In their application to “branding,” they propose as an example that some consumers
might confuse such brand labeling as “California Burgundy” for some cheap California
wine with the certified labeling “Burgundy” that applies to quality wines from the French
Burgundy region. In the four-product setting above, products (0,0) and (1,0) would be
two cheap California wines with comparable physical characteristics but the producer
might try to differentiate one of them (say (1,0)) by calling it California Burgundy. Prod-
ucts (0,1) and (1,1) would be two wines characterized by a quality difference so that only
product (1,1) can claim a certification label such as Burgundy. Formally, assume that the
producer of the generic cheap California wine, x
2
¼0, can choose a message
m 2 CB, DR
fg
, where CB stands for “California Burgundy” and DR stands for
“Delicious Red” (following the example in
Mullainathan et al., 2008). By contrast,
the wine producer in the alternative category, x
2
¼1, chooses a message m 2 B, T
fg
if it is (1,1) and m 2 T
fg
if it is (0,1), where B stands for Burgundy and T stands for Table.
The key point here is that only product (1,1) can use message B. The coarse thinker,
however, not knowing x
2
, confuses messages B or CB. She only realizes that x
1
¼1 when
reading such a message but is unsure whether this certifies a high quality or not.
If the consumer is not a coarse thinker, Mullainathan et al. call her a Bayesian, in which
case she knows which category of product she is dealing with, so she knows x
2
.Now
assume x
2
¼0. If a Bayesian consumer is endowed with beliefs about the product’s char-
acteristics x
1
, she updates her beliefs after observing the message m, depending on the equi-
librium messages she expects from products (0,0) and (0,1). Her willingness to pay,
however, does not depend on these beliefs. It is rmðÞ¼u for all m 2 CR, DR
fg
.Bycon-
trast, a coarse thinker believes that m ¼CB might certify quality in the event that x
2
¼1.
Assume now, as in Mullainathan et al., that the probability assigned by a coarse thinking
consumer to x
2
¼1 is exogenously fixed at some level strictly between zero and one.
66
A producer of cheap California wine will be able to charge a higher price to that consumer
if it announces m ¼CB, rather than m ¼DR. Mullainathan et al. show that, if the con-
sumer population comprises some Bayesians and some coarse thinkers, then it is optimal
for a monopoly producer of cheap California wine to propose two brands: Delicious
Red that is purchased by Bayesian consumers and California Burgundy that is purchased
by coarse thinkers where the latter brand is sold at a higher price than the former.
66
Mullainathan et al. (2008) also mention the possibility that coarse thinkers could be more sophisticated and
update their beliefs in view of the message they receive. For instance, if they believe that product (1,1) is
much more unlikely than product (0,1), then they would drastically revise the probability that x
2
¼1
downward after observing m ¼CB (assuming that m ¼CB is product (1,1)’s equilibrium strategy).
Lauga (2012) explores a similar idea in a setting where consumers are confused about the past experience
they have had with a product. When they remember a favorable experience, they cannot tell whether it
was their actual experience or whether they have been influenced by some advertising campaign. They
update their beliefs about the product quality accordingly, taking into account the firm’s equilibrium
advertising behavior.
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Advertising in Markets