the information transmitted through advertising is indirect. It looks more specifically at
the quality signaling argument and at the coordination role of advertising.
Section 4.5
focuses on various characteristics of the technology through which advertising conveys
information to consumers, considering in turn advertising costs, targeting, and informa-
tion congestion. I take a wider perspective in
Section 4.6 by allowing advertising to have
some role other than the transmission of information. In doing so, I reconsider the wel-
fare implications of advertising while incorporating elements of the persuasive and com-
plementary views. I also relax the strict consumer rationality assumption and I consider an
important function of advertising, which is to build some goodwill for a brand. I offer a
few final thoughts in
Section 4.7.
4.2. SEARCH AND ADVERTISING
As I have emphasized in the introduction, in order to capture the informative role of
advertising, it is necessary to consider a framework where the consumer’s access to infor-
mation is limited if firms do not advertise. I start by summarizing the two seminal papers
on consumer search by
Stigler (1961) and Diamond (1971). Stigler starts by arguing that
there is price dispersion in markets that leads consumers to search. Diamond, however,
shows that costly consumer search should lead to a one-price equilibrium under reason-
able assumptions. I will show that combining search and advertising yields price disper-
sion although it does not generate search in equilibrium. I end the section with an
overview of the literature on price advertising, first with homogeneous products and then
with differentiated products, with particular emphasis on arguments suggesting that
advertising is excessive or, on the contrary, insufficient as compared to a social optimum
benchmark.
4.2.1 Stigler's Question
Stigler (1961) argues that buyers cannot be aware of all prices that are charged by different
sellers of a given commodity. Obtaining such information takes time and effort and is
therefore costly. Stigler suggests that perfect price information for buyers might be
achieved if prices remained unchanged for a very long period of time. However, he dis-
misses this possibility as unrealistic. As a result of the buyers’ imperfect information, they
cannot systematically arbitrage price differences, which may therefore persist. This,
according to Stigler, explains the dispersion in prices that characterizes actual markets.
These considerations lead him to investigate how price information might reach buyers,
due to their own search activity and to the sellers’ advertising effort.
Much of Stigler’s attention is devoted to characterizing the optimal non-sequential
search rule for a consumer, given he expects some price distribution and faces a search
cost that is proportional to the number of searches. An additional search decreases the
expected lowest price observed by the buyer and the marginal impact on the expected
127Advertising in Markets
minimal price of an additional observation is decreasing. Hence, there is a well-defined
solution to the optimal search problem. Stigler then considers how advertising provides
buyers with additional search opportunities by letting them know about the existence of a
seller and how to reach him. Such advertising has some value to the buyer by increasing
the expected number of sellers he is aware of, and making it more likely that this number
exceeds the number of searches he wishes to perform.
The insights from Stigler’s contribution as to the impact of the buyers’ imperfect
information on the market outcome are very partial but critical. He makes the point that
buyers’ ignorance leads to dispersion, which in turn makes information provided by
advertising valuable. This is true even if that information is the most basic possible,
namely the existence of the advertising seller. In many respects, his analysis remains very
preliminary and his main merit is to set out a broad research agenda that remains relevant
today. For instance, he provides some brief discussions of such issues as the role of inter-
mediaries in facilitating the transmission of information from sellers to buyers or the
implications of charging media users rather than advertisers for advertising.
Before returning to the informative role of advertising, I turn to a decisive landmark
in the theory of search.
4.2.2 Diamond's Question
Although the work of Diamond (1971) may be perceived as a dramatic rebuff of the anal-
ysis of search by
Stigler (1961), its starting point is quite remote from Stigler’s consider-
ations.
3
Diamond positions his article as a critique of the analysis of the stability of
competitive equilibria. By contrast with that literature, he intends to propose a setup with
three appealing attributes. First, the adjustment should “… reflect some realistic process
…”. Second, “… agents in a disequilibrium process should be aware, at least in part, of
the disequilibrium …”. And finally, prices should be set by agents involved in the market,
buyers or sellers, rather than by an auctioneer. Diamond’s original construction does not
involve any price dispersion. Nor does it involve any consideration of the consumers’
optimal search behavior. Rather than a distribution of prices, there is a distribution of
threshold prices above which buyers would not buy. The values of these thresholds
evolve over time, taking into account the actual pricing behavior of firms. In particular,
a buyer’s threshold increases whenever she has not purchased in the previous period.
Each firm prices as a monopolist on its local demand. The source of competition is
the possibility that buyers postpone their purchase, but doing so involves some cost.
At any date, the profit-maximizing price is always at least as high as the lowest threshold,
implying that the minimum threshold should rise over time, either because the low-
threshold buyers drop out or because they observe prices at which they do not purchase.
The market finally reaches a steady state at which all firms charge the monopoly price.
3
As a matter of fact, Stigler is mentioned nowhere in Diamond (1971).
128
Handbook of Media Economics
As I now briefly explain, non-cooperative game theory affords a much simpler and the-
oretically consistent approach to the same problem.
4
Consider a market for a homogeneous product with n sellers. They share the same
constant marginal cost, denoted c 0. The market demand at price p 0 is denoted
dpðÞ0, where all buyers have the same demand.
5
The function d is such that the
monopoly profit dpðÞp cðÞis single peaked and reaches a maximum at some price
p
m
> c. Sellers choose prices simultaneously, where p
i
denotes the price of seller i. Con-
sumers may find out additional price quotes through sequential search. The cost of an
additional search is s > 0. All sellers are initially randomly matched with an equal fraction
of the total buyer population in such a way that the corresponding demand at price p is
d( p)/n.
6
Buyers matched with a seller get to observe its price at no cost before deciding
whether or not to search on through the other sellers.
7
At each round of search, if a con-
sumer decides to search on she is matched randomly with one of those sellers she has not
yet visited.
8
The cost of recalling a price quote from some previous round is zero. What
has come to be known as “the Diamond paradox” states that, in any sequential equilibrium
9
of this game, all firms charge the monopoly price p
m
and no consumer searches beyond the first firm
visited; furthermore such an equilibrium exists.
I now sketch a proof of the paradox. Existence is fairly immediate. If consumers
expect the same price from all sellers, it is optimal for them not to search. Each seller,
if it charges a price below p
m
, faces demand d( p)/n with a corresponding profit of 1/n
times monopoly profit. Hence profits are no larger than what the seller earns at price
p
m
. For larger prices, demand is clearly at least as elastic as monopoly demand (the seller
now competing with the option to search on as well as the outside option) so that pricing
above p
m
cannot be more profitable.
10
I now turn to the uniqueness argument for pure
strategies.
11
4
Although it is arguably not the same problem because the analysis below assumes an equilibrium behavior
by agents, whereas Diamond was interested in the convergence of a disequilibrium process to some long-
term equilibrium.
5
The result could also be derived assuming heterogeneous buyers with unit demands.
6
This will be approximately the case with random matching provided that the buyer population is large
enough.
7
The analysis would go through if the first price quote costs s and all buyers have a price-sensitive demand
with corresponding consumer surplus at p
m
of at least s.
8
Otherwise, search would no longer be random and other equilibrium outcomes are possible (see
Arbatskaya, 2007).
9
In this game, some players, namely the consumers, make moves at some information sets at which they are
not perfectly informed of the history of play. This is why the relevant equilibrium concept is the sequential
equilibrium: see
Kreps and Wilson (1982).
10
It is straightforward to specify off the equilibrium path behavior for consumers to complete the description
of the equilibrium.
11
The generalization to mixed strategies, though it is not too involved, would be slightly more technical
because the sellers’ strategy spaces are not countable.
129
Advertising in Markets
I first show that the lowest equilibrium price is at least p
m
. Suppose instead that the
lowest equilibrium price is
p < p
m
. Consider a seller i who is charging that price. First note
that, because all consumers have identical demands, marginal cost is constant and
p < p
m
,
the firm’s profit from selling to any particular consumer, is strictly increasing at
p (using
the assumption that monopoly profit is single peaked). I now show that if i increases its
price by some small amount, no buyer would prefer searching to buying from i. Consider
a buyer whose consumer surplus at price p is denoted v( p). By searching one more time,
she can expect at best v
p
s. Because consumer surplus is continuous in price, the firm
can increase its price slightly so that consumer surplus decreases by less than s and the
consumer prefers buying at that new price to searching on. Now, seller i faces two seg-
ments of buyers. First, buyers who end up with seller i after some rounds of search must be
holding at best a surplus of v
p
s from previous rounds. Otherwise they would not
have searched, expecting a price of at least
p. Such buyers would therefore all buy from
i if its price is slightly above
p. Second, demand at any price p from buyers matched in
the initial round with i is d( p)/n. It follows that i’s profit on the new buyers is (1/n) times
monopoly profit, which is strictly increasing at
p because p < p
m
. Seller i would therefore
wish to deviate by increasing its price.
The proof that the largest price cannot exceed p
m
proceeds similarly by contradiction.
Let p > p
m
denote that price. The basic argument is that a seller charging that price has at
most demand d pðÞ=n (which is what it would get if all other sellers are charging that
price). Hence it is better off charging p
m
which, from the previous argument, is less than
or equal to any other price charged in equilibrium so that the corresponding profit is at
least 1=nðÞdp
m
ðÞp
m
cðÞ.
The paradoxical nature of the result is threefold. First, introducing even the slightest
search cost wipes out all competition in the market. An extreme version of this is when
the buyers must incur the search cost even for the first price quote and they all have unit
demand. Then, even if they are heterogeneous in their willingness to pay, the market
unravels (this was initially pointed out by
Stiglitz, 1979). Second, monopoly pricing pre-
vails no matter how large the number of firms is. Third, this is a search model with no
search in equilibrium. The literature has proposed a number of alterations of the frame-
work that solve the paradox in one or more of the above dimensions. I exclusively con-
centrate on the role that can be attributed to informative advertising.
To conclude the discussion of the search framework inspired by
Diamond (1971),itis
worth noting that the type of advertising considered in
Stigler (1961) would not modify
the market outcome in terms of pricing or consumer search behavior. Recall that Stigler
only considered advertising that informs buyers of the existence of sellers so buyers must
still engage in search to uncover price information. Then a seller’s advertising activity
would only affect the share of buyers that show up at that seller’s shop to get a first price
quote. It would still be the case that each seller could act as a monopolist with the result-
ing demand and that there would be no search. This is why the research that I discuss
130 Handbook of Media Economics
below has considered price advertising through which each seller can commit to some
pricing behavior. This, however, does not disqualify Stigler’s approach altogether
because he was actually considering a search technology that is different from the sequen-
tial search of the Diamond environment.
Burdett and Judd (1983) have shown that, if
buyers use non-sequential search as in Stigler, although the monopoly price equilibrium
always exists, there can be equilibria with dispersed prices so that consumers find it opti-
mal to sample more than one seller with positive probability. In such a context, an
increased advertising intensity may be valuable to consumers and social surplus by
increasing the probability that a buyer is able to sample more than one seller.
I now present the main insights from the research on price advertising with homo-
geneous products with sequential search or no search at all.
4.2.3 Price Advertising and Price Dispersion
The idea that price advertising might constitute a sensible solution to the Diamond
paradox was first explored in the seminal paper by
Butters (1977). Although the article
does include a version of the model with consumer search, it is usually remembered as a
model where consumers may only purchase at firms that have reached them with an ad.
The ad provides them with price information and the opportunity to buy. As such, it has
inspired a number of variants where advertising informs consumers about both the exis-
tence of a firm and its price. Besides Butters himself,
Stegeman (1986) and Robert and
Stahl (1993)
have studied a model of price advertising with sequential consumer search.
I first present a streamlined model that I use to present the insights from both strands of
the literature.
The following stylized model shares many features with the model of
Robert and
Stahl (1993)
. Consider a duopoly for a homogeneous good. Both marginal costs are zero.
There is a continuum of consumers with measure 1. When the market opens, consumers
do not know a firm’s price unless they see it advertised. They may, however, find out
prices that are not advertised through sequential search. Each search costs s > 0. All con-
sumers have identical unit demands with a valuation of v > 3=2 for the product. I now
introduce the following simplifying assumption on the advertising and pricing game:
firms may either not advertise and price the product as they wish, or advertise, in which
case they must charge
p ¼1 (to be thought of as a low price). If firm i, i ¼1, 2, advertises,
it selects to reach a fraction Φ
i
2 0,1ðof the consumer population which costs 1/2Φ
i
2
.In
a first stage, firms simultaneously choose whether to advertise or not: if they advertise,
they select an advertising reach; and if they do not advertise, they select a price, p
i
, for
firm i. In a second stage, after observing advertisements that have reached them, if
any, consumers choose whether or not to enter the market, and if they do whether to
search and buy. If consumers enter the market without seeing an ad, they are matched
with equal probability with one of the two competitors.
131Advertising in Markets
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