the
consumer believes its type to be s
1
or s
2
. Then we may specify off the equilibrium path beliefs
that put all the weight on whichever type yields the lowest sale probability and it is clear that
the deviation profit of type s
1
cannot be larger than its equilibrium full information one.
This, however, is not a generalization of unraveling to a general match disclosure set-
ting. It merely says that full revelation is an equilibrium but it does not rule out others.
This can be illustrated by considering one special case of interest, investigated by
Sun
(2011)
, where the product attributes and consumer tastes are derived from the
Hotelling (1929) linear city model. To illustrate, assume the set of consumer types is
the unit interval T ¼ 0, 1½, and s
1
¼0, s
2
¼1=2 and s
3
¼1. Types are independent
and uniformly distributed. The match is given in a standard manner by
rs, t
ðÞ
¼R jr tj. In this simplified setting with only three product types, product type
s
2
in the middle of the segment is always revealed in equilibrium.
33
However, for R large
enough, there may be an equilibrium where the two extreme products s
1
and s
3
pool by not
33
When assuming that the product type is uniformly distributed over the whole interval Sun (2011) finds
that for R large enough, there exists a fully pooling equilibrium where no product information is revealed.
156
Handbook of Media Economics
revealing their product information. To see this note that, if this is the case, the expected
match is independent of the consumer type t and given by R 1=2ðÞ(the expected trans-
port cost does not depend on location). The profit-maximizing solution is therefore to
charge R 1=2
ðÞ
with corresponding profit R 1=2
ðÞ
. Now for R large, the best a firm
located at the extreme can achieve if consumers know its type is to sell to all consumer types
by charging R 1 (so even the consumer type at the other extreme buys). Hence it is not
profitable to deviate by revealing product information. However, for R < 1=2ðÞthe two
extreme firm types could not survive by pooling in this manner, whereas they can still sur-
vive by revealing product information and catering to their niche customers.
Sun (2011) shows that, in equilibrium with a continuum of firm types, firms selling
products that are sufficiently close to the center reveal product information and that the
set of such products becomes larger as R decreases. This means that, interpreting a low
R as low quality, if product quality is known to consumers, low-quality products tend
to provide more horizontal match information than high-quality products. However,
another insight from
Sun (2011) is that if quality as well as horizontal attributes are unknown
to consumers, then a quality difference might not be revealed in equilibrium if it is too small.
To illustrate, suppose now that a product type is characterized by a value of R in addition to a
location. Locations of the three types are as before but R ¼4 for types s
1
and s
3
and R ¼3:5
for type s
2
: matches are thus rs
1
, tðÞ¼4 t, rs
3
, tðÞ¼3+t,andrs
2
, tðÞ¼3:5 jt 1=2j .
Then there is an equilibrium where no information is revealed. It is then optimal for the
firm to serve the entire market at price 10/3. This is larger than the full information profits,
3 for all types. Hence the equilibrium can be sustained by specifying off the equilibrium
beliefs that put all the weight on s
1
if R ¼4 is revealed but the horizontal attribute is not.
The above example also illustrates a useful result due to
Koessler and Renault (2012).
Whenever a disclosure strategy guarantees each firm type at least as much as its full
revelation profit, then there exists an equilibrium in which the firm uses this disclosure
strategy. One application of this result is the case where the firm is able to implement a
threshold disclosure strategy which, from the analysis in
Section 4.3.3, is profit maximizing
for disclosing match information for both experience and search goods.
Anderson and
Renault (2006)
present a simple specification of firm and consumer types as well as a match
function r such that threshold disclosure is feasible. Then, as discussed by
Koessler and
Renault (2012)
for an experience good, there is an equilibrium where the firm achieves
the perfect discrimination profit, which is larger than the full disclosure one.
The above discussion highlights the multiplicity of equilibria that may arise, when
product information involves some horizontal attributes valued differently by different
consumer types.
34
This does not mean, however, that the only case in which full disclo-
sure is the unique equilibrium is when product information only concerns quality. First,
34
Standard forward induction refinements have no bite on this multiplicity. However, Celik (2014), using
the undefeated equilibrium of
Mailath et al. (1993), significantly refines the set of equilibria in the
Hotelling setting studied by
Sun (2011).
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Advertising in Markets
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