An Incentive-Aligned Mechanism for Conjoint Analysis Author(s

Transcription

An Incentive-Aligned Mechanism for Conjoint Analysis Author(s
An Incentive-Aligned Mechanism for Conjoint Analysis
Author(s): Min Ding
Source: Journal of Marketing Research, Vol. 44, No. 2 (May, 2007), pp. 214-223
Published by: American Marketing Association
Stable URL: http://www.jstor.org/stable/30162469
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MINDING*
Thisarticlespecifies,analyzes,and validatesa rigorousand practical
The mechanism
mechanism(game) forconjoint
applications.
truth-telling
and has truth
tellinginconjoint
requiresonlyone real productvariation
thusmakingit possibleto incentive
as its BayesianNash equilibrium,
in
most
Usingthe iPod package
conjointapplications.
alignparticipants
that the mechanism
as the context,the authorshows empirically
comparedwitha standard
substantially
improvespurchaseprediction
conjoint
procedure.
forConjoint
AnIncentive-Aligned
Mechanism
Analysis
research.
of marketing
Conjointanalysisis a centerpiece
Since the methodologywas introducedto marketing
30 yearsago in a seminalarticleby Green
approximately
realizhavebeencontinuously
and Rao (1971), researchers
ing new and majoradvancesin thefield,includinghierarchical Bayesian estimation(Allenby and Ginter1995),
polyhedralmethods(Toubia,Hauser,and Simester2004;
Toubiaet al. 2003), and partialconjointprofiles(Bradlow,
Hu, andHo 2004).
Almostwithoutexception,however,conjointdata have
thatofferno consebeen collectedin hypothetical
settings
economicsliterature
The
decisions.
for
quences participants'
and Hausman
Diamond
and
Camerer
1999;
Hogarth
(e.g.,
1994; List 2001) has longwarnedabouttheperilsof inferbecause
in such hypothetical
conditions,
ringpreferences
their
true
to
are
not
incentive
aligned report
participants
in
Grewal,
research,
Ding,
Recently marketing
preferences.
andLiechty(2005) showedthatdatacollectedin suchhypothandatacolhaveweakerexternal
theticalsettings
validity
lectedfromincentive-aligned
Theyfindthatthe
participants.
thehypothetichoiceconjointoutperforms
incentive-aligned
cal choiceconjointin out-of-sample
predictions.
Smeal Collegeof Busiof Marketing,
*MinDing is AssistantProfessor
ness, PennsylvaniaState University(e-mail: minding
@psu.edu). The
fromGaryLilienon several
comments
constructive
authoracknowledges
previousversionsof thisarticle,as well as thosefromRajdeep Grewal;
in presentations
givenat
GuangGuo; JohnLiechty;Bill Ross; participants
andtheMarketofTechnology,
Institute
Massachusetts
CornellUniversity,
JMRreviewin Atlanta;and thethreeanonymous
ing Scienceconference
financialsupportfromtheSmeal Colers.The authoralso acknowledges
and assistancefromthe
StateUniversity,
lege of Business,Pennsylvania
State
andAuctionsat Pennsylvania
forEconomicManagement
Laboratory
This articlewas processedunderRussellWiner,and William
University.
Mooreservedas guesteditor.
to reader and authordialogue on JMR, visit
To read and contribute
http:/lwww.marketingpowercom/jmrblog.
Association
(c)2007,AmericanMarketing
ISSN: 0022-2437(print),1547-7193(electronic)
it seems criticalthatconjoint
In lightof thisliterature,
to incorporate
properincentivesinto
attempt
practitioners
torevealtheir
aremotivated
theirstudiesso thatparticipants
thistaskis not trivialfor
truepreferences.
Unfortunately,
mostapplications.Standardguidelinesin theexperimental
economicsliterature
(Smith1976) requirethatparticipants
on all tasks,whichimplies
be paid fortheirperformance
is askedto evaluate
a participant
thatall productvariations
to purchaseor conshouldbe availablefortheparticipant
will
sumeif he or she so chooses.Anymissingvariations
In
most
the
make
prodconjointstudyhypothetical.
likely
have
and researchers
uct categories,conjointpractitioners
access to onlya fewproductvariations,
makingit unclear
howto incentive
usingtheestabalignconjointparticipants
and
in bothmarketing
lishedguidelines.Existingliterature
issue.
economicsis silenton howto addressthisimportant
An ideal solutionto thisproblemshouldsatisfyseveral
drivenandprovidegeneral
criteria.
First,itshouldbe theory
guidelinesfor conjointpractice.Second, it should not
changesto existingconjointpractice.
requiresignificant
Third,thesolutionshouldbe applicableto variedproduct
stagesby demandingas few
categoriesand development
variationsof real productsas possible.Fourth,the addishouldbe
and participants
tionalburdenon practitioners
minimal.
thatsatismechanism
Thisarticledevelopsa truth-telling
inforofincomplete
fiesthesefourcriteria
usingthetheory
mechanism
mationgames(morespecifically,
designtheory;
see Mas-Colell,Whinston,
foran accessibleintroduction,
thatit is in thebest
and Green1995). I showtheoretically
Nash
the
(BNE)equilibrium
interest-namely, Bayesian
in the proposedmechanismto respond
of a participant
in conjoint.In an empiricalstudyusing iPod
truthfully
betteroutleads to substantially
packages,thismechanism
of-sample predictionthan a standard (hypothetical)
bias (definedin
thathypothetical
approach.It also confirms
as thebias inducedby thehypotheeconomicsliterature
214
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Research
JournalofMarketing
Vol. XLIV (May 2007), 214-223
An Incentive-Aligned
MechanismforConjoint
Analysis
215
a real
a taskinwhich
a participant
canpurchase
byadding
or
to
on
his
her
inferred
willingness
pay
product,
depending
is thatan
behind
thismodification
(WTP).Theintuition
caninfer
a participant's
structure
experimenter
preference
the
on thebasisofhisorherresponses,
which
enables
to
the
WTP
for
variaexperimenter
predict participant's any
tionoftheproduct
Aslongastheparticipant
studied.
being
theidentity
comdoesnotknow
oftherealproduct
before
to
theconjoint
heorshewillbeincentivized
study,
pleting
THEORETICALFRAMEWORK
that
the
toallconjoint
toensure
respond
questions
carefully
inwhich
a
Mechanism
studies
design
theory
problems
willinfer
hisorherentire
structure
experimenter
preference
wants
to
obtain
certain
information
about
principal
private
As
a
it
is
to
result, possible appendconsebutagents
willnotreport
thisprivate
informationaccurately.
agents,
all
to
onerealproduct.
quences conjoint
responses
using
aregiven
theproper
unless
incentives
truthfully
they
bythe
I incorporate
theBDM (Becker,
and
DeGroot,
Finally,
Theobjective
ofa design
is toidentify
a mecha- Marschak
principal.
toensure
thatitis inthebest
1964)
procedure
itis in thebestinterest
nismforwhich
oftheagents
to
tohavetheinferred
interest
oftheparticipant
WTPequal
their
true
Unlike
most
theoretireport
types.
applied
game
hisorhertrue
WTP.TheBDMprocedure,
which
guarantees
in whichtherulesof thegamesaregiven that
cal models,
itis inthebestinterest
of
a
to
state
hisor
participant
is toidentify
andthetaskofresearchers
the hertrue
exogenously
hasbeenwidely
usedineconomics,
WTP,
though
behavior
of suchgames,mechanism
(e.g.,equilibrium)
introduced
intomarketing
and
(Wertenbroch
only
recently
focuses
on
the
of
the
and
itself,
design
design
game(rules)
Skiera
Theprocedure
involves
thefollowing
2002).
steps:
researchers
toidentify
a gamestructure
suchthat
a
attempt
states
hisorherWTPforanitem,
(1) A participant
(2) a
desirable
behavior
truth
in
the
is
embedded
(e.g.,
telling)
is drawn
from
a
distriuniform)
price
randomly
(typically,
A mechanism
contains
twoelements:
(1) a message
game.
and(3) theoutcome
isdetermined
as follows:
Ifthe
which
a player
canchoosetosenda message bution,
spacefrom
drawn
is
than
the
stated
the
WTP, participant
higher
and(2) anoutcome
function
that
determines
theoutcomes price
willnotbeabletopurchase
iftheprice
the
but
drawn
item,
foranygiven
ofmessages
combination
sentbyallplayers. islower
than
or
to
the
stated
will
the
WTP,
equal
participant
When
combined
with
andpayoff
a
beliefs,
functions,
types,
be
able
to
the
item
but
will
the
purchase
pay
only
randomly
mechanism
defines
anincomplete
information
game.
drawn
As a result,
either
orunderstating
price.
overstating
Ingeneral,
theexisting
mechanism
literature
stud- WTPwill
design
lead
to
an
inferior
outcome
for
the
participant,
iestwotopics:
socialefficiency
1971;Groves andthe
(e.g.,Clarke
is
to
hisorher
state
participant's
optimal
strategy
maximization
1973;Vickrey
1961)andrevenue
(e.g.,Myer- true
Inthemechanism
WTP.
I
the
herein,
proposed
replace
son1981;Wilson1993).However,
noneoftheexisting stated
WTPwith
inferred
WTP.
mechanisms
canbereadily
totheconjoint
context
applied
1 presents
thecomplete
mechanism
Figure
graphically.
because
to
that
either
are
cur- Note
pertain products/goods
they
that
areinformed
about
the
entire
participants
process
available
orwillbeavailable
in
rently
(e.g.,auction
design)
before
thestart
of
the
task.
The
mechanism
(game)
conjoint
thenearfuture
ifparticipants
sochoose
(e.g.,public
goods). proceeds
as follows:
eachparticipant
the
First,
completes
In addition,
theexisting
mechanism
literature
has
design
standard
task
as
which
can
use
usual,
conjoint
anytypeof
almost
restricted
itsattention
tocasesinwhich
exclusively
choice,
conjoint
methodology
(e.g.,
rating,
polyhedral).
theagent's
information
is onedimensional,
private
(type)
theexperimenter
reveals
onerealproduct
tothe
Second,
whereasconjointparticipants'
is
privateinformation
that
could
Third,
participants
they
potentially
purchase.
multidimensional.
after
allthedata,theexperimenter
estimates
the
collecting
I specify
a new,
sound
mechanism
to
Thus,
theoretically
their
preferences
(partworths)
using conjoint
motivate
truth
inconjoint
Theintuition
for participants'
telling
analysis.
andinfers
eachparticipant's
WTPforthereal
responses
theproposed
mechanism
comes
from
truth-telling
recasting product.
the
inferred
theBDMproceFourth,
WTP,
using
theconjoint
as a gamebetween
a participant
andthe duredetermines
study
a
whether
will
be abletopurparticipant
From
thisperspective,
a participant's
experimenter.
prefer- chasetherealproduct
if
at
what
and,
so,
price.1
encestructure
couldbe considered
hisorher
(partworths)
TheBDMprocedure
ensures
that
itisinthebestinterest
A
is
in
a
continuous
multidimentype. participant's
type
of participant
tohavehisorherinferred
WTPequaltohis
sionalspace,inwhich
thedimensions
num- oraher
equalthetotal
true
but
because
of
in conjoint
errors
WTP,
(e.g.,
beroflevelsstudied
ina given
Inturn,
conjoint
application.
and
of
estimation,
design,
quantity
quality
participants'
theparticipant's
totheconjoint
canbe
responses
questions
theBDMprocedure
itself
doesnotnecessarily
considered
hisorherstrategy.
Theinformation
inthisgame responses),
that
it
in
will
be
the
best
interest
ofa participant
guarantee
isasymmetric:
A participant's
isknown
tohimorher- to
type
in
The
respond
(a formal
truthfully
conjoint.
Appendix
selfbutnotto theexperimenter.
In standard
(unincentheexperimenter
tivized)
conjoint,
posesvarious
(conjoint)
to acquireinformation
abouttheparticipant's
questions
buttheparticipant
hasnoincentive
toadopt
a strategy 'An alternativeincentive-compatible
type,
procedurecommonlyused in the
economicsliterature
that
is theVickreyauction(Vickrey1961),whichis infeisconsistent
with
hisorhertype.
Whena conjoint
is recast
as anincomplete
infor- riorto BDM in thecurrentcontextforthreereasons:(1) It requiresmultistudy
in auctionsagainstotherpeopletend
players,(2) peopleparticipating
mation
the
task
of
game,
incentivizing
conjoint
participants ple
to deviatefromtheirtrueWTP,and(3) itsubstantially
reducestruth-telling
becomes
tomodifying
thisgamesuchthatthe incentivesforparticipantswho believethattheirWTPs
equivalent
are smallerthan
becomes
theBNE.I accomplish
this thoseofmostotherparticipants.
truth-telling
strategy
thetical
nature
ofa task)exists
forexpensive
durable
productsandforfrequently
(as
purchased
inexpensive
products
intheliterature).
Therestofthearticle
is organreported
I first
izedas follows:
themechanism
andpresent
specify
I then
and
theoretical
describe
theempirical
study
insights.
I conclude
discuss
theresults.
with
a general
discussion
and
somefruitful
directions
forfurther
research.
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JOURNAL OF MARKETING RESEARCH, MAY2007
216
Figure 1
A GRAPHIC REPRESENTATION OF THE TRUTH-TELLING MECHANISM
Conjoint Participant
Types
Preference
structure
Experimenter
Productvariation
to be used
Mechanism
Action
Responds to
conjointtask
Reveals the real productto
be used in purchase task
Infersa participant'sWTP
forthe real producton the
basis of his or her responses
in conjointtask
Actualpurchase price (x)
determinedby an incentivecompatiblemechanism
(BDM) and inferredWTP
Outcome
Utility
Depends on
outcome and
types
andpractice).As a result,
monlyassumedin conjointtheory
Theoreml a impliesthattruthtellingis alwaystheunique
BNE fortheexisting
(It is assumed
conjointmethodologies.
that conjointmethodologies[estimation]are not biased
state their preferences.)
when participantstruthfully
inFigure1,
Theorem
1: Underthemechanism
specified
Althoughthereis littlereasonto believethatan estimation
procedurewill producea smallervariancefora non-truthWTPforthetruth-telling
ofinferred
(a) Ifthevariance
strategy
thanforthetruth-telling
strategy,
practitionstrate- tellingstrategy
thanthatfornon-truth-telling
is equalto orsmaller
in thenotionthatevenif
erscan takecomfort
lb)
(Theorem
BNF
in
is
the
truth
gies,
telling conjoint unique
actuallyexistfora yetstrategies
superiornon-truth-telling
are able
method
and
to-be
participants
developedconjoint
WTP forthetruth-telling
of theinferred
(b) If thevariance
structures
the
discover
to
them,
by
represented
preference
thansomenon-truth-telling
is greater
strategies,
strategy
similar
to
will
be
these
as
the
BNE
as
is
the
in
truth
strategies
non-truth-telling
superior
long
unique
telling conjoint
thoseoftruepreferences.
WTP
inferred
havean expected
non-truth-telling
strategies
different
fromthetrueWTP (forthe
thatis substantially
seetheAppendix).
condition,
EMPIRICALIMPLEMENTATION
precise
The empiricalstudyhas two objectives.The firstis to
in conjoint(i.e.,
all inconsistent
strategies
Theoretically,
to
conthe
in
their
are
not
consistent
empiricalevidenceregardingwhetherthe truthprovide
responses
participants
tellingmechanismleads to improvedpredictiveperformjointquestions)shouldhavehighervariancethana consisincentives
itaimsto testwhether
ance.Furthermore,
whereasall consistentstrategies(including
tentstrategy,
lottery
selected
of
a
certain
truthtelling)shouldhave the same variance(as is comparticipants
percentage randomly
(only
showsthattruth
ofthemechanism)
treatment
tellingin contheuniqueBNE in thismechanism
jointindeedrepresents
The mainresultcan be statedas
undergeneralconditions.
Theorem1:
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An Incentive-Aligned
MechanismforConjointAnalysis
217
receive
rewards
basedontheir
theAppleWebsiterecommended.
workeffectively sories
that
onthe
Then,
decision)
forthemechanism.2
basis of a focusgroupsessionwithtenstudents
fromthe
Thesecond
istofurther
ofdif- university,
I selecteda subsetof this list for the actual
objective
explore
patterns
ferences
inpartworths
between
thehypothetical
condition experiments.
The subsetconsistsof an iPod (storage-size
andan incentive-aligned
condition
thetruth- variation),a case/holder,
(e.g.,under
headphones,speakers,car audio,
In
of
their
Chinese
dinner
a
and
The
mechanism).
telling
study
spe- power,
warranty. numbersof levelswithineach
cialsandsnack
andLiechty
arealso keptthesameinbothexperiments
to allow
combos,
(2005) attribute
Ding,Grewal,
establish
ininexpensive
tworeplicable
foodprod- foridenticalexperimental
findings
designs.The finalattribute
space
ucts:(1) Hypothetical
biasexists,
and(2) price
is
is 223541andincludesfourpricelevels.
sensitivity
bothsmaller
andlessheterogeneous
inthestandard
Experiment1 employsthe iPod Shuffle,the firstnew
(hypoI
condition.
these
in
addition
to the Apple iPod familyafterthe startof this
thetical)
investigate findingsproducts
from
thataredifferent
In
I
food.
research
2 uses thenextnew addition
addition,
inexpensive
project.Experiment
examine
there
arereplicable
whether
biaspat- to theiPod family,
theiPod Nano,whichwas launchednine
hypothetical
ternsassociated
withphysical
features.3
Taken monthsaftertheiPod Shuffle.Of thephysicalaccessories
product
thesetwoobjectives
call fortwoidentically in the iPod package (case/holders,
together,
headphones,speakers,
inthehypotheticalcar audio,and power),halfof them(twospeakers,twocar
(thus,
designed
experiments
anychanges
biaspattern
thetwoexperiments
between
forthesamefea- audio,and one power)appearin bothexperiments,4
which
turecanbe attributed
to
the
feature
itself
rather
than
makes
it
to
examine
of
differonly
possible
replicablepatterns
to[artificial]
totestpredictive
design
parameters)
perform- ence in partworthsassociatedwith these five physical
andtruth features.
ance;eachhas twoconditions
(hypothetical
andboth
usenewdurable
that
havea price ValidationTask
telling),
products
ofa fewhundred
dollars
andshareseveral
range
physical
Thepurpose
ofconjoint
is to predict
a conanalysis
features.
sumer's
real-life
decisions.
As a result,
thebestmetric
to
Therestofthissection
discusses
theproducts,
validation
a
new
method
is
to
examine
whether
can
it
conjoint
andfitandpredictive judge
task,
estimation,
design,
participants,
forchoicedecisions
to
similar
predictions
I discuss
ofdifference
inesti- leadtobetter
performance.
Finally,
patterns
those
encountered
in
real
life.
Because
consumers
mated
between
usually
thehypothetical
andtruth-telling
partworths
toa largenumber
ofoptions
when
make
forpriceandfivecommon
they
mechanism
conditions
physical areexposed
an
actual
decision
Best
carries
more
purchase
features
in
(e.g.,
both
Buy
Unless
otherwise
present
experiments.
than
20
different
in
cameras
its
retail
stores
at
alldescriptions
digital
to
any
both
noted,
apply
experiments.
ProductCategory
giventime),a good validationtask forconjointmethods
shouldnotonlybe wellconstructed
butalso includeenough
to real-life
choicesforthe
optionsto makeitcommensurate
productcategoryunderstudy.A validationtaskwithonly
threeorfouroptionsmaybe tooartificially
easyto discriminatetheperformance
amongdifferent
conjointmethods.5
In thecase of theiPod package,forexample,fourprofiles
chosenfroma space of 223541wouldlikelybe so different
fromone anotherthatpotentialhypothetical
bias probably
would not affectwhichof the fouroptionsa participant
ranksas themostpreferred.
Thatis, smallvalidationtasks
arenotappropriate
forestablishing
theusefulnessof a new
suchas thetruth-telling
mechanism.
Thisguideline
method,
is followedin theconstruction
ofthevalidationtask.
After
informal
discussions
with
students
ata major
U.S.
where
thestudy
wasconducted,
I selected
the
university
foritsoverall
match
with
the
AppleiPodproduct
category
selection
criteria.
Mostconsumers
several
accespurchase
sories
when
atthetimeoftheNano
they
buythisproduct;
andShuffle
launches,
Apple'sWebsiteevensuggested
seven
iPodgift
sets(Starter,
AthTeens,
Students,
College
andGadget
eachof
letes,Commuters,
Travelers,
Lovers),
which
ofoneversion
consisted
oftheiPodandseveral
different
accessories
the
Athletes
set
contains
the
1GB
(e.g.,
iPodShuffle,
armband
fortheShuffle,
andsport
case).Borthegift
setconcept
from
I define
theproduct
rowing
Apple,
intheempirical
as aniPodpackage
that
consists
ofa
study
Design
launched
iPodandseveral
different
accessories.
To
newly
In each experiment,
twoconditions
wereemployed:one
determine
thespecific
attributes
andlevelsforeachattrib- that
to thestandard(hypothetical)
choiceconcorresponds
aninitial
listbasedonthecommon
accesute,I developed
andone forthe
The
mechanism.
joint(control)
truth-telling
mechanismincludesfiveparts:introduction,
truth-telling
task(in whichtheidentity
of the
conjointtask,purchasing
2Inexisting
allparticipants
receive
rewards real productthatcould be purchasedis revealed),external
research,
incentive-aligned
basedontheir
orchoice.
Inrealconjoint
howThe controlconditiondoes
performance
applications,
validitytask,and a briefsurvey.
cannot
afford
toaward
toevery
ever,
practitioners
expensive
products
parnotincludethepurchasing
task.
Asa result,
itiscritical
totest
thevalidity
oflottery
reward
structicipant.
tures.
Notethat
theobjective
hereis nottocompare
theeffectiveness
of
incentives
with
incentives
that
reward
butrather
to
lottery
every
participant
examine
whether
incentives
work
when
itisnotpossible
toprovide
4Half
oftheaccessories
those
that
comewith
aniPod;e.g.,
lottery
(excluding
incentives
forevery
basicearphones)
wereintentionally
differed
toensure
sufficient
variance
participant.
3Ifa physical
feature
tobeexamined
ispresent
inatleasttwodifferent between
thetwoexperiments.
sizeandwarranty
arespecific
for
Storage
eachis usedina separate
Itis possible
totestfor
eachiPodversion
orNano)andthus
products,
arenotgoodcandidates
for
experiment.
(Shuffle
offeature-specific
biaspatterns
indifferent
contexts examining
biaspatterns.
possible
repetition
replicable
hypothetical
andthuscontribute
toempirical
inthefuture
5Thisis analogous
to measuring
A superior
generalization
(defined
by
computer
performance.
Bass[1995,
orregularity
that
overdifferent computer
willexcelindemanding
taskbutmost
p. G7]as "a pattern
willnotbenoticerepeats
likely
inhandling
circumstances").
tasks.
ablydifferent
simple
word-processing
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JOURNAL OF MARKETING RESEARCH, MAY2007
218
containsbothexperimental
instructions
The introduction
of theiPod and theaccessories
and a detaileddescription
The detaileddescriptions
usedin theexperiment.
(including
pictures),whichare identicalforbothconditionsin each
experiment,were reproducedfromApple's Web site.
in
Instructions
forthecontrolconditionmimicinstructions
standardchoice conjointstudies,exceptthatparticipants
wereaskedto selectone packagefroma listat theend of
the study(externalvaliditytask) and a randomlyselected
wouldbe givenhis
winner(fromevery40-50 participants)
or her chosenoption(whichincludesnotpurchasingany
betweena certain
packagefromthelist),plusthedifference
1 and $320 in Experiamountofcash ($250 in Experiment
in the
ment2) and thepriceof thatoption.All participants
controlreceived$10.
conditionweretoldthat
in thetruth-telling
Participants
theirresponsesin theconjointtaskwouldbe used to infer
theirWTP fora specificproductX, thattheywouldknow
theconjointtask,andthat
ofX aftercompleting
theidentity
they would participatein an externalvaliditytask, as
received$10, and a
All participants
describedpreviously.
wouldbe randomly
winner(fromevery40-50 participants)
For each winner,a
selectedat theend of each experiment.
whether
he or she wouldreceive
cointosswoulddetermine
WTP usingtheBDM proceX on thebasis of theinferred
dureor theoptionchosenin theexternalvaliditytask.If X
werechosen,a price(x) wouldbe drawnfroma uniform
thatincludesall reasonablevaluationsforan
distribution
iPod package.If x wereless thanor equal to theinferred
WTP,thewinnerwouldreceiveX atpricex, plusthedifferencebetweena certainamountofcash ($250 in Experiment
he or she
1 and $320 in Experiment
2) and x. In contrast,
wouldreceivethecash and no X if x werehigherthanthe
WTP. Finally,ifthecoin tossresultedin theexterinferred
nal validitytask, the winnerwould receive the option
selectedin the externalvaliditytask,plus the difference
betweenthecash andthepriceof thatoption.
threeparts(theconfortheremaining
The instructions
joint task,the purchasingtask, and the externalvalidity
andfollowthepracticein thefield;
task)arestraightforward
conditionwereurgedto "image
in
the
control
participants
thatyou wereaskedto choose RIGHT HERE and RIGHT
NOW" in the conjointtask.The productvariations(profiles) used in these threepartswere generatedby SAS
designmacrosto ensuredesignobjectivity,
experimental
whichindicatesthata 72-profile
designis themostefficient
space (223541).Then,SAS was used
designfortheattribute
with20 additional
72 profiles,
togenerate
nonduplicate
proand externalvaliditytasks.The 72
filesforthepurchasing
profilesweredividedinto24 groupsby meansof therandom sequencegeneratedby SAS (witha few rearrangementsto ensurethattherewas no dominant
profilein any
givengroup),and thegroupswereused as the 24 choice
was addedto each
tasks(afteran optionof notpurchasing
group)in theconjointtask.In each choice task,a particioptionout
pant'sjob was to pickhis or hermostpreferred
the
of four(threedifferent
not-purchasing
packagesplus
4 profilesthatwould
option).Of the20 additionalprofiles,
iPod at thelowest
dominate(packageswiththehigher-end
iPod
price)or be dominated(packageswiththelower-end
16 proThe remaining
atthehighestprice)wereeliminated.
filesappearedin theexternalvaliditytask,alongwiththe
optionof not purchasingany of the 16 profiles.In the
was usedas
one ofthefoureliminated
profiles
experiments,
taskin
thereal product(withoutprice)forthepurchasing
thetruth-telling
mechanism.
Participants
fromthe
in bothexperiments
wererecruited
Participants
same undergraduate
and graduatestudentpopulationat a
Experiment1 was conductedone
major U.S. university.
2 took
monthaftertheiPod Shuffle
launch,andExperiment
To
that
Nano
launch.
ensure
one
after
the
iPod
month
place
werepotentialbuyersof thenew product,the
participants
e-mail and advertisement
explicitlystatedthat
recruiting
in thestudyif theyhad no
studentsshouldnotparticipate
a digitalmusicplayer.A totalof 49
in purchasing
interest
1 and wererandomly
in Experiment
studentsparticipated
mechanism
and
the
to
the
control
(24)
truth-telling
assigned
2
in Experiment
(25); a totalof 117 studentsparticipated
and wererandomly
assignedto thecontrol(58) and truthtelling mechanism(59). No one participatedin both
experiments.
Estimation
hierarchicalBayesian multinomial
A random-effects
similarto thatspecified
logitmodelis used forestimation,6
and
Ginter
and
Arora,and Gin(1995)
Allenby,
byAllenby
chooses
thattheithparticipant
ter(1998). The probability
fromthetthchoicesetis givenby
thejthalternative
(1)
Pr(zit
in thetth
wherezitis thechoicemadeby theithparticipant
choiceset,ditidescribesthelthoptionin thetthchoiceset
and Pi is a vectorof partevaluatedby theithparticipant,
A priori,itis assumedthat
worthsfortheithparticipant.
(2)
Normal
are
that
there
and
vagueconjugatepriorsforB and A. The
hierarchical
Bayesianapproachmakesit possibleto estimate individual-level
parameters((3i), average
Eartworth
heterogeneity
(f3),and thepartworth
parameters
partworth
weremadeafteritwas ensuredthatthecon(A). Inferences
vergencepropertiesof the Markov chain Monte Carlo
prior
analysiswere met.In addition,a rangeof different
to
valueswas testedto ensurethattheresultswereinvariant
for
WTP was inferred
A participant's
thepriorspecification.
taskforeachdrawofthe
theiPodpackagein thepurchasing
and
the
after
averagewas takenas the
convergence,
sampler
finalestimate.
Fitand Predictive
Performance
forExperiment1 appear in
The estimatedpartworths
Table 1. To assess thein-samplegoodnessof fitforExperiidentiof timesthemodelcorrectly
ment1, thepercentage
fiedthechoicein eachofthe24 tasksin theconjointexperiThe averagesare
mentwas calculatedforeach participant.
from
6Thisparticularestimationapproachprecludesan experimenter
in the
WTP in real time.In the empiricalstudy,participants
estimating
weretoldthatthewinnerwouldbe invitedbackthe
condition
truth-telling
nextday fortheBDM procedure(if BDM is chosenon thebasis of the
coinflip).
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219
An Incentive-Aligned
MechanismforConjointAnalysis
Table 1
PARAMETER ESTIMATES FOR EXPERIMENT 1
Control(Hypothetical)
Attribute
Me
Level
Intercept
Storage
Base: 512 MB
1 GB
Mechanism
Truth-Telling
M
Heterogeneityf
Heterogeneity
6.19 (.87)
1.41 (1.43)
5.22 (.66)
1.35 (1.35)
3.44 (.43)
2.32 (1.25)
2.86 (.31)
1.13 (.68)
Case/holder
Base: none
Armband
forShuffle
Sportscase
1.73 (.36)
.91 (.28)
1.64 (.87)
.58 (.39)
.60 (.28)
.74 (.25)
.90 (.54)
.63 (.37)
Headphones
Base: Applea
Apple+ NikeVaporb
Apple+ NikeDuroc
.72 (.30)
.39 (.29)
.83 (.48)
.39 (.24)
.65 (.27)
.35 (.28)
.61 (.39)
.60 (.36)
Base: none
MonsteriSpeaker
Creativespeaker
1.17 (.27)
1.59 (.27)
.39 (.24)
.41 (.25)
1.56 (.27)
1.87 (.29)
.53 (.36)
.60 (.36)
.72 (.26)
1.89 (.30)
.45 (.29)
.92 (.60)
.24 (.29)
2.01 (.35)
.94 (.54)
1.66 (.97)
.06 (.25)
.17 (.24)
.36 (.23)
.33 (.19)
.38 (.24)
.61 (.24)
.42 (.26)
.46 (.26)
Speakers
Car audio
Base: none
Sonycassetteadapter
BelkinFM transmitter
Power
Base: USB
USB + battery
pack
USB + poweradapter
Warranty
Base: basic
Extended
Priced
.69 (.27)
.82 (.43)
.07 (.22)
.38 (.22)
-5.87 (.66)
6.12 (2.83)
-5.43 (.47)
1.96 (1.25)
aBasicAppleearphonethatcomeswithanyiPod Shuffle
purchase.
bNikeVaporsportbudheadphones.
CNikeDurobehind-the-head
headphones.
dPricelevelsare $129,$159, $189, and$219. Theyaredividedby 100 beforeestimation
forease ofpresentation.
meanand standard
deviationof 13.
ePosterior
Posteriormeanand standard
deviationofdiagonalofA.
Notes:The fivecommonphysicalfeatures
arein bold.
presentin bothexperiments
Table 2
PREDICTIVE PERFORMANCE FOR EXPERIMENT 1
ActualChoiceMatchestheTop
PredictedOption
Condition
Control
mechanism
Truth-telling
TotalNumber
24
25
ActualChoiceMatchesOne of
theTopTwoPredictedOptions
NumberCorrect
Percentage
NumberCorrect
4
9
17
36
9
16
identicalbetweenthetwo conditions(78%). However,the
predictiveperformancefor the externalvaliditytask
forthe truth-telling
mechanismin
improvesconsiderably
1 (Table 2). Thatis, thechoicesof 36% of the
Experiment
in thetruth-telling
mechanism
can be correctly
participants
predicted,
comparedwithonly17% in thecontrolcondition
(1 of 17). The
(p = .085)7 and 6% witha naiveprediction
of
in
the
choices
external
percentage
validitytask that
agreeswithone of thetop twopredictedoptionswas also
calculatedto measurethesensitivity
of thepredictive
performance.
Withthiscriterion,
64% of choicesin thetruthis used to obtaintheprobability
of observinga difference
in
7Bootstrap
thenumberofcorrectpredictions
betweenthecontrolandthetruth-telling
mechanism
thatwouldbe at leastthisextreme
iftheyweredrawnfromthe
same population(based on the standardprocedureof resamplingwith
The population
in thebootstrap
is createdbyaggregating
the
replacement).
outcomes(numbersof correctand incorrect
from
prediction
predictions)
thecontrolandtruth-telling
mechanism
undereach situation.
Percentage
38
64
tellingmechanismcan be correctly
predicted,compared
with38% in thecontrolcondition
(p = .043).
The estimatedpartworths
forExperiment2 appear in
Table 3. The in-samplefitsare almostidenticalto thosein
Experiment1: 78% and 79% for the controland truthThe out-of-sample
tellingmechanism,
respectively.
predictionsare also consistent
withthosein Experiment
1 (Table
in thetruth-telling
4). The choicesof 34% of participants
mechanism
can be correctly
predicted,
comparedwith21%
in thecontrolcondition(p = .067). Withthetop two predictedoptions,56% of choicesin thetruth-telling
mechanismcan be correctly
predicted,
comparedwith40% in the
controlcondition
(p = .047).8
8Todemonstrate
theimportance
of usinga largeand realisempirically
tic validationtaskin benchmarking
different
(see thedismethodologies
cussionunderthe"ValidationTask"subsection)and to providea baseline
to existingliterature,
wereaskedin Experiment
2 to complete
participants
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220
JOURNALOF MARKETING
RESEARCH,MAY2007
Table3
PARAMETER ESTIMATES FOR EXPERIMENT 2
Control(Hypothetical)
Attribute
Level
Mf
Storage
Case/holder
Headphones
Speakers
Car audio
Power
Warranty
M
Heterogeneityg
9.54 (1.11)
Intercept
Mechanism
Truth-Telling
44.81 (12.2)
Heterogeneity
9.56 (.50)
1.34 (.91)
Base: 2 GB
4 GB
3.01 (.25)
2.26
(.76)
2.96 (.25)
2.69 (.78)
Base: none
ArmbandforNano
Incaseleatherfolio
.83 (.17)
.80 (.15)
.55
.41
(.26)
(.20)
1.18 (.19)
.79 (.15)
.68 (.28)
.35 (.17)
Base: Applea
Apple+ lanyardb
Apple+ Sonye
.44 (.15)
.57 (.17)
.25
.45
(.10)
(.19)
.51 (.16)
.60 (.15)
.46 (.19)
.38 (.20)
Base: none
MonsteriSpeaker
Creativespeaker
1.00 (.17)
1.40 (.18)
.70
.68
(.30)
(.28)
1.26 (.21)
1.90 (.19)
1.60 (.56)
1.39 (.51)
.31 (.17)
1.43 (.17)
.79
.58
(.31)
(.26)
.32 (.21)
1.56 (.15)
1.22 (.45)
.35 (.16)
.80 (.16)
.79 (.14)
.52
.22
(.22)
(.09)
.79 (.20)
.81 (.18)
.54 (.21)
.33 (.16)
.62
(.23)
.51 (.15)
.63 (.23)
6.85 (1.78)
-5.63 (.25)
1.37 (.52)
Base: none
Sonycassetteadapter
BelkinFM transmitter
Base: USB
USB + Tekkeond
USB + poweradapter
Base: basic
Extended
.61 (.16)
Pricee
-5.21 (.42)
aBasicAppleearphonethatcomeswithanyiPod Nano purchase.
bAppleNano lanyardheadphones.
eSonyFontopiaearphones.
dTekkeon
foriPod Nano.
myPower
forease ofpresentation.
ePricelevelsare$209, $239, $269, and $299. Theyaredividedby 100 beforeestimation
Posteriormeanandstandard
deviationof f3.
meanand standard
gPosterior
deviationofdiagonalofA.
arein bold.
Notes:The fivecommonphysicalfeatures
presentin bothexperiments
Table4
PREDICTIVE PERFORMANCE FOR EXPERIMENT 2
ActualChoiceMatchesOne of
theTopTwoPredictedOptions
ActualChoiceMatchestheTop
PredictedOption
Condition
Control
mechanism
Truth-telling
TotalNumber
58
59
NumberCorrect
12
20
in out-of-sample
The improvement
performpredictive
ancesin bothexperiments
providesempiricalvalidationfor
this
mechanism.Furthermore,
the proposedtruth-telling
a
costachieved
in
is
by using
improvement performance
a practithusremoving
incentive
effective
structure,
lottery
mechaofthetruth-telling
cal hurdleto theimplementation
nismforexpensiveproducts.
validationtask(fourchoicequestions,
an additionaland moretraditional
iPod Nano packagesandtheoption
each of whichcontainedfourdifferent
of not purchasing).Accordingto both the top optionand the top two
butthedifled to betterpredictions,
mechanism
options,thetruth-telling
forthetopoption(p = .151) and is onlymarginferenceis notsignificant
theimporforthetoptwooptions(p = .088). Thisconfirms
allysignificant
tanceofusinglargeandrealisticvalidationtasksto comparemethods.
Percentage
NumberCorrect
21
34
23
33
Percentage
40
56
inPartworths
Patterns
forPriceandFive
ofDifferences
Features9
Common
Physical
under
fromthesuperiorpredictive
performance
Judging
it is conin bothexperiments,
mechanism
thetruth-telling
bias indeedexistsforexpensive
cluded thathypothetical
durablegoods,suchas iPods. This findinggeneralizesthe
previousevidencebased on inexpensivefood (Ding, Grewal, and Liechty2005) because iPods and foodrepresent
the poles on two key productdimensions(priceand frequencyofpurchase).
ofdifferences
associatedwithpricesensitivThe patterns
by a similarmean
ityforiPod packagesare characterized
of difference
is availableon
9A morerigorousanalysisof thepatterns
request.
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An Incentive-Aligned
MechanismforConjointAnalysis
221
"simi- under
thetruth-telling
mechanism
inboth
andhigher
variance
and,asa result,
(Theterms
mayhave
experiments.
this
in
WTPforan iPodpackagethatincludes
a higher
or"higher"
areusedtorefer
tothepatterns
"lower,"
lar,"
orvariance]
thehypotheticalspeaker.
thevalue[mean
under
which
issimilar
orhigher
than
that
under
condition
to,lower
than,
Theseresults
difthetruth-telling
mechanism,
respectively.)
GENERALDISCUSSION
in
both
ecothosepreviously
Research
ferfrom
reported.
onthemechanism
thisarticle
literature,
design
Building
andHausman
nomics
1994;List2001)andmar(Diamond
a
mechanism
that
embeds
standard
specifies
truth-telling
on
andLiechty
that,
Grewal,
2005)hasshown
keting
(Ding,
in
information
and
studies
an
conjoint
incomplete
game
inhypothetical
conarelesspricesensitive
average,
people
it
is
the
BNE
for
to
reveal
their
true
that
participants
con- proves
todiscount
their
ditions
because
theyappear
budget
inconjoint
In addition
toitsrigorous
studies.
inthemean preferences
Itis hypothesized
that
thisdifference
straints.
several
theoretical
this
mechanism
contains
foundation,
is likely
dueto experimental
patterns
design(e.g.,price desirable
will
its
features
that
facilitate
among
adoption
whoisnotpaying
closeattenintervals
used).A participant
It
not
in
does
require
changes
existing
practitioners.
any
constraints
willlikely
small
tiontohisorherbudget
ignore
andcouldbe usedforallofthem
conjoint
methodologies
in
andLiechty
[2005],
(cf.Ding,Grewal,
pricedifferences
Asa result,
a practitioner
choice,
polyhedral).
isonly$1between
which
theprice
difference
thetwoclos- (e.g.,rating,
or
in
still
could
on
his
her
conrely
any
expertise specific
is $2).Inconestprice
levelsandthemaximum
difference
and
the
same
data
collection
perform
joint
methodology
aremuch
lesslikely
toignore
thediffertrast,
participants
thismechanism
removes
Equally
important,
inthisstudy
difference
is $90, andanalysis.
enceinprice
(themaximum
the
burden
of
all
variations
onerous
that
requiring
product
is $30).Ding,Grewal,
and
andtheminimum
difference
atthetime
oftheexperiment
(asisrequired
by
that
inhypotheticalbeavailable
(2005)alsoreport
participants
Liechty
such
that
one
existing
incentive-alignment
guidelines),
only
for
conditions
havelessheterogeneous
sensitivities
price
isneeded
atthetime
oftheconjoint
variation
product
study.
to
theChinese
dinner
andthesnack
combo,
contrary
special
In
of
nonfinancial
terms
additional
the
effort,
only
major
foriPodpackages.
whatis observed
Further
research
is
itimposes
onpractitioners
is tocalculate
eachpartounderstand
howpricesensitivity
needed
under burden
changes
WTP
for
a
variation
the
ticipant's
product
using
conjoint
conditions.
hypothetical
results
after
the
The
additional
financial
burden
experiment.
Of thefivecommon
features
be
can
(which
physical
is
also
will
to
need
real
limited;
practitioners
provide prodof differences
in partexamined
forreplicable
patterns
uctsas theprizeofrandom
butonlytotheextent
drawings
three
Creative
and
the
worths), (Monster
iSpeaker,
speaker,
that
theexpected
valueoftherandom
foreachpardrawing
arecharacterized
adapter)
power
bythesametypeofpator
is
than
his
her
cost(e.g.,a
ticipant
higher
opportunity
lowermeansandlowervariances.10
With
terns-namely,
of
a
television
a
1
in
10
chance
of
$200
study
may
require
ofthemeanpattern
theexception
forthepower
adapter
of
whereas
a
a
$2,000
winning,
study
refrigerator
may
inExperiment
mean
in
observed
2),allthepatterns
(similar
ofwinning).
this
onlya 1 in 100chance
Finally,
1 werereplicated
inExperiment
2.Thepattern require
Experiment
mechanism
not
does
additional
burdens
on
impose
any
parofdifferences
associated
with
theSonycassette
is
adapter
other
than
toreadextended
(but
ticipants,
needing
easy-toa
characterized
mean
and
lower
variance,
by higher
except understand)
instructions.
needsto
(Notethata participant
thatthedifference
inmeandisappeared
inExperiment
2.
learn
if
or
once
he
she
in
different
only
participates
many
Thepattern
ofdifferences
withtheBelkin
FM
associated
studies
that
contain
thismechanism.)
conjoint
transmitter
is characterized
similar
a
mean
and
lower
by
Theempirical
tests
conducted
theiPodShuffle
and
using
variance
inExperiment
1.Although
themeanpattern
was
Nano
iPod
the
demonstrate
external
packages
superior
inExperiment
inExperi2, itsvariance
replicated
pattern
ofthetruth-telling
mechanism
andshowthatsuch
2 contrasts
ment
with
that
inExperiment
1.Theempirical validity
can
be
achieved
incentives,
improvement
using
lottery
evidence
heresuggests
that
ofdifferthepatterns
presented
reduces
thefinancial
which
costassociated
with
theimpleencesassociated
with
features
are
physical
mostly
replica- mentation
of
this
mechanism.
The
also
study
empirical
ble anddepend
on thephysical
features.
It appears
that
demonstrates
the
bias
exists
not
(1)
following:
Hypothetical
these
arerelated
tohowlikely
itis that
theowner
patterns
in
and
cateonly
inexpensive
frequently
purchased
product
willusea physical
Itisconjectured
feature,
given
purchase.
butalsoinexpensive
durable
(2)
gories
product
categories,
that
under
onaverage,
conditions,
hypothetical
participants the
ofdifferences
associated
with
patterns
price
sensitivity
tendtounderstate
their
valuation
forphysical
features
they for
durable
aredifferent
from
those
for
expensive
products
arelikely
touse(e.g.,speakers,
thepower
andto
adapter)
and
the
(3)
frequently
purchased
inexpensive
products,
patoverstate
theirvaluation
forphysical
features
theyare
ofdifferences
terns
inpartworths
associated
with
physical
touse(cassette
Further
isneeded
to
unlikely
adapter).
study
attributes
are
feature
specific.
testthisconjecture.
Given
itssound
theoretical
foundation
andempirical
supOnthebasisofthese
itisclearthat
the
results,
empirical
this
mechanism
should
lead
port,
incentive-aligned
conjoint
WTPfora complex
will
not
be
lower
product
necessarily
tobecome
field
tested
andthen
tobecome
perhaps
under
an incentive-aligned
In thecaseofthe studies
condition.
standard
which
will
external
practice,
provide
greater
fora speaker
iPod,a participant
mayhavehigher
utility
areasstilldeserve
conHowever,
validity.
many
promising
active
research.
thisgeneral
mechanism
tinued,
First,
may
wIfformal
were
tobemade,
ratios
of
between-experiment
comparisons
not
be
effective
for
a
box
of
inexpensive
products
(e.g.,
coefficients
theprice
should
beused.However,
(e.g.,against
sensitivity)
cereal
that
retails
for
is
It
to
$2.99). unlikelygenerate
large
theresults
would
bemuch
notlikely
inthisstudy,
different
because
the
incentives
forsomeparticipants
totellthetruth
in
sensitivities
aresufficiently
similar
between
theexperiments.
I thank enough
price
ananonymous
reviewer
forpointing
this
out.
these
thepotential
isinherently
limcases,because
penalty
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JOURNALOF MARKETING
RESEARCH,MAY2007
222
inline action
issimply
toreveal
therealproduct
valueoftheproduct.
itedbythemaximum
Second,
(type
t2).Theoutinwhich
a ranthewinner comefunction
with
theguidelines
ofexperimental
economics,
(o) is theBDMprocedure,
of
from
distribution
and
a certain
domprice(x) is drawn
a uniform
with
amount
inthemechanism
willbeendowed
WTP(wi).Ifxisequaltoorless
with
theinferred
thanthehighest
price compared
(equaltoorslightly
larger
money
receives
butonly
willbeusedtopur- than
theproduct
ofwhich
usedina study),
themajority
wi,theparticipant
paysx.
is
if
x
the
The
cannot
inthestudy.
chasetherealproduct
However,
participant purchase product greater
peoplemay
of
wi:
than
wouldinreallifebecause
behave
thanthey
differently
toinvestigate D4: The
thispotential
gain.It wouldbe worthwhile
by theoututility
eui(--)is determined
participant's
iftheymust
howparticipants
behave
payfortheproduct
o: A1x A2-p Z, hisorhertypet1,andthe
comefunction
ownmoney.
someconjoint
withtheir
Third,
participants
experimenter's
typet2.
butmay
understand
themechanism
not
may completely
The
payoff
(utility)
eui--)is theexpected
participant's
offifthey
harder
tofillit
that
willbebetter
believe
try
they
if
the
or
were
abletopurchase
in
he
she
increase
It
utility
as possible.
outas conscientiously
(andas truthfully)
x.
This
drawn
at
the
expected
utility
themental
to investigate
wouldbe worthwhile
process product randomly price
three
levelsofexpectabyconsidering
ofthelot- couldbe obtained
with
totheeffectiveness
involved.
Fourth,
regard
ofthe
over(1) theexperimenter's
type
t2(theidentity
toconduct tions
itwould
beworthwhile
incentive
structure,
tery
the
at
time
of
revealed
the
is
not
real
(2)
conjoint),
product
the
effectiverelative
and
controlled
experimentscompare
buthaserror
dueto
is unbiased
WTP(estimation
that inferred
structure
with
anincentive
incentive
nessofthelottery
ofparorquality
andquantity
estimation
method,
isnotfinancially design,
thelatter
rewards
though
every
participant,
of
variance
x.
the
characteristics
and
the ticipants), (3) Using
suchasaniPod.Finally,
forexpensive
feasible
products,
the
valueof continuous
distributions,
oftheproduct andtheexpected
that
oneversion
mechanism
current
requires
canbe obtained,
fora givenparticipant
utility
to
expected
As a result,
itis notapplicable
available.
be physically
is stated
A1:
asLemma
nophysical
forwhich
newproduct
product which
concepts
really
an
This
is
available.
even
a
(not
represents
prototype)
thatthepurchase
LemmaAl: Ifitis assumed
price(x) is ranresearch.
forfurther
andfruitful
direction
x E [c1,
drawn
from
a uniform
distribution,
important
domly
forpractitioners
toconduct
itis critical
fora type
In conclusion,
utility
c2]andw1E [c1,c2],theexpected
whochoosesstrategy
becauseof their
al in theconti participant
conjoint
applications
incentive-aligned
is
that
the
It
is
external
jointstudy
truth-telling
validity. hoped
greater
todo
herein
willenable
described
mechanism
practitioners
SO.
APPENDIX: FORMALSPECIFICATION OF THE
MECHANISM
TRUTH-TELLING
(Al)
eui
ofwi,respecm andv arethemeanandvariance
where
theproposed
incom- tively,
WTP.
andWisthetrue
ThisAppendix
formally
specifies
itskeytheoretical The mainresultfollowsdirectly
fromLemmaAl
gameanddescribes
pleteinformation
Whinif truth-telling
unbiased
that
method
is
the
structure
a
In
line
with
Mas-Colell,
(assumingconjoint
properties.
informationstrategy
isadopted):
ston,andGreen(1995)use,theincomplete
(D3)
(D2) probability,
by (D1) types,
gameis defined
in a conjoint
Al: Truth
studyis theunique
and (D4) payoff(utility)functions. Theorem BNEiftelling
mechanism,
andonlyif
Specifically,
has an N1-dimensional
D1: Each participant
typet1= (t1[1],
of
t1[2], ti[Ni])E RN1,whereN1is thetotalnumber
A specific
levelsacrossallattributes.
typecorreparticipant
Theexperimenter
structure.
preference
spondstoa specific
hasanN2-dimensional
typet2= (t2[1],t2[2], t2[N2])E
A specific
ofattributes.
RN2,whereN2is thetotalnumber
variatoa specific
product
typecorresponds
experimenter
tion(profile).
T1,T2 denotethesetsofpossibletypesfor
Alternaand experimenter,
the participant
respectively.
ofa participant's
thetotaldimensions
typecouldbe
tively,
levelsofmorethan
as thesumoftheattribute
interpreted
andtheexperimenter's
oneproduct
typeis a comcategory,
thesecategories.
from
ofproducts
bination
D2: Eachplayerknowshisorherowntypebutnottheother
distriknowstheprobability
type.Theparticipant
player's
as pi(t2).
denoted
bution
oftheexperimenter's
type,
sets
F = (A1,A2,o--) haspossible
D3: Themechanism
strategy
x
--->
o:
function
an
and
outcome
Z
Al
A2
(A1,A2)
(A2) Equ+
(A3)
E{
to
chooses
ofwiiftheparticipant
V is thevariance
where
intheconjoint
tellthetruth
study.
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