Download Persuasive Advertising with Sophisticated but

Persuasive Advertising with Sophisticated but
Impressionable Consumers∗
Dominique Olié Lauga†
February 2010
Abstract
I propose a model in which consumers base their purchasing decisions upon their recollections
of product quality, and in which firms can use persuasive advertising to change these recollections.
Although consumers are aware that such advertising has occurred when updating their beliefs, they
cannot prevent their memories from being affected. I show that persuasive advertising may be used
even though consumers are fully aware of it, and that persuasive advertising does not necessarily
signal high-quality products. The model is extended to incorporate informative advertising in which
firms reveal some verifiable information. When firms choose between persuasive and informative
advertising, persuasive advertising may block the full unraveling of information.
Keywords: advertising, persuasion, memory, postexperience advertising
∗
I am deeply indebted to Abhijit Banerjee, Glenn Ellison, and Elie Ofek for time, advice, and encouragement. I
thank Antara Dutta, Sara Ellison, Xavier Gabaix, Sergei Izmalkov, Paul Joskow, Nancy Rose, Jean Tirole, and seminar
participants at Babson College, Kellogg School of Management Northwestern University, Massachusetts Institute of
Technology, Paris School of Economics, Rady School of Management University of California San Diego, Simon Graduate
School of Business University of Rochester, University College London, and the 2nd Workshop on the Economics of
Advertising and Marketing (2009) for helpful comments.
†
Rady School of Management, University of California, San Diego. Email: [email protected].
1
1
Introduction
The goals of advertising campaigns are diverse; they vary from creating awareness for a new product
to affecting repeated purchases. To achieve these goals, firms decide not only how much to advertise
but also how to advertise their products. Firms may select the content of their advertisements to
convey information about their product quality directly to consumers. Firms may also choose uninformative advertisements. One explanation behind uninformative advertising is to signal product
quality to consumer by "burning money."1 The message contents of advertisements are, in that case,
irrelevant and their only effect is to reveal information indirectly to consumers. However, the content
of uninformative advertisements might have a direct effect on consumers in itself, through persuasion for example. A vast literature documents and uses cognitive psychology to analyze persuasion
in advertising.2 Firms may therefore select uninformative advertising because of its direct effect on
consumers through the persuasive elements of its message. This strategic decision may also convey
information to consumers indirectly and signal the product quality. The focus of this paper is to
address the following questions about persuasive advertising. When consumers understand how persuasion works, will persuasive advertising ever be optimal for a firm? If the answer to the previous
question is yes, will persuasive advertising always be associated with high-quality products? Finally,
when firms can select persuasive or informative advertising, does one type of advertising dominate
the other one?
I propose a model in which consumers are uncertain about the quality of a product sold by a
monopolist. At the time of purchase, consumers do not know the exact product quality but try to
assess it using their prior beliefs about quality. These beliefs can be, for instance, the recollections
that consumers have of the product, which are generated by all past interactions between consumers
and the product, including past personal experiences, word-of-mouth, official consumer reports, and of
course advertisements. Different prior beliefs about quality are generated by some consumers having
1
Nelson (1974) describes the idea of advertising signaling quality by dissipating part of the profits and Kihlstrom
and Riordan (1984) and Milgrom and Roberts (1986) formalize the money-burning effect.
2
See Braun (1999) and Braun-Latour and Zaltman (2006) for studies on how memory can be changed by advertising;
and Friestad and Wright (1995) about the similarity of lay people’s and researchers’ beliefs about persuasive advertising.
2
positive recollections and some consumers having negative recollections. The likelihood of having a
positive recollection is an increasing function of quality thus recollections reveal some information
about product quality. Furthermore, the firm may engage in persuasive advertising to increase the
number of positive recollection. Specifically, in this paper, persuasive advertising is assumed to change
the distribution of prior beliefs that consumers have about product quality.3 After being exposed to an
advertisement, consumers are, for example, more likely to remember the positive aspects of their last
experience with the product than they would have remembered without the advertisement (further
examples are provided in Section 2.2). In addition, consumers are sophisticated as they are fully
aware that the firm can choose to engage in persuasive advertising which increases the likelihood of
positive recollections.4 They know whether they have seen persuasive advertisements and that they
might be affected by them. However, they do not know if a positive recollection is the consequence of
persuasive advertising or true experience as, of course, they do not know the recollection they would
have had without persuasive advertising.
This paper shows that consumers cannot fully undo the effects of advertising, and engaging in
persuasive advertising might be optimal even with sophisticated consumers. In addition, I show that
persuasive advertising is not necessarily a signal of high quality. Under some market conditions, the
fact that consumers fully understand the effects of advertising allows firms to signal a high quality
by choosing a high price and by not engaging in advertising. Indeed, if a firm chooses not to engage
in persuasive advertising, consumers with positive signals know that their signals come only from
the intrinsic product quality and were not artificially improved by a marketing campaign. Consumers
with negative signals do not buy and, therefore, the product quality has to be high enough to generate
substantial positive signals and make choosing a high price profitable. As a result, choosing a high
price and not engaging in advertising can help signal a high-quality product. Depending on market
conditions and the degree of advertising persuasion, persuasive advertising can signal an intermediate3
By contrast, persuasive advertising enters directly in the utility function in Becker and Murphy (1993), creates loyal
customer in Baye and Morgan (2009) and Bala and Bhardwaj (2010), and refers to a shift in the demand of consumers
in Bagwell (2007), Chen, Joshi, Raju, and Zhang (2009), Amaldoss and He (2009), and Wu, Chen, and Wang (2009).
4
See Mehta, Chen, and Narasimhan (2008) for an empirical study that takes into account that "consumers perceive
ads to be biased, because they realize that ads are coming from a partisan source."
3
quality range, a high-quality range, or even a low-quality range.
Similarly, persuasive advertising is not naturally associated with high prices. Two factors drive the
relationship between persuasive advertising and prices. First, firms use both price and advertising to
signal their quality. therefore, when advertising does not signal high quality, it is not associated with
high prices. Second, keeping everything else constant, exposure to persuasive advertising lowers the
expectation of product quality which reflects the consumers willingness to pay.5 Indeed, a positive
signal with persuasive advertising does not carry as much good news as a positive signal without
persuasive advertising. The latter signal was generated only through the intrinsic product quality
while the former could be spurious and could have been negative without persuasive advertising.
After characterizing, without specifying any functional form, the full set of equilibria and their
properties, I study the case of a uniform distribution of qualities coupled with a particular persuasion
technology. I find that when the degree of persuasion is high, advertising does not signal high quality
as, with a high degree of persuasion, persuasive advertising has a homogenizing effect. Since firms do
not look that different after engaging in persuasive advertising, advertising cannot signal high-quality
firms. Similarly, if the range of quality is small, quality is not signaled through advertising as the
differential effect of advertising on firms is too small to allow quality signaling.
Finally, I introduce informative advertising to study how firms use different types of advertising
strategically. Informative advertising is based on a claim which is a hard/verifiable piece of information about the product.6 The monopolist chooses now between persuasive advertising, informative
advertising, or no advertising. I show that the option of engaging in persuasive advertising might
block the full unraveling of information in equilibrium. Some firms, instead of releasing some information in informative advertisements, choose persuasive advertising. Moreover, high-quality products
are not always promoted with the same type of advertising. Specifically, persuasive advertising can
signal a higher or lower quality product than a product promoted with informative advertising.
5
Anand and Shachar (2005) also find that advertising exposure can have a negative effect when the beliefs of a
consumer are worsened by exposure to an advertisement revealing that the attributes of a promoted product are below
his average match. The negative effect arises from what consumers learn from the content of an advertisement, whereas,
in the current paper, the negative effect comes from the inferences of sophisticated consumers.
6
See Tirole (1988) for a discussion about hard versus soft information.
4
Literature Review
This paper contributes to the literature on advertising with direct behavioral effects on consumers.
Previous analyses vary in the degree of consumer rationality they assume. Consumers can either be
irrational and not think about the decisions of firms (Schmalensee (1978)), or be rational and form
their beliefs by taking into account that firms behave strategically (Gabaix and Laibson (2006) and
Shapiro (2006)). The current paper falls in the latter category, and is related to Shapiro (2006)
which studies advertising in a limited memory set-up. Specifically, that paper examines how the
level of advertising expenditure is affected by consumer experience and by product quality when
consumers do not remember whether they have been exposed to advertising. By contrast, I analyze
here the situation when consumers are aware of being exposed to persuasive advertising, and use this
information to form their beliefs about product quality. This allows me to examine how a firm choose
strategically its advertising type, as well as its price level.
The current paper also adds to three other lines of research in advertising, namely its signaling
ability, its content, and the different types of advertising. First, my findings that persuasive advertising
does not necessarily signal high quality and is not always associated with high prices are in contrast
with the series of papers in which advertising is simply a money-burning device (Nelson (1974),
Kihlstrom and Riordan (1984), and Milgrom and Roberts (1986)).7 In these papers, the signaling
power of advertising stems from the fact that a firm with a large potential profit is willing to sacrifice
some of it to signal its type, while a firm with a smaller profit would not do so. Recent empirical
studies also disagree on whether advertising signals quality or not. Erdem, Keane, and Sun (2008) find
that firms use both price and advertising to signal quality, while Clark, Doraszelski, and Draganska
(2009) obtain that advertising has no effect on quality perception.
Second, the current paper is related to the literature on advertising content. Anand and Shachar
(2009) study how informative advertising can convey indirect information by signaling product attributes in addition to the direct information included in the messages. They found that consumers
use the content of advertising to form their out-of-equilibrium beliefs, but ignore the ad content on
the equilibrium path. In my paper, however, the persuasive elements of the advertisements matter
7
For a review of the literature on advertising as a signaling device, see Bagwell (2007).
5
on and off the equilibrium path. Anderson and Renault (2006) also study ad content and find that
a monopolist might not reveal all its information when consumers face a search cost.8 The current
paper suggests a different explanation: firms may not reveal all their information as they choose to
engage in another type of advertising. Finally, Shaffer and Zettelmeyer (2009) analyze comparative
advertisements and how in-store displays can reinforce their messages, while Anderson and Renault
(2009) show that welfare goes down due to comparative advertising.
Third, empirical studies have tried to disentangle the different effects of advertising. Studying the
yogurt industry, Ackerberg (2001) and Ackerberg (2003) find that consumers are primarily affected by
the informative elements of the advertisements over the persuasive effects. Finally, the current paper
focuses on the persuasive and informative elements in advertising even if an advertising campaign
entails more than that, for example targeting (Iyer, Soberman, and Villas-Boas (2005)).
The rest of the paper proceeds as follows. Section 2 describes the set-up of the model and provides
some support for its assumptions. Section 3 derives the equilibrium when the firm cannot advertise.
Section 4 characterizes the equilibrium of the model with persuasive advertising. Section 5 studies
the case of a uniform distribution of qualities and a particular persuasion technology. Section 6
characterizes the equilibrium with persuasive and informative advertising. Section 7 concludes the
paper.
2
The model
In this section, I first present the model set-up and then explain in more detail what quality represents,
how signals are generated, and how an advertising campaign can be persuasive.
2.1
Model Set-up
A monopolist sells a product of quality q, drawn from a distribution with probability distribution
function f on the support [q, q] ⊂ (0, 1]. There is a unit-mass of consumers who demand at most
one unit of the product. If consumers buy a product of quality q and price p, their utility is q − p,
8
See Koessler and Renault (2009) for a condition about full disclosure when firms do not know the consumers’ tastes.
6
their outside option being normalized to zero. Consumers do not know the product quality, but
they know the quality distribution f and, furthermore, each consumer receives a signal s about the
product quality. These signals are either positive, s = 1, or neutral/negative, s = 0. The probability
of positive signals, α(q) ≡ Pr(s = 1| q), is an increasing function of the true product quality. As
more consumers have positive signals about the product when the product quality is high, signals
reveal information about the underlying product quality. In addition, the worst quality is assumed
to generate few positive signals. Specifically, the worst-quality firm prefers selling to all consumers at
the lowest price p = q over selling only to consumers with positive signals (i.e., α(q) consumers get a
positive signal) at p = E[q|s = 1], the expected quality when consumers have a positive signal.
Assumption 1 The distribution of qualities satisfies q > α(q)E[q|s = 1].
The firm cannot communicate its product quality directly to consumers. It can, however, run a
persuasive advertising campaign to increase the probability that consumers receive positive signals
about the product. After a persuasive advertising campaign, the probability of positive signals is
ϕ(q) ≡ Pr(s = 1|P, q), which is larger than α(q), the probability of positive signals without advertising
(ϕ(q) ≥ α(q)).9 ϕ is also an increasing function of q so that better products generate more positive
signals even after an advertising campaign. For example, if persuasive advertising converts a share
θ of negative signals into positive signals, then the probability of positive signals becomes ϕ(q) =
α(q) + θ(1 − α(q)). As the focus of this paper is on the demand-side effects, i.e., how firms can use
the direct effect of advertising on consumers to signal their quality, a persuasive advertising campaign
covers the full market at no cost.10 Similarly, marginal costs are assumed to be constant and without
loss of generality, equal to zero.
Finally, consumers are fully aware of the effects of persuasive advertising. They observe whether
the firm engages in persuasive advertising and form Bayesian beliefs about the product quality.
9
In the conditional probabilities, P means conditional on the firm engaged in persuasive advertising while ∅ means
conditional on no advertising (α(q) = Pr(s = 1|∅, q)).
10
Introducing small fixed costs would not change the nature of the results. A more detailed discussion about costs
can be found at the end of Section 4.
7
The timing of the model is illustrated in Figure 1. After learning its product quality, the firm
chooses its advertising campaign and its price. Consumers see the advertising campaign if there
is one, then they receive their signal, observe the price and decide whether to buy. I analyze purestrategy perfect Bayesian Nash equilibria, with a tie-breaking rule such that a firm indifferent between
advertising and no advertising picks no advertising.
Before analyzing the model, I give more detail and provide some support for the different assumptions of the model in the next section.
time
The monopolist
learns q.
The monopolist
chooses
advertising
and price.
Consumers see
advertising
(if any).
Consumers learn
their signals, the price,
and decide whether to buy.
Figure 1: Time line of the model.
2.2
Motivation
In this paper, product quality refers to the probability that the good delivers a satisfactory experience
when it is consumed. The level of satisfaction may vary for several reasons. First, consumers do
not always use the product in the same situations. In the case of cough medicine, for example,
non-drowsiness is not crucial if the medicine is taken before going to bed whereas it involves safety
issues if taken before driving or operating machinery. Secondly, consumers have heterogeneous needs.
For example, some people take allergy drugs to treat a specific allergy, while others need help for all
possible sources of allergy. Finally, the quality of some goods, such as restaurant meals, varies from
one production batch to another.
Another assumption of this paper is that firms cannot communicate their product quality directly.
This could be the case because the information is too difficult to process for a non-expert consumer
and/or the information would not fit into the format of an advertisement or on the package of the
good. On the other hand, consumers might have used the product in the past or might have talked
to someone who has some experience with it. They have a prior about the product at the time of
8
purchase, which is captured in the model by the signal consumers have about the product quality.11
One example based on a limited-memory assumption, is that consumers remember whether their last
experience with the product was satisfactory, in that case α(q) = q. The origin of the signal can be
more complex. The signal could be the memory of one experience randomly drawn from all the past
experiences, weighting them differently depending on whether the experience was good or bad, how far
in the past it happened, and on their ordering (first and last experiences might be more salient). The
effects of confirmation bias, namely the fact that consumers put more weight on experiences confirming
their first experience, can be incorporated.12 In addition, the firm might be able to interfere with
these signals by engaging in persuasive advertising, which increases the probability that a consumer
receives a positive signal about the product.
The characterization of how advertising affects consumers is consistent with behavioral research
done in marketing and psychology. Braun (1999) and Braun, Ellis, and Loftus (2002) demonstrate
and cite many studies that support the effectiveness of post-experience advertising, namely, exposure
to advertising after the last time a product was consumed. Their papers show that the memory of
consumers can be altered by advertisements viewed after they have consumed a product, even after
an unpleasant experience. In these studies, recollections of products are closer to what advertisements
claim products are than to the true experiences as remembered by the control group. Post-experience
advertising might create suggested experiences. For example, if consumers mostly remember whether
their last experience with a product was positive, their experience does not have to stem from actually
using the product themselves. It could simply be a suggested experience as consumers cannot distinguish between memories arising out of suggested experiences from memories generated by personal
experiences. Marketers can therefore generate more positive memories than what products would
generate by themselves. Another way advertising works is mood congruence memory, which means
that people more easily remember memories that match their current mood (Teasdale and Russell
(1983)). Product advertising may activate mood elements, and from that may also activate memories
11
See Boatwright, Kalra, and Zhang (2008) about consumers forming product evaluations in the case of experience
attributes.
12
In Iyer and Kuksov (2010), the signals that consumers get about the product quality depend on the true product
quality and also on the affects of the consumers at the time of purchase.
9
of the product sharing the same mood elements. For example, when Nescafé advertisements were
centered around "Making time for friends...," positive memories about drinking coffee while spending
time with friends might have been retrieved more frequently. Finally, state-dependent learning could
also play a role in persuasive advertising. Eich, Weingartner, Stillman, and Gillin (1975) show that a
memory is more easily retrieved if one is in the same emotional or physical state as when the memory
was formed. The memories about a drug treating depression or migraine can be very different depending on whether people are currently depressed or having a migraine. Therefore, marketers could
change recollections about a drug by helping potential consumers remember how they feel when they
are sick.
Finally, I briefly present a model providing some micro-foundations for post-experience advertising.
First, consumers use the product and their experience is either satisfactory or neutral, and q is the
probability of having a satisfactory experience. Then time elapses and consumers might forget about
their satisfactory experience. At the time of the next purchase, α(q) consumers remember a positive
experience, while 1 − α(q) consumers have a neutral memory as they either had a neutral experience
or they forgot about their satisfactory experience. In that context, persuasive advertising serves as
a reminder for consumers. It reminds them why their experience was satisfactory and decreases the
number of consumers forgetting.13
The next section describes the effects of persuasive advertising in more detail.
2.3
Positive and Negative Effects of Persuasive Advertising
At this point, one might ask why a firm would forgo persuasive advertising as it is free and increases
the number of consumers with a positive prior about the product. Before answering that point, I first
present an assumption about the persuasive advertising technology and discuss its implications.
13
In this example, advertising helps consumers remember their own experiential level of satisfaction. Depending on
one’s interpretation of the results on post-experience advertising, it could also suggest a positive memory to someone
who had a negative experience. It is easy to imagine that a consumer had a negative experience because the last time
he used the product he was under a lot of stress and nothing seemed pleasant. An ad depicting a nice experience might
show him what he could experience when consuming the product. In the end, that consumer might remember the
positive suggested memory over the negative experienced one.
10
Assumption 2
ϕ(q)
α(q)
and
1−ϕ(q)
1−α(q)
are non-increasing.
The first part of Assumption 2 means that the share of positive signals after persuasive advertising relative to the positive signals generated solely by the product does not become larger as quality
increases. Similarly, the second part means that the share of remaining negative signals after persuasive advertising relative to the negative signals generated by the product does not become larger
as quality increases. In particular, this assumption is satisfied in the previous example in which advertising converts a fixed share of negative signals into positive signals. Assumption 2 implies that
holding the signal constant, persuasive advertising decreases the average consumer willingness to pay,
i.e. E[q|P, s, q1 ≤ q ≤ q2 ] ≤ E[q|∅, s, q1 ≤ q ≤ q2 ].14 I will refer this as the negative direct effect
of persuasive advertising. Sophisticated consumers understand that getting a positive signal with
persuasive advertising conveys less good information about the quality than getting a positive signal
without persuasive advertising as some positive signals result from the marketing strategy and not the
product quality. Overall, the negative direct effect of persuasive advertising has to be compared with
its positive direct effect, which is the generation of more consumers with positive signals, translating
into a demand expansion if the firm sells only to consumers with positive signals. These two effects are
illustrated in Figure 2. Firstly, as consumers respond to persuasive advertising, the share of consumers
with positive signals increase with persuasive advertising (arrow pointing to the right in Figure 2).
Secondly, consumers are sophisticated and take into account that their signals might be changed by
persuasive advertising. Thus, their willingness to pay decreases with persuasive advertising (arrows
pointing to the left in Figure 2). In the end, a firm may choose to engage in persuasive advertising if
the positive effect dominates, i.e., selling to more consumers at a lower price is more profitable than
selling to fewer consumers at a higher price.
Furthermore, advertising does not change consumers’ preferences as, with or without persuasive
advertising, consumers have the same ex-ante expected quality E[q] = Es [E[q|∅, s]] = Es [E[q|P, s]].
Persuasive advertising changes the dispersion around the mean, i.e. the variance. In the above example, where persuasive advertising converts a fixed share of negative memories into positive memories,
14
Conditional on signal s and q ∈ [q1 , q2 ], the distribution of q with no persuasive advertising first-order stochastically
dominates the distribution with persuasive advertising: F (q|∅, s, q1 ≤ q ≤ q2 ) ≤ F (q|P, s, q1 ≤ q ≤ q2 ).
11
persuasive advertising reduces the variance.
Share of Consumers
With Persuasive Advertising
With No Advertising
Impressionable
Sophisticated
Sophisticated
Expected Quality
E[q|P, s = 0] E[q|∅, s = 0]
E[q] E[q|P, s = 1] E[q|∅, s = 1]
Figure 2: Distribution of the expected quality with and without persuasive advertising. The difference
in the two distributions can be analyzed in two steps. First, the share of consumers with s = 1 increases as a direct
effect of persuasive advertising. Secondly, sophisticated consumers understand that a positive signal with persuasive
advertising could have been generated by persuasion and not because of the true product quality. Hence the decrease
in the expected quality given a positive signal.
3
No advertising case
I start by analyzing a simpler model where firms cannot advertise. This provides some useful insight
into the role played by prices in this model.15 In this section, a pure-strategy equilibrium is characterized by a triplet (p(q), b(s, p), µ(q|s, p)). p(q) is the price chosen by the firm as a function of its
quality q. b(s, p) is the decision of the consumers to buy or not to buy and µ(q|s, p) are their beliefs
when they receive signal s and observe price p. The beliefs are a probability distribution over the set
of qualities.
The support of µ(q|s, p) when p is on the equilibrium path does not depend on s as the choice of the
15
See Wolinsky (1983) and Bagwell and Riordan (1991) for studies about how prices signal product quality in other
contexts.
12
firm p(q) is independent of the signals received by consumers, and as each signal occurs with a positive
probability for every quality. Specifically, when p is chosen in equilibrium, consumers with neutral
signals and consumers with positive signals believe the same set of firms could have chosen that price.
The beliefs with a neutral signal put however more weight on the low-quality firms than the beliefs
with a positive signal. This implies that on the equilibrium path, if consumers with neutral signals
are willing to buy at p, consumers with positive signals are also willing to buy, namely b(0, p) =buy
implies b(1, p) =buy. On the equilibrium path, firms either sell to everybody or to consumers with
positive signals only. In addition, as consumers always buy if the price is equal to the worst quality,
the profits of the firms are larger than q in equilibrium.
The next lemma shows formally that in equilibrium two prices at most are chosen. It proves that
when exactly two prices are on the equilibrium path, every consumer buys at the lower price while
only consumers with positive signals buy at the higher price. It also pins down the ordering in terms
of quality: a low-quality firm chooses a low price and a high-quality firm chooses a high price.
Lemma 1 In the model with no advertising,
i. At most two prices are chosen on the equilibrium path.
ii. When exactly two prices (pL , pH ) are on the equilibrium path, there exists qL such that
- p(q) = pL if q ≤ qL and pH if qL < q,
- b(s, pL ) = buy for any s and b(s, pH ) = buy iff s = 1.
Intuitively, firms choose between the highest price where all consumers buy and the highest price
where only consumers with positive signals buy as firms always want to increase their prices as long as
demand remains constant. The trade-off is between selling at a low price to the full market or selling
at a high price to one segment. This effect is the usual monopoly trade-off between increasing the
price and reducing the demand. Setting up a high price allows firms to signal their high quality by
forgoing some demand. Indeed, when consumers with positive signals observe a high price, they know
that consumers with negative signals never buy at that price. It is profitable for a firm to choose that
13
price only if the firm generates enough positive signals. Therefore, only high-quality firms choose the
high price over the low price and consumers with positive signals buy at the high price.
Lemma 1 states that any equilibrium has exactly one or two prices on the equilibrium path.
They are referred to as pooling equilibrium or as semi-separating equilibrium, respectively. A pooling
equilibrium is characterized by a price pL such that the strategies and beliefs along the equilibrium
path are p(q) = pL , b(pL , s) = buy, and µ(q|pL , s) =
Rq
q
g∅ (q|s)
.16
g∅ (y|s)dy
Moreover, a semi-separating
equilibrium is characterized by two prices (pL , pH ) and one quality cutoff qL such that the strategies
©
L
and beliefs along the equilibrium path are p(q) = ppHL ifif q≤q
qL <q , b(s, pL ) = buy, b(s, pH ) = buy iff s = 1,
and µ(q|s, pL ) and µ(q|s, pH ) are derived using Bayes’ rule.17
Figure 3 illustrates graphically these two types of equilibria while Proposition 1 states the necessary
conditions that have to be satisfied by each equilibrium. Proposition 1 is general as it is stated with
general functional forms of the distribution of qualities f and the signal function α. E[q|s] represents
the expected quality conditional on having received signal s.
Proposition 1 In the model with no advertising, any pure-strategy equilibrium is either:
i. a pooling equilibrium characterized by pL such that pL ∈ [q, E[q|0]];
ii. a semi-separating equilibrium characterized by (pL , pH ) and qL such that
pL = α(qL )pH
with pL ∈ [q, E[q|0, q ≤ qL ]] and pH ∈ (E[q|0, qL < q], E[q|1, qL < q]].
These necessary conditions are also sufficient in the case of the worst out-of-equilibrium beliefs.
The next two corollaries present some additional results related to which equilibrium has the
highest profit or the highest welfare. Corollary 1 shows that the pooling equilibrium in which firms
extract the full surplus of consumers with neutral signals has the highest profits among all the pooling
16
g∅ (q|s) = α(q)s (1 − α(q))1−s f (q) is, up to a multiplicative constant, the density function over the qualities given
that signal s was received.
17
µ(q|pL , s) =
g (q|s)
R qL ∅
g∅ (y|s)dy
q
if q ≤ qL , 0 otherwise. µ(q|pH , s) =
14
g∅ (q|s)
qL g∅ (y|s)dy
Rq
if qL < q, 0 otherwise.
p
p
buy if s = 1
buy if s = 0
pH
pL
pL
q
qL
q
q
q
q
q
Figure 3: No advertising case: The product quality varies along the horizontal axis and equilibrium prices along
the vertical axis. The purchasing decision on the equilibrium path is represented by a dashed line for consumers with
negative signals and by a solid line for consumers with positive signals. The left graph illustrates a semi-separating
equilibrium in which high-quality firms signal themselves by choosing a high price and forgoing selling to consumers
with a negative signal. The right graph illustrates a pooling equilibrium.
equilibria. This pooling equilibrium has the highest profits if the profit achieved by the highest-quality
firm when selling only to consumers with positive signals is lower than the expected quality after
receiving a negative signal. Furthermore, the profits of any semi-separating equilibrium are smaller
than the profits of a semi-separating equilibrium in which low-quality firms extract the full surplus of
consumers with negative signals. These results give some support in favor of studying the equilibria
with binding upper constraints on prices.
Corollary 1 In the model with no advertising,
i. among all pooling equilibria, the one with pL = E[q|0] has the highest profits ,
ii. if α(q)q ≤ E[q|0], the pooling equilibrium with pL = E[q|0] has the highest profits among all
equilibria,
iii. among the semi-separating equilibria, the highest profits are achieved in a semi-separating equilibrium with pL = E[q|0, q ≤ qL ].
It is intuitive that the pooling equilibrium with the full consumer surplus being extracted leads
to the highest profit among all the pooling equilibria. How do these profits compare with the profits
15
of a semi-separating equilibrium? Assume that the highest-quality product generates so few positive
signals that, even if consumers with positive signals believed the product to have the highest quality,
the firm would still prefer to sell to all consumers at p = E[q|0]. It must be the case that this pooling
equilibrium has the highest profits. Finally, if the monopolist does not extract the full surplus of the
consumers with neutral signals when its quality is low, then there is some scope for increasing the
profit by increasing the price so another equilibrium with higher profits exists in which the price has
been increased.
In addition, the highest welfare is achieved by any pooling equilibrium as all consumers buy in
these equilibria. The highest welfare among all semi-separating equilibria is achieved by a semiseparating equilibrium in which low-quality firms extract the full surplus of consumers with negative
signals. These results are presented in the next corollary.
Corollary 2 In the model with no advertising,
i. a pooling equilibrium leads to higher welfare than a semi-separating equilibrium,
ii. all pooling equilibria have the same welfare,
iii. the highest welfare among all semi-separating equilibria is achieved by a semi-separating equilibrium satisfying pL = E[q|0, q ≤ qL ].
This section has illustrated how firms use price to signal their quality. A high-quality firm can
signal its type by choosing a price high enough to forgo the demand of consumers with neutral signals
while a low-quality firm would never find it profitable. In the next section, I analyze how firms signal
their quality when they can use not only their price but also their advertising decision to communicate
with their customers.
4
Persuasive advertising case
In this section, I analyze the full model where firms choose both their advertising and their price.
Two new insights about persuasive advertising are developed. First, persuasive advertising does not
16
naturally signal high quality. When the price is high, a firm doing no persuasive advertising relies only
on its intrinsic product quality to create positive signals. Consequently, if the share of positive signals
has to be high to make that choice optimal, consumers understand that the quality is high. Second,
persuasive advertising helps the monopolist extract rents. In the extreme case where the expected
quality conditional on a signal does not depend on the value of the signal, the firm can extract the
full surplus simply by charging a price equal to the expected quality. Nevertheless, when the expected
quality conditional on a signal has some variance, the firm cannot extract the full surplus. The firm
either sells to every consumer at a low price, leaving some surplus to the consumers with positive
signals, or it does not sell to consumers with neutral signals, extracting only the surplus of consumers
with positive signals. When it is more profitable to sell only to consumers with positive signals,
persuasive advertising helps extract the surplus from additional consumers as more of them get a
positive signal after persuasive advertising.
An equilibrium is ((p(q), a(q)), b(s, p, a), µ(q|s, p, a)). (p(q), a(q)) ∈ R+ ×{∅, P } is the price and the
advertising chosen by the firm as a function of its quality.18 b(s, p, a) is the decision of the consumers
to buy or not to buy and µ(q|s, p, a) their beliefs when they receive signal s and observe price p and
advertising a. The beliefs are a probability distribution over the set of qualities. The support of
µ(q|s, p, a) when (p, a) is on the equilibrium path does not depend on s as the choice of the firm p(q)
is independent of the signals received by consumers and each signal occurs with a positive probability
for every quality. Therefore, using a similar reasoning as the one in the no-advertising case, on the
equilibrium path, firms either sell to everybody or only to consumers with positive signals.
Intuitively, firms face three kinds of demand: sell to all consumers D = 1; sell to consumers
with positive signals with persuasive advertising D = ϕ(q); or sell to consumers with positive signals
without persuasive advertising D = α(q). Obviously, the highest price is always chosen when demand
is unchanged. The trade-off is thus between increasing the price and decreasing the demand. If these
three kinds of demand occur in equilibrium, as they are ordered from the largest to the smallest (1 ≥
ϕ(q) ≥ α(q)), they must be associated with prices with reverse ordering. The following lemma proves
formally that a firm selling only to consumers with positive signals without engaging in persuasive
18
a = ∅ represents no advertising while a = P represents persuasive advertising.
17
advertising chooses the highest price, and that a firm selling to all consumers chooses the lowest price.
This lemma also shows that a firm selling only to consumers with positive signals without engaging
in persuasive advertising is part of the high-quality range and that a firm selling to all consumers
belongs to the low-quality range.
Lemma 2 In the model with persuasive advertising, at most three different prices are on the equilibrium path.
If there exists q0 such that (p(q0 ), a(q0 )) = (p0 , ∅), then
i. if b(s, p0 , ∅) =buy iff s = 1,
then for any q > q0 , (p(q), a(q)) = (p0 , ∅), and for any q, p(q) ≤ p0 ,
ii. if b(s, p0 , ∅) =buy for any s,
then for any q < q0 , (p(q), a(q)) = (p0 , ∅), and for any q, p(q) ≥ p0 .
How do firms use persuasive advertising to signal their types? Assume for the moment that a firm
can choose to sell to consumers with positive signals either at a high price without advertising (price
pH and α(q) consumers) or at a low price with persuasive advertising (price pL and ϕ(q) consumers).
The trade-off is once again between price and quantity. The firm chooses no advertising and a high
price if the proportional increase in quantity
Per Assumption 2,
ϕ(q)
α(q) ,
ϕ(q)
α(q)
is smaller than the proportional increase in price
pH
pL .
the share of positive signals with persuasive advertising relative to the share of
positive signals without persuasive advertising, becomes smaller when the product quality increases.
Therefore by not engaging in persuasive advertising and choosing a high price, high-quality firms can
be separated from firms engaging in persuasive advertising and selling at a low price. Specifically,
forgoing the extra demand created by persuasive advertising allows firms to signal their high quality.
The exact nature of the equilibria is presented in the rest of the section.
According to Lemma 2, in an equilibrium with three different prices, low-quality firms choose a
low price and no advertising, intermediate-quality firms choose an intermediate price and persuasive
advertising while high-quality firms choose a high price and no advertising. In addition, low-quality
firms sell to all consumers whereas intermediate and high-quality firms sell only to consumers with
18
positive signals. That equilibrium is characterized by three prices (pL , pM , pH ) and two quality
cutoffs (qL , qM ) such that the strategies and beliefs along the equilibrium path are a(q) = ∅ if q ≤ qL
or qM ≤ q and = P if qL < q ≤ qH , p(q) = pL if q ≤ qL , = pM if qL < q < qM , = pH if qM ≤ q,
b(pM , P, s) = b(pH , ∅, s) = buy iff s = 1, µ(q|pL , ∅, s), µ(q|pM , P, s) and µ(q|pH , ∅, s) are derived using
Bayes’ rule.19
Proposition 2 characterizes a set of necessary conditions of any equilibrium where persuasive
advertising signals intermediate quality. The cutoff qualities are given by firms being indifferent
between two strategies. Moreover, prices are such that the purchasing decisions are rational. This
equilibrium is shown graphically in Figure 4.
Proposition 2 In the model with persuasive advertising, any equilibrium with three different prices
is characterized by (pL , pM , pH ) and two quality cutoffs (qL , qM ) such that
pL = ϕ(qL )pM and ϕ(qM )pM = α(qM )pH
with pL ∈ [q, E[q|∅, 0, q ≤ qL ]], pM ∈ (E[q|P, 0, qL < q < qM ], E[q|P, 1, qL < q < qM ]], and pH ∈
(E[q|∅, 0, qM ≤ q], E[q|∅, 1, qM ≤ q]].20
These necessary conditions are also sufficient in the case of the worst out-of-equilibrium beliefs.
In the equilibrium of Proposition 2, persuasive advertising signals intermediate-quality products.
Firms have a choice between a high price with a regular demand or a medium price with an expanded
demand. Since the demand expansion expressed as a share of the regular demand becomes smaller as
quality increases,21 the demand expansion created by persuasive advertising for intermediate-quality
firms is large enough to overcome the price decrease from a high price to a medium price, while it
is too small for high-quality firms. As for the low quality firms, they generate too many consumers
19
Define g∅ (q|s) = α(q)s (1 − α(q))1−s f (q) and gP (q|s) = ϕ(q)s (1 − ϕ(q))1−s f (q). µ(q|pL , ∅, s) =
q ≤ qL , 0 otherwise. µ(q|pM , P, s) =
g (q|s)
R qM P
qL gP (y|s)dy
if qL < q < qM , 0 otherwise. µ(q|pH , ∅, s) =
g (q|s)
R qL ∅
g∅ (y|s)dy
q
g (q|s)
Rq ∅
g∅ (y|s)dy
q
M
if
if qM ≤ q, 0
otherwise
20
To be fully exhaustive, if pL ≤ E[q|P, 0, q ≤ qL ], there exists another equilibrium identical to the previous one except
when q ≤ qL , a(q) = P , and µ(q|pL , P, s) is derived using Bayes’ rule.
21
For example if the regular demand is α(q) = .5, the demand expansion can go up to 200% while if the regular
demand is α(q) = .8, the demand expansion cannot exceed 125%.
19
p
buy if s = 1
buy if s = 0
pH
Persuasive
Advertising
pM
pL
q
qL
qM
q
q
Figure 4: Persuasive advertising signals intermediate quality. The product quality varies along the horizontal
axis and the equilibrium prices along the vertical axis. The purchasing decision on the equilibrium path is represented by
a dashed line for consumers with neutral signals and by a solid line for consumers with positive signals. The equilibrium
advertising choice is shown on top of the price level.
with neutral signals to be able to forgo them by selling at a higher price with or without persuasive
advertising.
The result that persuasive advertising does not signal high quality is in contrast with the previous
literature describing advertising as a means of burning money. If the advertising content is irrelevant
and advertising matters only because it is costly, firms with higher profits can signal themselves by
burning some of these profits as firms with lower profits cannot afford to burn the same amount of
money. In that case, only high-quality firms engage in advertising, whereas Proposition 2 shows that
if the direct effect of advertising is taken into account, advertising can signal intermediate quality
while high-quality firms signal themselves by not engaging in persuasive advertising. The burningmoney story also implies that the relationship between price and advertising is monotonic; advertising
is associated with the highest price while Proposition 2 shows that a non-monotonic relationship
between price and advertising can arise. No advertising is coupled with prices that are either higher
or lower than the price associated with persuasive advertising.22
22
Organic milk can be purchased in most supermarkets, not just the ones specializing in organic food. It is not
associated with any advertising and it is sold at a higher price than its closest substitute which is non-organic milk.
20
Furthermore, persuasive advertising does not necessarily signal intermediate-quality products.
First, it signals high quality when high-quality firms choose persuasive advertising while low-quality
firms opt out of advertising. Such an equilibrium is characterized by two prices (pL , pM ) and one
©
L
quality cutoff qL such that the strategies and beliefs along the equilibrium path are a(q) = P∅ ifif q≤q
qL <q ,
© L if q≤qL
p(q) = ppM
if qL <q , b(pL , ∅, s) = buy, b(pM , P, s) = buy iff s = 1, and µ(q|pL , ∅, s), and µ(q|pM , P, s)
are derived using Bayes’ rule. Second, persuasive advertising signals low-quality products when the
ordering of the firms engaging in persuasive advertising is reversed. In that case, only consumers
with positive signals buy, even for the worst-quality firm. That equilibrium is characterized by two
prices (pM , pH ) and one quality cutoff qM such that the strategies and beliefs along the equilibrium
©pM if q<qM
©
M
,
p(q)
=
path a(q) = P∅ ifif qq<q
pH if qM ≤q , b(pM , P, s) = b(pH , ∅, s) = buy iff s = 1, and µ(q|pM , P, s)
≤q
M
and µ(q|pH , ∅, s) are derived using Bayes’ rule. Finally, in some cases persuasive advertising has no
signaling power if all firms choose it. Such an equilibrium is characterized by one price pM such that,
on the equilibrium path, a(q) = P , p(q) = pM , b(pM , P, s) = buy iff s = 1, µ(q|pM , P, s) = gP (q|s).
Proposition 3 gives some necessary conditions for any equilibrium with one or two different prices
on the equilibrium path. In part (i), persuasive advertising signals high quality while it signals low
quality in part (ii). Part (iii) describes a pooling equilibrium in which all firms engage in persuasive
advertising. Finally the equilibria in part (iv) have no advertising occurring in equilibrium. In the
last two cases, advertising has no signaling value either because all firms run a persuasive campaign
or because none of them do.
Proposition 3 In the model with persuasive advertising, any equilibrium with less than three different
prices is characterized by either:
i. two prices (pL , pM ) and one quality cutoff qL such that pL = ϕ(qL )pM
with pL ∈ [q, E[q|∅, 0, q ≤ qL ]] and pM ∈ (E[q|P, 0, qL < q], E[q|P, 1, qL < q]];
ii. two prices (pM , pH ) and one quality cutoff qM such that ϕ(qM )pM = α(qM )pH and
ϕ(q)pM ≥ q with pM ∈ (E[q|P, 0, q < qM ], E[q|P, 1, q < qM ]] and
pH ∈ (E[q|∅, 0, qM ≤ q], E[q|∅, 1, qM ≤ q]];
21
iii. one price pM such that ϕ(q)pM ≥ q with pM ∈ (E[q|P, 0], E[q|P, 1]];
iv. the conditions described in Proposition 1.23
These necessary conditions are also sufficient in the case of the worst out-of-equilibrium beliefs.
In the equilibrium drawn on the left of Figure 5, persuasive advertising signals high-quality firms
while low-quality firms opt out of advertising and sell to the full market at a lower price. In the
equilibrium drawn on the right of Figure 5, the reverse takes place in terms of advertising signaling
quality and pricing. Persuasive advertising signals low-quality firms while high-quality firms choose
a higher price and no advertising. Consumers with neutral signals never buy in this equilibrium.
p
p
buy if s = 1
buy if s = 0
pH
Persuasive
Advertising
pM
Persuasive
Advertising
pM
pL
q
qL
q
q
q
qM
q
q
Figure 5: Persuasive advertising signals high or low quality. The left graph illustrates an equilibrium in
which persuasive advertising signals high quality while the right graph illustrates an equilibrium in which persuasive
advertising signals low quality. The product quality varies along the horizontal axis and the equilibrium prices along
the vertical axis. The purchasing decision on the equilibrium path is represented by a dashed line for consumers with
negative signals and by a solid line for consumers with positive signals. The equilibrium advertising choice is shown on
top of the price level.
I now discuss three important assumptions of the model, namely, that in addition to advertising
decisions firms also choose their price, that advertising has no cost in this model, and that consumers
are ex-ante homogeneous.
23
To be fully rigorous, b(p, s) should be replaced by b(p, ∅, s) and the expectations should also be conditional on no
advertising.
22
Variable price
Assuming that firms choose both their advertising and their price is a key assumption and reflects
the fact that firms do use several instruments to communicate with their consumers. To illustrate this
point, assume in this paragraph that prices are fixed and that the firm chooses only its advertising
campaign. If the price is low, p ≤ E[q|∅, 0], all firms sell to all consumers and do not engage in
persuasive advertising. If the price is intermediate, E[q|∅, 0] < p ≤ E[q|P, 1], all firms engage in
persuasive advertising and sell to consumers with positive signals. Persuasive advertising has no
signaling power in that case; it is used only to take advantage of its demand expansion effect. Finally,
if the price is high, E[q|P, 1] ≤ p < E[q|∅, 1], all firms opt out of persuasive advertising and are able to
sell only to consumers with positive signals. A firm would like to expand its demand with persuasive
advertising and have more consumers with positive signals but it is not possible due to the negative
direct effect of persuasive advertising. Recall that consumers are sophisticated and that persuasive
advertising lowers their willingness to pay. If a firm engages in persuasive advertising, the share of
consumers will certainly be larger but none of them are willing to buy at that price. Therefore, with
a fixed price, advertising loses all its signaling power. It is important to study how firms use both
advertising and price when communicating with consumers.
Advertising costs
Advertising is assumed to come at no cost for the firms. If a small fixed cost for advertising is
introduced, the results are qualitatively unchanged. More specifically, in a given type of equilibrium,
the quality cutoffs would become larger and the prices would also be larger. By small cost, I mean
that the cost does not completely overshadow the direct effect of advertising. If the cost becomes
large, then the main effect is a burning-money effect and the equilibria in which persuasive advertising
signals an intermediate quality or a low quality disappear. Nevertheless, advertising has to be more
than a means of burning money since some advertising campaigns are famous for failing. They did
not fail because consumers did not understand that they were expensive. They failed because of the
message they conveyed. Hence the advertising message is a strategic choice for firms.
Consumer Homogeneity
Consumers are supposed to be ex-ante identical. Once they receive their signal, the firm faces two
23
types of consumers: the ones with a positive prior about the product and the ones with a negative
prior. If all consumers are still assumed to value quality, and if their disutilities of price were drawn
from a continuous distribution, the monopolist would be facing a continuous distribution of consumers
instead of facing a distribution of consumers with two types. The drawback would be to introduce
some equilibria where prices would be a continuous function of quality. The consumers’ beliefs would
be extremely sensitive to slight variations in prices. However, the results presented above are still
valid when the beliefs of consumers are the limit of beliefs when firms make small errors when setting
prices.
5
Application to a uniform distribution
In this section, I focus on the case of a uniform distribution of qualities coupled with a particular
persuasive technology. More results are given about the sustainability of the different equilibria
depending on the market characteristics. In particular, I analyze how the existence of an equilibrium
depends on the degree of persuasion of the advertising technology.
Consider the model of the previous section with a uniform distribution of qualities between q
and q, i.e. f (q) =
1
q−q .
The signal without persuasive advertising is the memory of the outcome of
the last experience with the product, namely α(q) = q. Moreover, persuasive advertising transforms
a fixed share of negative experiential memories into positive suggested memories, which leads to
ϕ(q) = q + θ(1 − q). It is easily checked that the assumptions of the model are satisfied as α(q)E[q|s =
1] = qE[q|s = 1] < q,
ϕ(q)
α(q)
= (1 − θ) +
θ
q
and
1−ϕ(q)
1−α(q)
= 1 − θ are non-increasing. The model has three
parameters which are the range of qualities, q and q, and the degree of advertising persuasion, θ.
In this section, I focus on the equilibria where the upper constraints on prices are binding. The
prices are simply equal to the expected quality of the marginal consumers. Furthermore, in order to
determine when persuasive advertising cannot signal high-quality firms, the worst out-of-equilibrium
beliefs are used, that is, if an out-of-equilibrium action is observed, consumers believe they are facing
the worst-quality firm. If an equilibrium in which persuasive advertising signals high quality firms
does not exist with the worst out-of-equilibrium beliefs, such an equilibrium will not exist with any
24
other beliefs system. The next proposition shows that if the degree of persuasion is high, persuasive
advertising cannot signal high quality. If a high share of negative signals is transformed into positive
signals, persuasive advertising has a homogenizing effect on firms. After engaging in advertising, firms
do not look that different as they generate mainly positive signals. Therefore low-quality firms and
high-quality firms have similar profits when engaging in persuasive advertising and as a consequence,
persuasive advertising cannot signal high quality. Likewise when the range of quality is small and
the degree of persuasion is small, persuasive advertising cannot signal high quality. Indeed, when
the range of quality is small, all firms generate a similar number of positive signals. If persuasive
advertising has a small impact, even after engaging in persuasive advertising, all firms still have a
similar share of positive signals. Hence, persuasive advertising does not help signal high quality.
Proposition 4 Consider the model with persuasive advertising with f (q) =
1
q−q ,
α(q) = q and ϕ(q) =
q + θ(1 − q). There exist θ∗ ∈ (0, 1) and θ∗∗ ∈ [0, θ∗ ) such that persuasive advertising never signals
high quality if
θ < θ∗∗ or θ∗ < θ
There exists q ∗ (q) such that θ∗∗ = 0 iff
√
4− 7
3
≤ q and q < q ∗ (q).
The proposition states that if the degree of persuasion is large, persuasive advertising cannot
signal high quality in equilibrium. Besides, when the range of quality is large, persuasive advertising
might signal high-quality products for any low degree of persuasion. But if the range of quality is
small, persuasive advertising cannot signal high quality in equilibrium when the degree of persuasion
is too small. In that case, persuasive advertising might signal high-quality products only if the
degree of persuasion is in between two cutoff values. Figure 6 illustrates when the equilibrium in
which persuasive advertising signals high quality does not exist depending on the value of the highest
quality q and the degree of persuasion θ.
Similarly, Figure 7 illustrates when the equilibrium in which persuasive advertising signals low
quality does not exist depending on the value of the highest quality q and the degree of persuasion
θ. Recall that, in this equilibrium, all firms sell only to consumers with positive signals. Therefore,
when the degree of persuasion is low, by engaging in persuasive advertising, low-quality firms do not
25
θ
θ
q = 0.25
q = 0.75
Persuasive advertising
signals high quality
q
Persuasive advertising
signals high quality
q
Figure 6: Persuasive advertising signals high quality. The upper range of quality q ∈ (q, 1) varies along the
horizontal axis and the level of persuasion θ along the vertical axis. The left figure is drawn for q = 0.25 and the right
one for q = 0.75. The region where persuasive advertising signals high quality, is located in between the two curves.
get a large demand expansion. Instead they prefer to mimic high-quality firms by selling at a higher
price with no advertising. This explains why persuasive advertising does not signal low quality when
the degree of persuasion is low. On the other hand, when the range of qualities is small, the share
of positive signals is similar across firms. In this case, high-quality firms cannot signal themselves by
not engaging in persuasive advertising.
The findings of this section are in sharp contrast to the results in the previous literature. When
advertising has no direct effect and is only a means of burning money, only the high-quality firms
signal their type with advertising and advertising is coupled with the highest price. If, however,
the direct effect of advertising is taken into account and if consumers are sophisticated, high quality
cannot be signaled with persuasive advertising when the degree of persuasion is high or when the
range of quality is small. Furthermore, persuasive advertising does not necessarily signal low quality
either. That is, when the degree of persuasion is low or when the range of quality is small, persuasive
advertising cannot signal low-quality products.
26
θ
θ
q = 0.25
q = 0.75
Persuasive advertising
signals low quality
Persuasive advertising
signals low quality
q
q
Figure 7: Persuasive advertising signals low quality. The upper range of quality q ∈ (q, 1) varies along the
horizontal axis and the level of persuasion θ along the vertical axis. The left figure is drawn for q = 0.25 and the right
one for q = 0.75. The region where persuasive advertising signals low quality, is located in between the two curves.
6
Two types of advertising
After studying how firms choose between persuasive advertising and no advertising, I analyze how
firms choose between two types of advertising and no advertising. Informative advertising is introduced as a second type of advertising with a different direct effect on consumers from that of persuasive
advertising.
I analyze the choice of a monopolist when it chooses between two types of advertising that differ
in how they affect consumers. Persuasive advertising interacts with the private signal received by
consumers while informative advertising is a way to convey a piece of hard/verifiable information to
consumers. Firms are assumed to choose only one type of advertising or no advertising at all.24 I
start by presenting how informative advertising works, then I analyze the equilibrium focusing on the
interaction between persuasive advertising and informative advertising.
24
This assumption is consistent with the fact that advertisements compete to grab the attention of consumers; there-
fore, an ad conveys principally one message.
27
6.1
Informative Advertising
Suppose that prior to deciding on the advertising campaign, the monopolist performs marketing tests
which might deliver a claim about the product that can fit in the format of an advertisement. An
example of such a claim is “this toothpaste was clinically proven to fight germs for twelve hours.”
The probability η(q) ≡ Pr(σ = 1|q) that a firm gets a positive claim is an increasing function of the
product quality, where σ = 1 represents the fact that a claim was produced and σ = 0 means no
claim was created. The firm can engage in informative advertising only the marketing tests delivered
a positive claim. Informative advertising is thus noisy in this paper (see Anand and Shachar (2009)
for stylized facts about formulating informative advertising as a noisy process).
Note that for both types of advertising, the effect of advertising depends on the product quality.
The share of extra positive signals created by persuasive advertising varies with the underlying product
quality. Similarly, the probability to generate a positive claim about the product also depends on
the quality. The crucial point is that they affect consumers differently. Informative advertising adds
an element to consumers’ information set while persuasive advertising changes the information set
without allowing consumers to know what their information would have been without persuasive
advertising. Hence informative advertising has only a positive direct effect—increase in willingness to
pay—while persuasive advertising has both a positive and a negative direct effect–demand expansion
and decrease in willingness to pay.
The only difference with Section 4 is that firms with a positive claim choose between informative,
persuasive advertising, or no advertising while firms with no claim chooses between persuasive advertising or no advertising. The timing of the model is unchanged and I analyze pure-strategy perfect
Bayesian Nash equilibrium.
6.2
Equilibrium Analysis
An equilibrium is ((p(q, σ), a(q, σ)), b(s, p, a), µ(q|s, p, a)). (p(q, σ), a(q, σ)) ∈ R+ ×{∅, P, I} is the price
and the advertising chosen by the firm as a function of its quality and its claim status.25 b(s, p, a)
is the decision of the consumers to buy or not to buy and µ(q|s, p, a) their beliefs when they receive
25
a = I represents informative advertising.
28
message s and observe price p and advertising a. Using the same reasoning as in the previous model,
on the equilibrium path, firms either sell to all the consumers or only to the consumers with positive
signals.
In equilibrium, only five situations can arise. The firm chooses a high price associated with either
informative advertising or no advertising and sells only to consumers with positive signals. Conversely,
the firm chooses a low price while choosing either informative advertising or no advertising, and sells
to all consumers. Finally, the firm chooses persuasive advertising and sells only to consumers with
positive signals. These results are described formally in the next lemma.
Lemma 3 In the model with persuasive and informative advertising, at most five different prices are
on the equilibrium path.
If there exists (q0 , σ 0 ) such that (p(q0 , σ 0 ), a(q0 , σ 0 )) = (p0 , I), then
i. if b(s, p0 , I) =buy iff s = 1,
then for any q > q0 (p(q, 1), a(q, 1)) = (p0 , I), and for any (q, σ) p(q, σ) ≤ p0 ,
ii. if b(s, p0 , I) =buy for any s,
then for any q < q0 (p(q, 1), a(q, I)) = (p0 , 1), and if p = p(q, σ) < p0 then a(q, σ) = ∅ and
b(s, p, ∅) =buy for any s.
If there exists (q0 , σ 0 ) such that (p(q0 , σ 0 ), a(q0 , σ 0 )) = (p0 , ∅), then
i. if b(s, p0 , ∅) =buy iff s = 1,
then for any q > q0 (p(q, 0), a(q, 0)) = (p0 , ∅), and if p = p(q, σ) > p0 then a(q, σ) = I and
b(s, p, I) =buy iff s = 1,
ii. if b(s, p0 , ∅) =buy for any s,
then for any q < q0 (p(q, 0), a(q, 0)) = (p0 , ∅), and for any (q, σ) p(q, σ) ≥ p0 .
Lemma 3 shows that in an equilibrium with five different prices on the equilibrium path, lowquality firms sell to all consumers at a low price. If the firm has a claim, it reveals it through informa29
tive advertising and is able to charge a higher price than firms with no claim who chooses not to advertise. Intermediate-quality firms choose an intermediate price, engage in persuasive advertising and sell
only to consumers with positive signals. Finally, high-quality firms with a claim choose an informative
campaign and charge the highest price, while high-quality firms with no claim signal their type with a
high price and no advertising. That equilibrium is characterized by five prices (p0L , p1L , pM , p0H , p1H )
0 , q 1 ) such that the strategies and beliefs on the equilibrium path
and four quality cutoffs (qL0 , qL1 , qM
M
are



∅ if q≤qL0



0
a(q, 0) =
P if qL0 <q<qM




 ∅ if q 0 ≤q
M



I if q≤qL1



1
, a(q, 1) =
P if qL1 <q<qM




 I if q1 ≤q
M



pσ if q≤qLσ


 L
σ ,
, p(q, σ) =
pM if qLσ <q<qM




 pσ if q σ ≤q
H
M
b(p0L , ∅, s) = b(p1L , I, s) = buy, b(pM , P, s) = b(p0H , ∅, s) = b(p1H , I, s) = buy iff s = 1, and µ on the
equilibrium path is derived using Bayes’ rule.26
The next proposition gives a set of necessary conditions for an equilibrium with five prices on the
equilibrium path. The cutoff qualities are given by the indifferent firms, while the prices are such
that the purchasing decisions are rational. That equilibrium is also depicted graphically in Figure 8.
Proposition 5 In the model with persuasive or informative advertising, any equilibrium with five
0 , q1 )
different prices is characterized by (p0L , p1L , pM , p0H , p1H ) and four quality cutoffs (qL0 , qL1 , qM
M
such that
σ
σ
pσL = ϕ(qLσ )pM and ϕ(qM
)pM = α(qM
)pσH
0 } ∪ {P, 1, 0, q 1 < q < q 1 }],
with pσL ∈ [q, E[q|∅, σ, 0, q ≤ qLσ ]], pM ∈ (E[q|{P, 0, 0, qL0 < q < qM
L
M
0 } ∪ {P, 1, 1, q 1 < q < q 1 }]], and pσ ∈ (E[q|∅, σ, 0, q
E[q|{P, 0, 1, qL0 < q < qM
M ≤ q], E[q|∅, σ, 1, qM ≤
L
M
H
q]].27
26
Define g∅ (q|s, σ) = α(q)s (1 − α(q))1−s η(q)σ (1 − η(q))1−σ f(q) , gP (q|s, 0) = ϕ(q)s (1 − ϕ(q))1−s (1 − η(q))f (q), and
gP (q|s) = ϕ(q)s (1−ϕ(q))1−s f (q). Let aσ = I if σ = 1 and ∅ if σ = 0. µ(q|pσL , aσ , s) =
wise. µ(q|pσH , aσ , s) =
g∅ (q|s,σ)
qM g∅ (y|s,σ)dy
Rq
1
0
if qL0 < q < qL1 or qM
< q < qM
,=
27
R
σ
if qM
< q , 0 otherwise. µ(q|pM , P, s) =
(q0 ,q 0 )∪(q 1 ,q 1 )
L M
M L
gP (q|s)
R q1
gP (y|s,0)dy+ 1M gP (y|s)dy
q
L
g∅ (q|s,σ)
σ
R qL
g∅ (y|s,σ)dy
q
if q ≤ qLσ , 0 other-
gP (q|s,0)
R q1
g (y|s,0)dy+ 1M gP (y|s)dy
0
0
1
1
(q ,q )∪(q ,q ) P
q
L M
M L
L
R
1
if qL1 < q < qM
, 0 otherwise.
0
The ordering of the elements in the conditional expectations is a, σ, s, q. For example E[q|∅, 0, 0, q ≤ qL
] represents
0
the expected quality when a = ∅, σ = 0, s = 0 and q ≤ qL
.
30
These necessary conditions are also sufficient in the case of the worst out-of-equilibrium beliefs.
p
Firms: s=0
Consumers:
buy if s=1
buy if s=0
p1H
p0H
Persuasive Adv
pM
p1L
p0L
q qL0 qL1
1
qM
0
qM
q
q
p
Firms: s=1
Consumers:
p1H
buy if s=1
buy if s=0
Informative Adv
p0H
pM
p1L
Persuasive Adv
Informative Adv
p0L
q qL0 qL1
1
qM
0
qM
q
q
Figure 8: Informative and persuasive advertising case. On the top graph, the pricing and advertising choices
of a firm without a claim are drawn with respect to its quality. On the bottom graph, the pricing and advertising
choices of a firm with a claim are drawn with respect to its quality. The purchasing decision on the equilibrium path, is
represented by a dashed line for consumers with neutral signals and by a solid line for consumers with positive signals.
Low-quality firms choose a low price p0L if they choose no advertising or p1L if they reveal a positive
claim through informative advertising. These firms sell to all consumers. Intermediate-quality firms
run a persuasive campaign and choose an intermediate price pM . They sell only to consumers with
positive signals. High-quality firms also sell only to consumers with positive signals. They choose a
high price p0H and no advertising if they have no claim to reveal and they choose the highest price p1H
and informative advertising if they can.
In addition, the set of qualities of firms with a claim choosing persuasive advertising is strictly
included in the set of qualities of firms with no claim engaging in persuasive advertising. In terms
31
1 < q 0 . The low price for a firm without a
of quality cutoffs this translates into qL0 < qL1 < qM
M
claim is lower than the low price for a firm with a claim as the firm with a claim can always forgo
informative advertising and mimic the firm without the claim. Therefore, the profit of the firm
without a claim indifferent between no advertising with the lowest price and persuasive advertising
is equal to p0L which is smaller than p1L . On the other hand, with or without a claim there is a single
price associated with persuasive advertising. Hence the quality of the indifferent firm with a claim is
higher than the quality of the indifferent firm without a claim. The intuition is similar in the case
of the cutoff qualities between persuasive advertising with the intermediate price and no advertising
with the high price.
It is striking that some firms with a claim choose persuasive advertising; these firms have a claim
to reveal but choose not to reveal it to consumers. In this equilibrium, the information does not fully
unravel. Consumers do not know whether a firm that engages in persuasive advertising has a claim.
On the other hand, consumers rationally infer that a firm engaging in no advertising has no positive
claim to reveal.
This equilibrium also illustrates the important role played by prices. When consumers observe an
informative campaign, they cannot distinguish between low and high quality. They need to check the
price to be able to form their final beliefs. Depending on the price level, they think the product is
from the bottom quality group or from the top quality group.
Finally, these results show that no clear ordering exists between the two types of advertising.
Persuasive advertising can signal a higher or a lower quality than informative advertising.
7
Conclusion
Manufacturers of personal care products spent more than 5 billion dollars in 2006 on advertising in
the United States.28 Total advertising spending across all categories and media was estimated at 285
billion dollars. Firms have large advertising budgets and their choice of advertising is an important
strategic decision.
28
See AdvertisingAge (2007).
32
In this paper, I analyze how firms can signal their product quality when consumers are sophisticated and understand that they can be affected by the persuasive side of advertising. I show that
some firms engage in persuasive advertising even if consumers are fully aware of their motivation for
choosing this form of advertising. In addition, firms can strategically signal their product quality by
launching or not launching a persuasive advertising campaign. I show that neither the relationship
between advertising and quality nor the one between advertising and price are monotonic. Specifically, persuasive advertising does not naturally signal high-quality products and is not necessarily
associated with the highest price. Depending on the market conditions, persuasive advertising can
signal low-quality firms, high-quality firms, or even an intermediate range of qualities. In particular,
if the persuasion technology is very effective or if the range of qualities is small, persuasive advertising
cannot signal high quality since firms engaging in persuasive advertising look very similar from the
consumers point of view. Finally, when choosing between persuasive or informative advertising, firms
may prefer to withhold their information and instead engage in persuasive advertising.
These results were obtained by developing a model where persuasive advertising has a direct
effect on consumers. Unlike in the previous literature where persuasive advertising was included
as a direct element in the utility of consumers or where it shifted their preferences, in this paper
persuasive advertising affects the memory of consumers in a way that is consistent with results found
in the psychology and marketing literature on post-experience advertising. Furthermore, the results
of this paper could also be applied to other strategic choices made by a firm as long as they affect
the distribution of signals that consumers get about the product (see Brown, Camerer, and Lovallo
(2009) for the effects of movie cold on box office revenue and Milgrom (2008) for a review on disclosure
models).29
The effects of competition has yet to be studied in this context. It will raise some interesting
issues about the effect of mentioning a competitive product in an advertisement. In particular, is this
always a signal that the competitive product has a higher quality? Will it depend on the advertising
type chosen by the competitor?
Lastly, there remains a general issue on how to precisely classify the different types of advertising.
29
I thank
for pointing out this interesting remark.
33
Johnson and Myatt (2006) suggest to use a different taxonomy: hype versus real information. Their
distinction comes from a vertical versus horizontal differentiation, while the distinction that I used
is based on the notion of soft versus hard information. The more appropriate taxonomy depends of
course on the context, but the important point is that the type of advertising matters and affects
consumers differently. It is therefore a strategic tool that firms can use to communicate with their
customers.
Appendix
Proof of Lemma 1.
Consider two firms q and qe choosing p and pe in equilibrium, respectively.
First, assume that consumers buy only when they receive a positive signal for both prices or that all
consumers buy when they observe either price. It must be the case that the prices are equal. Otherwise, the firm with the lower price deviates and chooses the higher price. Its demand is unchanged
but it now sells at a higher price. As firms either sell to everybody or to consumers with positive
signals only, at most two prices are on the equilibrium path. Now assume that consumers buy only
when they receive a positive signal when they see one price and buy irrespectively of the value of their
signal when they observe the other price. Wlog assume that b(s, p) =buy iff s = 1 and b(s, pe) =buy
for any s. The profits of firm q after choosing p must be at least as large as its profits would have
been if it had chosen pe. Its no-deviation condition is α(q)p ≥ pe which implies that p ≥ pe. Similarly,
the no-deviation condition for firm qe is pe ≥ α(e
q)p. As the signal function α is non-decreasing, these
conditions imply that q ≥ qe.
Proof of Proposition 1.
Lemma 1 states that an equilibrium has at most 2 prices on the
equilibrium path. Firms can always choose to price at q and sell to everybody, hence any equilibrium
price is larger than q. Consider first a pooling equilibrium around pL . Assume that consumers buy
at pL only if their signal is positive, which is the case iff E[q|0] < pL ≤ E[q|1]. Thus, the profit
of the worst-quality firm is π(q) = α(q)pL ≤ α(q)E[q|1] < q.30 This firm can deviate to p = q and
increase its profit. Therefore, in a pooling equilibrium all consumers buy irrespectively of their signals.
30
The last inequality is Assumption 1.
34
Bayes’ rule pins down their beliefs when they observe pL and consumers with a negative signal are
willing to buy iff pL ≤ E[q|0]. Consider now an equilibrium with two prices. Lemma 1 shows that
©
L
p(q) = ppHL ifif q≤q
qL <q , b(s, pL ) = buy, b(s, pH ) = buy iff s = 1. The condition pL = α(qL )pH simply states
that the firm with the cutoff quality is indifferent between the two prices. Bayes’ rule delivers the
beliefs of the consumers on the equilibrium path. Finally, consumers with negative signals buy at pL
iff pL ≤ E[q|0, q ≤ qL ] while they do not buy at pH iff E[q|0, qL < q] < pH . Consumers with positive
signals buy at pH iff pH ≤ E[q|1, qL < q].
Proof of Corollary 1.
In a pooling equilibrium, the profits are π(q) = pL implying the first
result. In a semi-separating equilibrium, profits are non-decreasing with respect to quality and π(q) =
α(q)pH ≤ α(q)q. Hence, if α(q)q ≤ E[q|0], the equilibrium with the highest profits is the pooling
equilibrium with pL = E[q|0]. Consider a semi-separating equilibrium such that pL < E[q|0, q ≤ qL ]
and pH < E[q|1, qL < q], then there exists a semi-separating equilibrium with (pL + δpL , pH + δpH , qL )
such that δpL > 0, δpH > 0, δpL = α(qL )δpH and pH + δpH ≤ E[q|1, qL < q] with strictly higher
profits for any quality. Consider a semi-separating equilibrium such that pL < E[q|0, q ≤ qL ] and
pH = E[q|1, qL < q], then there exists a semi-separating equilibrium with (pL + δpL , pH , qL + δqL )
such that δpL > 0, δqL > 0, pL + δpL = α(qL + δqL )pH and E[q|0, qL + δqL < q] < pH with higher
profits, strictly higher for the low qualities. Therefore, the semi-separating equilibrium with the
highest profits among all semi-separating equilibria satisfies pL = E[q|0, q ≤ qL ].
The total surplus in a pooling equilibrium is simply E[q] as all the
Rq
Rq
consumers buy. In a semi-separating equilibrium the total surplus is q L qf (q)dq + qL α(q)qf (q)dq ≤
Rq
R qL
q qf (q)dq + qL qf (q)dq = E[q]. Note that the inequality is an equality iff all the consumers of the
Proof of Corollary 2.
high-quality firms receive positive signals, i.e., q > qL ⇒ α(q) = 1. Part iii. is immediately derived
from the last part of the proof of the previous corollary.
Proof of Lemma 2.
Consider two firms q and qe choosing (p, a) and (e
p, e
a) in equilibrium. If
all consumers buy whenever they observe (p, a) or (e
p, e
a) then the prices must be equal. Otherwise,
the firm with the lower price could increase its profit by choosing the same price and advertising
as the other firm. Now assume that only consumers with positive signals buy when they observe
(p, a) or (e
p, e
a). If the advertising choices are equal, the prices must be equal, i.e., a = e
a ⇒ p = pe.
35
If the advertising choices are different, wlog assume that a = ∅ and e
a = P . The profits of firm q
after choosing (p, a) must be at least as large as if it had chosen (e
p, e
a); its no-deviation condition is
α(q)p ≥ ϕ(q)e
p. Similarly for firm qe, the no-deviation condition is ϕ(e
q )e
p ≥ α(e
q)p. Recall that the
signal function ϕ/α is non-increasing and larger than 1. Therefore these conditions imply that q ≥ qe
and p ≥ pe. Finally, consider the case when only consumers with positive signals buy if they observe
(p, a) and when all consumers buy if they observe (e
p, e
a). Firm q can choose (e
p, e
a) and sell to all
consumers. As firm q prefers to sell to a smaller share of consumers, it must sell at a higher price:
p ≥ pe. Furthermore, the share of consumers with positive signals of firm qe is too small to make the
deviation to a higher price profitable. In particular, the no-deviation condition implies q ≥ qe. In the
end, at most one price corresponds to firms selling to all consumers, and at most two prices correspond
to firms selling only to consumers with positive signals with or without persuasive advertising.
Proof of Proposition 2. Lemma 2 implies that in an equilibrium with three prices, pL < pM < pH ,
high-quality firms (qH ≤ q) choose pH , no advertising and sell to consumers with positive signals
while low-quality firms (q ≤ qL ) choose pL , no advertising and sell to every consumer. Hence, the
intermediate price pM and persuasive advertising is chosen by intermediate-quality firms (qL < q <
qM ) and only consumers with positive signals buy. pL = ϕ(qL )pM and ϕ(qM )pM = α(qM )pH are
the indifference conditions for cutoff firms qL and qM , respectively. The beliefs of consumers are
determined by Bayes’ rule on the equilibrium path. The inequalities on prices are derived from the
rationality of the purchasing decision by consumers depending on their private signals and from the
fact that prices have to be larger than q.
The proof of Proposition 3 is derived by using a reasoning similar to the proof of Proposition 2.
Proof of Proposition 4.
Equilibrium (i) in Proposition 3 is the only equilibrium where per-
suasive advertising signals high-quality firms. This equilibrium is sustainable iff there exist two
prices (pL , pM ) and one quality cutoff qL such that pL = ϕ(qL )pM and pL = E[q|∅, 0, q ≤ qL ] and
pM = E[q|P, 1, qL < q]. Thus, this equilibrium exists iff E[q|∅, 0, q ≤ qL ] = ϕ(qL )E[q|P, 1, qL < q] has
a solution qL in (q, q). The LHS is an increasing function of qL and it is concave as
4(1−q)2
∂ 2 E[q|∅,0,q≤qL ]
2
∂qL
=
− 3(1−q+1−qL )3 . The RHS is an increasing function of qL and it is convex.31 Note that the LHS is
3 1 ∂ 2 ϕ(qL )E[q|P,1,qL <q]
2
∂qL
=
num
3((1−θ)(q+qL )+2θ)3
where num is a polynomial function of degree 2 in q with a positive
36
actually independent of θ and the RHS is increasing in θ.32 Besides when θ = 1, no solution exists
as the LHS is strictly smaller than the RHS. Indeed LHS = E[q|∅, 0, q ≤ qL ] < qL < E[q|P, 1, qL <
q] = RHS|θ=1 . Let’s analyze what happens when θ = 0. When qL tends to q, the LHS tends to q
and the RHS tends to qE[q|∅, 1] which is smaller. When qL tends to q, the LHS tends to E[q|∅, 0]
and the RHS tends to qq. Hence the LHS is larger than the RHS when θ = 0 and when qL tends
to q iff E[q|∅, 0] > q 2 ⇔
q+q
2
q 2 +qq+q 2
q+q
−
− q 2 (1 − 2 ) > 0 which is a polynomial function of degree
3
´
³
³
√ ´
p
2 in q. Let’s define q∗ (q) = 14 3q 2 − 2q + 3 − 9q4 + 12q 3 − 42q 2 + 12q + 9 .When q < 4−3 7 or
´
³ √
4− 7
∗ (q) ≤ q , E[q|∅, 0] ≥ q 2 which implies that no solution exists when θ = 0. And
≤
q
and
q
3
when
√
4− 7
3
≤ q and q < q∗ (q), E[q|∅, 0] < q 2 which implies that a unique solution exists when θ = 1.
Hence the results of the proposition.
The proofs of Lemma 3 and Proposition 5 are derived by using a reasoning similar to the ones of
Lemma 2 and Proposition 2.
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