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Conspicuous Consumption and Sophisticated Thinking
Wilfred AmaldossSanjay Jain
March 2003
Wilfred Amaldoss is an Assistant Professor of Marketing at the Fuqua School of Business, DukeUniversity, Durham, NC 27708, email: [email protected]. Sanjay Jain is an AssistantProfessor of Marketing, Robert H. Smith School of Business, University of Maryland, College Park,MD 20742, email: [email protected]. Both have contributed equally to the paper.
Conspicuous Consumption and Sophisticated Thinking
Abstract
Consumers purchase conspicuous goods to satisfy not just material needs but also socialneeds such as prestige. In an attempt to meet these social needs, producers of conspicuousgoods like cars, perfumes, and watches highlight the exclusivity of their products. In thispaper, we study how consumers’ purchase decisions are affected by the desire for exclusivityand conformity. Toward this goal, we propose a model of conspicuous consumption usingthe rational expectations framework. Contrary to some intuition, we find the desire forexclusivity can increase the demand for a good as price rises, when there is a segment ofconsumers who are (weakly) conformists. A laboratory test lends support for this modelprediction and also for the rational expectations framework. With the help of SophisticatedEWA model proposed by Camerer, Ho and Chong (2002), we attempt to understand howconsumers learn to play such games and also unravel the level of sophisticated thinkingamong our subjects. Our results show that the expectations based on the SEWA modelclosely tracks the stated expectation of subjects as well as their purchase decisions.
Keywords: Strategic thinking, Experimental Economics, Game Theory, RationalExpectations,Conspicuous Consumption, Prestige Pricing.
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1 Introduction
It is generally accepted that the decision to purchase a “conspicuous” product depends not
only on the material needs satisfied by the product, but also on social needs such as prestige
(see for example Belk 1988, Grubb and Grathwohl 1967). Recognizing such social needs,
firms highlight the exclusivity of their products. For example, in an effort to maintain
its exclusive image, Ferrari promises not to produce more than 4300 vehicles every year,
despite a more than two-year waiting list for its cars (Betts 2002). The strategy of limiting
production quantity is also practiced in categories such as coins, watches and jewelry. Other
firms use exclusive distribution channels to restrict the availability of their products. For
instance, fearing that wide availability could hurt its exclusive image, Christian Dior sued
supermarkets for carrying its products (Marketing Week, July 3, 1997).1 These strategies
are in part driven by the belief that some consumers would find a product less valuable if
it is widely available, and that exclusivity will enable the firm to charge a high price and
potentially earn higher profits.2
In this paper, we examine how consumers’ purchase decisions are affected by the desire for
exclusivity or conformity. Toward this goal, we develop a model of conspicuous consumption
using the rational expectations framework. We capture consumers’ desire for exclusivity and
conformity by allowing the utility derived from a product to depend not only on its intrinsic
value but also on consumption externality. Consistent with the classic work of Leibenstien
(1950), we model snobs as consumers whose utility from a product decreases as more people
consume the same product. For example, a BMW in every driveway could dilute the value of
the car to potential buyers (cf. Bagwell and Bernheim 1996).3 In a similar fashion, we model
followers as consumers whose utility from a product increases as more people consume the
product (Ross, Bierbrauer and Hoffman 1976, Jones 1984, also see Becker 1991 for a similar
formulation).4 For instance, often teenagers view MTV because their friends watch it (Sun
and Lull 1986). We also see evidence of conformism in the purchase of books, toys and
1Luxury good manufacturers are also advised not to sell their products over the internet since this willdilute their image (Marketing, August 24, 2000).
2Research has shown that rarity of products can increase the perceived value of products even for itemssuch as cookies (see Worchel, Lee and Adewole 1975).
3See also Nagel and Holden (2002, p.92) who say that exclusivity adds to the objective value of a product.4Leibenstein (1950) uses the term bandwagon effect to describe what we call the follower-effect. We prefer
to use the terms followers and conformist (Bagwell and Bernheim 1996) since bandwagon effects are oftenassociated with adoption in large blocks (see for example Farrell and Saloner 1985) which is not our focushere.
2
garments.5
Our theoretical analysis suggests that if the market is comprised of only snobs or fol-
lowers, then consumers would not demand more as price increases. However, if the market
is comprised of both snobs and followers, then snobs might buy more as price increases.6
It is commonly believed that exclusivity leads to higher prices. We show that this belief is
not always valid. Corroborating evidence for these results is found in an empirical study of
visible status goods purchased by women (Chao and Schor 1998).
At the heart of our model is the concept of rational expectations, and sophisticated
thinking. However, the empirical evidence in support of rational expectations is mixed.
Individual-level studies comparing forecasts made by subjects of stochastic variables against
the actual outcomes suggest that people might not be good at forming rational expectations
(Schmalansee 1976, Garner 1982, Williams 1987, Smith et al. 1988). On the the other hand,
experimental asset markets seem to converge toward the predictions of rational expectations
equilibria (Sunder 1995). Further, prior research has not attempted to probe the expectations
that guide the decisions as it is difficult to measure expectations, especially in a field setting
(Leiderman 1980, Dwyer 1981, and Mishkin 1981). Thus, we have limited knowledge of
how rational expectations shape decisions in strategic contexts. To fill this gap in our
understanding, we conducted a controlled laboratory study where it is possible to track both
the behavior and beliefs of decision makers. To the best of our knowledge, our empirical
investigation is the first to track both expectations and outcomes in a rational expectations
game (see Sunder 1995 for a survey of experimental research on rational expectations models).
Then, using the Sophisticated EWA (SEWA) model proposed by Camerer, Ho and Chong
(2002), we attempt to unravel the level of sophisticated thinking among our subjects.
The experimental results are qualitatively consistent with the model predictions for both
snobs and followers. On average, the expectations are closely aligned with the actual out-
comes and the equilibrium solution. But we observe variation in the expectations of indi-
vidual subjects. The experimental investigation shows that snobs buy more as price rises,
5The innate desire to conform is often used to explain the persistence of social customs. Similar argumentsare also advanced to explain participation in trade unions (Naylor and Cripps 1993), and fair wages (Romer1984). An alternative explanation for conformism is herd behavior caused by Bayesian learning (Bikchandaniet al. 1992). See Frank (1985) for a discussion of the socio-biological bases of human needs such as desirefor exclusivity and conformity.
6In fact, we can observe an upward-sloping demand curve for snobs even if there is a segment of consumerswhose utilities are unaffected by consumption externalities. In other words, the result goes through if themarket is comprised of snobs and consumers who are (weakly) conformists.
3
even though the products have neither quality differences nor any signal value. Furthermore,
we find some support for the rational expectations framework at the aggregate level. We
also show that the Sophisticated EWA model proposed by Camerer, Ho and Chong (2002)
closely tracks the subjects’ stated expectations and purchase decisions thereby providing
useful insights into the learning process of our subjects.
Related Literature and Contributions. Researchers have for long studied the role
of products as a means of self expression (see, e.g., Belk 1988, Grubb and Grathwohl 1967).
This research has identified the existence of two competing social needs among consumers:
a need for uniqueness and a countervailing need for similarity (Brewer 1991, Fromkin and
Snyder 1980). These needs form the basis of what we refer to as the desire for exclusivity
and conformity. Prior research examines from a psychological perspective how these needs
influence consumer choice processes (Lynn 1991, Snyder 1992, Simonson and Nowlis 2000).
Unlike our research, the behavioral literature does not examine the effect of social factors on
aggregate demand or firm behavior.
Our research is related to the work in economics that incorporates social factors in formal
economic analysis. Liebenstein (1950) drew the attention of economists to the importance
of social factors in consumption (see also Veblen 1899). Becker (1991) used conformism to
explain why similar restaurants might eventually experience vastly different sales pattern.
He showed that in equilibrium the demand curve for followers could be upward sloping,
though the equilibrium is not stable. There are several signaling models on conspicuous con-
sumption. For instance, Bernheim (1994) showed that when status is sufficiently important
relative to intrinsic utility, then many individuals conform to a single standard of behavior,
despite heterogeneous underlying preferences. Bagwell and Bernheim (1996) and Corneo
and Jeanne (1997a) have argued that conspicuous consumption is a consequence of the de-
sire of consumers to signal their wealth. However, Corneo and Jeanne (1997a) find that the
demand curve for a conspicuous product is downward sloping for snobs. The intuition for
this result is that if more consumers buy the good, then the signal value of the good must
decrease for snobs. Consequently, the firm needs to decrease prices in order to increase de-
mand, implying a downward-sloping demand curve. Thus, they show that under a signaling
framework, snobbish behavior cannot lead to an upward-sloping demand curve. Another
stream of research which studies consumption externality is the research on network goods
(see for example, Besen and Farrell 1994, Katz and Shapiro 1994). However, the motivation
4
for consumption externality in this literature is technological, rather than social.
Our research is also related to the literature on strategic thinking and learning in games.
Our theoretical model, like standard non cooperative game theoretic analyses, assumes that
all players think strategically. Consequently, consumers should instantaneously be able
to arrive at the equilibrium solution. A large body of experimental data shows that eco-
nomic agents rarely reach the equilibrium solution immediately through sheer introspection.
Rather, if boundedly rational agents ever reach equilibrium, they converge toward it over
time. In prior literature on learning in games, beliefs have been operationalized as a function
of past actions as in fictitious play. This implies, in contrast to much of the theoretical lit-
erature, that players do not think in a sophisticated way. Recent research has attempted to
bridge this gap between theoretical models based on strategic thinking and learning models
(see Camerer 2001 for an excellent review of strategic thinking in games). Camerer, Ho and
Chong (2002) develop a learning that allows a fraction of consumers to be strategic thinkers.
We use their model to understand how subjects learn to play the game and also uncover the
level of sophisticated thinking among our subjects.
Our research is different from the prior research in several important ways. First, in
contrast to the signaling models in economics, we model snobs and followers using a con-
sumption externality. Second, unlike the extant literature we show that snobs can have an
upward-sloping demand curve and also examine the impact of social factors on equilibrium
prices and profits. Third, we demonstrate the existence of an upward sloping demand curve
for snobs in the laboratory. Fourth, unlike prior experimental research, we tracked both the
actions and beliefs of the subjects. This enables us to test both the consequences as well as
the assumptions of the rational expectations model. We show that stated expectations are
consistent with rational expectations equilibrium. Further, we show that such anticipatory
beliefs of subjects could be accurately predicted using the Sophisticated EWA model.
The rest of the paper is organized as follows. In §2, we describe a model of conspicuous
consumption and examine its implications. §3 discusses a laboratory test of the model.
§4 discusses Sophisticated EWA model and how subjects came to conform to equilibrium
behavior. Finally, §5 concludes the paper.
5
2 Model
We assume that the market consists of two groups of consumers: snobs and followers. Snobs
value exclusivity, and consequently the utility derived from a product depends not only on
its base value, but also on the expected number of people who will buy the product. Thus,
the expected (indirect) utility of purchasing a product is given by:
U(ze, p) = v − p− g(ze) (1)
where v is the base valuation, p is the price for the product, and ze is the expected number
of buyers. Assume that g(0) = 0, g(ze) ≥ 0 ∀ze > 0, g(1) < ∞, and g′(·) ≥ 07. These
conditions capture an important characteristic of snobs: They value the product less as
more people buy it. We assume that each consumer only buys at most one unit of the
conspicuous good at a time. Such an assumption is tenable for many conspicuous goods
like cars. Suppose that v is distributed across the populations according to a continuous
distribution F1(·) with pdf f1(·). We assume that F1(·) is common knowledge.
Similarly, we model followers as consumers who are not looking for exclusivity, but instead
like to follow others. The expected (indirect) utility of such a consumer is given by:
U(ze, p) = v − p + h(ze) (2)
where h(0) = 0, h(1) < ∞, h(·) ≥ 0 and h′ ≥ 0. Therefore, followers value a product more
as more people purchase it. We assume that the value distribution for followers is given by
F2(·) with pdf f2(·). Note that we allow the two groups to have different value distributions.8
The proportion of snobs in the market is β ∈ [0, 1] while (1− β) consumers are assumed
to be followers. We normalize the total market size to be 1. Given the above formulation,
the number of snobs who will buy the product is given by:
x = β (1− F1(p + g(ze))) (3)
7Note that we are assuming that this group of consumers are “weakly” snobbish. If g(·) ≡ 0 then theconsumers do not care as to how many others buy the product.
8An alternate formulation would be to assume that snobs dislike followers adopting the product andtherefore g(ze) should be replaced by g(ye) where ye is the expected number of followers buying the product.Also, it is possible that followers look at the snobs as their aspirational group and therefore, h(ze) shouldbe replaced by h(xe) where xe is the expected number of snobs that will buy the product. This alternateformulation is consistent with the notion of reference groups and less so with the notions of exclusivity andconformity, which is the main focus of this paper. Also, this alternate formulation would require consumersto have more precise estimates of segmentwise demand, which may be more difficult. Nevertheless, thequalitative implications of our results would remain unchanged if we use this alternate formulation.
6
where ze is the expected sales of the product. Similarly, the number of followers who buy
the product is given by:
y = (1− β) (1− F2(p− h(ze))) (4)
Using (3) and (4), we obtain the total demand z for the product:
z = β (1− F1(p + g(ze))) + (1− β) (1− F2(p− h(ze))) (5)
Each consumer is assumed to have the same expectation about the number of people
who will buy the product. Further, these expectations are rational, implying that they are
correct in equilibrium. Such assumptions are fairly common in the literature (see for example
Becker 1991, Katz and Shapiro 1985). Thus,
z − ze = 0. (6)
Using (5) and (6) we can derive the rational expectations equilibrium. The relevant equation
is:
Λ1(z) = z − β (1− F1(p + g(z))) + (1− β) (1− F2(p− h(z))) = 0. (7)
Equation (7) implicitly describes the total demand z(p) under the rational expectations
condition. Note that if (7) defines a unique z for a given p, then from (4) and (5) we can see
that for any given price p, there will be unique numbers x and y which will define the sales
to the snobs and the followers, respectively. The next lemma establishes the condition for
existence and uniqueness.
Lemma 1 There exists a rational expectations equilibrium that satisfies (7). The equilibrium
is unique if and only if:.
h′(z)f2[p− h(z)] <1 + βf1[p + g(z)]g′(z)
(1− β)(8)
where z is the equilibrium total demand at price p.
Proofs of all the results are in Appendix A.
The condition included in the lemma places a useful restriction on the size of the con-
formity effect. If the conformity effect is very large, then the system can become unstable
leading to multiple possible solutions.9 But, if there are no followers then there always exists
9This is due to the possibility of bandwagons in which all consumers decide to either buy or not buy theproduct.
7
a unique rational expectations equilibrium. It is useful to note that the condition places no
upper bound on the magnitude of the exclusivity effect.10 For the remainder of the analysis,
we will assume that the condition specified in Lemma 1 holds.
Effect of Price Changes on total demand.
On investigating how changes in price affects the aggregate demand as well as the demand
from snobs and followers, we have the following result:
Proposition 1 The total market demand and the demand from followers falls as price rises.
However, snobs buy more as price increases if and only if:
(1− β)f2[p− h(z)] (h′(z) + g′(z)) > 1. (9)
This result shows that snobs can have an upward sloping demand curve. To better
appreciate the intuition for this proposition, we will systematically examine first a market
consisting only of snobs (β = 1); and then a market consisting of both snobs and followers,
that is β ∈ [0, 1).
Market comprised of only snobs. First, note that (9) implies that in this case snobs
will buy less as prices increase. We have, ze = xe, and the utility that a snobs gets from
consuming the product is given by:
Us = v − p− g(xe) (10)
The impact of price on the consumer’s utility is:
∂Us
∂p= −1− g′(xe)
∂xe
∂p(11)
Consumers could possibly expect ∂xe/∂p to be negative, probably based on everyday obser-
vation in the demand pattern of fast moving consumer goods. Then for a sufficiently large
g′(·), it is possible that consumer utility increases in price. This outcome, however, implies
that as the price increases, the total number of consumers who will buy the product would
increase - thus giving rise to an upward sloping demand curve. Such a line of reasoning could
potentially form the basis of naıve intuition, which suggests that more snobs would buy as
price rises.
10In fact, a higher exclusivity effect helps in that (8) is more likely to be satisfied.
8
Now let us examine the implications of consumers forming rational expectations. If util-
ity increases with price, then demand is likely to grow with price implying that ∂xe/∂p > 0.
However, if ∂xe/∂p > 0, then we know from (11) that consumer utility must decrease with
price, irrespective of the size of g′(·). Thus, if consumers expect an upward sloping demand
curve, then the realized demand curve would be downward sloping. Hence, such an expec-
tation is not rational. The only situation which is consistent with the rational expectations
condition is the one in which the expected demand curve of snobs is downward sloping and
consumers’ utility is decreasing in price. This analysis provides a useful clarification: if a
market is comprised of only snobs, then demand would not grow as price rises.
Market comprised of both snobs and followers. In the presence of followers and snobs,
(11) becomes:∂Us
∂p= −1− g′(ze)
∂ze
∂p(12)
If the consumer expects the total demand to drop as price increases, then for sufficiently
large g′(·) it is possible that consumer utility increases as price rises – thus giving rise to an
upward sloping demand curve for snobs. Indeed, it is possible that the total demand curve
is downward sloping (i.e., ∂ze/∂p < 0) while the demand from snobs is growing as price
increases, when there are enough followers 11
The arguments made above highlight the importance of rational expectations for Proposi-
tion 1. In the empirical section, we will examine the validity of both the rational expectations
assumption and its consequences.12
Proposition 1 provides a plausible explanation for why upward sloping demand curve
seems to be empirically associated with snobs rather than followers. This is because the
demand curve for snobs can be upward sloping at the optimal price. But this cannot be
true for the followers. Further, the result highlights that the upward-sloping demand curve
for snobs is likely to be observed only when the market includes a group of consumers
whose utilities do not exhibit negative consumption externality. That is, there is a group
11To illustrate the possibility that there will exist situations in which (8) and (9) are satisfied, considerthe case where f1(·) and f2(·) are uniform with range (0, 1), β = 1/2 and g(·) and h(·) are linear withg′ ≡ λ1 = 0.8 and h′ ≡ λ2 then (8) is always satisfied and (9) is satisfied as long as λ2 > 1.2. That is, if thesnob effect is large enough, then these consumers will demand more as price increases.
12 We derived Proposition 1 using the implicit function theorem (which requires local differentiability). Thecontinuity assumptions were useful to prove uniqueness and existence of rational expectations equilibrium.But as our discussion of the intuition using equations (11) and (12) shows, the proof would go through evenif F1(·) and F2(·) were not continuous. Also, it is easy to see that the arguments would hold even if demandwas discrete. For example, in the empirical section we consider a discrete version of this model.
9
of consumers who are (weakly) conformists.13 Note that our result contradicts the claim of
Liebenstein (1950) who argues that the demand curve for snobs would always be downward
sloping. Nevertheless, the result is consistent with anecdotal and empirical evidence.
Support for our results is seen in the study of Chao and Schor (1998). They find that
the demand curve for conspicuous cosmetics like lipsticks, mascara and eyeshadow is upward
sloping for college educated women. To the extent that these women are more likely to
be status conscious and desire exclusivity, these results are consistent with our theoretical
results. However, the overall demand curve is downward sloping. Interestingly, the demand
curve for women who have not graduated from college is downward sloping as we would
expect. Finally, they also find that non-conspicuous products like facial cleanser exhibit
downward sloping demand curves for all segments. This is also consistent with our results.14
Impact on Profits
Next we examine how a monopolist’s profit is affected by snobbishness and conformism.
Without any loss in generality, assume that the marginal cost of the product is zero. The
profit function is:
Π(p) = z(p)p (13)
We assume that the profit function is concave in price, and we focus on situations where
there is an interior solution. In order to evaluate the impact of the snobbish behavior, we
define g(·) = λ1g(·) where g(·) ≥ 0 and g′ ≥ 0. Thus, as λ1 increases consumers become
more snobbish. Similarly, we define h(·) = λ2h(·), h(·) ≥ 0 and h′ ≥ 0. Therefore, when λ2
grows, conformism becomes stronger.
We have the following result:
Proposition 2 Firm’s profits decrease with snobbishness, but increase with conformism.
It is commonly believed that manufacturers of luxury good items earn supra-normal
profits, and the reason for this is intimately related to consumers’ desire for exclusivity. Our
13It is important to note that the result does not require the presence of followers. In particular, thedemand curve for snobs could be upward sloping even if h′ ≡ 0; that is, there exists a segment of consumerswhose utility is unaffected by the choices of other consumers.
14For example, the price coefficient for lipsticks, equals -0.19 for women with high school diploma. Butfor women with college degree the price coefficient is +0.117. However, the overall price coefficient is -0.157.Chao and Schor (1998) also find that the correlation between quality and price in this category is zero.Therefore, price could not be a credible signal of quality in this case. Similar results were also observed inthe case of mascara and eyeshadow.
10
result shows that at least in a monopoly setting with rational consumers this is not true.
To understand the reason for this result, note that as snobbishness increases, the demand
decreases. This is because each additional sale exerts a negative externality on the sale of
other units. Consequently, the firm sells less as snobbish behavior increases. On using the
Envelope theorem, we have:∂Π∗
∂λ1
= p∂z
∂λ1
< 0. (14)
This inequality is formally established in Appendix A. Thus, firm’s profits are hurt by the
negative impact of snobbish behavior on the demand. Similarly,
∂Π∗
∂λ2
= p∂z
∂λ2
> 0. (15)
Again, this inequality is formally established in Appendix A. Thus conformism has a
positive impact on firm profits, and it is in direct contrast to the effect of snobbishness
discussed earlier. This result is consistent with the observation that some firms employ
marketing strategies to create a bandwagon effect for their products. Often such companies
are able to charge high prices and make higher than normal profits.15 To understand the
intuition note that each additional unit that the firm sells exerts a positive externality on
the sale of other units. Consequently, as the degree of conformism increases, the total sales
and thereby the total profits are higher.
A related question is: How does snobbism and conformism affect optimal prices? As
snobbishness increases, the total demand tends to decrease. However, increase in snobbish-
ness can also make the consumer less price sensitive, which tends to increase price. It can
be seen that the sign of ∂p∗/∂λ1 is the same as the sign of:16
∂2Π
∂p∂λ1
=∂z
∂λ1
+ p∂2z
∂p∂λ1
(16)
The first term on the right hand side of the above equation represents how the demand
changes as snobbishness increases. This term is always negative. It implies that in order to
15For example, Corneo and Jeanne (1997b) discuss the case of a French company which introduced anobject called POG which were plastic disks with little usefulness or aesthetic quality. However, with someclever marketing campaign the company started a craze among French children for POGs. The companysold more than 15 million POGs in a month, at a price which far exceeded the production cost.
16To see this, note that by the implicit function theorem it follows that:
∂p
∂λ1= −∂2Π/∂p∂λ1
∂2Π/∂p2
Since ∂2Π/∂p2 < 0, the sign of ∂p/∂λ1 is the same as the sign of ∂2Π/∂p∂λ1.
11
sell additional units the firm needs to decrease its price more as snobbishness increases. The
second term, however, tends to be positive because as the desire for exclusivity increases,
consumers usually become less price sensitive. The combined effect of these two terms is
ambiguous. In the case of uniform f(·) and linear g(·) these two effects completely counter-
balance each other, and the prices are independent of the degree of snobbishness! However,
this is not a general result. Note that this ambiguous result is in contrast to some claims
that products associated with desire for exclusivity would be higher priced (see for example
Groth and McDaniel 1993). These claims are sometimes based on the fact that desire for
exclusivity can make consumers less price sensitive. However, as (16) shows this effect is
counteracted by the negative demand-effect of snobbishness, which tends to reduce price. In
fact, it is easy to construct examples where the price decreases as snobbishness increases.
Now, let us consider the impact of conformism on prices. As in the case of snobs, there
are two effects that we need to consider. The first effect is the demand-effect, which tends to
increase price since the value of the product increases with each additional sale. Thus, the
firm has less incentive to decrease prices. However, as in the case of snobs, there is another
effect: the effect of conformism on price-sensitivity. Usually, consumers tend to become more
price-sensitive as conformism increases. These two effects tend to counteract each other. For
the case where we have uniform f(·) and linear h(·), the two forces balance out, and thus
conformism has no effect on prices! Nevertheless, in more general cases the overall effect is
ambiguous, and prices can be higher as conformism increases.
3 Empirical Investigation
The theoretical analysis makes an important prediction: snobs might actually buy more if
the price is higher, implying that the demand curve could be upward sloping. This result
depends on individuals forming rational expectations. With little reflection, we can see that
it is not easy for individuals to form correct expectations: the expectations that shaped
the decisions of individuals should be identical with ensuing aggregate behavior. Indeed,
the current evidence on rational expectations is mixed. Individual-level studies reject the
possibility that individuals can form rational expectations (Schmalansee 1976, Garner 1982,
Williams 1987, Smith et al. 1988). But market-level studies support the rational expectations
model. For example, experimental assets markets seem to converge toward the predictions
of rational expectations equilibria (see Sunder 1995 for a survey). However, in these markets
12
the beliefs that guided actions were not tracked. Consequently, we have no knowledge of
expectations in these markets. It is also not clear whether the results of asset market studies
are generalizable to retail markets, which are generally less efficient (Smith 1982 and Holt
1995). Thus, it would be useful to test our model in a laboratory setting, where we can track
both actions and expectations. Such an investigation will add to our understanding of the
rational expectations model of conspicuous consumption, over and above the support we see
in the empirical study of Chao and Shor (1998).
We first address two key questions:
1. Do snobs buy more as price increases? In our laboratory test, snobs purchased more
when price was increased. In addition to finding strong support for the qualitative pre-
dictions of the model, we have moderate support for the point predictions. Relatedly,
theory predicts that the demand curves for followers and the total market should be
down sloping, and we also find support for this claim.
2. Are the expectations of subjects consistent with the rational expectations model? Prior
experimental literature has not attempted to explore whether the beliefs of economic
agents conform to rational expectations model. Thus, an answer to this question is a
useful addition to our knowledge of behavior in games. We tracked the beliefs that
guided the purchase decisions of subjects in every trial of the experiment. On aver-
age, the expected demand was consistent with the actual demand and the rational
expectations equilibrium predictions. We observe variation in the behavior of individ-
ual subjects, implying that the model prediction survives at the aggregate level rather
than the individual level.17
The details of the experimental investigation are presented below.
Empirical Model. Our analytical model assumes continuous distribution in values. It
is difficult to validate such a model in a laboratory setting with a small sample of subjects.
However the analytical results do not crucially depend on the continuity assumption as can
be seen in the discussion of the intuition for the results and footnote 12. Hence, we use a
discrete distribution of valuations that is conducive to test the model with a population of
20 subjects. The approach of testing a continuous model using a discrete version is common
17Similar observation has been made in several experimental games (e.g., ONeill 1987, Rapoport andBoebel 1992).
13
in experimental economics (e.g., Smith 1982). Table 1 presents the distribution of valuations
for ten snobs (labeled Type A buyers in our experiment) and ten followers (Type B buyers
in our experiment).18 We used g(z) = 0.5z and h(z) = 0.6z. The resulting equilibrium
demands for the snobs, the followers, and the total market are shown in Figure 1. We see
that the demand curve for snobs is (weakly) upward sloping, while it is (weakly) downward
sloping for followers and the total market. In our experiment, we use two price points to
trace the slope of the demand curve.
–Insert Table 1 –
–Insert Fig. 1 –
Subjects. The subjects who participated in the experiment were business school stu-
dents. They were paid a show-up fee of $5 in addition to monetary reward contingent on
their performance. All transactions were in an experimental currency called “francs” that
were converted into US dollars at the end of the experiment.
Experimental Design. We used a within-subject design with two levels of prices: 5.9
and 6.9 francs. Using these two price points we trace the changes in demand among snobs
and followers. We ran two groups comprised of twenty subjects each. In Group 1 the price
was low in the first thirty trials and high in the next thirty trials. In Group 2 the order of
price presentation was reversed.
Procedure. In our experiment, subjects played the role of buyers, while the computer
played the role of a seller. The instructions that we provided to the subjects are in Appendix
B. In keeping with the spirit of the complete information theoretical model, subjects were
informed of g(z), h(z), and the value distribution.
Seller: We simulated the retail market environment, where a seller posts price and
promises to supply its product to all buyers who are willing to pay the posted price (see
Smith 1982 and Holt 1995 for a discussion on posted prices market, and its implications for
market efficiency). In this posted-price market, buyers cannot negotiate the price with the
seller.
Buyers: Each subject was randomly assigned to play the role of either a Type A or
Type B buyer.
Type A buyers: Type A buyers value the product less when more people own the product.
18We named the two types of buyers as Type A and Type B buyers, rather than as snobs and followers,so that the behavior of subjects is purely guided by the negative and positively externality captured in ourmodel.
14
Consequently, the actual value of the product systematically drops below the base value when
more people choose to buy the product. For example, consider the Type A buyer whose base
valuation for the product is 9.5 francs. If a total of five Type A and Type B buyers purchase
the product, the actual value of the product will fall to 7 francs (that is, 9.5− 0.5× 5 = 7).
Type B buyers: Type B buyers value the product more when more people own the prod-
uct. Hence, the actual value of the product rises above the base value when more people
choose to buy the product. For example, consider the Type B buyer whose base valuation
is 2 francs. If a total of five Type A and Type B buyers purchase the product, the actual
value of the product will increase to 5 francs (that is, 2 + 0.6× 5 = 5).
At the commencement of each trial, subjects were endowed with 7 francs so that they
had sufficient funds to pay for the product if they decide to buy it. Consistent with our
theoretical model, subjects were informed of their valuation, the distribution of valuations
and the price of the product. The type of a subject, the total number of subjects, and the
base valuations remained fixed in all trials.
In every trial, each subject had to decide whether or not to purchase the product. Sub-
jects were asked to provide demand projections. Then using these demand projections, the
computer showed the expected value of the product. Subjects could revise their demand pro-
jections, and obtain new estimates of the likely value of the product. We used the demand
projections to track the expectations that guide the decisions of the subjects.
After all the buyers made their decisions, the computer counted the total number of
subjects who purchased the product. Then, based on the total number of subjects who
bought the product, the actual value of the product for each subject was assessed. The
payoff to a subject who bought the product is: endowment + actual value of the product
- price paid. The subjects who did not buy the product kept the endowment. At the end
of every trial, each subject was informed of the number of Type A and Type B buyers who
purchased the product, and the payoff for the trial.
In order to make subjects familiar with the structure of the game, they were allowed
to play three practice trials for which they received no monetary reward. Following the
common practice in tests of rational expectations games, we allowed our subjects to play
several iterations of the game to test for equilibrium behavior (Sunder 1995). Note that the
equilibrium demand is not affected by the multiple iterations. We changed the prices after
the first thirty trials, and the experiment concluded at the end of sixty trials. Then subjects
15
were paid according to their cumulative earnings, debriefed, and dismissed.
3.0.1 Results.
In this section, we assess the descriptive power of the rational expectations equilibrium. We
begin our analyses by examining the quantity demanded by snobs and followers. Thereafter,
we investigate the expectations that could have guided the behavior of our subjects. Qualita-
tively, the experimental results are consistent with the predictions of the model. We observe
an upward-sloping demand curve for Type A buyers (snobs), and a downward-sloping de-
mand curve for Type B buyers. On average, the expected demand is also consistent with
the rational expectations equilibrium solution. However, we observe variations in the beliefs
and actions of individual subjects.
Analysis of Demand. Table 2 presents the mean quantity demanded by the two types
of buyers, and the corresponding equilibrium predictions. The empirical results are consistent
with the qualitative predictions of the equilibrium solution. However, we see some departures
from the point predictions of model. Also, there is a significant trend in the demand pattern
over the several iterations of the game.
Qualitative Predictions. The model makes four qualitative predictions. First, the demand
for the product among Type A buyers (snobs) should grow as the price increases. The
average demand was 1.53 units, when the product was priced 5.9 francs. But when the price
increased to 6.9 francs, the demand rose to 3.57 units. We can reject the null hypothesis
that these demand levels are the same (F(1,118) = 92.83, p < 0.0001). We obtain similar
results in each of the two groups. In Group 1, the average demand grew from 1.33 to 3.43
units, as the price rose from 5.9 to 6.9 francs, and this difference in demand is significant
(F(1,58) = 94.25, p < 0.0001). In Group 2, the mean demand correspondingly increased from
1.93 to 3.7 units (F(1,58) = 27.66, p < 0.0001).
Second, in equilibrium the followers should demand less as the price increases. In ac-
tuality, the average demand of Type B buyers across the two groups declined from 9.12 to
3.08 units, when the price rose from 5.9 to 6.9 francs. This shift in demand is significant
(F(1,118) = 573.31, p < 0.0001). We see similar results at the level of individual groups.
In Group 1, on average the demand dropped from 9.03 to 2.9 units (F(1,58) = 749.48, p <
0.0001). In Group 2 the demand declined from 9.2 to 3.26 units, as the price increased
(F(1,58) = 171, p < 0.0001).
Third, the model predicts that the overall demand should fall as price increases. The
16
mean actual demand dropped from 10.65 to 6.65 units, when price rose from 5.9 to 6.9.
This change in average demand is significant (F(1,118) = 199.93, p < 0.0001). We obtain
similar results in each of the two groups (Group 1: F(1,58) = 134.81, p < 0.0001; Group 2:
F(1,58) = 89.67, p < 0.0001).
Fourth, when the price is 5.9 francs, followers should demand the product more than
snobs. Consistent with this prediction, the followers demanded on the average 9.12 units
across both groups. On average, snobs demanded only 1.53 units. A paired comparison of
the units demanded by snobs and followers reveals that the observed difference in demands
is significant (t = 42.15, p < 0.0001). We observe similar results in both Group 1 and Group
2. In Group 1, the average demand of followers was 9.03, and it is more than the 1.13 units
demanded by snobs (t = 45.10, p < 0.0001). In Group 2, the followers and snobs bought on
the average 9.2 and 1.93 units, respectively (t = 23.69, p < 0.0001).
Finally, when the price is 6.9 francs, snobs should demand more than followers. On
average across the two groups, snobs and followers bought 3.56 and 3.08 units, respectively.
We cannot reject the null hypothesis that these quantities are the same (t = 1.5, p > 0.13).
On closer examination, we note that the difference in demand is marginally significant in
Group 1, but not in Group 2. In Group 1, the mean quantity purchased by snobs and
followers is 3.43 and 2.9 units, respectively (t = 1.97, p < 0.058). Whereas in Group 2, snobs
and followers purchased 3.7 and 3.26 units (t = 0.73, p > 0.2).
–Insert Table 2 –
Distribution of Demand. The equilibrium solution provides unique point predictions about
demand. But the actual demand varies over the several trials of the experiment. Fig. 2
presents the empirical distribution of demand for the product among snobs and followers.
The model predicts that if the price is 5.9 francs, then one snob should buy the product.
Over the sixty trials across the two groups, the actual quantity demanded ranges from 0 to
4, with mean = 1.53, median = 2, and mode = 2. But if the price rises to 6.9 francs, then in
theory four snobs should buy the product. We observe that the actual demand ranges from
1 to 6, with mean = 3.56, median = 4, and mode = 4.
In equilibrium, the followers should demand ten units when the price is 5.9 francs. The
actual demand ranged from 7 to 10 units, with mean = 9.11, median = 9, and mode = 9.
If the price is increased to 6.9 francs, then in theory the demand should drop to 2 units.
The observed demand ranged from 0 to 8 units, with mean = 3.08, median = 3, and
17
mode = 2. This suggests that, though the observed behavior is consistent with the qualitative
predictions of the model, there are departures from the point predictions of the equilibrium
solution.
–Insert Fig. 2 –
Trends in Demand. In the analyses discussed above, we have aggregated the demand
across groups and trials, and it could mask the trends in demand. In Fig. 3 we present
the moving average for blocks of five trials. These block means were computed across the
two groups. Statistical analysis of the block means suggests that followers evince significant
trend in demand, when the price was 6.9 francs (F(5,20) = 9.76, p < 0.0001), but only a
marginal trend when the price was 5.9 francs (F(5,20) = 2.34, p < 0.08). The trends in
the demand pattern of snobs is much weaker. It is marginally significant at 6.9 francs
(F(5,20) = 2.87, p < 0.05), and not significant at 5.9 francs (p < 0.2). This suggests that we
observe some learning in the experiment.
–Insert Fig. 3 –
Variation by Valuation. Whether or not a subject buys the product depends on her base
valuation and the expected number of people likely to buy the product. In equilibrium,
each player should play a pure strategy, and it changes with the base value of the product.
For instance, when the price is 5.9 francs then only the Type A buyer with a base value
of 11.4 francs should buy the product. All others should not buy the product. On the
other hand, when the price is 6.9 francs, then only the Type A buyers with the four top base
valuations should buy the product. Fig. 4 presents the number of trials in which the different
Type A buyers purchased the product. The players are arranged in the ascending order of
their base valuations. Hence, player 1 has the lowest base valuation, and player 10 has the
highest valuation. We see that subjects did not always play the predicted strategies. Yet,
the aggregate behavior is directionally consistent with the model prediction. We observe
similar behavior among Type B buyers as well.
–Insert Fig. 4 –
Analysis of Expectations. Thus far we have examined how the purchase behavior
conforms to the rational expectations equilibrium solution. In every trial of the experiment,
subjects were asked to guess the likely number of Type A and Type B buyers who might
purchase the product. Using these demand projections, we can explore whether the expecta-
tions of our subjects are consistent with the outcomes and the equilibrium solution. Table 3
18
presents the mean expected demand, along with the rational expectations equilibrium solu-
tion.19 It is reassuring to observe that the expected demand is in keeping with the observed
outcomes and the qualitative predictions of the model. But there is a wide variation in
expectations. Further, we discern a trend in the expectation over multiple iterations of the
game.
–Insert Table 3 –
Qualitative Predictions. In keeping with the theory, our subjects expected snobs to buy
more when the price was high. Across the two groups, the mean expected demand of
snobs increased from 1.63 to 3.38 units as the price rose from 5.9 to 6.9 francs (F(1,2398) =
853.65, p < 0.0001). On the other hand, followers were expected to buy less as the price
rose. The average expected demand dropped from 8.08 to 3.52 units as the price increased
(F(1,2398) = 2126.39, p < 0.0001). The changes in expected demand follow a similar pattern
within each group. Finally, consistent with theory, the mean aggregate demand was expected
to drop as price increased (F(1,2398) = 554.01, p < 0.0001). The results are similar within
each group.
The model assumes that expectations are correct. That is, the actual demand and
the expected demand are the same. Indeed, the mean observed demand and the expected
demands are similar. When the price was 6.9 francs, the average actual and expected total
demand were 6.65 and 6.89 units, respectively. We can not reject the null hypothesis that
these demands are the same (t = 0.11, p > 0.2). When the price dropped to 5.9 francs, the
actual and expected demand were on average 8.45 and 9.11 units, respectively. Again, we
can not reject the null hypothesis that these demands are the same (t = 0.39, p > 0.2).
Distribution of Expectations. Fig. 5 shows the distribution of expected demand across the
two groups. In equilibrium, one snob should buy if the price is 5.9 francs. The expectations
range from 0 to 10, with mean = 1.63, median = 1 and mode = 1. In theory, the demand
should be four units, if the price is increased to 6.9 francs. We note that the expectations
range from 0 to 10, with mean = 3.38, median = 3, and mode = 4. Thus, though the
expectations vary widely, they conform to the qualitative predictions of the model.
–Insert Fig. 5 –
Our subjects expected all the way from none to all the followers to buy the product
at both prices. Yet, as before, the distributions of expectations is qualitatively consistent
19Each subject forecast the number of Type A and Type B buyers who will purchase the product. Themean expected demand is computed by averaging the expectations of all the subjects.
19
with the equilibrium solution. If price is 5.9 all followers should buy. The corresponding
expectations followed a distribution with mean = 8.86, median = 9, mode = 9. But if
the price is 6.9 then two followers should buy. The expectations were distributed with
mean = 3.51, median = 3, and mode = 3.
Trends in Expectations. Fig. 6 traces the trend in expected demand over blocks of five
trials. An analysis of variance suggests that the block means are significantly different for
snobs (Price = 5.9: F(5,780) = 66.79, p < 0.001; Price= 6.9: F(5,780) = 4.35, p < 0.001). The
results are similar with followers.
–Insert Fig. 6 –
Our experimental results show that the behavior of financially motivated individuals is
directionally consistent with the predictions of the rational expectations equilibrium. How-
ever, we see variations in the demand from trial to trial as well from player to player. Further,
the beliefs of our subjects are qualitatively consistent with the observed outcomes and the
equilibrium predictions.
4 Learning with Sophistication
Earlier we reported the trends in demand and expectations, and also showed how closely
the equilibrium solution tracks the aggregate behavior. In this section, we explore whether
learning can account for the observed behavior and self-reported expectations of our subjects.
An important feature of our model of conspicuous consumption is that the purchase decision
is contingent on the expected behavior of other consumers. Traditional adaptive learning
models do not allow for players to anticipate the behavior of others, and consequently there
is no scope for sophisticated thinking in those models (e.g., Camerer and Ho 1999, Roth and
Erev 1995). Clearly, human beings are capable of sophisticated thinking and can potentially
outguess other players. Recognizing this potential, a few researchers have proposed models
that allow for sophisticated thinking (Stahl 1996, Selten 1991, Tang 2001). We chose to
estimate the parameters of Sophisticated EWA (SEWA) model proposed by Camerer, Ho
and Chong (2002) for two reasons:
1. The SEWA model is an extension of the EWA model, which has proven to be superior to
belief and reinforcement models in 31 data sets spanning over a dozen different games
(Camerer, Ho and Chong 2002). The EWA model hybridizes the intuition of both
20
reinforcement and belief based learning models and includes these as special cases.20
In turn, the EWA is a special case of SEWA.
2. The SEWA is the only model that could predict the purchase decisions of subjects
and also forecast the foward-looking beliefs of subjects. These forward-looking beliefs
are based on anticipated behavior, and are not a pure function of past actions as in
fictitious play. Thus, SEWA predictions can be compared with both the actions and
the expectations of subjects.
The SEWA Learning Model
The model allows for both adaptive and sophisticated players. The adaptive players best
respond to past actions. Whereas, the sophisticated players form expectations of the behavior
of others, and then best respond to this expectation. Next we describe in more detail the
learning process of these two types of decision makers.
Adaptive players. In every trial of the game, each player has to decide whether or not
to purchase the product. The probability of adaptive player i choosing strategy j from the
m available strategies on trial t + 1 can be given by the logit function:
P ji (a, t + 1) =
eλAji (a,t)∑m
k=1 eλAki (a,t)
(17)
where Aji (a, t) is the attraction for an adaptive player i of choosing strategy j at time
t. The parameter λ measures sensitivity of the players to attractions, and it can also be
interpreted as a measure of noise in the strategy choice process. At the end of every trial,
a player updates the attractiveness of a strategy based on the actual payoff and also the
expected payoffs corresponding to strategies that were not chosen. While updating the
attraction of a strategy, payoffs corresponding to chosen strategies are given a weight equal
to 1, while expected payoffs corresponding to unchosen strategies are given a weight of δ
(0 ≤ δ ≤ 1). The parameter δ measures the relative weight given to foregone payoffs,
compared to actual payoffs, in updating attractions. It can also be interpreted as a kind of
20The key point of EWA is that the seemingly different belief-based and reinforcement-based learning areindeed very closely related: Reinforcement models are based on some weighted average of previously receivedpayoffs, and exclude foregone payoffs. Whereas, in belief models the expected payoffs are exactly equal toa weighted average of previously received payoffs, and foregone payoffs of strategies which were not chosen.Thus, the fundamental difference between reinforcement and belief models is the extent to which foregonepayoffs are assumed to influence the choice of strategies. In EWA model, the effect of foregone payoffs onchoice of strategies is captured in a single parameter, δ ∈ [0, 1].
21
‘imagination’ of foregone payoffs. Previous attractions are depreciated by another parameter
φ (0 ≤ φ ≤ 1). The decay rate φ reflects a combination of forgetting, and the degree to
which players recognize that other players are adapting and thereby place lower weight on
the history of the game. If φ is lower, players discard old observations more quickly, and
become more responsive to the most recent observations.
In updating the attractiveness of a strategy, the model also uses another parameter de-
noted by N(t). This parameter can be interpreted as the number of observations-equivalents
of past experience. In other words, this is a weighted combination of the number of times
the game has been played. The updating rule employed is:
N(t) = (1− κ) · φ ·N(t− 1) + 1, t ≥ 1 (18)
where the parameter κ (0 ≤ κ ≤ 1) captures the growth of attractions. When κ = 0,
current attractions are weighted average of past attractions, and they not grow outside the
bounds of the payoff in the game. But when κ = 1 the attractions could grow beyond the
payoffs of the game. The parameter N(t) is used to combine the prior attractiveness with
the actual/expected payoffs from the current period. The attraction of choosing strategy j,
namely Aji (a, t), is a weighted average of the payoff for period t and the previous attraction
Aji (a, t− 1) :
Aji (a, t) =
φN(t− 1)Aji (a, t− 1) + [δ + (1− δ)I(sj
i , si(t))]πi(sji (t), s−i(t))
N(t)(19)
where πi(sji (t), s−i(t)) is the payoff received by player i by choosing strategy j in period
t given that the other players chose s−i(t) in time period t. The I(sji , si(t)) function is an
indicator variable, which is defined as:
I(sji , si(t)) =
{1 if si(t) = sj
i ,0 otherwise.
(20)
Thus, if player i chooses strategy j on trial t, then the payoff is added to the attraction
of the strategy j, Aji (a, t − 1) . But if the player does not play strategy j on trial t, then
only δ fraction of the payoff is added to the attraction of strategy j. The initial values of
the two parameters of the model are denoted by N(0) and Aji (a, 0).
Adaptive learning nests both reinforcement and belief learning as special cases. For
instance, if δ = 0, κ = 1, and N(0) = 1, then the attractions are mathematically equivalent
to the reinforcement of classical reinforcement-based learning models. But if δ = 1 and
22
κ = 0, then the attractions are exactly the same as updated expected payoffs as in belief-
based learning models (See Camerer and Ho 1999 for a proof of this claim).
Sophisticated Players. In contrast to the adaptive learners, these players form expec-
tation of the likely behavior of other players, and then best respond to this forecast. Let α
fraction of the players be sophisticated. While forming expectation about the likely behav-
ior of other players, the sophisticated players assume that (1− α′) proportion of players are
adaptive. By allowing α′ to be different from α, we can investigate the extent to which these
players over/under estimate the sophistication of others. It is useful to note that by allowing
for sophisticated players SEWA creates room for recursive thinking, and consequently nests
equilibrium concepts. For example, the Quantal Response Equilibrium (QRE) is a special
case of SEWA, where all players are sophisticated (α = 1, and α = α′).
These players update attractions of strategies as follows:
Aji (s, t) =
m−i∑k=1
[α′P k−i(s, t + 1) + (1− α′) · P k
i (a, t + 1)] · πi(sji , s
k−i) (21)
where sk−i is the strategy vector k ∈ S−i chosen by all players except i, where S−i is the
available strategy space for all players except i, m−i is the cardinality of S−i, P k−i(s, t + 1)
is the probability that the sophisticated players (except i) will choose strategy vector k at
time (t + 1) and P k−i(a, t + 1) is the corresponding probability for adaptive players. Note
that P k−i(a, t+1) can be easily derived from (17). Camerer, Ho and Chong (2002) define the
probability of a sophisticated player i using strategy j on period t + 1 as:
P ji (s, t + 1) =
eλAji (s,t)∑m
k=1 eλAki (s,t)
(22)
Note that (21) and (22) define a set of recursive equations which need to be solved at
every time period in order to derive the probabilities that a player would choose strategy j
at time (t + 1) and to determine the updated attractiveness. We estimated the model using
the maximum likelihood method. Following Camerer, Ho and Chong (2002), we used the
purchase decisions made in the first trial of each price condition to initialize the model.21
21This procedure of computing the prior attraction is equivalent to choosing initial attractions that wouldmaximize the likelihood of the first period data, separately from the rest of the data (for a value of λ derivedfrom the overall maximum likelihood). Suppose the empirically observed frequency of strategy j in the firsttrial is f j . Let the attraction of strategy j with the lowest frequency to be Aj(0) = 0. Then we can derive
the initial attractions using the following equation: eλA
ji(0)∑m
k=1e
λAki(s,t)
= f j . We also set N(0) = 1. For a more
detailed discussion on the computation of initial attractions see Camerer et al. (2002, p 18).
23
The model was calibrated on the next twenty trials, and validated on the last 9 trials of each
price condition.
Results
Table 4 reports the parameter estimates of the SEWA model, and goodness of fit statistics
for the model. We conducted separate analysis for Group 1 and 2 in each price condition,
and they are summarized below.
–Insert Table 4–
Overall Model Fit. The fit statistics attest to the predictive accuracy of SEWA model.
Table 4 presents the log-likelihood (LL), Akaike Information Criterion (AIC), Bayesian
Information Criterion (BIC), pseudo-R2(ρ2), and average probability.22 We observe that
the pseudo-ρ2 for Group 1 and Group 2 in the low-price condition are 0.435 and 0.480,
respectively. The corresponding values for Group 1 and Group 2 in the high-price condition
are 0.284 and 0.23. The average predicted probability for the chosen strategies is more than
0.77 and 0.65 for the groups in the low and high-price conditions. Next, we discuss the ability
of the model to predict the pattern of demand and expectation observed in the experiment.
Demand Predictions. The model correctly predicted over 86% and 75% of the purchase
decisions of subjects in the low and high-price conditions. On average, SEWA predicted
that subjects in Group 1 of the low-reward condition would demand a total of 10.85 units
in each trial, while actual demand was 10.35. We can not reject the null hypothesis that
the predicted and actual demand are the same (p > 0.4). Similarly, there is no significant
difference between the actual demand and SEWA prediction for subjects in Group 2 in the
same price condition (Actual Demand:11.15, SEWA prediction: 11.55, p > 0.4). We obtain
similar results for the two groups in the high-price condition.
Expected Demand. As we have highlighted earlier, the SEWA provides forward-looking
beliefs for each subject in each trial. We find that purchase decisions consistent with these be-
liefs are similar to the purchase decisions predicted by the reported expectations of subjects.
The corresponding hit ratio is 85.3% and 79.8% for Group 1 and Group 2 in the low-price
condition. The hit ratios for Group 1 and Group 2 in the high-price condition are 74.5%
22The pseudo-ρ2 of the EWA model indicates the extent to which the EWA model can perform betterthan the null model. More precisely, the pseudo-ρ2 is the difference between the AIC measure and the log-likelihood (LL) of a model of random choices, normalized by the random model log-likelihood. AIC = LL−k,and BIC = LL−(k/2)log(M), where k is the number of degrees of freedom and M is the sample size. Averageprobability is the mean predicted probability of the choices made by subjects
24
and 76.3%, respectively. Further, the expectation based on SEWA model closely tracks the
stated expectation. For instance, the mean stated expectation of subjects in Group 1 of the
low-price condition is 10.345 while the SEWA-based mean expectation is 10.8 (p > 0.2). We
obtain similar results in all the four groups.
Interpretation of the parameter values. We observe that only a small fraction of sub-
jects in each of the four groups are sophisticated decision makers, as α is small (α < 0.118).
Further α′ < α, implying that subjects in general seem to underestimate the sophistication of
others. A similar overconfidence effect have been reported in other experimental settings.23
We note that δ = 0, suggesting that purchase decisions were strongly influenced by past
payoffs, rather than foregone payoffs. This finding is consistent with the high proportion of
adaptive decision makers.
Model Validation. We validated the model in two types of hold-out samples. First, we
assessed the predictive accuracy of the model in the last 9 trials of the same group. Second,
we validated the model on the group of subjects who were not used for calibration. That is,
we predicted the behavior of subjects in Group 1 using the estimates of subjects in Group
2, and vice versa.
To assess the predictive accuracy of the model, we used log-likelihood, AIC, BIC, pseudo-
ρ2, average predicted probability of purchases actually made by subjects, the mean predicted
demand, percentage of purchases correctly predicted by the model (hit ratio-demand), per-
centage of consistency in the purchase decision based on stated expectations and SEWA
predicted expectations (hit ratio-expectation) and mean predicted expectation. In Table 5,
we report these summary statistics for the hold-out sample of 9 trials, and hold-out sample
of 20 subjects (members of the other group).24 The fit statistics suggest that SEWA model
closely tracks the purchase decisions and expectations of subjects.
On average, the percentage of purchase decisions correctly predicted in the four cali-
bration samples is 81.4%. The corresponding average hit ratio for the validation sample
comprised of the last 9 trials is 85.8%. When the model is validated using the alternate
group, the average hit ratio is 76.3%. Likewise, the average hit ratio for expectations is
85.8% in the last 9 trials of the same group, and it is comparable to that in the calibra-
tion sample. The average hit ratio is 76.4%, when the validation sample was the alternate
23For example, Camerer et al. (2002) report empirical estimates of α′ larger than the corresponding α inp-beauty contests using both experienced and inexperienced subjects.
24The subjects in the hold-out sample played 30 trials. Like before, we used the first trial to estimate theinitial attractions and used the remaining sample for validation.
25
groups. Also, as in the calibration sample, we can not reject the null hypothesis that actual
and SEWA predicted demand are the same. We obtain similar results for expectations as
well.
–Insert Table 5–
Discussion. The SEWA model accounts for the major behavioral regularities observed
in our experiments. The model performs well in the hold-out sample of trials, as well in the
hold-out sample of subjects. This learning analysis highlights that a small fraction of subjects
are sophisticated in their decision making, while most of them are adaptive decision makers.
Further, we see some tendency to underestimate the sophistication of others. Finally, we find
that the SEWA model predicts well the expectations of subjects. This suggests that SEWA
model can potentially be used to infer the latent beliefs of decision makers, in contexts where
it is difficult for players to report their beliefs.
5 Conclusion
This paper was motivated by a desire to understand the impact of social factors on conspicu-
ous consumption. Toward this goal, we have developed a parsimonious model of conspicuous
consumption using the rational expectations framework. Our theoretical and empirical in-
vestigation provides useful insights on a few questions about conspicuous consumption and
sophisticated thinking.
1. Would consumers buy a conspicuous product more as price increases, even if the product
has neither quality difference nor signal value? We show that in a market comprised
of both snobs and followers, the demand curve of snobs could be upward sloping. But
the demand curve of followers and the total market is always downward sloping. The
intuition for this result is that snobs prefer a higher priced product if they expect
the overall demand to be lower at the higher price, and such an expectation will be
rational only if the followers have a downward-sloping demand curve. Hence, in a
market comprised of only either snobs or followers the demand curve is downward
sloping. It is useful to note that our result does not rely on signaling either product
quality or wealth of consumers.25
25In fact, an explanation based on signaling status cannot account for an upward-sloping demand curvefor snobs (see Corneo and Jeanne 1997a).
26
Consistent with our findings, Chao and Shor (1998) report that the demand for visible
women’s cosmetics grows as price increases in a sub-segment of the market, though
the overall demand curve has a downward slope. Moving beyond this correlational
support, we see in the laboratory study that price increases cause demand to increase
among snobs.
2. What is the descriptive validity of the rational expectations framework? To the best of
our knowledge, our study is the first to track both beliefs and outcomes in the context
of a rational expectations game. In our studies, we find the subjects’ expectations are
on average consistent with the observed outcome and also consistent with the rational
expectations equilibrium. Thus our empirical analysis makes a useful contribution to
the experimental literature on rational expectations models.
3. How do subjects learn to play the game in a fashion that is consistent with equilib-
rium predictions? In the case of a small fraction of subjects, sophisticated thinking
shaped their purchase decisions. But most of the players were adaptive in their deci-
sion making. We also note a tendency on the part of subjects to underestimate the
sophistication of others. Finally, the SEWA predicts well both the purchase decisions
and expectations of subjects.
There are several avenues for future research. One important extension would be to
examine the role of conspicuous consumption when there are multiple firms in the market.
Also, future research can examine how other variables like advertising can affect conspicuous
consumption. Our empirical results show that the SEWA model of Camerer, Ho and Chong
(2002) performs well in predicting individual choices and beliefs in our rational expectations
based model. It would be useful to replicate this result in other contexts.
27
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30
Table 1: Value Distribution for the Empirical ModelSA
1 SA2 SA
3 SA4 SA
5 SA6 SA
7 SA8 SA
9 SA10
Type A 2 3 4 5 6 9.5 10.1 10.6 11.2 11.4SB
1 SB2 SB
3 SB4 SB
5 SB6 SB
7 SB8 SB
9 SB10
Type B 0.1 0.2 0.5 0.55 0.7 1.5 2 2.5 3.5 5
Note: Sij refers to Subject j of Type i.
Table 2: Mean DemandType A Buyers (Snobs) Type B Buyers (Followers)
Price Actual Demand Prediction Actual Demand PredictionGroup 1 Group 2 Both Group 1 Group 2 Both
5.9 1.33 1.93 1.53 1 9.03 9.2 9.12 106.9 3.43 3.70 3.57 4 2.90 3.26 3.08 2
Table 3: Mean Expected DemandType A Buyers (Snobs) Type B Buyers (Followers)
Price Expected Demand Prediction Expected Demand PredictionGroup 1 Group 2 Both Group 1 Group 2 Both
5.9 1.40 1.86 1.63 1 8.82 7.35 8.08 106.9 3.56 3.20 3.38 4 3.17 3.86 3.52 2
Table 4: Estimation of SEWA model parametersPrice = 5.9 Price = 6.9
Parameter Group 1 Group 2 Group 1 Group 2κ 0.999∗∗∗ 0.999∗∗∗ 0.999∗∗∗ 0.999∗∗∗
φ 0.729∗∗∗ 0.728∗∗∗ 0.753∗∗∗ 0.497∗∗∗
δ 0.489∗∗∗ 0.488∗∗∗ 0.001 0.335∗∗∗
λ 0.191∗∗∗ 0.190∗∗∗ 0.091∗∗∗ 0.189∗∗∗
α′ 0.001 0.001 0.001 0.001α 0.118∗∗∗ 0.096∗∗∗ 0.064∗∗∗ 0.082∗∗∗
Average Probability 0.773 0.777 0.677 0.651Log-Likelihood -156.576 -144.309 -198.401 -213.287AIC -162.576 -150.309 -204.401 -219.287BIC -174.551 -162.284 -216.375 -231.261Pseudo R2 0.435 0.480 0.284 0.231Hit ratio (demand) 0.865 0.865 0.770 0.755Hit ratio(expectation) 0.853 0.798 0.745 0.763Actual Mean Demand 10.350 11.150 6.150 7.700SEWA Predicted Demand 10.850 11.550 6.250 7.500Stated Expectation 10.345 9.200 6.655 7.553SEWA Predicted Expectation 10.800 11.550 7.000 8.400
∗∗∗ significant with p < 0.001.
31
Table 5: Performance of SEWA model in Validation Samples
Price = 5.9 Price = 6.9Validation Sample Performance Measure Group 1 Group 2 Group 1 Group 2
Average Probability 0.652 0.688 0.533 0.504Log-Likelihood -61.197 -62.164 -74.052 -77.756AIC -67.197 -68.164 -80.052 -83.756BIC -76.776 -77.743 -89.631 -93.335Pseudo R2 0.510 0.502 0.406 0.377
Last 9 trials (same group) Hit ratio (demand) 0.878 0.872 0.828 0.856Hit ratio (expectation) 0.878 0.789 0.844 0.839Actual Mean Demand 10.000 11.110 6.889 5.444SEWA Predicted Demand 10.000 11.110 6.333 5.667Stated Expectation 9.883 9.244 6.806 5.872SEWA Predicted Expectation 10.000 11.110 6.889 5.444Average Probability 0.800 0.774 0.696 0.668Log-Likelihood -207.474 -218.526 -293.063 -282.649AIC -213.474 -224.526 -299.063 -288.649BIC -226.563 -237.615 -312.152 -301.738Pseudo R2 0.484 0.456 0.271 0.297
Alternative group trials Hit ratio (demand) 0.886 0.597 0.783 0.788in the same price condition Hit ratio (expectation) 0.814 0.588 0.793 0.779
Actual Mean Demand 11.138 10.241 7.000 6.379SEWA Predicted Demand 11.345 10.688 6.931 6.276Stated Expectation 9.214 10.202 7.031 6.702SEWA Predicted Expectation 11.448 10.550 7.483 6.965
Figure 1
Figure 2
Figure 3
Distribution of the Demand from Snobs
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7 8 9 10
Demand Level
Freq
uenc
y
5.96.9
Distribution of Demand of Followers
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7 8 9 10
Demand Level
Freq
uenc
y
5.96.9
Trends in Demand of Followers
0123456789
10
1 2 3 4 5 6
Blocks of Trials
Ave
rage
Dem
and
5.96.9
Empirical ModelDemand as a Function of Price
02468
1012
5.8 6 6.2 6.4 6.6 6.8 7
Price
Dem
and
Snobs
Followers
Total
Trends in the Demand of Snobs
0123456789
10
1 2 3 4 5 6
Blocks of trials
Ave
rage
Dem
and
5.96.9
Figure 4
Figure 5
Figure 6
Distribution of Expected Demand of Snobs
0100200
300400500
0 1 2 3 4 5 6 7 8 9 10
Demand Level
Freq
uenc
y
5.96.9
Distribution of Expected Demand of Followers
0
50
100
150
200
250
300
350
400
450
500
0 1 2 3 4 5 6 7 8 9 10
Demand Level
Freq
uenc
y
5.96.9
Trends in the Expected Demand of Followers
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6
Blocks of Trials
Ave
rage
Dem
and
5.96.9
Trends in the Expected Demand of Snobs
0
0.5
1
1.5
2
2.5
3
3.5
4
1 2 3 4 5 6
Blocks of ten trials
Dem
and
5.96.9
Variation in Purchase Frequency among Snobs
0102030405060
1 2 3 4 5 6 7 8 9 10
Type A Buyers (1 to 10)
Freq
uenc
y of
Pu
rcha
se
5.96.9
Variation in Purchase Frequency among Followers
0102030405060
1 2 3 4 5 6 7 8 9 10
Type B Buyers (1 to 10)
Freq
uenc
y of
Pu
rcha
se
5.96.9
