The Rationality of Prices and Volume in

ORGANIZATIONAL BEHAVIOR AND HUMAN DECISION PROCESSES5I.237_272
O992)
The Rationalito
y f P r i c e sa n d V o l u m ei n
ExperimentalMarkets
CoLrNrCelaBnen
U niv er s ity of P ennsy lv ania
Market experiments designed to test whether individual errors are reduced
by markets generally indicate that errors do make prices or trading volume
irrational. For example, in markets for assets of uncertain value a "representativeness"-based theory predicts deviations of prices from Bayesian predictions. Endowment effects and optimism about relative trading ability lead
to trading volumes which are too low or too high. Forecasts of future prices in
markets violate rational expectations restrictions. And subjects do not ignore
their own information when making forecasts of the forecasts of others. These
data suggest that individual errors are often reduced, but not eliminated, in
experimental markets under ideal learning conditions. They cast doubt on the
optimistic presumption that prices negotiated in competitive market settings
will reflect true values. The markets are unusually competitive, but the results
suggest that errors are likely to be important in two-party negotiations and
press,
other settings too. @ 1992
Academic
Inc.
A market for a good or serviceis competitiveif there are many buyers
and sellers,so no singletraderexertsmuch influenceon the good'sprice.
Most of the articlesin this volume concernnegotiationsin "thin" (lowvolume)markets- often, betweenone buyer and one seller.In thin markets (see Fig. la) there is a wide rangeof "competitiveequilibrium"l
prices betweenPnirn?rd P16q7,
creatingplenty of room for negotiatinga
price.
In thin marketsit is hard to detect many errors in judgmentsof value
becausethere is a wide rangeof possibleprices.A buyer and sellercould
both misjudgethe value of the good they trade (as shownby dotted lines
in Fig. 1b), but still agreeon a price in the rational-valuerange (Pro*,
Pnt*n)'
I will discusssimpleexperimentalmarketsin which competitionamong
The financial support of the Wharton Risk and Decision Processes Center and the National Science Foundation (SES 87-08566, 88-09299)is gratefully acknowledged. The author
thanks the editors of this volume, and three anonymous reviewers, for many helpful comments. Address correspondence and reprint requests to Colin Camerer, Graduate School of
Business, University of Chicago, Chicago IL 60637.
1 The competitive
equilibrium price is the price at which the number of units demanded
equals the number of units for sale. With one buyer and one seller ("bilateral monopoly"),
as in Fig. la, there is a wide range of price at which demand equals supply.
237
0749-5978t92$3.00
Copyright O lD2 by Academic Press, Inc.
All rights of reproduction in any form reserved.
238
COLIN CAMERER
pn ce
pnce
buver values:
mrsludeed*
buver
vafues
I
rn'o'
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mislidged
pnces
I
r a n q eo f
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Frc. L (a) The rangeof pricesin a one-trademarket.(b) The rangeof misjudgedprices
in a one-trademarket.(c) Pricein a competitivemarket.(d) Misjudgedpricein a competitive
market.
several buyers and sellerspushes prices toward a single equilibrium price
(see Fig. lc). There is little room for negotiation over prices because
traders are constantly outbid or undercut by others. The lack of negotiating room enables us to focus more sharply on judgment issues. Errors
injudging value (the dotted lines in Fig. 1d) will translateimmediately into
a price different than the rational equilibrium price, denoted P.. The
amount of trading volume might be different than the amount predicted,
too. My focus is therefore on judgment errors subjects make in experimental markets. The crucial questions are whether errors affect prices
and trading volume, and whether experience reduces errors.
The article has three main sections. In the next section, I describe
several ways in which psychologists and economists view behavior in
markets differently, and how their presumptions generate methodological
differences in the way economists and psychologists construct experiments. The approach of experimental economists is described in some
RATIONALITY
OF PRICES AND VOLUME
239
detail, presuming it is not well known to readers. (The reader thirsty for
data may want to skip through this section.)
The other sections discuss evidence from market experiments about
two types of judgment errors. The second section describes errors in
judging exogeneous events that affect the value of assets. The third section describes errors in judging variables that are endogeneously created
by market activity, such as prices in future trading periods. The paper
ends with a conclusion, some implications for negotiations research, and
general ideas for future experiments.
H O W P S Y C H O L O G I C A LA N D E C O N O M l C V I E W S O F M A R K E T S
A N D E X P E R I M E N T SD I F F E R
The study ofjudgment errors in markets lies squarely at the intersection
of psychology and economics. Both fields have their point of view. The
essential difference is that economists are mostly interested in aggregate
behavior (psychologists are generally not2), and therefore make do with
models of individuals that are deliberately made too simple so they can be
mathematically aggregated.The defense of these models rests on several
hypotheses explaining how rational aggregate behavior can arise from
mostly irrational individuals. I will review these hypotheses and critique
them.
The presumptions of economists and psychologistsalso influence their
experimental methods. I review some criticisms economists often make
of psychology experiments, and give a brief primer on methods economists use in experimentation.
Mechanisms for Rational Aggregation of Judgment Errors
Before proceeding, it is necessary to define the slippery term "rational." I take rational behavior to be judgment consistent with laws of
statistics and probability (including Bayes' rule) and choice consistent
with expected utility. I speak of "bias" when judgments and choices are
inconsistent with these normative rules in a predictable direction (e.9.,
when 70% of subjects overestimatea quantity and307o underestimateit).
A market outcome is irrational if it is inconsistentwith collective behavior
of rational individuals.
In economics there is a long tradition of using admittedly unrealistic
models of individuals as building blocks for theories of aggregatebehavior
2 One reason psychologists are uninterested in markets is that a market combines several
treatment variables that are important to disentangle-the presence of others, social comparison, arousal, information cues, conformity pressures, etc. Nonetheless, a few social
psychologists (e.g., Schachter, Hood, Gerin, Andreassen, & Kennert, 1985)and sociologists
(e.g., Baker, 1984; Abolafia & Kilduff, 1988) have studied markets.
240
COLTN CAMERER
in households,firms, markets,and societies.3There are severalspecific
mechanismsby which the rational model could capturemarket behavior
even though it is a poor descriptionof individuals.To understandthese
mechanisms,it helps to think of market outcomesas a complicatedaverageof the bias in individualjudgmentsand actions(denotedb,, for the
ith individual), weighted by each individual's market activity (denoted
w,). Denote the bias in the market averageby 2b,w,.
A marketmay be a rational,unbiasedaverageof individualopinionsfor
many reasons.We call these reasonsthe cancellationhypothesis,the
smart few hypothesis,the learninghypothesis,and the evolutionaryhypothesis. Each is discussedin turn, along with counterarguments(cf.
Russell& Thaler, 1985).The discussionis summarizedin Table l.
i. A market will be rational if individualerrorsare random(the "cancellation hypothesis").If individualjudgmentsare randomly distributed
around the rationaljudgment, then a market with many participantswill
show no bias (zero averageerror). Formally, if the biasesbi, zra independentlydistributedaround0, then if there are enoughtradersand their
activity weights are not too extreme the market averageZb,w, will be
close to zero (by the law of large numbers).
However, the only interestingjudgment errors are those which create
systematicbias-people mostly err in the samedirection(thebiasesb, are
positively correlated),so their errors will not cancelout. In fact, market
errors may thereforebe even more statisticallyreliable than individual
errors.
ii. A market will be rational tf active tradersare rational (the "smert
').
few hypothesis' If more active tradersmake lesserror than less active
traders (i.e., if o21b,)and w, are negativelycorrelated),an activityweightedaveragewill show less error than the unweightedaverageindividual. The activity of a few smart traders could wipe out individual
errorsby all others.
The smart few hypothesismay hold in some specialmarkets. Equity
3 The philosophical
defense of this practice (e.g., Friedman, 1953)is that the implications
of a theory could be approximately true (e.g., markets could be rational) even if its presumptions are badly violated (people are actually irrational). For example, Plott (1986)
notes:
Almost all economic models postulate the existence (on an "as if ' basis) of a
transitive preference over lotteries. Thus, transitive choice over lotteries can be
viewed as a prediction made by the models. We know . . . that those particular
predictions of the models will be disconfirmed . . . Logic thus compels us to realize
that the "truth" of the models is not necessarily the only goal of the research effort
because we already have the answer to that question. Instead, the research question becomes the degree to which one model is better than another at capturing
market behavior. (p. 5305, my emphasis)
RATIONALITY
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COLIN CAMERER
markets are a good candidate: Persistent mistakes by a thousand investors trading 100-shareblocks can be corrected by a few rational agents
trading 100,000-shareblocks. (Of course, the argument only works if large
traders are smarter than small ones.)
ln other settings, activity-weighting will not produce unbiased market
judgprices. The market for sports betting is a pure weighted median of
ments, because bookmakers deliberately choose a "price" (usually a
point spread or handicap) to balance the amount of money bet for and
against a team. But a very smart trader cannot bet all she wants to exploit
because the most a person can bet is limited in order to prevent
un
"*or,
insiders from betting too much ("steam").
In general, activity-weighting will only eliminate individual errors if
traders who make less error than others know they make less error, have
(cf.
access to capital, and are willing and able to trade all they want
Z ec k haus er , 19 8 6 ).
iii. A market will be rational if traders who make errors learnfrom other
traders or buy advice (the "learning hypothesis"). In Somemarkets traders can learn to avoid errors (biasesb, shrink over time). In other markets,
like those for housing, education, marriages, and consumer durables,
people trade infrequently so they have few opportunities to learn from
their own experience. But people may learn by observing others who they
think are successful, or by buying advice. Imitation and advice-giving
could therefore reduce market-wide bias. (This is a kind of activityweighting in which imitation or advice induces a correlation between
birf br: 0, increasingthe implicit activity weight
biases, such that br:
of unbiased agents.)
However, there are reasons to think that imitation and advice may only
reduce bias slowly, or not at all. Learning from one's own experience is
difficult enough (Einhorn & Hogarth, 1978);learning by imitation may be
even harder. For example, suppose the psychological reasons for imitating someone'sbehavior include its memorability, social acceptability, and
simplicity. Then successful people who are mild-mannered, outrageous,
o, ur" complicated systems will not be imitated'a
Buying and selling advice is tricky too. To buy advice correctly, people
must be aware of their own biases, then shop around sufficiently before
(1985)
a In theirbookon evolutionary
Boyd& Richerson
of culturaltransmission,
models
their behavior.
describe..indirect bias": Children imitate successful people by copying
may adopt
When success is initially correlated with trait X, but not caused by it, children
becomes
X
then
trait
Having
successful.
them
will
make
it
that
trait X in the mistaken belief
include the peculiar
a self-perpetuating mark of success, even if it is maladaptive. Examples
tattooing in
Micronesian practice of contributing enormous yams to feasts, and extensive
Polynesia.
RATIONALITY
OF PRICES AND VOLUME
243
buying advice. Evidence of "cognitive conceit" (Dawes, 1976) suggests
that they are unaware of biases; insufficient search for information in
many domains (Connolly & Thorn, 1987; Cox & Oaxaca, 1988) suggests
that they will not shop around enough.
Even if people try to buy advice wisely, the supply side of the advice
market will crumble if knowledge is tacit and hard to articulate. And even
when knowledge can be articulated, it may be difficult to sell because
advice is hard for consumers to value without sampling it, and advice is
inherently difficult to divide and sample (unlike cheese and wallpaper); a
small free sample might be all the advice one needs.
iv. A market will be rational if traders who make errors are selectedout
(the "evolutionary hypothesis''). E,volutionary analogies are popular in
economics (e.g., Alchian, 1950;Becker, 1976 Hirshleifer, 1985).A common argument is that traders who make persistent errors will become
bankrupt; eventually, only unbiased traders will remain (bias b, shrinks
over time by extinction of biased traders) and markets will be unbiased.
The evolutionary analogy is appealing, but there are several reasons why
evolution is unlikely to be as successfulin explaining economic behavior
a s i n biology .
For example, economic evolution may work very slowly. Products
which are inefficient or become obsolete-COBOl
programming, the
clumsy grammar of English, vinyl LP records, the QWERTY keyboardmay persist for decades alongside superior new products. (Old products
persist if the short-run individual benefit of using the same product as
everyone else outweighs the gain from switching to a better product.5)
Evolution may also work in favor of bias rather than against it. If
rational behavior is not an optimal response to irrationality (Keynes,
1936; Arrow, 1982), then rational traders may be selected out in a world
with many irrational traders. For instance, Shleifer and Summers (1990)
describe stock market models with irrational "noise traders."6 Suppose
noise traders misperceive risk-return tradeoffs, overestimating the returns to bearing risk. Then they will invest more in risky stocks than
rational traders (who perceive the return to risk correctly). Since stocks
do have larger returns on average, noise traders will grow richer, on
average, than traders who are rational and thus more conservative.
There is also evidence that people who are biased about their relative
s This is a specific example of "coevolution," or simultaneous
evolution with externalities between parties. Quick evolution may be maladaptive if others in the population are
evolving slowly.
6 The harshest definition of noise traders is people who trade based on random information they think is accurate. More generally, in behavioral finance many types of agents who
are less than fully rational-preferably in systematic ways-are called noise traders.
244
COLIN CAMERER
abilities and personal control are less likely to be depressed than rational
people who judge their ability and control accurately (Alloy & Abramson,
1979; Taylor & Brown, 1988).Accurate self-perception may therefore be
psychologically maladaptive and get selected against by evolutionary
forces.
For population bias to be reduced by evolution, capital must be increasingly controlled by unbiased traders. But many markets have a steady
supply of new biased traders, which prevents unbiased traders from perpetually dominating markets.T Even if successful unbiased traders control
increasing amounts of resources, there is no guarantee that they will
continue to be unbiased. Diminishing returns to scale in organizationsthe economic equivalent of a swelled head-may cause more errors as
agents grow successful.
Which Mechanisms Can Experimental Markets Test?
The cancellation, smart few, evolutionary, and learning hypotheses
(i-iv above) underlie the instinctive belief in economics that collective
activity will reduce judgment error. The arguments are routinely applied
without careful thought.s Whether markets reduce error is not a matter of
faith, but a fundamental empirical question which experimental evidence
can help answer.
Experimental markets can test three of the four hypotheses rather easily. The hypotheses that errors cancel, are eliminated by a smart few, or
disappear with learning can be tested in experiments with many traders
and repeated trials. The hypotheses that advice markets correct errors or
error-prone traders are selected out are harder to test but not impossible.
Some Economic Criticisms of Psychology Experiments
Many studies which show judgment error (though not all) use the standard methods in experimental psychology: Subjects are paid a flat fee for
participating (not according to their performance) and often have no opportunity to learn from feedback. Many economistsdismiss this evidence
on methodological grounds (e.9., Merton, 1987).Why?
t As a group small
speculators have lost a large amount of money in futures markets for
decades. Presumably individual speculators either lose money and quit trading or make
money and become large speculators (who do make money, as a group). Since the small
speculators' collective record is persistently bad, quitters and big winners must be getting
replaced by new speculators who lose money too.
8 In a 1989 seminar on
choice theory, the speaker mentioned experiments in which subjects violate stochastic dominance when it is not transparent (alluding to Tversky &
Kahneman, 1986, pp. 5263-264). A famous economist (editor of a leading journal) said,
"Surely a businessman who violated dominance would be firedl" Is the editor right?
RATIONALITY
OF PRICES AND VOLUME
245
Economiststhink of peopleas allocatingscarcecognitiveeffort (e.g.,
Smith & Walker, 1990).If subjectsare not paid for their performance,the
argumentgoes,they will not think hard enoughto avoid instinctivejudgment errors. And even if subjectscannotpossiblybe instinctivelyrational, the argumentcontinues,they will learnto be over time. Hence,many
economistsdismiss experimentswith no performanceincentives and
learningopportunities.(Note that thesecriticismspresumepeoplehave
enoughfinancial incentiveand learningopportunitiesin natural settings
to avoid errors there.)
Empirical evidenceof incentiveeffectsis mixed. Performanceincentives usually reduce the rate of errors due to confusionor carelessness
(Smith & Walker, 1990),but do not typically improve average performanceor prevent rejectionof theoriesbasedon rationality (Camerer&
Hogarth, in preparation).
Learningeffectsare mixed too. There is rapid learningin somesimple
market environments(e.g., in doubleauctionsfor commodities,Smith,
1982)but not in more complicatedenvironments(Smith, Suchanek,&
williams, 1988;camerer & weigelt, 1990;Ball, Bazermatr,& carroll, in
press).Furthermore,many studiessuggestthat experienceor expertise
are no guaranteeof superior performancein naturally occurring tasks
(e.g.,Northcraft & Neale, 1987;Camerer& Johnson,l99l).
A Primer on ExperimentalEconomicsMethodology
The studiesdescribedbelow are consideredexperimentaleconomics,
which is often quite differentin methodologythan experimentalpsychology. Before discussingspecificstudiesit is useful to review someof the
principles underlying experimentaleconomicsand contrast them with
conventionsin experimentalpsychology.
In both economicsand psychologyexperiments,some parametersor
relationshipsare controlled(in settingswhich are thereforeartificial, by
necessity),to establishwhetherone variablecausesanother.An economics experimentconsistsof subjectsmakingchoicesand sendingmessages
usinga prescribedexchangeinstitutionein an environmentcontrolledby
the experimenter(Smith, 1982).(A psychologyexperimentis similar,but
usuallywithout an exchangeinstitution.)The main featuresof the envie An exchange
institution is a set of clear rules for making exchanges. The rules of an
English (ascending-price) auction, New York Stock Exchange rules, and the implicit contract that forces stores to sell goods they have in stock at prices they have posted publicly
are all exchange institutions. Note that economists carefully distinguish the skeleton of an
institution-its rules-from the conventions, history, and physical location which are its
flesh.
246
COLIN CAMERER
and its
ronment are the good being traded (or the choice being made)
"induced"
good
is
typically
value or cost to pirticipants. A value for the
on the
by paying subject, u pt.tpecified sum of money which depends
what
at
sell,
goods
they
outcome of market eichange (e.g., how many
outinto
subjects
by
prices). The exchange institution transforms choices
comes according to a specified set of rules'
in ecoTheoreticat viltdtty, incentives, and learning. Formal theory
Expernomics circumscribes the design of most economics experiments'
all the
imental economists strive to achieve "theoretical validity"-*.re
"internal
validas
well
assumptions of the economic theory met?ro-as
(do
"external
validity"
ity" ldid the treatment cause the effect?) and
conclusions from the experiment generalize to natural settings?)'
Since economic theory almost always assumes rational, self-interested
incentive to
agents and focuses on equilibrium (when people have no
validtheir behavior), the most important elements of theoretical
"f,ung.
ity have to do with incentives and learning'
must be
Incentives; Smith (1982) argued that a subject's payoffs
than the
(greater
"salient" (connected to her actions) and "dominant"
ecotest
to
subjective costs of thinking and acting) for an experiment
lacks
nomic theory. Since paying a subject a small sum for participating
of such
salience and dominance, experimental economists are skeptical
psychic payoff
experiments. Of course, intrinsic motivation provides a
power of intrinwhich does connect (psychic) payoffs to actions, but the
are wary of
sic payoffs is hard to judge and experimental economists
them.
with
Learning; Repeating the entire process of endowing subjects
their
announcing
and
actions,
choose
them
goods and money, letting
for converoutcomes ("stationary replication") are usually necessary
describes
usually
tested
being
theory
the
gence to equilibrium- Since
to
required
is
feedback
with
replication
equilibrium behavior, stationary
validity).
(i.e.,
theoretical
for
teit the theory fairly
Dataandtheiranalltsis.Thedataexperimentaleconomistsgather'and
presumptions
the way they analyze them, are largely circumscribed by
behaviorists:
essentially
are
economists
and theory in economics. Most
is connected
which
behavior
actual
are
the data they take most seriously
of
explanations
subjects'
about
skeptical
to payoffs ("salient"). They are
ro The economists' idea of theoretical validity is kin to construct validity in psychology'
constructs-usually tastes'
The idea is that a good economics experiment operationalizes
The difference in the two fields is
intended.
iheorists
way
messages-the
and
endowments,
so the proper way to
that the theory in economics is typically expressed mathematically,
have about methodology
economists
<lebates
the
result,
As
a
clear.
more
it
is
operationalize
often appear petty and picayune to outsiders'
RATIONALITY
OF PRICES AND VOLUME
247
behavior, and reports of intended behavior, so they usually do not gather
su ch dat a. lI
Labeling. Experimental economists dislike using realistic labels for elements of the experimental environment, for fear of inducing a nonmonetary utility for labeled actions (which ruins their control over a subject's
incentives). Shares of stock will thus be called "certificates"; two ran'.(A"
dom states of nature representing good and bad times will be called
and "8"; levels of effort will be called "decision numbers."
In sum, methodology in experimental economics is more theoretically
driven and fastidious than in experimental psychology. Experimental
economists seek to control incentives by inducing value for an object,
then test theoretical predictions about equilibrium behavior when subjects send messagesor trade using a specific set of rules. Careful instructions and repetition are required to lest equilibrium (long-run) behavior,
bland labels are required to avoid inducing uncontrolled incentives; and
individual-level data are often ignored because the theory makes no predictions about them. This style is virtually the opposite of most psychology experiments, which study individuals in richly labeled environments,
usually without learning opportunities or financial incentives.
J U D G M E N T S O F A S S E T V A L U E I N E X P E R I M E N T A LM A R K E T S
There are two ways in which judgment errors could affect behavior in
experimental markets. This section discussesways in which people may
misjudge the exogeneous value of the asset or good they buy and sell. The
next section discussesjudgments about endogeneoasmarket activity (like
future prices).
Som e judgm ents o f e x o g e n e o u s v a l u e a re B ayesi an. In expl i ci tl y
Bayesian experiments, subjectsknow that assetvalues are determined by
a statistical process with known prior probabilities and likelihoods. In
implicitly Bayesian experiments, the likelihoods are generatedby trading
behavior; subjects must update their beliefs about information conveyed
by price signals.
Other judgments of value are not Bayesian, but appear to be irrational
because of endowment effects or optimism ("hubris"). Endowment effects and optimism will not necessarily affect the level of prices, as errors
in Bayesian judgment will, but they will affect the volume of trade.
tt Studies comparing reports of intended trading behavior with actual trading have shown
some differences-people would say they would never pay more than $2.50, then pay $2.75
minutes later-but
the reports predicted actual behavior better than rational theory did
(Knez, Smith, & Williams, 1985; Knez & Smith, 1986). In Camerer & Kunreuther (1989),
reports of intended trading predicted market prices quite well because reporting errors either
were small or were large but far away from equilibrium.
248
COLIN CAMERER
In most experimental markets, precise values are induced by paying
subjects certain amounts of cash for objects they buy or sell. In such
markets, prices are usually close to competitive equilibrium levels (e.g.,
Smith, 1982), but it is virtually impossible for subjects to misjudge the
private value of the objects they trade. When subjects must make jud7ments of the value of goods or assets, a broad range of data suggest that
Bayesian errors in prices, and errors in the amount of trade stemming
from endowment effects or optimism, are common in experimental marke ts .
Errors in Explicit Bayesian Judgments
Suppose the value of assetsdependson a random "state ," X or Y. The
states might represent "strong economy" and "weak economy" or high
and low demand for a product. Before investing in assets,people usually
would not know the state but they would see signals which are correlated
with the state-expert forecasts about the econoffiy, or results of test
marketing. Investors face a classic Bayesianjudgment task: They must
infer the posterior probabilities of the states (i.e., the probabilities after
accounting for sample or signal information), and hence the expected
asset value, from the signals and the states' prior probabilities.
Camerer (1987) studied an experimental market in which a Bayesian
judgment task was embedded. (Duh & Sunder, 1986, did so earlier, and
independently.) There were two states, X and IZ. Occurrence of X was
physically represented by drawing a ball numbered 1-6 from a bingo cage;
drawing 7-10 meant Y had occurred. (The bingo cages were intended to
induce the subjective probabilities P(X; : .6 and P(Y) : .4.)
Subjects did not know the state. But if X had occurred, three balls were
drawn with replacement from a bingo cage with I red ball and two black
balls. If I'occurred three balls were drawn with replacement from a cage
with two reds and I black. The draws gave subjects clues about which
state had occurred. Black draws suggested X, red draws pointed to IZ.
Figure 2 shows the bingo cage setup.
In each trading period, subjects were given two shares of an asset.
Subjects got a dividend for each share they held at the end of the period,
which depended on whether X or I' had occurred. Half the subjects
(called type I) got 500 "francs" for X (equal to $.75) and 200 for Y. The
other half of the subjects, type II, got 350 for X and 650 for )'.12
The value of the assets to subjects depends on their subjective probabilities of X and I', which depends on the sample of balls drawn from the
X or Xbingo cage. Suppose the sample of draws was two blacks and 1 red
r2 These asset dividends were chosen so that the two theories
of most interest would make
different predictions.
RATIONALITY
OF PRICES AND VOLUME
249
l0 balls
N u m b e r e d1 - 1 0
I n i t i a lC a g e
Ftc. 2. The bingo cagedesign.Reproduced,by permissionof the publisher,from Came r e r( 1 9 8 7 ) .
("1 red"), which indicatesthe stateis likely to be X. A Bayesiansubject
would calculateP(Xll red) : .75.If the subjecthad type I dividends(and
was risk-neutral)shewould thereforepay up to (.75X500)+ (.25)(200):
425francsfor a shareof the asset.Bayesiantype IIs would pay up to 425
francstoo. Thus, if subjectsare Bayesianpricesshouldrise near 425and
we cannottell whethertype I or type II traderswill buy shares.
The Bayesiancalculationsare difficult and counterintuitive.Many alternativepsychological
hypotheses
are suggested
by behavioraldecision
theory studiesof judgment.The hypothesiswhich is clearest(and turns
(Kahneman& Tverout to fit best)is a variantof "representativeness"
sky, 1972b).
An intuitiveheuristicfor judgingP(statelsample)
is to assesshow representativethe sampleis of the state.A sampleof 1 red and two blacksis
maximallyrepresentative
becauseit exactlymatchesthe contentsof the
X-statebingo cage.One could interpretrepresentativeness
to then imply
P(Xll red) : 1, but that predictionis too extremeand can be easily
rejected.Instead,I take representativeness
to imply P(Xll red) > .75.
Then market priceswill be greaterthan 425francs and type I traderswill
buy the assetsfrom type II traders.
Each experimentalsessionwas a seriesof trading periods.In each
period a statewas determinedand three balls were drawn from the X or
Y cagesand announced.Subjectstradedassetsin a double-oralauction:
Tradingone shareat a time, both sidesshoutedout bids to buy, offers to
sell, and acceptancesof others' bids or offers. At the end of a trading
periodthe statewas announced,dividendswere paid, subjectsfiguredout
250
COLIN CAMERER
their profits, and their shares expired. In the next period each subject got
two m or e s har es a n d th e w h o l e p ro c e s s b egan agai n (" stati onary
re p lic at ion" ) .
Figure 3 shows prices in an experiment. The four panels show the mean
prices in those periods of an experiment which had the same sample of
balls. In Experiment 6, for instance, there were two periods when the
sample of balls was three blacks and 0 reds (denoted "0 red"). These
periods occurred randomly throughout the experiment, but Fig. 3 shows
mean prices in the two periods taken out of chronological order and
plotted consecutively. The thin horizontal line is the Bayesian prediction.
The arrow marked '5R" shows the direction of deviation from the
Bayesian line predicted by representativeness.In the l-red periods of
Experiment 6, prices began far below the equilibrium price and converged
within a period or two to the Bayesian level, then went above it as representativenesspredicts. Prices did not converge to a precise equilibrium,
but they show no tendency to decline back toward the Bayesian level.
Prices in these experiments were generally volatile, but tended to be
higher than the Bayesian predictions when the samplesof balls have 1 or
two reds and lower when the samples have 0 or three reds. One way to
analyze the data from many experiments is to use prices at the end of the
experiment to infer an implicir probability. If the price in a 1-red period
was 441 francs and type I traders bought most of the shares, we infer their
subjective P(n from 441 : 500P(X) + 200(l - P(n), yielding P(X) :
.8 0 3. ( T his pr oc e d u re i s c ru d e -i t a s s u mes expected uti l i ty, ri skneutrality, and perfect competition-but tells us something.)
R
R
/
Ir 4
mean
0
3 redr
r5
IO
n u m b eor f p e r i o d s
FIc. 3. Average trading prices: Experiment 6. Reproduced, by permissionof the publisher, from Camerer (1987). Horizontal line denotes Bayesian prediction.R, directionof
representativeness deviation from Bayesian.
RATIONALITY
25r
OF PRICES AND VOLUME
Figure 4 shows a probability line, with the Bayesianposterior probabilities marked for each of the four samplesof balls. Open circles show
the averageimplicit probabilitiesfor each of the four samples,averaged
acrossnine experimentswith inexperiencedsubjects.Closedcirclesshow
the same for six experimentswith experiencedsubjects.The implicit
probabilitiesare extremelycloseto Bayesianin 0- and 3-redperiods.The
implicit probabilitieserr in the directionpredictedby representativeness
(shownby an arrow marked"R") in l- and 2-redperiods,rather strongly.
Inexperiencedsubjectsregarda sampleof I red as beingalmostas indicative of the X stateas a sampleof 0 reds. Experiencereducesthe size of
representativeness
bias-that is, the closedcircles are always closer to
the Bayesianposteriorsthan open circles-but doesnot eliminateit.
Duh and Sunder(1986)and Andersonand Sunder(1989)report roughly
similarresultswith students,but two experimentswith professionaltraders suggestless bias. The professionalstraded at higherprices than studentsdid, which happenedto be closerto Bayesianlevels,but they also
showedlessunderweightingof baseratesin the blue-greentaxicabproblem used by Kahnemanand Tversky (1972a)to demonstraterepresentativeness.
Subjectsgot an enormousamount of compactedexperiencein these
experiments.Subjectsmade 20 Bayesianjudgments before trading so
they could understandthe bingo cagearrangement.Then they tradedfor
2G35 periods. Experiencedsubjectsdid everythingtwice so they saw
8f100 sampleswith feedback.A hundredrepeatedtrials is /essexperience than tradersmight have in natural settings,but the ability to learn
from this laboratoryexperiencemay be greaterbecausethe environment
r--T-
P(X/O reds)
l.oo |
.923
Bayesian
posteriors
T--l
P(X/2 reds)
l
P(X/l red)
|
.750
P(X/3 reds)
l
kgend:
U
:.
N
A
FIc.
mean, inexperienced-subjectexperimenls,N-red sample
mean, eperienced-subject experiments,N-red sample
direction of predicted representativeness
bias
4. Graphical
comparison
of probabilities
implicit
in market
prices,
and Bayesian
posteriors.Reproduced,by permissionof the publisher,from Camerer(1990).
252
COLIN CAMERER
is stationary and feedback is frequent, immediate, and clear (see, e.g.,
Einhorn & Hogarth, 1978).
Representativeness biases might be common and large for infrequent
events which are rare and difficult to learn from. For example, stock
market traders were nervous over the weekend in mid-October 1989,
because the previous Friday's large market drop was highly representative of the big Friday drop before the 500-point crash on Monday, October
19,1987. They braced for a similar Monday crash; the market went up
instead (Wall Street Journal, l989a,b).
Another example: In the summer of 1990film studios released several
big-budget movies which resembled the blockbuster "Batman" from the
previous summer (Wall Street Journal,l990). Most of the 1990movies did
poorly. Perhaps the representativeness of the movies to "Batman"
caused studios to ignore the low probability of such expensive films making money.l3
Errors in Implicit Bayesian Judgments
Many market experiments are implicitly Bayesian; they test a theory
which assumesthat people are making some kind of Bayesianjudgment,
even if priors and likelihood data are not made clear using bingo cages.
Markets with insiders. Plott and Sunder (1982)studied markets in which
assetslived one period, then paid either a high or a low dividend. Before
trading, all subjectsreceived a "clue card"; 6 of l2 subjectsgot clue cards
saying whether the dividend was high or low. Could "clueless" subjects
(noninsiders)learn the dividend by observing prices?
When the dividend was high, six insiders knew it and bid prices up. An
observant noninsider trader should infer from the bidding that the insiders
knew the dividend was high instead of low. That inference requires an
implicit Bayesianjudgment: traders must figure out P(high dividendlrising
prices) from the prior P(high dividend) and the observation that P(rising
priceslhighdividend) is usually greater than P(rising pricesllow dividend).
(The judgment is only implicitly Bayesian because P(rising priceslhigh
dividend) and P(rising pricesllow dividend) are learned by subjects, rather
than told to them.)
Figure 5 shows a typical experiment. The graph plots the time series of
prices in each of several periods. (A different dividend and fresh clue
cards were used each period.) The solid line shows the rational price; the
13The much-hyped "Dick Tracy" was most representative:
Like "Batman," it had a
large production budget of $25 million (and an even larger ad budget); both movies were
based on comic strips, had famous actors starring as villains, offered many commercial
product tie-ins, etc. "Dick Tracy" grossed more than $100 million, only half of what
"Batman" earned (but hardly a box-office flop).
RATIONALITY
253
OF PRICES AND VOLUME
l{n
Tiansacted
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200
ATE
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FIc.5. Trade prices, in insider experiments. Horizontal line denotes predicted prices:
solid line is the "fully revealing," rational expectations price; dotted line is naive, private
information price. Reproduced, by permission of the University of Chicago, from Plott &
S u n d e r( 1 9 8 2 ) .
dotted line shows the price predicted if noninsiders ignore information
conveyed by prices. Most noninsiders ignored price signals in the early
periods with insiders (marked "private information to six insiders"). In
later periods, noninsiders learned from price signals and prices rose or fell
to "fully reveal" the true dividend (see period 9, for instance). Others
have largely replicated these results (Banks, 1985;Friedman, Harrison, &
Salmon, 19841'
Plott & Sunder,1982; Forsythe & Lundholm, 1990).
While convergence in insider markets is persistent, it is not clear evidence of Bayesian updating. Simple heuristics which use prices as an
indication of inside information could generate convergence too, even if
254
COLIN CAMERER
they violate Bayes rule. An indirect way to test whether traders are truly
Bayesian is to put them in more complicated settings which require more
difficult Bayesianjudgments.
Mirages. Keith Weigelt and I (1991)studied one such complicated setting. Our experiments were virtually identical to Plott and Sunder's, except for one twist: Before each period a coin was flipped to determine
whether there would be any insiders in that period. If there were insiders,
then six traders got clue cards with the dividend value (high or low). If
there were no insiders, everyone got a blank card.
A trader with a blank card could not tell whether six others knew the
dividend or whether everyone saw blank cards. Therefore, a few random
price changes might trigger an avalanche of mistaken Bayesian updating
in periods with no insiders. One trader could mistakenly take price movements as a sign that others knew the dividend was high, then Bayesianupdate and begin bidding prices up. Others would observe her and conclude that she knew the dividend was high, "learn" from her mistake, and
bid prices up further. Once prices rise to the high dividend level subjects
are unlikely to question their inference that others knew the dividend was
high, so prices will not fall.
We observed only a few mirages which lasted through an entire trading
period. Figure 6 shows them. Each of the four pairs of trading periods
comes from a different experimental session. In each pair, the first period
shows trading with insiders and the second period shows trading with no
insiders. The thick line representsa time series of prices at which trades
took place; the thin line is the rational price.
For example, the upper left shows periods 5 and 6 in one session.Prices
in period 5, in which there are insiders, rose to the rational level (375).
Prices in period 6 (with no insiders) began at the high level where prices
in period 5 had left off, falsely signaling that some insiders knew the
dividend was high. Prices never fell becauseeveryone thought someone
else knew that the dividend was high.
The mirages shown in Fig. 6 always occurred early in the experimentra
and had the following form: In period T, there were six insiders and prices
moved to the appropriate dividend level. In period T + 1 there were no
insiders, but for some reason the first few trades resembled the path of
prices in period T (see Fig. 6). Traders in period T + | overreacted to the
initial trades, mistakenly inferring that there were insiders, and prices
rose to the same level as in period T.
Endowment Effects and Trading Volume
Some judgment elTors will affect the amount of trade rather than prices.
to Later in the experiments
subjects learned that the pace of trading was a sign of whether
there were insiders present or not. (Trading was slower when there were no insiders.)
RATIONALITY
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An example is the "endowment effect," which leads people to overvalue
objects they own. For example, Knetsch (1989) gave some subjects a
coffee mug and allowed them to exchange it for a candy bar. Only llVo
made the exchange. when given candy instead, only l0% chose to exchange it for a mug. (Given a choice with no initial endowment,56To took
mugs and 447o took candy.)
Kahneman, Knetsch, and Thaler (in press) studied endowment effects
in a market setting. In a typical experiment they gave 36 subjects coffee
mugs; 36 others got nothing. Mug-owners gave the lowest price they
would sell their mug for; others gave the most they would buy a mug for.
Supply and demand curves were constructed by ordering selling prices
from low to high and ordering buying prices from high to low. Where the
curves crossed determined the market price of mugs: Everyone who said
they would pay that much (or more) then actually bought a mug, at the
market price, from the mug-owners who said they would sell for that
p ric e.
The normative prediction is that about 18 of the mugs will be traded,
but only about 6 were. Selling prices were much higher (median : $7.12)
than buying prices ($2.S2).In this market it is not clear whether selling or
buying prices (or both!) are irrational,r5 but the low volume of trade is
clearly irrational (i.e., inconsistent with endowment-free preferences).
Endowment effects arise becauseselling prices must be especially high
to salve the pain of losing an item. A similar "disposition effect" occurs
in trading assetswhich vary in value, such as shares of stock (Shefrin &
Statman, 1985).People are often eager to sell assetswhich have gained
value and reluctant to sell assets which have lost value. For example,
trading volume is lower for stocks that recently fell in price (Ferris, Haug en, & M ak hija, 1 9 8 8 ).
Disposition effects seem strongest in housing markets, where losses
and gains can be large and there are few professional investors accustomed to absorbing losses. When prices fall, people seem to keep their
houses on the market longer rather than cutting prices and selling at a
loss.t6 When prices rise (as in southern California in the 1980s)people
15A third group
of "chooser" subjects chose between having a mug and a sum of money,
for several possible sums. Their valuations (the smallest sum they would rather have instead
of a mug) had a median of $3.12,much closer to buying prices than to selling prices. This
result suggeststhat sellers are overvaluing the mugs, because choosing between a mug and
money is exactly what a mug-owner does in setting a selling price. The difference between
choosing and selling is simply the endowment effect of actually owning a mug.
16Of course, there
are good reasons to avoid selling at a loss, like belief in an imminent
market upturn or arrival of a special buyer. But these reasons should also make people less
eager to sell their houses at a profit.
RATIONALITY
OF PRICES AND VOLUME
257
often buy and sell housesrepeatedly.Agents and stockbrokersmay encouragethe dispositioneffect rather than extinguishit.17
Optimismand Trading Volume
Endowmenteffectswill createtoo little tradein somegoodsand assets.
Then why is there so much trading in many assets?Securitiesare an
example.It is sensibleto trade sharesto speculateon their future value,
for tax-relatedreasons,or to adjust liquidity or risk of a portfolio of
assets.The speculativemotive seemsto be the most important; but two
peoplewho tradewith eachother cannotboth expect,rationally,to make
money by pure speculation.(In economicsthis is called the no-tradeor
Groucho Marx theorem,namedafter the comedianwho said he "did not
want to join any club that would have me as a member;" seeMilgrom &
Stokey, 1982.)
The GrouchoMarx theoremassumespeopleare rationaland humbleall think their expectedtrading profits are equal. But most people think
they are above averagein luck, ability, future prospects(Weinstein,
1980),drivingability (Svenson,1981),etc. (Taylor& Brown, 1988).A
similaroptimismabout one's tradingability or informationwill lead to an
irrationally high volume of trade. (Roll, 1986,explainedthe takeover
boom this way.)
In sum: Subjects in market experimentsappear to err in making
Bayesianjudgments of events that affect or convey information about
assetvalue. Their behaviorsuggestsa tendencytoward representativeness,though experienceand possiblyexpertise(in one study with professionaltraders)reducethe degreeof representativeness
bias.Two other
kinds of irrationality,overvaluinggoodsin one's endowmentand being
optimisticaboutone's relativetradingperformance,may not affectprices
but affect whetherthere is too little or too much tradingcomparedto the
benchmarkof rationalbehavior.
J U D G M E N T SO F E N D O G E N E O U SM A R K E TV A R I A B L E S
In the last section we saw examples of how judgment errors about
exogeneouslydetermined asset value affected prices and volume in market experiments. People might also make biased judgments about variables generated endogeneously by their own collective activity-future
prices, for instance. To test for bias in such judgments, studies of the
r7 When selling a house that had
only increased in value slightly, my agent picked an
asking price by figuring out what price would keep me from suffering a loss (after paying
commissions and taxes). I explained that the price should depend on what the market would
bear, not on the initial purchase price. A polite discussion followed, in which both of us
thoueht the other was an idiot.
258
COLIN CAMERER
rationalityof forecastsof future pricesare reviewedbelow. (Forecastsare
typically not rational.)Then a market study of "iterated expectations"forecastsof others' forecasts-is described,and somenew data are presented.
Expectationsof Future Prices
There are many studies of whether price expectationsare rational.
Most of the studiesuse publishedforecastsby consumers,businessmen,
or professionaleconomists(see Lovell, 1986,and Williams, 1987,for
reviews).Generally,they find that forecastsare biased:That is, forecast
errors (differencesbetweenforecastsand actual results)have a nonzero
mean. Forecastsare usually irrationaltoo: They are correlatedwith observablevariables(typicallypastforecasterrors and currentforecastlevels), implyingthat someavailableinformationis ignoredwhen forecasts
are made. Forecastsalso usuallyfollow an adaptiveprocessin which
forecastchangesare relatedto pastforecasterrors(Nerlove, 1958).Expectationsare adaptiveif the adaptationcoefficientb is positive in the
formula
E(P,) - E(P, ) : blP,-r - E(P, ,)1,
(l)
where E(P,) denotesthe forecast of prices in period r and P t - r is the
actualprice in period I - 1.
Apparentviolationsof rationalityof naturallyoccurringforecastscould
be due to Bayesianlearningin an economywherethe statisticalprocess
generating
outcomeskeepschanging(Caskey,1985;Lewis, 1989).Therefore, severalexperimentsexaminedforecastsof outcomesof a statistical
processthat is unknown but fixed throughoutthe experiment(Schmalansee,1976;Garner, 1982;Bolle, 1988).Their resultsare generallyinconsistentwith rationalityof expectations
too, but suggestsomelearning
and rationalityin specialsettings(Dwyer, Williams,Battalio,& Mason,
1989).Severalresearchers
have studiedforecaststhat subjectsin an experimentalmarketmakeof the future priceswhich they themselvesgenerate.
Williams(1987)was the first. He studiedforecastsin doubleauctionsrs
for one-periodgoods. In his simple market, subjectshave a lot more
information and learningopportunitiesthan forecastersin most natural
settings.But subjects'forecastswere still biased(a penny too high, r :
4.3) and only weakly correlatedwith actualprices.Forecasterrorswere
r8 ln a double auction, buyers and sellers both shout
or post bids to buy goods and offers
to sell goods. Securities and commodities exchanges are the most familiar and important
examples.
RATIONALITY
OF PRICES AND VOLUME
259
autocorrelated(r : .15) and highly adaptive(b : .86). Forecastsof
experiencedsubjectswere slightly lessbiasedand error-prone.
Wellford (1989)studied "cobweb" markets in which suppliersmade
productiondecisions,basedonly on pastprices,and then sold their supply in a market (see also Carlson, 1967).leIn her markets,prices and
quantitiesmay cycle aroundin an unstablepattern(resemblingthe web of
a spider)if suppliers'expectationsaboutfuture pricesadapttoo readilyto
past prices(i.e., if b is too closeto I in Eq. (1)).Rationalityof expectations is therefore crucial to avoiding boom-and-bustcycles in cobweb
markets.
In Carlson's cobweb experiments,quantity and price choicesconvergedafter severalperiods.Wellford'sexperimentsconvergedin six of
eightcases,but two experimentsexhibitedchronicfluctuations.In both
studies,estimatesof the adaptationcoefficientb rangedfrom .5-.7.
Smith et al. (1988)studiedforecastsin a more complexmarket.Their
subjectstradedassetswhich lived l5 periodsand paid a randomdividend
D eachperiod.If subjectswere rational,priceswould beginat l5D and
fall by D cents each period. But prices often beganbelow the intrinsic
value, rose a couple of dollars above it in a speculativebubble, then
crashedtoward the end of the experiment.
While the price dynamicsin the l5-period assetmarketsare quite different from the one-periodmarketsstudiedby Williams and the cobweb
marketsof Carlsonand Wellford, the forecastpropertiesare remarkably
similar.Forecastsin the assetmarketswerebiased(a nickeltoo high,/ :
(r : .28)and correlatedwith
3.0). Forecasterrors were autocorrelated
price levels (errors were negativeduring price rises and positive during
crashes).Forecastswere adaptive(b : .82),not rational.
Camerer and Weigelt (1990)studied markets in which assetspaid a
constant(marginal)dividendD eachperiodand lived from periodto period with a probabilityp. The intrinsicvalueof assetsis ^D + (1 - p) D
+ (1 - ilzD +... : Dlp.PricedynamicsweresimilartothoseinSmith
et al. (1988):Priceswere very slow to convergeand sometimesovershot
(r : .39), negatively
the intrinsic value. Forecastswere autocorrelated
correlatedwith forecastlevels (when forecastswere low they were too
low; when they were high, they were too high),and adaptive(b : .77).
Danielsand Plott (1988)ran experiments
for one-periodgoodsin which
supplyand demandcurveswere shiftedupwardby 15%eachperiod.The
shifts createdprice inflation, which subjectslearnedto anticipate.Forecasterrorsappearto be autocorrelatedandcorrelatedwith price levels,as
re Cobwebs could occur in any
market with a steep demand curve and a flat supply curve,
where there are time lags between production and sale (like markets for clothing, labor,
consumer durables, housing or office space, agricultural products; e.g., Ezekiel, 1938).
260
COLIN CAMERER
in the other studies (but no direct tests were reported). However, subjects
did learn to forecast the inflation rather well, and forecasts did not depend
on previous forecasts as in adaptive models (b was around 0).
In sum: The assumption that forecasts are rational is repeatedly rejected in a wide variety of experiments in different environments, using
both forecasts of an exogeneous time series and subjects' forecasts of a
time series of prices they create themselves. Forecasts are usually slightly
biased (too low if prices are rising; too high if prices are falling). Forecast
errors are autocorrelated and correlated with observables (previous price
changes or current forecast levels). And forecasts are invariably adaptive-the current forecast equals the previous forecast plus a coefficient
b times the previous forecast error, and estimates of b are remarkably
constant, between .6 and .8. The only exceptions showing rational expectations are the random walk experiment of Dwyer et al. (1989)and the
inflation markets of Daniels and Plott (1988).
Iterated Expectations of Prices
Sports handicappers post opening or "morning-line" odds which forecast what odds will be at the time of a game or race, hours or days later.
The game-time odds are themselves a forecast by bettors of a game's
outcome. The handicappers are therefore forecasting a forecast.
There are many other examples of such "iterated expectations." Investment bankers price a new issue of common stock by forecasting what
investors will think the stock is worth; the price investors pay is itself a
forecast of future earnings. Gallery owners show art, corporate agents
buy wine and clothes, and theater owners show movies after guessing
whether the public will buy their products; the public's purchasesdepend
on their own forecasts of product quality. In all these cases, agents forecast the forecasts of others.
When a well-informed agent forecasts the forecast of a less-informed
agent, her sophistication may get in the way. Her additional information
is psychologically available (Tversky & Kahneman, 1973) and hard to
forget when imagining how much others know. For instance, teaching is
difficult because it is hard to imagine how little students know. People
give poor directions to their homes because they forget to mention landmarks only newcomers would notice. Product designers overestimate
how easy it is for regular folks to master tricky functions on high-tech
devices (cf. Norman, 1988). And information about an event that occurred causes "hindsight bias" in recollections of what event people
expected (Fischhoff , 1975).
All these examples reflect a "curse of knowledge": people who know
a lot are cursed by their knowledge when guessing what less-informed
people know. Formally, the more-informed agents in these examples have
RATIONALITY
OF PRICES AND VOLUME
26r
a large set of information,1-or".The eventor variablebeingforecastedis
X. In forecastingthe forecastsof otherswho know only 1,... (where11...
is a subset of 1-o..), the more-informedagentscalculatean "iterated
expectation" EfE(X11,..r)11n.,or.]-the
expectation,knowing1_or",of what
people who know less (1r",.)will expect. It is a simple mathematical
exercise2oto show that EIE(X11,",.)11-.."1
should equal E(X11,..,)if 1,.,. is
a subsetof 1*o,". The curseof knowledgeoccurswhen EIE(XVrc,,)l/.,,o."]
is closer ro E(xll^o.") than it shouldbe. A simpledescriptivemodel is
EIE(XVrc,,)l/-o,"1: wE(XlI-o,") * (l - w)E(X11,",,).
(Z)
If w : 0 subjectsbehavenormatively;w: l is pure curseof knowledge
(peoplewho know more are sure that others do too). The weight w representsthe degreeof curse of knowledge.
Camerer,Loewenstein,and weber (1989)looked for curse of knowledge in experimentalmarkets. Before the marketsbegan,one group of
"uninformed" subjectsguessedthe 1980earnings-per-share
(EPS)of several actualcompanies,basedon accountingdata from 1970to 1979anda
value Line profile of the firm's 1980EPS prospects,written very early in
1980.Call their averageestimateE(EPSldata).
Subjectsin the marketstradeda one-periodassetwhich paid a dividend
equal to the averageestimateof uninformedsubjects,E(EPSldata).To
value the assetcorrectly, market subjectshad to make the best possible
guessof what uninformedsubjectsthought 1980EPS would be. The twist
is that market subjectsknew Lheactual EPS. Their guessabout the uninformed subjects'averageestimateis thereforean iteratedexpectation,
EtE(EPsldata)ldata
and EPSI. If market subjectssufferfrom the curseof
knowledge,assetpriceswill generallybe closerto 1980EPS than they
shouldbe.
Subjectstraded assetsbasedon the earningsof eight different companies,for two tradingperiodseach.Beforeand after every tradingperiod,
eachsubjectguessedthe assetvalue.We cancomparetheir guesses,
after
two tradingperiods,with guessesmadeby a separategroup of individual
subjectswho also knew the actual EPS but did not trade in markets.
Figure 7 showsthe degreeof hindsightbias or curse of knowledge(an
estimateof the weight w in Eq. (2) above)for eight companies,for subjects who participatedin markets("market judgments")and subjectswho
simply madeguessesas individuals("individualjudgments").The curse
of knowledgeoccursin marketsubjects(w is positive)but marketsubjects
show half as much curseas individuals.(The /-statistictestingfor a market-individualdifferenceis given below eachcompany;it is significantat
20The claim that "it
is a simple mathematical exercise" illustrates curse of knowledge.
262
COLIN CAMERER
l n d r v r d r r aJ lu d g m e n t s
Pl:R(l:NT
101'(.
I i l N D S t C tl T
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t0,)b
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Ftc. 7. Degree of hindsight (or curse of knowledge) in individuals (dotted line) and market
traders (solid line). Reproduced, by permission of the University of Chicago, from Camerer,
Loewenstein. & Weber (1989).
p < .05 for three of eight companies).The curse also varies a bit across
companies, indicating some difference in surprisingness of actual earnings.
The market experiments test some of the arguments economists have
for market erosion of individual errors. The errors do not cancel out
because they are systematically biased toward actual EPS. Separate samples of individual subjects (not trading in markets) showed that incentives
and feedback did not reduce biases. We did not test the influence of
evolutionary selection and availability of advice on reduction of bias.
Consistent with the smart few hypothesis, we did find that less biased
traders were slightly more active-S6% of the bids to buy, offers to sell,
and trades were made by less biased traders, and 447o by more biased
ones. Traders' biases were also reduced by trading with others 63Voof
the changesin their judgments between trading periods reduced bias,37Vo
increased bias.
Some new experiments. One implication of the curse of knowledge is
that more information might hurt, becauseit makes the curse worse.2r A
worthless good that is freely disposable-used motor oil, or curseproducing information-should have a price of zero. In two new experi2r In semesters when you
are teaching negotiations to MBAs, do not attend technical
game theory seminars. lf you must attend, close your eyes and listen to a Walkman or hum;
what you see or hear can only hurt your teaching.
RATIONALITY
OF PRICES AND VOLUME
263
ments, we auctioned off the actual EPS to market subjects. Since it does
not help subjects establish the value of assets,the information is worthless. Would subjects bid zero for it?
The actual EPS was sold to the four highest bidders in each period, at
the fifth highest price.22Their bids are shown in Tables 2 and 3. Rows
represent different subjects; columns represent different companies (in
chronological order).
Many subjects apparently had no idea how to value the information at
first, or were confused, since bids for information began in the first (Diamond) period at high prices close to the assetvalue ($3.+S;.By the fourth
or fifth auction prices converged to zero. Some subjectseven made small
negative bids-they had to be paid to know something worthless! (Of
course, worthless information is not freelv disposable, because of its
availability in memory; hence its negative price may actually be ration a l .23)
The information auction separated traders into those who knew the
actual EPS (and were vulnerable to curse of knowledge) and those who
did not. We can then analyze the trading activity of informed and uninformed traders. The results are an interesting mixture of evidence for and
against market forces. Within each group of four informed traders, the
two least-biased traders did not bid, offer, or trade any more often
(50.4%, n : 262) than the two most-biasedtraders.2aHowever, the four
informed traders were disproportionately active compared to the five
uninformed traders (thev took 52.6% of actions instead of 44%, n : 576,
z : 4.2).
Theinformation
in theformof tradesbroughtthejudgments
exchanged
of the two types of traders closer: Informed traders were more likely to
move away from the pure-curse prediction (55% away, n : 60, z : .8);
uninformed traders were more likely to move toward it(57% toward, n :
6 1 ,z : 1 . 2 ) .
2 2l n a " h i g h e s t - r e j e c t e d - b i d " o r " r z * l s t - p r i c e " a u c t i o n ( V i c k r e y , 1 9 6 l ) , b i d d e r s
should simply bid their true value for an object, since their bids never determine the price
they pay. Such auctions do not reveal valuations perfectly in experimental settings, but no
auction is known to be better for revealing valuations.
2r Robyn Dawes once used a Ph.D. admissions application with a section allowing applicants to state additional information about themselves. One student added something Dawes
knew he should ignore but could not. He eventually paid to have the forms changed so
applicants could not add anything extra, thus providing an example of someone paying to
nol know information.
24The lack of difference in trading activity between less- and more-biased traders here
contradicts the finding that less-biasedtraders took more action in the original experiments.
The smaller sample of "informed" traders in the new experiments may account for the
difference.
264
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Market prices were slightly less biased than in the original experiments,
in which all traders knew the EPS. As in the other experiments reviewed
above, the possibility of some unbiasedtraders in these markets does nol
guarantee that markets will be unbiased (contrary to the smart few hyp o t hes is ) .
C O N C L U S I O N S ,I M P L I C A T I O N SA, N D R E S E A R C HD I R E C T I O N S
Many markets are competitive in the sense that no single trader has
much influence over prices. In such markets, it is natural to turn attention
from where in a zone of agreement negotiated outcomes lie, to whether
traders can properly estimate the value of the good they trade. The shift
in focus to trader judgment then raises the difficult question of whether
mistakes individuals make will aggregate into a market-wide error in
p ric es .
Economists instinctively believe that markets are likely to price goods
correctly even if individuals make mistakes, for any of several reasons.If
errors cancel out, a few smart traders control the market, or irrational
traders learn or go bankrupt, then the market will reduce individual errors. Whether these conditions hold, and hence whether errors aggregate
or not, is fundamentally an empirical question.
Several studies of markets by experimental economists shed light on
this question. Experiments can test the hypothesesthat errors cancel or
are extinguished by a few smart traders or by learning (but experiments
are less well suited to studying evolutionary effects).
Conclusions
The studies generally indicate that errors in judgment, of the kind investigated by psychologists studying individuals, do persist in market
prices and measures of trading volume.25However, experience usually
reduces errors.
For example, studies of markets for assetsof uncertain value (Duh &
Sunder, 1986; Camerer, 1987) indicate that a theory based on "representativeness" judgments predicts prices better than a theory based on
Bayes' rule. Overreactions to market price signalswhich are mistakenly
thought to convey information-"mirages"-suggest
representativeness
to o ( Cam er er & W e i g e l t, l 9 9 l ).
Irrationality, in the two forms of instinctive preferences for goods in
one's endowment and the tendency to overestimateone's relative perforz-sMy conclusion disagrees sharply with Plott's (1986). The important
difference is that in
all the settings reviewed here, individual error was expected. The open question was
whether market errors would be smaller than individual errors. Plott surveyed several
experimental domains in which individual error was not predicted.
RATIONALITY
OF PRICES AND VOLUME
267
mance in trading, is also observed in market experiments (Kahneman et
al., in press). These brands of irrationality can explain why the amount of
trading is either lower or higher than predicted by rational models.
Forecasts subjects make about future prices in market experiments are
typically not rational either. Their forecasts are biased, and errors in
forecasting are autocorrelated and correlated with price levels and other
observable variables. Forecasts usually are adaptive, too: they are adjusted based on previous forecast errors (rather than on knowledge of
underlying economic structure, as "rational expectations" are). In forming "iterated expectations" (expectations about other subjects' expectations) subjects are unable to ignore extraneous information they have that
others do not have.
The data suggest that individual errors are sometimes reduced, but not
eliminated, in experimental markets under ideal learning conditions. They
cast doubt on the optimistic presumption that prices negotiated in competitive market settings will always reflect true values.
Some Implications for Negotiation
The kinds of judgment and forecasting tasks studied in experimental
markets are present in most negotiations too. Errors that were apparent in
market prices and trading volumes are likely to appear, perhaps magnified, in less competitive settings (like trade between one buyer and one
seller).
Negotiators often struggle to forecast an event or numerical value
based on a sample of information. The influence of representativenessin
the experimental markets suggeststhat negotiators will succumb to representativeness too, overweighting small samples of information and underweighting the effects of base rates, regression-toward-the-mean, and
event conjunction. For example, I suspect novice labor negotiators form
beliefs about the likelihood and length of a strike by recalling or imagining
a particularly long, destructive "representative" strike and thinking
strikes must be rare. Strikes are actually quite common (lVl\% of major
wage negotiations end in strikes) but relatively short, lasting only a month
on average (Card, 1990). The fact that forecasts of future prices are so
strongly adaptive in experimental markets suggests that negotiators will
overreact to previous errors in negotiation (cf. the old adage that "generals always fight the last war").
Mirages may occur when negotiators think the actions of others convey
more information than they do. In "The Big Picture," a satire of Hollywood, an unsuccessful screenwriter gets a call from his agent while he is
busy making toast. The toast burns so he says he must call the agent back.
The agent suspects his client is actually talking to other agents about a
script (rather than burning toast) and calls some others to check. Each
268
COLIN CAMERER
agentwho gets called then immediatelycalls the screenwriter.Since he
has gone out for the afternoon, nobody can reach the screenwriter,so all
the agentswho call him assumethat he is meetingwith other agents.He
returnsto find dozensof messages
on his answeringmachinefrom agents
offering giant sums for his wonderful script. One can imagine similar
miragesin bidding for highly prized workers, target firms, initial stock
offeringsof companies,etc.
Optimismabout relativeperformancesuggeststhe oppositeerror: Negotiatorswill ignorethe informationsignalsthat actionsof othersconvey.
The "winner's curse" is a famous example (Samuelson& Bazerman,
1985).Failure to end strikes or settle legal casesout of court might be
other examples(cf. Thompson& Loewenstein,1992).
The curseof knowledgemay be importantfor negotiationstoo. Models
of asymmetricinformationtend to focus on how well the less-informed
agentscan infer a better-informedagent'sknowledgefrom actions.The
presumption in such models is that better-informedagents can act
"inscrutably," pretendingthey know nothing,if they needto. The curse
of knowledgemakesit hard to be inscrutable.
There is a deliciousirony here: Sufferingfrom the curse of knowledge
(an irrationality) may reduceperceived information asymmetry, which
can lead a well-informedagentto shareinformation,thus mitigatingmarket failure and bargainingbreakdown(improving social rationality). Of
course, the curse only helps if peoplereveal informationthat improves
bargainingefficiencywhen it is shared(preferences,for example).Further researchcould help show whether the right kind of information is
overrevealed,or not.
The curse of knowledge implies that people will overestimatehow
much of their informationothers share."False consensus"refers to the
related tendency to overestimatehow many people share your tastes,
beliefs,and attitudesto a greaterextentthan they do (Ross,Greene,&
House, 1977;cf. Dawes,1990).Sincefalseconsensus
makeit difficultfor
people to realize how different their valuesare, it may reduce the perceivedgainsfrom integrativebargaining(cf. the "reactive devaluation"
documentedby Stillingeret al., in press, and the "mythical fixed-pie
bias" describedby Bazerman,Magliozzi& Neale, 1985).
Future ResearchDirections
Competitive markets and bilateral monopoly (one buyer, one seller)
spanthe continuumof competitiveness.
There is relativelylittle negotiation researchtoward the marketend of the continuum(but seeBazerman
et al. 1985;Sondak & Bazerman,1989).Subjectsare usually told a
"BATNA" or reservationprice which is meantto representthe best offer
they have been made,or expectto get, from anotherbuyer or seller. By
RATIONALITY
OF PRICES AND VOLUME
269
embeddinga negotiationin a market, subjectsare actually forced to make
judgmentsof the best availableoffers (or BATNA), thus increasingthe
complexity of their task and the range of what we might learn about
negotiation.
Bringing richer negotiationtasks and variablesinto experimentalmarkets could benefitexperimentaleconomicstoo. For instance,fairnesshas
rarely been studied in experimentalmarkets. And the use of abstract,
blandly labeledstimuli has made it easy for experimentaleconomiststo
ignore interestingquestionsof memory, attribution, and emotion. One
field's nuisancevariableis often anotherfield's main effect. For negotiation researchand experimentaleconomics,that truism posesinteresting
opportunitiesfor new research.
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