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Does Informative Advertising Increase Market Price?
An Experiment
Wilfred Amaldoss∗ Chuan He†
2011
∗Professor of Marketing, Fuqua School of Business, Duke University, Durham, NC 27708; email:[email protected].†Associate Professor of Marketing, Leeds School of Business, University of Colorado, Boulder,
CO, 80309; email: [email protected].
Abstract
Does Informative Advertising Increase Market Price?
An Experiment
Does informative advertising increase price or does it decrease price? The answer to this
empirical question is mixed and not conclusive, despite its significance for public policy and
marketing. Using the tools of experimental economics, we seek answer to this empirical
question in this paper. Our experiments constitute the first laboratory test of the effect of
informative advertising in a horizontally differentiated market. Study 1 shows that informa-
tive advertising can lead to higher prices if consumer valuations are low. Study 2, on the
other hand, points to the possibility that informative advertising can lead to lower prices if
consumer valuations are high. Thus these studies provide evidence on the causal relationship
between price and advertising and more importantly clarify the conditions under which we
may observe divergent results. Furthermore, our experimental analysis is the first to study
competition involving multiple firms (n = 7) in a horizontally differentiated market using
the spokes framework.
Keywords: Informative Advertising, Competition, Game Theory, Experimental Economics.
1. INTRODUCTION
In theory, advertising plays two important communication roles. Advertising informs
consumers about a product’s features including its price. Advertising persuades consumers
about a product’s superiority by influencing their perception of the product. One can argue
that persuasive advertising can increase the price of a product by raising consumers’ valuation
of the product. But informative advertising merely informs consumers about a product
without affecting consumers’ valuation of the product. Can informative advertising also
raise market price? Or, will informative advertising only lower prices by intensifying price
competition. Although a clear answer to this empirical question has significant public policy
and managerial implications, it still remains elusive.
On one hand, researchers have shown that the prices of heavily advertised products are
higher (Nickell and Metcalf 1978, Krishnamurthi and Raj 1985, Connor and Peterson 1992).
A potential explanation for this finding is that the heavily advertised products are of higher
quality, suggesting that unobserved factors rather than advertising levels can account for the
finding. On the other hand, Benham (1972) presents evidence suggesting that informative
advertising could lead to lower prices. Specifically, on comparing the prices of eyeglasses in
U.S. states where advertising was prohibited in the 1960s against the prices for the same
product in states where advertising was allowed, Benham found that market prices were
lower in states that allowed price advertising. In another field study, Cady (1976) examined
the prices of prescription drugs in 1970 when legal restrictions on retail advertising varied
across U.S. states. As in Benham’s natural experiment, retail prices were lower in markets
where advertising was permitted. Although these field studies may lead one to believe that
informative advertising causes prices to be lower, Milyo and Waldfogel (1999) note that these
investigations ignore the possible endogeneity of the regulations and that they do not control
for omitted firm-specific and market-specific factors in their single cross-sectional data. To
address this shortcoming, Milyo and Waldfogel used longitudinal data to analyze how lifting
the prohibition for price advertising on May 13, 1996 affected the average market price for
liquor products in Rhode Island. Unlike the previous field studies, they did not see any
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significant reduction in consumer prices for a full year after the change in regulation. Thus
the empirical evidence on the effect of informative advertising on price is not conclusive.
Instead of providing any further empirical evidence on this issue, Amaldoss and He (2010)
have recently attempted to examine this issue using a game-theoretic model. They consider a
horizontally differentiated market where consumers’ tastes are diverse and advertising merely
informs consumers about product characteristics including price. Their analysis shows that
market price increases with informative advertising for low valued products, although price
decreases with advertising when products are highly valued.1 Thus they suggest that adver-
tising can cause price to increase as well as decrease by merely informing consumers without
invoking its persuasive power. To gain a glimpse into the intuition for this result note that if
the base valuation of products is low, then some of the informed consumers can purchase any
product in their consideration set whereas others may be able to purchase at best only one
product. The consequent reduced substitutability of competing products and softens price
competition. Furthermore, the marginal consumer who is indifferent between buying any
of the products in her consideration set is less sensitive to a price cut in comparison to the
marginal consumer who is indifferent between buying the only product in her consideration
set or buying nothing. In this context, informative advertising increases the relative impor-
tance of consumers who are less sensitive to price, and thereby encourages firms to charge a
higher price. Next consider the situation where consumers’ valuations are high enough that
all informed consumers can gain a surplus by buying any product in their consideration set.
In this situation, informative advertising increases the substitutability of competing products
and thereby raises price elasticity of demand. Hence price decreases with advertising reach
when products are highly valued.
While the theoretical analysis of Amaldoss and He (2010) is interesting, its usefulness is
limited as its predictions have not been empirically validated. The need for empirical vali-
dation is especially strong for two important reasons. First, the theoretical analysis assumes
that each firm understands how a change in its price will directly affect its demand, and
1In their model consumers are distributed on a plane along different taste dimensions (spokes), each firmdirectly competes with every other firm in the market (nonlocal competition) and the market can be partiallycovered.
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also how all the competing firms will respond to its price change and thereby indirectly in-
fluence its demand. However, prior empirical research suggests that when faced with several
competitors, firms may overreact to competition in the sense that they act far more aggres-
sively than what noncooperative game theory would anticipate (e.g., Huck et al. 1999 and
2000). Thus it is not clear that agents will precisely vary prices as predicted by their analy-
sis. Second, the spokes framework used in the theoretical analysis has not been empirically
validated. Even more generally, as we discuss later, the predictive accuracy of horizontal
differentiation models has been scrutinized in a very limited way.
Motivation for experimental investigation. One potential avenue to further study the
effect of informative advertising on price is to analyze field data along the lines of Milyo
and Waldfogel (1999) for an even more protracted period. But such data is typically not
available to marketing researchers, and it is prohibitively costly to conduct such a field study.
Moreover, in a field setting it is difficult to exogenously vary the level of advertising level
as well as randomly assign firms to treatment and then study the effect of advertising on
price. In fact, this is the major weakness of the field studies of Benham (1972) and Cady
(1976). However, it is possible to exercise this level of control in a laboratory setting and
establish a causal link between advertising level and price. Next, economic agents typically
attain equilibrium through trial and error rather than mere introspection (Camerer and Ho
1999). Even Milyo and Waldfogel (1999) wonder whether their null result would hold if the
Rhode Island liquor market had been tracked for a longer period. In a laboratory setting,
it is feasible to track the behavior of firms over multiple iterations of a game and explore
whether equilibration is feasible (see also Wang and Krishna 2006, Lim and Ho 2007, Ho and
Zhang 2008). These advantages motivate us to use a theory-guided laboratory experiment
to understand the effect of advertising on price.
As noted earlier, prior experimental research on horizontal differentiation models is very
limited. This is particularly striking because of the extensive body of theoretical research on
product differentiation spawned by the seminal work of Hotelling (1929) and Salop (1979).
Much of the extant experimental research has focused attention on location choices rather
than price competition (Brown-Kruse Cronshaw and Shenk 1993, Brown-Kruse and Shenk
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2003). A common finding in this work is that players tend to differentiate less in their
location choices. In a working paper, Barreda et al. (2000) report that when allowed to
choose both location and price, players differentiate less than the normative prediction. Prior
theoretical work on the role of imperfect information in a horizontally differentiated market
is limited and it includes Grossman and Shapiro (1984) and Soberman (2004). To the best
of our knowledge, prior experimental literature has not investigated the effect of informative
advertising on price in a horizontally differentiated market despite its significance for both
public policy and marketing.
Overview of results. The theoretical analysis of Amaldoss and He (2010) focuses on the
limiting case when the number of competing firms is sufficiently large (that is, n tends to
infinity). In an experimental investigation, we can only study cases where the number of
competing firms is small. Hence to facilitate our experimental investigation, we first analyze
the effect of informative advertising on price when a small number of firms (2 < n <
∞) compete in a horizontally differentiated market. The results of this analysis form the
normative benchmark for evaluating our experimental results.
A key insight of the normative analysis is that the causal relationship between informa-
tive advertising and price is moderated by consumer valuation. In particular, if consumer
valuations are low, market price increases with the reach of informative advertising. But if
consumer valuations are high, market price decreases with the reach of informative adver-
tising. Study 1 examines whether market price does increase with informative advertising
when consumer valuation is low. The observed prices increased with informative advertising
as predicted by the normative analysis. Next we examine whether informative advertising
can also have the opposite effect. Specifically, Study 2 explores whether market price can
decrease with informative advertising when consumer valuation is high. In Study 2, the
actual prices declined as the level of informative advertising increased.
While the experimental results are consistent with the qualitative predictions of the equi-
librium solution, we observe a pattern in pricing behavior not anticipated by the equilibrium
analysis. Specifically, we observed very aggressive undercutting of prices in Study 2 but not
in Study 1. The direction and magnitude of the departures from the normative benchmarks
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raise the possibility that agents may not be fully anticipating competitive response to their
pricing decisions. For instance, in Study 2 a consumer can purchase any product in her
consideration set because of the high valuation of products, and a price cut by a firm will
attract the marginal consumer to purchase its products. In this context, if the firm antici-
pates the competing firms also to offer a lower price in response to its price cut, then it may
not venture to lower its price. But if the competing firms fail to fully anticipate competitive
reaction to their pricing decisions, they may engage in very aggressive price competition.
Without communication, it is indeed difficult for firms to de-escalate from intense price
competition as we see in Study 2. In Study 1, some consumers can purchase any product
in their consideration but some cannot do so because the products have low valuation. The
reduced substitutability of products deters firms from aggressively cutting their prices and
to a certain extent also buffers them against the negative consequences of poor strategic
foresight. Even in Study 1 the observed prices are lower than the equilibrium predictions.
However, now the departures from equilibrium point predictions are not as large as that
observed in Study 2.
These experiments also help us to better appreciate the prior field research on how infor-
mative advertising influences market price. It is interesting to note that, notwithstanding
the methodological criticisms of the field studies, qualitatively similar results can be ob-
tained in the laboratory. In particular, we see that advertising can have divergent effects
on price. More importantly, the experiments suggest that consumer valuation can moderate
the observed divergent effects of informative advertising on price.
The rest of the paper is organized as follows. Section 2 outlines the theoretical framework
and predictions. Section 3 describes Study 1 which investigates whether price could increase
with the level of informative advertising. Section 4 reports Study 2 which explores whether
the opposite results can also be induced by informative advertising. Finally, Section 4
summarizes the findings and concludes the research.
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2. THEORETICAL PREDICTIONS
As reported in prior literature, the effect of informative advertising on prices is divergent
and furthermore not conclusive (e.g., Nickel and Metcalf 1978, Benham 1972, Milyo and
Waldfogel 1999). While it is possible to advance different context specific explanations for
the divergent results, we search for evidence whether the divergent results can be induced by
informative advertising. Moreover, we strive to probe into the factor that might moderate
the causal relationship between price and informative advertising. Toward this goal, in this
section we introduce the model that guides our investigation. Although the structure of
our model closely follows Amaldoss and He (2010), it does not assume that the number of
competing firms is arbitrarily large. Specifically, we focus on the case where the number
of competing firms is finite and small. This case is particularly relevant for any empirical
analysis as the number of competing firms in any market is finite. Next we provide an
overview of the model, outline the approach for partitioning consumers into segments and
deriving the aggregate demand, and discuss the theoretical predictions.
Model Overview. We examine a market with n horizontally differentiated firms. Each
firm offers a product, and informs consumers about its characteristics and price through
advertising. Denote the reach of a firm’s advertising by φ (0 ≤ φ ≤ 1). The cost of reaching
φ fraction of the market is αφ2, where α is a scale parameter representing the advertising
technology. The marginal cost of production is a constant and assumed to be zero.
A unit mass of consumers are uniformly distributed on N spokes. N can be interpreted
as the number of varieties (flavors) that consumers desire. Of the N spokes, 2 ≤ n ≤ N are
occupied in that firms offer those product varieties. In this spokes network, a consumer who
prefers variety i (i = 1, 2, . . . N) and is located at distance x ∈[0, 1
2
]from the origin of spoke
i, is denoted by (li, x). Note that x = 12
is at the center of the spokes network and x = 0 at
the origin of a spoke. The familiar Hotelling model (Hotelling 1929) is a special case of the
spokes network when N = n = 2. Figure 1 illustrates a market with eight spokes (N = 8)
and seven firms (n = 7). Consumers have the same valuation, v, for all products.
It is assumed that consumers are completely uninformed about a product unless they are
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Fig. 1. An Illustrative Spokes Model: A market with eight spokes (N = 8) and seven firms(n = 7)
li
exposed to its advertisement. Furthermore, each consumer considers at most two products at
the time of purchase. All consumers consider their local product and it is their first preferred
product. The probability of being informed about it is φ. The second preferred product in
the consideration set is one of the nonlocal products of which the consumer is informed.
Thus the composition of the consideration set is endogenous to the model. The assumption
that consumers prefer at most two products helps to obtain pure strategy equilibrium and
is consistent with the notion that consumers have finite consideration set (Nedungadi 1990).
Now we outline the approach to deriving the demand for firm j’s product for any given price
profile (p1, p2, . . . , pn), relegating the detailed derivation to the appendix. Note that Firm j’s
product could be the first preferred (local) product or the second preferred (nonlocal) product
in a consumer’s consideration set, and that consumers could be informed or uniformed about
it. Hence, we can partition consumers who purchase product j into four segments as shown
in Figure 2. In Segment 1, Firm j’s product is the first preferred product in the consideration
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Fig. 2. Partitioning of Consumers into Four Segments
j is available and known
j is the first preferred product
j is the second preferred product
k (the second preferred product) is available
k (second preferred)is not available
k (first preferred)is not available k (the first preferred product)
is available
k is known k is not known
Segment 1Consumers are awareof their first preferred product j and the second preferred product k
Already included in the demand formulation of
Segment 1
Not possible
Segment 2Consumers are aware of their first preferred product jand are not aware of their second preferred product k
Segment 3Consumers are awareof their second preferred product jand their first preferred product k is not available
Segment 4Consumers are aware of their second preferred product jand are not aware of their first preferred product k
k is not knownk is known
set. Consumers in this segment are also informed of their second preferred product k. In
Segment 2, Firm j’s product is the first preferred product in the consideration set. But now
consumers are uninformed about their second preferred even though it is available in the
market. In Segment 3, Firm j’s product is the second preferred product in the consideration
set. The first preferred product of the consumers in this segment is not produced by any of
the firms. Finally, in Segment 4 product j is the second preferred product in the consideration
set, but now consumers are uninformed of their first preferred product.2
As shown in the appendix, we obtain the demand for firm j’s product by adding the
demand from all the four segments of consumers. Then using this demand function we
compute the firm j’s profits and derive the equilibrium price.
Model Predictions. To understand the effect of advertising reach on price, we first focus
2At this point, it is useful to clarify why it is not possible to find a consumer for whom product j is thefirst preferred product and her second preferred product is not available (See Figure 2). As the number ofproducts available in the market is n ≥ 2 and n − 1 of these products are equally likely to be the secondpreferred product in the consideration set of the consumer located at (lj , x), some second preferred productwill be available for this consumer.
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on the case where consumer valuation is low. Specifically, we consider the case where for
some consumers the valuation is lower than the traveling cost and the purchase price of the
second preferred product, that is 12<
v−pjt
< 1. These consumers can still purchase their
first preferred product. On examining the equilibrium price corresponding to this case, we
have the following prediction.
Prediction 1 When consumer valuations are low, equilibrium price can increase with ad-
vertising reach.
We prove this claim in the Appendix. The intuition for Prediction 1 is as follows. As
consumers become better informed, some consumer segments expand while others contract.
Specifically, the proportion of consumers whose first and second preferred products are both
available (Segment 1) and consumers whose first preferred product is non-existent (Segment
3) increases in size, while the proportion of consumers who are unaware of the existence of
their first or second preferred product (Segment 2 and Segment 4) declines in size. Further-
more, being better informed helps consumers to find their desired product variety and gives
firms an opportunity to charge a higher price (anti-competitive effect). At the same time,
informative advertising also makes consumers more aware of competing product alternatives
and thereby increase price competition (pro-competitive effect). The anti-competitive effect
dominates when consumer valuation is low. Put differently, although a higher advertising
reach increases the proportion of consumers who are aware of both of their preferred prod-
ucts, price elasticity can decrease. This is because when valuation is low, some consumers
do not find it worthwhile to engage in comparison shopping regardless of awareness. Con-
sequently, the substitutability between the first and second preferred products is lower. In
this context, higher advertising reach increases the proportion of consumers who are aware
of one of their preferred products only. Hence, when consumer valuations are low, higher
advertising reach reduces price elasticity. For an example, consider the case when advertis-
ing reach is low with φ = 0.1, v = $1.2, N = 8, n = 7, t = 1, α = $0.1. In this case, the
symmetric pure strategy equilibrium price is 39.12 cents. Now if advertising reach rises to
φ = 0.5, the equilibrium price increases to 45.82 cents. The proof for this claim can be seen
in the Appendix (Claim 1). Next we explore whether this finding can be reversed.
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When consumer valuation is high, all consumers gain a surplus by buying any product
in their consideration set implying that valuation is more than the traveling cost and the
purchase price of even the second preferred product, that isv−pjt≥ 1. On analyzing the
equilibrium price for this case, we have the following prediction.
Prediction 2 When consumer valuations are sufficiently high, price decreases with adver-
tising reach.
As discussed earlier, informative advertising creates both an anti-competitive effect and a
pro-competitive effect. Together, Prediction 1 and Prediction 2 clarify that the net influence
of these two forces is moderated by consumer valuation. In particular, when consumer
valuation is high the marginal consumer is willing to consider all the product alternatives
she is aware of and this strengthens the pro-competitive effect. That is, when consumer
valuation is sufficiently high, a higher level advertising reach increases the substitutability
between the first and second preferred products, raises price elasticity and lowers prices. For
an illustration of the equilibrium prediction, consider the low φ condition where φ = 0.2,
v = $10, N = 8, n = 7, and α = $1. In equilibrium, price should be 61.20 dimes in
this condition. Now if we increase advertising reach to φ = 0.5 keeping all other variables
constant, the equilibrium price reduces to 23.04 dimes. The proof for this claim is presented
in the Appendix (Claim 2). Next, we proceed to subject these theoretical predictions to an
experimental test.
STUDY 1
The purpose of Study 1 is to assess whether price increases with informative advertising
when consumer valuations are low (Proposition 1). To make causal inference about the
relationship between advertising level and price, we need to exogenously vary the level of
advertising and study its effect on observed price. Furthermore, we need to randomly assign
firms to the different levels of advertising so that all other variables are kept constant. We
exercise this level of control in our experiment. The experimental results provide evidence
that informative advertising can increase price. On further comparing the observed prices
10
against the normative benchmarks, we notice small but significant departures from the equi-
librium predictions. Although the equilibrium solution is the same for all players, we observe
heterogeneity in the behavior of individual participants. We also see trends in the prices over
the several iterations of the game raising the possibility that our participants might have
engaged in adaptive learning. Next we outline the experimental design and then discuss this
findings.
Experimental Design. Treating the level of advertising reach as a between-participant
variable, we ran two groups where the level of advertising reach was low (φ = 0.1) and
another two groups where it was high (φ = 0.5). The other variables of the model were held
constant in all the four groups: N = 8, n = 7, t = 1, v = $1.2, and α = $0.1. We chose this
set of parameters because it leads to a significant rise in equilibrium price if advertising reach
increases from 0.1 to 0.5 (as shown in the previous section). Each group was comprised of
fourteen participants. In each trial, the fourteen participants were randomly divided into two
oligopolies of seven participants. By varying the composition of each oligopoly from trial to
trial and not revealing the identity of the players, we obtained data on multiple replications
of our game (see also Carare, Haruvy and Prasad 2007, Amaldoss and Jain 2005).
Procedure. We invited graduate and undergraduate students to participate in a decision
making study promising them a show-up fee and additional monetary reward contingent on
their performance. On average, participants earned $28.47. As the focus of our experimental
investigation is on the pricing behavior of firms, we abstract away from the demand side of
the market by using the aggregate demand function derived from our consumer model (see
Selten and Apesteguia 2005 for a similar design). Hence, participants played the role of
firms, while the computer played the role of consumers. The detailed instructions provided
to participants can be seen in the Appendix.
Although computer played the role of consumers as per the demand function, we still
provided participants a verbal description of the market. The market was described as a
town with eight streets emanating from the center of the town. At the end of seven of
these streets there is a store, but there is no store in one of the streets. All the stores offer
products of the same quality level. Each street is half a unit long with an equal number
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of consumers residing in each street. Furthermore, consumers are spread uniformly along
each street. Consumers in each street prefer the product that is available in their local
store. In addition to this product, their consideration set may include another product from
the set of products whose advertisements they have seen. In the low φ treatment, there
is a 10% chance that consumers are aware of the advertisement of a store, whereas in the
high φ treatment the probability of consumers being aware of a store’s product is 50%. It
costs money for consumer to travel from their house to a store. It costs less to travel to a
store if the consumer resides in the same street where the store is located, but more if the
consumer has to travel to another street to purchase its product. The travel cost is equal
to the distance traveled. The total cost of purchasing a product thus includes the price of
the product and the travel cost. Now depending on the total cost of purchasing each of the
products in her consideration set, a consumer first decides whether or not to purchase any
product. If she decides to buy, then she selects the store from which to buy its product.
Note that we can project the demand for a given store’s product if we know the focal
firm’s price and the expected average price of all other competing firms (see Equation (A–14)
in the Appendix). We used this simplification to help our participants appreciate the profit
implications of their price and the likely average price of their competitors. At the beginning
of each trial, each participant was asked to indicate her product’s price and the likely average
price of all the other products in the market. The prices were expressed in cents. Based
on these two inputs, the likely profits of the participant were computed using the simplified
demand formulation. After viewing the likely profits, the participant could revise her price
as well as the expected average price of her competitors. It was clarified to each participant
that her competitors might not behave as predicted by her. Furthermore, her actual earnings
only depended on the actual prices charged by her competitors, not her expected average
price. That is, a participant’s likely profits would be close to her actual profits only to
the extent her expectation about competitors’ average price was accurate. The calculator
thus served as a mere computational tool without providing any guidance on normative
behavior. By providing this calculator, we are able to rule out poor computational skills as
a potential explanation for our results. Perhaps, seeing the likely profit impact of a pricing
12
decision (conditional on their belief about competitors’ actions) might help our participants
to think more about how to improve their profits. Furthermore, as noted earlier, it helps us
to focus our investigation on the supply side while abstracting away from the demand side
of the market (Selten and Apesteguia 2005). After all the players confirmed their prices,
the computer displayed the results of the trial: own prices, own profits, average price of
competitors, average profits of competitors.
To familiarize participants with the structure of the game, they were asked to play three
practice trials for which they were not compensated. If they had any questions about the
instructions, the supervisor answered them. After all the participants became familiar with
the structure of the game, they played thirty five actual trials. Participants played the game
anonymously in the sense that neither their identity nor the identities of the competing
players were revealed. This anonymity, coupled with random assignments of participants to
the two oligopolies of seven firms in each trial, reduced scope for building reputation over
the course of the experiment. The goal of our participants was to maximize their individual
profits over several replications of the game. At the end of the experiment, their cumulative
earnings in the experiment were converted into dollars and paid.3
Results. We begin our analysis of the experimental data by examining the aggregate
behavior of our participants. Later we investigate the variation in the behavior of individual
participants, and analyze the trends in prices over the course of the experiment. The second
row of Table 1 presents the average prices observed in Group 1 and Group 2 corresponding to
each treatment of Study 1 and also compares them to the point predictions of the equilibrium
solution. Below, we report the major results.
Experimental Result 1 On average, the observed prices increased with advertising reach
when consumer valuation was low.
3In our experiment, we did not provide any financial incentive for participants to truthfully reveal theirexpectations. Such an incentive has to be in addition to the profits earned in a trial, and it may add alayer of complexity to an already complicated game and potentially impede comprehension. Thus in ourexperiment, it is quite possible that after gaining experience a participant could enter a random number asher expectation, and yet set her price to maximize actual profits (rather than the expected profits displayedby the calculator). Thus, although the calculator is at the disposal of participants, they can choose not touse it. Thus, we only tracked the actual prices and profits, not the expectations. As we discuss later, we caninfer each participant’s expectations about competitors’ prices from her price.
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Support: In each of the 35 trials of the experiment, we observed the prices in two oligopolies.
Across the two groups of each treatment, we have accumulated 280 data points (2 oligopolies
× 35 trials × 2 groups × 2 treatments = 280 data points). On analyzing this body of data,
we observe that the average market price increased from 38.592 to 42.681 cents as the reach
of advertising increased from 0.1 to 0.5. We can reject the null hypothesis that these two
prices are the same (t = 25.70, p < 0.0001). A nonparametric analysis based on the Wilcoxon
test also rejects the possibility that all these 280 data points are drawn from the same dis-
tribution (Z = 14.14, p < 0.0001). Instead of focusing on the average price in each duopoly,
if we focus on the average price of each individual participant over the course of thirty five
trials and perform a nonparametric analysis on the resulting 56 data points, we obtain sim-
ilar results. Specifically, we can reject the null hypothesis that the average prices of the 56
participants across the two treatments were drawn from the same distribution (Wilcoxon
Z = 5.82, p < 0.0001). If we conduct repeated measures analysis using the data on price
charged by each individual participant in each trial, we again find that price increased with
advertising reach (F(1,54) = 61.62, p < 0.0001). Next we compare the observed prices against
the point predictions of the equilibrium solution.
Experimental Result 2 The observed average prices are statistically different from the
point predictions.
In theory, the price should be 39.115 when φ = 0.1. On average, the participants charged
38.749 and 38.435 in Group 1 and Group 2, respectively. Though these observed prices look
very close to the equilibrium prediction, the differences from the equilibrium prediction are
still statistically significant (Group 1: t = 2.08, p < 0.001; Group 2: t = 4.7, p < 0.001). In
equilibrium, price should rise to 45.824 if φ = 0.5. In actuality, the average prices observed
in Group 1 and Group 2 were 42.591 and 42.771, respectively. We can reject the null
hypothesis that the observed prices and equilibrium price are the same (Group 1: t = 19.70,
p < 0.0001; Group 2: t = 20.49, p < 0.0001). Thus, although the observed average prices
are directionally consistent with predictions of the equilibrium solution, they are statistically
different from the point predictions.
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Experimental Result 3 We see evidence of time trends in the prices over the several it-
erations of the game.
Support: On examining the average price of duopolies, we note that both the main effect of
trials (F(34,1890) = 1.53, p < 0.026) and its interaction effect with the level of advertising reach
(F(34,1890) = 1.51, p < 0.031) are marginally significant. It is easy to see the trends in Figure
3 (top panel), which presents the average price in the duopolies over blocks of five trials. A
nonparametric analysis based on the ranks of the average prices of the oligopolies also rejects
the hypothesis that prices are the same over the course of the experiment (p < 0.0001).
On further probing into the trends in the prices charged by individual participants using
repeated measures analysis, we note the trends observed in the data are significant (main
effect: F(34,1836) = 2.12, p < 0.001; interaction effect: F(34,1836) = 2.08, p < 0.001). The
significant interaction effect raises the possibility that participants might have adaptively
learned how to set prices over the course of the experiment but perhaps in different ways in
the two treatments (see Camerer and Ho 1999 for a discussion on adaptive learning).
Experimental Result 4 Although participants are symmetric, their average prices are het-
erogeneous.
Support: Across the two groups of a treatment, we have data on the behavior of twenty
eight participants. The bottom panel of Figure 3 presents the distribution of average price
charged by each of these individual participants. When advertising reach is low, the average
price ranges all the way from 37.41 to 43.37. But when reach is higher, the average price
charged ranges from 39.47 to 48.54. It is easy to see a shift in the empirical distribution
of prices as advertising reach increases. Using a nonparametric test, we can reject the null
hypothesis that the average prices charged by participants in the two treatments are drawn
from the same distribution (Wilcoxon Z = 5.82, p < 0.0001). Thus although the participants
are symmetric in theory, they do not set the same price. Such individual level variation is
commonly observed in experimental tests of games (e.g Amaldoss and He 2009)
Discussion. Consistent with Prediction 1, observed prices increased as advertising reach
increased. Interestingly, our participants did not aggressively cut their prices compared
15
to the equilibrium predictions. What can explain this departure from prior experimental
research on competitive games (e.g., Huck 2000)? Note that when consumer valuation is low,
for some consumers the products in their consideration set are substitutable but not so for
others. This substitutability will be further hampered if consumer are not informed of all the
products in the products in their consideration set because of low advertising reach. Hence,
while setting price each participant in Study 1 implicitly weighs the benefits of aggressively
cutting her price to attract some customers away from the competing products (Segment 1)
against the opportunity to charge a higher price to her captive market (Segments 2, 3 and
4). Perhaps the presence of a captive market deterred our participants from charging prices
far lower than the equilibrium prediction.
To further probe into this speculation, we estimated each participant’s belief about oppo-
nents’ average price that is consistent with the best response function and the price charged
by the participant in each trial. On average, the estimated expected price of competitors
was 15.93 and it is much lower that the actually price observed in the low φ treatment.
Similarly, in the high φ treatment the expected price of competitors was 23.35 which is again
lower than the observed price. Thus in Study 1, even though players held very pessimistic
beliefs about competitors prices it was still profitable not to aggressively undercut the price
because of the existence of some consumers in Segments 2, 3 and 4.
As the focus of Prediction 1 is on the effect of advertising reach on price, the analysis and
discussion thus far were centered on prices. In our experiment, we did observe profits. On
average, profits increased as the reach of advertising increased (t = 22.8, p < 0.001). At the
level of individual participants, we see variation in profits, but we can reject the hypothesis
that the average profits of individual participants in the two treatments are drawn from the
same distribution (Wilcoxon Z = 6.41, p < 0.001). Thus, as one may anticipate, the effect
on profits is qualitatively similar to that observed in prices. Having assessed the predictive
accuracy of Prediction 1, we next test Prediction 2.
16
STUDY 2
In Study 2, we seek answer to the question: Is it possible for informative advertising to
cause firms to lower price? According to Prediction 2, the answer is yes. It is useful to
note that this pattern of result is exactly the opposite of the finding reported in Study 1.
In theory, when the valuations are high, consumers could potentially buy either product in
their consideration set. In such a case, when advertising reach increases, the size of the
consumer segment that is aware of both its preferred products grows and the resulting price
competition lowers price. Next we describe experimental procedure and discuss the results
of Study 2.
Experimental Design. Like the previous experiment, Study 2 was designed to focus on
the supply side of the market while abstracting away from the demand side. Consumer valu-
ation was set at v = 10 so that a consumer could purchase any product in her consideration
set. Using a between-participants design, we ran two groups where the level of advertising
reach was low (φ = 0.2) and another two groups where it was high (φ = 0.5). In all these
groups we kept the other model parameters constant, namely N = 8, n = 7, and α = 1.
Each group was comprised of fourteen participants and they were randomly divided in each
trial into two oligopolies of seven participants. The experimental sessions lasted for 35 trials,
excluding three practice trials.
Procedure. We recruited a fresh set of 56 participants for this study and they were
compensated as in the previous study. On average, the participants in this study earned
$28.95. The experimental protocol was similar to the previous study except that we now
used a different set of model parameters.
As in the previous study, in each trial each participant was asked to indicate her product’s
price and the likely average price of all the competitors in the market. The prices were
expressed in dimes. Based on these two prices and the simplified demand function, the
computer displayed the expected profits. The derivation of the simplified demand function
is presented in the Appendix. It was highlighted to each participant that her competitors
might not behave as predicted by her. Further, a participant’s expected profits would be
17
close to actual profits only to the extent her expectation about competitors’ average price
was accurate. Without providing any guidance on equilibrium behavior, the calculator thus
helped our participants to avoid computational error and better understand the likely profit
impact of their decisions. After all the players confirmed their decisions, the results of the
trial were announced and the experiment progressed to the next trial. At the end of 35 trials,
the participants were paid according to their cumulative earnings, debriefed and dismissed.
Results. Table 1 presents the average prices observed in Group 1 and Group 2 for the
two levels of reach and the corresponding equilibrium predictions (see third row). Next we
discuss the major experimental findings.
Experimental Result 5 The average observed price decreased as advertising level increased.
Support. We investigated the aggregate behavior of duopolies using the average price
observed in each of the 280 oligopolies in the study (2 oligopolies × 35 trials × 2 groups
× 2 treatments = 280). On average, price decreased from 41.418 to 21.332 dimes when the
reach of advertising increased from 0.2 to 0.5. We can easily reject the null hypothesis that
these two prices are the same (t = 35.44, p < 0.001). A nonparametric analysis of the 280
data points also leads to the same conclusion (Wilcoxon Z = 14.44, p < 0.001). Thus in
contrast to Study 1, in the current study prices decreased with advertising reach. Instead
of treating each oligopoly as the unit of observation, if we treat the average price of each
individual participant as the unit of observation and perform a Wilcoxon rank sums test,
we find that advertising reach has a significant effect (Wilcoxon Z = 5.96, p < 0.0001). A
repeated measures analysis of the prices set by individual participants in each trial also leads
to the same conclusion (F(1,54) = 132.94, p < 0.0001). Next we compare the observed prices
against the equilibrium point predictions.
Experimental Result 6 The observed prices are statistically different from the equilibrium
point predictions.
According to the equilibrium solution, the price should be 61.203 dimes when φ = 0.2. On
average, the participants charged 42.521 and 40.315 in Group 1 and Group 2, respectively.
18
These observed prices are substantially lower than the predicted prices (Group 1: t = 46.69,
p < 0.001; Group 2: t = 41.42, p < 0.001). If φ = 0.5, the equilibrium price should
decline to 23.039 dimes. In actuality, the average prices of Group 1 and Group 2 were
22.877 and 19.788, respectively. We can reject the null hypothesis that the observed prices
and equilibrium prices are the same in Group 2, but not in Group 1 (Group 1: t = 0.22,
p > 0.80; Group 2: t = 6.62, p < 0.001). Now we proceed to examine whether there were
any trends in the prices set by our participants over the course of the experiment.
Experimental Result 7 In Study 2, we see significant trends in prices
Support. The average price in the oligopolies varied over the trials of the experiment but
in different ways in the two treatments (main effect of trials: F(34,1890) = 4.30, p < 0.001;
interaction effect with ad reach:F(34,1890) = 2.03, p < 0.001 ). We obtain similar results if
we conduct a repeated measures analysis using the data on the prices charged by individual
participants in each trial (main effect of trials: F(34,1836) = 7.65, p < 0.001; interaction
effect:F(34,1836) = 3.62, p < 0.001). The top panel of Figure 4 presents the trends in the
average prices over seven blocks of five trials each. On studying further the behavior of
individual participants, we have the following result.
Experimental Result 8 Although our participants are symmetric, the average price charged
by individual participants are heterogeneous.
Support. The bottom panel of Figure 4 presents the distribution of average prices charged
by each of the twenty eight participants in the two treatments. When advertising reach is
low, the average price charged extends from 28.94 to 55.54. But when reach is higher, the
average price ranges from 17.18 to 55.91. In Figure 4, it is easier to see a leftward shift
in the empirical distribution of prices as advertising reach increased (Wilcoxon Z = 5.96,
p < 0.0001).
Discussion. In contrast to Study 1, prices decreased in the current study when advertising
reach increased. Furthermore, we see very large departures from the point predictions in
Study 2, suggesting that our participants aggressively cut their prices in the latter study. To
19
understand the behavioral basis for this outcome, note that a consumer can gain a surplus
by buying any product in her consideration set as now the valuations are high enough.
Consequently, the products in a consumer’s consideration set are substitutable and hence
a firm can gain share from all its competitors by lowering its price. Furthermore, if the
participant fails to see that its competitors can also cut their prices, then it may trigger
intense price competition. In the absence of any communication among our participants, it
becomes difficult to de-escalate such aggressive behavior and consequently we observe prices
that are far lower than the equilibrium predictions. Our Study 2 results are consistent with
the overreaction to competition seen in Huck et al. (2000).4
As in the previous study, we also estimated the average price that each participant ex-
pected her competitors to charge in a given trial. In the low φ treatment, we find that
the expected average price of competitors was 21.632. Despite such pessimistic views of
their competitors’ prices, participants still charged on average 41.418. This is because, even
though the valuation is high enough that consumers could buy either product in their con-
sideration set, all consumers may not be aware of both the products in their consideration
set because of the low and this makes it less profitable to aggressively cut prices. But when
the reach of advertising grows larger this deterrent effect should weaken. Indeed, in the high
φ treatment, the expected average price of competitors was 19.625 and the price charged
by participants was 21.332. Thus in the high φ treatment the deterrent effect was almost
negligible. This additional analysis helps us to understand how participant’s belief’s come
to influence the market price.
For completeness, we briefly outline the profits observed in Study 2. On average, the
profits decreased when the reach of advertising increased (t = 14.53, p < 0.001). Although
we observe heterogeneity in the average profits of individuals participants, we can easily
reject the hypothesis that the profits in the two treatments are from the same distribution
4For example, in their experiment the observed prices were on average 52.17 though the equilibriumprediction was 76.5 (see p. 47). Their experiments studied oligopolies of three, four or five players; andin general cooperative plays decreased as the number of competitors increased. In our games, as there areseven players in each oligopoly, it reduces further the likelihood of cooperation. While Huck et al. 1999 and2000 test the predictions of Cournot and Bertrand competition using an aggregate demand formulation, weexamine price competition in a horizontally differentiated market.
20
(Wilcoxon Z = 6.41, p < 0.001). As in the previous study, the effect on profits is qualitatively
similar to that observed in prices. Next we test the effect of diverse consumers’ taste on
market price.
In sum, Study 1 and Study 2 show that the effect of advertising on price could vary
with consumer valuation of goods. As noted earlier, in Benham’s natural experiment the
prices of eyeglasses were found to be substantially lower in states that permitted advertising
compared to states that prohibited restrictions. As eyeglasses improve vision as well as how
one looks, consumers are likely to place a high value on eyeglasses (Blumenthal 1983). If
they did so, then Benham’s empirical findings are directionally consistent with Prediction
2. Also consistent with Prediction 1, heavily advertised low valuation goods like cornflakes
are priced higher (Nickell and Metcalf 1978; see also Farris and Reibstein 1979). As we can
only speculate about the valuations of goods covered in these empirical studies, any claim
of even correlational support is open for debate. These prior studies are also vulnerable
to other standard criticisms of cross-sectional analysis. Our laboratory experiment, on the
other hand, is a direct test of the theoretical predictions, and the results are directionally
consistent with the equilibrium solution.
4. CONCLUSIONS
Prior empirical research reports divergent results on the effects of advertising on price. For
example, heavily advertised breakfast cereals were high priced (Nickell and Metcalf 1978; see
also Farris and Reibstein 1979, and Boulding et al. 1994), but prices of eyeglasses declined
with advertising (Benham 1972). A potential way to resolve such divergent findings is to
conduct new field experiments (e.g. Wang and Krishna 2006, Tucker and Zhang 2009), take
advantage of natural experiments (e.g., Milyo and Waldfogel 1999) or use more sophisti-
cated estimation methods (e.g., Ackerberg 2003). Alternatively, one can conduct a tightly
controlled laboratory experiment which is grounded in a game-theoretic model. We pursued
the latter path in the current paper.
Study 1 shows that if consumer valuations are low then market price increases with the
reach of informative advertising. On the contrary, Study 2 establishes that if consumer
21
valuations are high, price declines with advertising. We obtain this result because when
valuation is low the products in a consumer’s consideration set are less substitutable. Fur-
thermore, price sensitivity varies across the different segments of consumers that contribute
to a firm’s demand. Furthermore, when consumer valuation is low, informative advertising
increases the relative importance of consumers who are less sensitive to price, and thereby
motivates firms to charge a higher price. But when consumer valuation is sufficiently high,
all informed consumers obtain a surplus by purchasing any product in their consideration
set. This induces firms to attract the marginal consumer by cutting their prices and conse-
quently market price declines. These experimental findings are reassuring in an important
way: Notwithstanding the methodological criticisms of prior empirical findings on the effects
of advertising, qualitatively similar results can be obtained in the laboratory. Furthermore,
our experiments demonstrate that consumer valuation can moderate the effect of informative
advertising on price.
Our experiments also offer an insight into when we may observe very aggressive under-
cutting of price. The observed prices are close to the equilibrium predictions in Study 1,
but not in Study 2. Why do we observe such a pattern of results? Note that while setting
price, each firm in Study 1 implicitly weighs the prospect of cutting its price (and attracting
some customers away from its competitor) against the benefit of charging a higher price to
her captive market and forgoing some of the competitive market. In this situation, if prod-
ucts are less substitutable because of low valuation or low advertising reach, it deters firms
from engaging in aggressive undercutting of prices. If this deterrent force weakens, we may
observe a downward spiral in prices. In the absence of communication, it is difficult for an
individual firm in an oligopoly to unilaterally extricate itself from aggressive undercutting
of prices. Interestingly, our participants’ beliefs about competitors’ prices are even harsher
than the market reality. Consequently in Study 2 we observe substantial departures from
the equilibrium price.
In several product categories consumers’ taste are very diverse and firms also offer a wide
variety of products. This raises an interesting empirical question: How does diversity in
consumers’ tastes affect market price? Extant empirical literature is yet to answer this
22
question for an important reason. Although it is easy to measure the variety of products
available in a market, it is difficult to reliably assess the variety of products that consumers
seek in a product category. Consequently, it is an even greater empirical challenge to study
the relationship between diversity in consumers’ tastes and price in markets where consumers
are not fully informed about all the competing products. However, it is possible to use our
experimental protocol to study this phenomenon in the laboratory. This will be a fruitful
avenue for further research.
More broadly, experimental investigations could become a useful complement to the em-
pirical literature on the effects of advertising. While laboratory studies have a high degree of
internal validity, one needs to exercise caution in extrapolating the findings to a field setting.
Cross-sectional field studies, on the other hand, guarantee external validity although it is
more challenging to establish causal relationships with such data. Field experiments can
overcome this issue but such an investigation is often costly and impossible to implement in
some settings. A judicious use of these different methods can augment our understanding of
markets (e.g. Krishna and Unver 2008).
The spokes model used in this paper is a very attractive framework for studying spatial
competition and it has several advantages over the traditional models of horizontal differen-
tiation. In contrast to the circle model (Salop 1979), the spokes model allows products and
firms to be symmetric without the need to change the location of the incumbents when a
new firm enters the market. Furthermore, each firm is in direct competition with all other
products in the market. The market also is not assumed to be fully covered and the extent
of coverage actually depends on the number of competing firms and consumer valuations.
Moreover, as demonstrated in this paper, the spokes model has both descriptive validity and
analytical tractability. These benefits should stimulate researchers to apply this framework
to study new issues in horizontally differentiated markets with a large number of competing
firms.
23
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26
Table 1.
EquilibriumGroup 1 Group 2 Overall Prediction
Low φ 38.749 38.435 38.592 39.115High φ 42.591 42.771 42.681 45.824Low φ 42.521 40.315 41.418 61.203High φ 22.877 19.788 21.332 23.039
Study 2 High
Observed Average PriceStudy Consumer Valuation Treatment
Study 1 Low
Note: The prices corresponding to Study 1 are expressed in cents, whereas the prices corresponding to Study
2 are expressed in dimes.
27
Fig. 3. Study 1
0246810121416182037-38 38-39 39-40 40-41 41-42 42-43 43-44 44-45 45-46 46-47 47-48 48-49Number of Participants Average Price of Individual Participants
Study 1: Individual Differences Low φHigh φ32343638404244
1 2 3 4 5 6 7Average Price Blocks of Five TrialsStudy 1: Trends in Prices Low φHigh φ
28
Fig. 4. Study 2
02468101214161817-20 20-23 23-26 26-29 29-32 32-35 35-38 38-41 41-44 44-47 47-50 50-53 53-56Number of Participants Average Price of Individual Participants
Study 2: Individual Differences Low φHigh φ15202530354045505560
1 2 3 4 5 6 7Average Price Blocks of Five TrialsStudy 2: Trends in Prices Low φHigh φ
29
APPENDIX
In this appendix, we derive the aggregate demand function and equilibrium price. We then
provide proofs to the theoretical predictions and claims (numerical examples) presented in
the paper. The appendix is organized as follows. We first derive the aggregate demand,
and the equilibrium price for the case where consumer valuations are low (Lemma 1). Next,
we show that price can increase with advertising reach when consumer valuations are low
(Prediction 1). We then derive the equilibrium point predictions for Study 1 (Claim 1).
Turning attention the case where consumer valuations are high, we derive the equilibrium
price (Lemma 2), show that price increases decreases with advertising reach (Prediction 2),
and then derive the equilibrium point predictions for Study 2 (Claim 2).
We derive the demand for firm j, j ∈ {1, . . . , n}, for any given price profile (p1, p2, . . . , pn).
Based on product availability and information (see Figure 2 on page 8), we can classify
consumers into four relevant segments as we described below. To eliminate the trivial cases,
we assumev−pjt
> 12
and|pk−pj |
t≤ 1.
Segment 1. Firm j’s product is the local product and hence the first preferred product
in the consideration set of a consumer in this group. The probability that a consumer is
aware of her first preferred product j is φ. Any nonlocal product about which the consumer
is informed could be the second preferred product in her consideration set. Thus the second
preferred product in the consideration set, namely k 6= j where k ∈ {1, . . . , n}, is drawn from
the set of products to which an individual consumer has been exposed through advertising.
The joint probability that the consideration set of a consumer located on spoke lj includes
products j and k is given by 1n−1φ
[1−
(1− φ̂
)n−1].5 The density of such consumers is 2
N,
and the demand from this group of consumers is given by:
2
N
1
n− 1φ
[1−
(1− φ̂
)n−1] ∑k 6=j,k∈{1,...,n}
(1
2+pk − pj
2t
). (A–1)
Segment 2. Firm j’s product is the first preferred product in the consideration set of
a consumer in this group also. However, the consumer is uninformed about their second
5Please see Amaldoss and He (2010) for a proof.
30
preferred product. In this case the probability that the consumer located on spoke lj only
considers product j is given by φ(
1− φ̂)n−1
. The demand from this group of consumers is
given by1
Nφ(1− φ̂)n−1. (A–2)
Next we turn attention to cases where firm j’s product is the second preferred product
in the consideration sets of consumers. As the number of products available in the market
is n ≥ 2 and n − 1 of these products are equally likely to be the second preferred product
in the consideration set of the consumer located at (lj, x), some second preferred product
will always be available for the consumer at (lj, x). However, consumers may be uninformed
about their second preferred products.
Segment 3. The first preferred product (variety) k preferred by consumers in this group is
not produced by any of the n firms, and product j is the second preferred product in their
consideration set. The demand from this group of consumers is given by
2NN−nn
[1− (1− φ)
(1− φ̂
)n−1] (v−pjt− 1
2
)for 1
2<
v−pjt
< 1
1NN−nn
[1− (1− φ)
(1− φ̂
)n−1]for
v−pjt≥ 1
(A–3)
The region 12<
v−pjt
< 1 corresponds to the situation where consumers always derive positive
surplus from purchasing their first preferred product but the valuation is not high enough for
some consumers to obtain positive surplus from purchasing their second preferred product.
By contrast, whenv−pjt≥ 1, consumers derive positive surplus from purchasing both their
first and second preferred products.
Segment 4. Consumers in this segment are uninformed of their first preferred product and
product j is the second preferred product in their consideration set. The demand from this
group of consumers is given by
2N
1−φ̂n−1
[1− (1− φ)
(1− φ̂
)n−2] ∑k 6=j,k∈{1,...,n}
(v−pjt− 1
2
)for 1
2<
v−pjt
< 1
2N
1−φ̂n−1
[1− (1− φ)
(1− φ̂
)n−2] ∑k 6=j,k∈{1,...,n}
12
forv−pjt≥ 1
(A–4)
31
When consumer valuations are low (that is, 12<
v−pjt
< 1), the demand function for firm
j’s product is given by
qj =
1Nφ
[1−
(1− φ̂
)n−1](1 + 1
n−1
n∑i=1
pi−pjt
)+ 1
Nφ(1− φ̂)n−1
+ 2N
N−nn
[1− (1− φ)
(1− φ̂
)n−1]+(
1− φ̂)[
1− (1− φ)(
1− φ̂)n−2]
(v−pj
t− 1
2
) (A–5)
We assume that firms set their prices simultaneously and focus on symmetric pure strategy
equilibrium.
When consumer valuations are sufficiently high (i.e.,v−pjt≥ 1), the demand function for
firm j’s product is given by
qj =
1Nφ
[1−
(1− φ̂
)n−1](1 + 1
n−1
n∑i=1
pi−pjt
)+ 1
Nφ(
1− φ̂)n−1
+ 1N
N−nn
[1− (1− φ)
(1− φ̂
)n−1]+(
1− φ̂)[
1− (1− φ)(
1− φ̂)n−2]
(A–6)
Lemma 1 When 12<
v−pjt
< 1, the equilibrium price is
p∗j =N (2v − t) [1− (1− φ)n]− 2nφ (v − t)
4N [1− (1− φ)n]− nφ (1− φ)n−1 − 3nφ. (A–7)
Proof. Using the demand function given in Equation (A–5) and the cost functionA (φ;α) =
αφ2, we obtain the following profits for firm j:
πj = pj
1Nφ
[1−
(1− φ̂
)n−1](1 + 1
n−1
n∑i=1
pi−pjt
)+ 1
Nφ(1− φ̂)n−1
+ 2N
N−nn
[1− (1− φ)
(1− φ̂
)n−1]+(
1− φ̂)[
1− (1− φ)(
1− φ̂)n−2]
(v−pj
t− 1
2
)− αφ2 (A–8)
Using the first-order condition∂πj
∂pj= 0 and noting that in the symmetric pure strategy
equilibrium, p∗j = p∗k and φ = φ̂, we solve for the optimal price and find that p∗j is as given
32
in Equation (A–7).
Prediction 1 When consumer valuations are low, (that is, 12<
v−pjt
< 1), equilibrium
price can increase with advertising reach.
Proof. When consumer valuations are low, the equilibrium price is given by Equation
(A–7). It follows that
∂p∗
∂φ= − n
(1− φ)2{
4N [1− (1− φ)n]− 3nφ− nφ (1− φ)n−1}2 ·
N (1− φ)2 (2v − 5t) +N (1− φ)2n (2v − t)
+ (1− φ)n
2N ((3t− 2v) + φ (2nt+ 2v − 5t))
−φ2 (n− 1) (5Nt− 2nt− 2v (N − n))
(A–9)
The case when N = 8 and n = 7 forms the basis for the experimental investigations presented
in the paper. For this case, we have:
limφ→0
∂p∗
∂φ= −(21v − 33t)
196> 0 for v ≤ 33
21t
limφ→1
∂p∗
∂φ= −(112v − 280t)
121> 0 (A–10)
Similarly, we can establish the comparative statics for any given n and N . For a more
general proof, readers are referred to Amaldoss and He (2010).
Claim 1 When v = $1.2, N = 8, n = 7, t = 1, α = $0.1, the symmetric pure strategy
equilibrium price is 39.12 cents if φ = 0.1. The equilibrium price increases to 45.82 cents
when advertising reach rises to φ = 0.5.
On substituting v = $1.2, N = 8, n = 7, t = 1, α = $0.1, and φ = 0.1 into Equation
(A–7), we have p∗j = 39.12 cents. The equilibrium price increases further to 45.82 cents when
advertising reach rises to φ = 0.5.
Note that in equilibrium when φ = 0.1, we havev−pjt
= 0.809; and similarly when φ = 0.5
we obtainv−pjt
= 0.742. Thus in both treatments 12<
v−pjt
< 1.
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Lemma 2 Whenv−pjt≥ 1, the equilibrium price is
p∗j =Nt (1− φ)
nφ
1− (1− φ)n
1− φ− (1− φ)n. (A–11)
Proof. On inserting firm j’s demand given in Equation (A–6) and the cost function
A (φ;α) = αφ2 into the profit function, we can express firm j’s profits as:
πj = pj
1Nφ
[1−
(1− φ̂
)n−1](1 + 1
n−1
n∑i=1
pi−pjt
)+ 1
Nφ(
1− φ̂)n−1
+ 1N
N−nn
[1− (1− φ)
(1− φ̂
)n−1]+(
1− φ̂)[
1− (1− φ)(
1− φ̂)n−2]
− αφ2 (A–12)
Solving∂πj
∂pj= 0 and noting that in the symmetric pure strategy equilibrium, p∗j = p∗k and
φ = φ̂, we obtain p∗j as given in Equation (A–11).
Prediction 2 When consumer valuations are sufficiently high (i.e.,v−pjt≥ 1), price
decreases with advertising reach.
Proof. When consumer valuations are high, the equilibrium price is given by Equation
(A–11). Therefore, we obtain:
∂p∗
∂φ=
∂
∂φ
{Nt [1− (1− φ)n]
nφ[1− (1− φ)n−1
]}
= Nt
[2 (1− φ)− (n− 1)φ2 − (1− φ)n
](1− φ)n − (1− φ)2
nφ2 (1− φ)2[1− (1− φ)n−1
]2 (A–13)
Note that the denominator of ∂p∗
∂φis positive for φ ∈ (0, 1). It can be shown that the
numerator is always negative for any φ ∈ (0, 1). Therefore, it follows that ∂p∗
∂φ< 0.
Claim 2 When v = $10, N = 8, n = 7, and α = $1, the symmetric pure strategy equilibrium
price is 61.20 dimes if φ = 0.2. The equilibrium price p∗ reduces to 23.04 dimes when
advertising reach increases to φ = 0.5.
Inserting v = $10, N = 8, n = 7, α = $1, and φ = 0.2 into Equation (A–11), we obtain
p∗j = 61.20 dimes. The equilibrium price p∗j reduces to 23.04 dimes when advertising reach
34
increases to φ = 0.5.
Also in equilibrium,v−pjt
is 3.88 when φ = 0.2, and it becomes 7.7 when φ = 0.5. Thus,
in both treatmentsv−pjt
> 1.
SIMPLIFIED EXPECTED DEMAND
When consumer valuation is low, the demand function given in Equation (A–5) can be
simplified as follows to obtain the expected demand of firm j:
qj =
1Nφ
[1−
(1− φ̂
)n−1](1 +
p−j−pjt
)+ 1
Nφ(1− φ̂)n−1
+ 2N
N−nn
[1− (1− φ)
(1− φ̂
)n−1]+(
1− φ̂)[
1− (1− φ)(
1− φ̂)n−2]
(v−pj
t− 1
2
) (A–14)
Thus, we can project the demand for a given store’s product if we know the focal firm’s
price and the average price of all other competing firms. In our experimental investigation,
we used this simplification to help our participants appreciate the profit implications of their
price and the likely average price of their competitors.
When consumer valuation is high, the demand function given in Equation (A–6) can be
further simplified to obtain the following expected demand of firm j:
qj =
1Nφ
[1−
(1− φ̂
)n−1](1 +
p−j−pjt
)+ 1
Nφ(
1− φ̂)n−1
+ 1N
N−nn
[1− (1− φ)
(1− φ̂
)n−1]+(
1− φ̂)[
1− (1− φ)(
1− φ̂)n−2]
(A–15)
35