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CESifo Area Conference on
Applied Microeconomics
4 – 5 March 2005
CESifo Conference Centre, Munich
Negative Advertising a New Product!
Simon P. Anderson and Régis Renault
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
E-mail: [email protected]
Internet: http://www.cesifo.de
Negative Advertising a New Product!
Simon P. Anderson∗and Régis Renault†
This version February 2004.
COMMENTS WELCOME
Abstract
An entrant introduces a new product and consumers do not know how much they
value it, while they know how they value an incumbent’s product. If the product
is low quality, the entrant will advertise detailed product information that enables
consumers to determine their matches: it will not if it is high quality. By contrast, the
incumbent would like to advertise match information about the new product only if
it is high quality. Such ”negative” advertising may improve welfare if entry costs are
low. If they are high, it may deter desirable entry of high quality products. We extend
the model to allow consumers to not know quality unless it is advertised (we assume
that consumers know that there is a positive probability that neither firm knows the
entrant’s quality, and this enables us to circumvent unravelling by which quality would
always be disclosed by the entrant) Then a high quality entrant will advertise quality,
and the incumbent will advertise match information. The reverse happens for a low
quality entrant. The policy implications for negative advertising are discussed.
Keywords: persuasion game, advertising, search, content analysis, information,
quality
JEL Classification: D42 L15 M37
Acknowledgement 1 We gratefully acknowledge travel funding from the CNRS and
NSF under grants INT-9815703 and GA10273, and research funding under grant SES0137001. We thank various seminar participants and IDEI (University of Toulouse I)
for its hospitality.
∗
Department of Economics, University of Virginia, PO Box 400182, Charlottesville VA 22904-4128, USA.
[email protected].
†
ThEMA, Université de Cergy-Pontoise, 33 Bd. du Port, 95011, Cergy Cedex, FRANCE and Institut
Universitaire de France. [email protected]
1
1
Introduction
Negative advertising is pervasive in the political arena and often viewed with distaste by
voters. For firms, negative advertising could cast rival’s products in a bad light to persuade
people not to buy them, and instead buy the firm’s own product. However, laws about
misleading ads apply also to negative ads (by which we mean those ads that compare or
contrast one’s own product, or just point out aspects of rival products) so claims ought to
have truth behind them. Here we assume that all information is truthful, and we consider a
game between rival firms and their incentives to provide information.
The paper is novel in several dimensions. First, we address the advertising decision of a
firm introducing a new product and faced with an incumbent rival. The asymmetry, which
is presumably the germane case in most market situations, is crystallized in asymmetric
information of consumers. Specifically, consumers know the characteristics of the existing
firm, but do not know those of the new firm’s product. We assume that the incumbent
is fully aware of the new product’s attributes, but consumers are not, although they have
(correct) priors about their evaluations of it. If negative advertising is not permitted, then
it is solely up to the new firm launching its product what to communicate about its good.
If negative advertising is permitted, then the incumbent can also inform consumers about
some product attributes that perhaps the new product does not wish to communicate. The
analysis also treats the welfare economics of negative advertising.
Here we present the general model and some results for an example with a uniform
distribution of matches. We end by presenting some extention o fthe current model.
2
Launching a new product with advertising
There is an incumbent product, sold by Firm 0. Consumers differ with respect to their
evaluations of this product, and know these in advance. Each consumer is in the market for
2
one unit of the good, and will buy from either the “old” or the “new” firm. Let F (r0 ) be
the fraction of consumers with valuations below r0 , with density f (r0 ), and suppose that the
support of r0 is [a, b] and we suppose for the sequel that a is large enough that all consumers
buy one of the two products. There is a visit cost of c0 for consumers who visit Firm 0.
The valuation of product 1, the new product sold by Firm 1, is r1 , whose distribution is
also given by F (.), and this valuation is independently distributed from that of r0 . The visit
cost for consumers who visit Firm 1 is c1 . We shall in the sequel be able to interpret the visit
costs as equal, and different values of c0 and c1 will be interpreted as inherent differences in
product qualities (so c0 > c1 will be interpreted as a new product of higher quality” than
the incumbent product).
Firms are able to advertise the prices they charge, and the new firm is allowed to advertise
the realization of r1 if it so wishes. If the incumbent is allowed to advertise r1 and does so,
we refer to this as negative advertising. Even though there is nothing untruthful in it, it
may be information that Firm 1 would not choose to reveal on its own. Now, if there is
no information on the value of r1 , consumers must form (rational) expectations of their
expected benefits from visiting Firm 1 (at cost c1 ) given that they anticipate the option of
later visiting and buying from Firm 0.
3
Some preliminary results
We first give two results for duopoly pricing that are important to the analysis that follows.
Since they are used quite extensively, we give them first. The demand curves considered
below will satisfy the properties used in these results.
Suppose that there are two products. They are priced at p0 and p1 . Demand for product
˜ which represents the full-price
1 depends in an increasing manner on a variable called ∆,
advantage of product 1. It is useful for what follows to write the full price of product i as
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˜ = (p0 + c0 ) − (p1 + c1 ).
pfi = pi + ci , and so ∆
˜ and so this is an increasing function.
Let then the demand for Firm 1’s product be D1 (∆)
Let the demand for Firm 0’s product be given by D0 = 1 − D1 , representing the idea that
there is a unit mass of consumers, and each consumer buys one unit of the good from one
firm or the other. We further assume that D1 (0) =
1
2
so that firms have an equal share of
the market when full prices are equal.
Then we have the following result.
Lemma 1 If c0 = c1 , then equilibrium prices satisfy p1 = p0 =
D0 (0)
−D0 (0)
and full prices are
equal. If c1 > c0 , then equilibrium prices satisfy p1 < p0 and full prices satisfy pf1 > pf0 , with
equilibrium sales satisfying D1 < D0 . The opposite pattern arises for c0 > c1 .
˜)
−Di (∆
˜ =
Proof.The first order conditions are pi = D ∆˜ . Since in any equilibrium, D0 ∆
i( )
˜ , then higher prices are associated to higher demands. But this means that, since we
D1 ∆
have D0 (0) = 1/2, the firm with the lower demand has a higher full price. That is, p1 < p0
holds if and only if D1 < D0 .and if and only if pf1 > pf0 . Taking the first and last inequalities,
this can be only true if c1 > c0 . The other results follow immediately along similar lines.
This result means intuitively that a cost (or quality) disadvantage is reflected in a lower
mark-up and yet lower demand since the cost disadvantage is only partially “passed on.”.
Assume too that demands are such that the associated revenue functions are quasiconcave.
˜ and DB (∆)
˜ for Firm 1 that are each increasing
Lemma 2 Consider two demands, DA (∆)
in their argument, with the properties that DA (0) = DB (0), and DA
(0) = DB
(0). Let
˜ =
these demands generate revenue functions that are quasiconcave in p1 (recalling that ∆
(p0 + c0 ) − (p1 + c1 )). Then, if the best reply to some price p0 under demand curve DB
˜ > 0 (resp. ∆
˜ < 0), with DA (∆)
˜ < DB (∆)
˜ for all ∆
˜ > 0 (resp. ∆
˜ < 0), then the
involves ∆
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corresponding revenue is higher than the highest revenue that can be achieved with demand
curve DA . Conversely, if the best reply to some price p0 under demand curve DB involves
˜ > 0 (resp. ∆
˜ < 0), with DA (∆)
˜ > DB (∆)
˜ for all ∆
˜ > 0 (resp. ∆
˜ < 0), then the
∆
corresponding revenue is lower than the highest revenue that can be achieved with demand
curve DA .
Proof.The last part is straightforward since demand DA dominates DB when evaluated
at the optimal best response for the latter demand curve, it must be strictly more profitable.
The other part is more subtle because, while it is true that the A demand is less attractive
at equal prices, the option remains of moving onto the part where A dominates B. We show
this is not profitable.
˜ > 0. It is straightforward to reverse the argument for ∆
˜ < 0.
We prove the result for ∆
˜ = 0, on
Consider Firm 1’s first-order profit derivative with respect to price, evaluated at ∆
(0) and this is positive under our assumption that
demand curve B It is p0 DB (0) + DB
˜ > 0 (which
profit is quasicocave and the maximizing price under demand curve B entails ∆
˜ = 0). But, Firm 1’s first-order profit derivative with respect
involves a higher price than at ∆
˜ = 0, on demand curve A is p0 DA (0) + D (0) = p0 DB (0) + D (0)
to price, evaluated at ∆
A
B
under our assumptions. This is therefore also positive, and so the profit maximizing price
˜ > 0. Now, since this means that the relevant section
under demand curve A also entails ∆
of the demand curve A is strictly dominated by demand curve B, we have that situation B
is more profitable.
3.1
Perfect information
We first use Lemma 1 above to characterize the equilibrium outcome under perfect information that will prevail if information about the new product is disclosed through advertising.
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Then a consumer purchases the new product if and only if
ε1 − p 1 − c 1 ≥ ε0 − p 0 − c 0
or equivalently
˜
r1 ≥ r0 − ∆.
It follows that demand for Firm 1 is given by
˜ =
D1 (∆)
a
b
˜ (f0 )dr0 .
[1 − F (r0 − ∆)]f
Since evaluations for the two products are I.I.d. we have D1 (0) = 12 . Results from Caplin and
Nalebuff (1991) may be used to establish the existence of a price equilibrium assuming the
match distirbution satisfy the increasing hazard rate condition. Furthermore, all assumptions
of Lemma 1 are satisfied. Thus the firm for which the visit cost is the lowest will charge the
lowest full price and thus a larger share of demand, even it charges the highest price.
3.2
No advertising
Here we characterize the equilibrium prices that ensue when neither firm advertises the
valuation information associated to Firm 1’s product. This describes an equilibrium when
either both firms are allowed to advertise full match information (and this is technologically
feasible, of course) and neither wishes to do so, or else only the new product can advertise this
information, and it does not wish to. We also refer to this case as “price only” information.
Note that if prices are not advertised they are correctly anticipated in equilibrium and,
since there is no cost of advertising, a firm might as well advertise its price. We must first
determine the allocation of consumers to firms in such a situation.
Suppose that the firms set observable prices, p0 and p1 . Then consider the problem of
a consumer who knows her valuation r0 (as we assume, these are known already) and must
decide whether or not to check out Firm 1. She knows that once she goes there and uncovers
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her true valuation, r1 , she will buy the other product zero, if
r1 − p 1 ≥ r 0 − p 0 − c 0 .
(1)
Note here that there is an extra cost in going to Firm 0 once the consumer is already at
Firm 1, which is a source of (hold-up) market power for Firm 1; however, there is a similar
power for Firm 0 stemming from the initial cost of going to 1. A priori, it is unclear which
way these forces will net out, but we show below that either firm may benefit from this
structure.
Hence, the expected benefit from going to Firm 1 to check it out is
b
(r1 − (r0 − p0 − c0 + p1 )) f (r1 ) dr1
r0 −p0 −c0 +p1
and the consumer will indeed visit if this benefit exceeds the search cost c1 . When interior,
the indifferent consumer who visits is then characterized by a critical value, r̂0 , that satisfies
b
(r1 − (r̂0 − p0 − c0 + p1 )) f (r1 ) dr1 = c1 ,
r̂0 −p0 −c0 +p1
and this value therefore determines an extensive margin in the sense that all consumers with
r0 > r̂0 never visit 1.1 It is convenient to define x̂ as the critical adjusted valuation. It is
defined by
x̂
1
(r1 − x̂) f (r1 )dr1 = c1 .
˜ + c1 .
which does not depend on prices set by firms and we have r̂0 = x̂ + p0 + c0 − p1 = x̂ + ∆
It is readily verified that the derivative of the right hand side with respect to c1 is F (x̂) > 0
so that less consumers visit Firm 1 if c1 increases.
Conditional on visiting, demand is determined by the “stay” condition (1). This means
˜ as
we can write Firm 1’s demand as a function of ∆
x̂+∆+c
˜ 1
˜
˜ − c1 f (r0 ) dr0 .
D1 (∆) =
1 − F r0 − ∆
a
1
If the resulting r̂0 is less than a, then no-one visits Firm 1. Conversely, if the r̂0 value exceeds b, then
everyone checks out Firm 1.
7
Similarly, Firm 0’s demand is 1 − D1 .
Candidate prices therefore solve the first-order conditions; for Firm i, it is given simply
by
pi =
Di
,
−Di
i = 0, 1,
(2)
where the prime denotes the own price derivative. A key property is that D0 = D1 , stemming
from the fact that each consumer buys one unit from one of the two firms. We may then
write the price difference as
p1 − p0 =
2D1 − 1
−D1
(3)
Note that demands are equal if and only if prices are equal. However, contrary to the perfect
information case it is no more true that D1 (0) = 12 , unless c1 = 0, in which case x̂ = b and
we are back in the perfect information case. Thus Lemma 1 may not be used in general. We
show below that both Lemmas 1 and 2 may be used to derive the equilibrium outcome if
valuations with the two products are i.i.d. uniform.
3.3
Equilibrium information disclosure
Suppose that we normalize a = 0 and set b = 1 and that product valuations are i.i.d.
uniform. We now provide a characterization of the equilibrium information disclosure.
3.3.1
Demands
We start by deriving demand curves under perfect information ant no information for a
uniform distribution of matches and show that they have appropriate properties in order to
apply lemmas 1 and 2.
We first determine demand when no information is disclosed. The first step is to find the
critical valuation, r̂0 , that constitutes the extensive margin of demand. Here x̂ = r̂0 − p0 −
c0 + p1 the critical adjusted valuation is defined by
1
(r1 − x̂) dr1 = c1 .
x̂
8
This simplifies to
x̂ = 1 −
√
2c1 ,
if c1 ≤ 1/2 and
x̂ =
1
− c1
2
˜ + c1 .
if c1 > 1/2. The marginal searcher’s identity is then given by r̂0 = x̂ + ∆
For demand, and restricting attention to case where demand is strictly between 0 and 1,
we have:
˜ =
D1 (∆)
min{r̂0 ,1}
˜ 1}
max{0,∆+c
˜ + c1 dr0 + max{0, ∆
˜ + c1 }
1 − r0 + ∆
˜ ≥ −c1 (which arises if the entrant’s price is low relative to the ”full price” – i.e., price
For ∆
plus search cost – of going to the incumbent) we have
˜
˜ = 1 + ∆,
D1 (∆)
2
if r̂0 ≤ 1 whether c1 is above or below 1/2, and
˜ + c1 )2 + ∆
˜ = 1 − 1 (∆
˜ + c1
D1 (∆)
2 2
if r̂0 > 1, a case that arrises only for c1 ≤ 12 .
˜ < −c1 , r̂0 ≤ 1 and we have
For ∆
˜ + c1 dr0
1 − r0 + ∆
0
2 r̂0
1
˜ + c1
= − 1 − r0 + ∆
2
0
2
˜ + c1
1+∆
.
= −c1 +
2
˜ =
D1 (∆)
r̂0
As shown above, with perfect information, demand facing Firm 1 is
1 (∆)
˜ =
D
a
b
˜ (f0 )dr0 ,
[1 − F (r0 − ∆)]f
9
which, for the uniform distribution, boils down to
˜ =
1 (∆)
D
˜ )
min(1+∆,1
˜ )
max(∆,0
˜
˜
[1 − r0 + ∆]dr0 + max ∆, 0
˜ ∈ (−1, 1) for both firms to have positive demands. Any best reply price for
Notice that ∆
Firm 1 must satisfy p1 ∈ [0, p0 + c0 − c1 − 1], where the upper bound is where Firm 1’s
demand disappears. Hence Firm 1’s profit is a continuous function that is defined over a
compact set, and so has a maximum.
˜ < 0, Firm 1’s demand becomes:
In the case ∆
˜ 2
˜ = (1 + ∆)
1 (∆)
D
2
˜ > 0, Firm 1’s demand is
For ∆
˜ =
D1 (∆)
˜2
1−∆
˜
+ ∆.
2
It is now straightforward to compare demands under no information and perfect infor˜ We first show that if ∆
˜ < 0, then demand for Firm 1
mation depending on the sign of ∆
is larger if information is revealed. We have
˜ −D
1 (∆)
˜ = 1 − 2c1 + ∆ −
D1 (∆)
2
˜2
∆
< 0.
= −
2
2
˜
1+∆
2
˜ ≥ −c1 . If ∆
˜ < −c1 , then
This expression holds for ∆
2
˜2
˜
˜ −D
1 (∆)
˜ = (∆ + c1 ) − ∆ < 0.
D1 (∆)
2
> 0. First note that if r̂0 > 1, then all consumers are perfectly informed
Now suppose ∆
when they make their purchase decision. However, without advertising, they take this decision after having already incurred c1 whereas with advertising they need to incur c1 if and
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only if she purchases good 1. Thus demand for the new product is clearly higher with no
information. For r̂0 ≤ 1
˜2
1−∆
1 − 2c1
+∆−
−∆
2
2
˜2
∆
>0
=
2
˜ −D
1 (∆)
˜ =
D1 (∆)
1 if and only if ∆
˜ > 0 and D1 < D
1 if and only if ∆
˙ < 0. Furthermore,
To sum up, D1 > D
(0) = 1. Thus Lemma 2 applies and, as we show below, it may be used
we have D1 (0) = D
1
to characterize the firms’ equilibrium disclosure strategies.
3.4
Equilibrium pricing and optimal information disclosure.
We start by using Lemma 1 to characterize the firm’s pricing behavior depending on whether
the visit cost for the new firm is above or below that of the incumbent. The analysis above
1 are
shows that both D1 and D
1
2
˜ = 0. We therefore know from Lemma
when evaluated at ∆
˜ > 0 if and only if
1 that, independently of the firm’s decision on information disclosure,; ∆
˜ < 0 if and only if c1 < c0 .
c0 > c1 and ∆
Consider first a situation where negative advertising is ruled out so that only the new firm
may disclose information about its own product. If c0 > c1 , then both the full information
˜ > 0. As shown in the previous section,
and no information price equilibria are such that ∆
this implies that the no information demand for Firm 1 dominates the full information
˜ > 0. Then Lemma 2 implies that it is profitable for Firm
demand and this is true for all ∆
1 to deviate from the full information equilibrium by not disclosing information while Firm
0 is keeping its price unchanged. Conversely, it is not optimal for Firm 1 to deviate from
the no information equilibrium because there is no price that would yield a higher revenue
with the full information demand even if Firm 1 changes its price while Firm 0 keeps its
price unchanged. Thus, if c0 > c1 then the new firm does not advertize product information
in equilibrium. Similar arguments may be used to show that if c0 < c1 , then the new firm
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advertises product information in equilibrium.
Now suppose that negative advertising is allowed. Note that since D0 = 1 − D1 , our
˜ > 0, demand for the incumbent is higher under perfect inresults above show that for ∆
˜ < 0, demand for the incumbent is higher with no information. Then
formation while for ∆
the arguments above may readily be adapted to establish that if co > c1 , then the incumbent would choose to resort to negative advertising in equilibrium and the entrant does not
advertise its product while if c0 < c1 the reverse happens (here we use the tie breaking rule
that when a firm is indifferent between disclosing information and not disclosing, it chooses
not to: indeed here disclosure by both firms would be an equilibrium since once one firm discloses information, the other is indifferent about information disclosure). Allowing negative
advertising is welfare enhancing to the extent that it improves the match of consumers with
products when c1 < c0 . However, if entree costs are too high, it may deter desirable entree.
Intuition for these results is as follows. If the cost of finding out about the new product
is small relative to the visit cost for the incumbent, most consumers check out Firm 1 before
making their purchase decision; this puts the new firm in a strong position because, when
they decide, they have sunk their visit cost c1 whereas they need to incur a visit cost c0 to
purchase the old product. If these consumers were fully informed before starting to search,
they would choose between the two products knowing that they would have to incur a visit
cost in any case. By contrast, if c1 is relatively high few consumers would choose to visit the
new comer if they have no prior information, even though they might like that new product
a lot. The entrant is therefore better off disclosing product information so that those who
really like the new product know it from the outset.
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4
Products with different qualities
The model may readily be reinterpreted as one where the visit cost is identical for both
firms but products have different qualities and quality comes in additively in the consumer’s
surplus. Suppose that the common visit cost is c and qualities are given by q0 for the existing
product and q1 for the new one. Then, if we define c1 = c and c0 = c + q1 − q0 , then the above
model may be reinterpreted as one where when c1 > c0 , the new product’s quality is lower
than that of the incumbent, whereas if c1 < c0 the new product’s quality is higher. Then
predictions are that a new firm with a high quality product chooses not to disclose match
information and would be negatively advertised by an incumbent if such a practice is allowed;
by contrast if the new product’s quality is low the entrant advertises match information and
the incumbent would not wish to negatively advertize.
One interesting extension would be one where the new product’s quality would be unknown to consumers before they visit the new firm. If the entrant knows quality perfectly
and consumers know this, then standard results would show that the entrant would always
advertise quality (see the persuasion game in Milgrom 1981 and Grossman, 1981). Then
the analysis would be as above. A more interesting case is one where consumers are unsure
whether firm’s are aware of the new product’s quality (a firm may be uncertain about the
demand for its new product). Then we conjecture an outcome where, if the new product’s
quality is low, then it would be negatively advertised by the incumbent while the entrant
would provide match information, whereas if it is high, it would be advertised by the entrant
and the incumbent would negatively advertise match information.
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