Designing Pricing Contracts for Boundedly

Designing Pricing Contracts for Boundedly

Vol.54,No.4,April2008,pp.686–700issn0025-1909??eissn1526-5501??08??5404??0686MANAGEMENT SCIENCEinf®doi10.1287/mnsc.1070.0788©2008INFORMS

DesigningPricingContractsforBoundedlyRationalCustomers:DoestheFramingoftheFixedFeeMatter?

HaasSchoolofBusiness,UniversityofCaliforniaatBerkeley,Berkeley,California94720,hoteck@haas.berkeley.edu

SloanSchoolofManagement,MassachusettsInstituteofTechnology,Cambridge,Massachusetts02142,jjzhang@mit.eduTeck-HuaHoJuanjuanZhang

Theformatofpricingcontractsvariessubstantiallyacrossbusinesscontexts,amajorvariablebeingwhetheracontractimposesa?xedfeepayment.Thispaperexamineshowtheuseofthe?xedfeeinpricingcontractsaffectsmarketoutcomesofamanufacturer-retailerchannel.Standardeconomictheoriespredictthatchannelef?ciencyincreaseswiththeintroductionofthe?xedfeeandisinvarianttoitsframing.Weconductalaboratoryexperimenttotestthesepredictions.Surprisingly,theintroductionofthe?xedfeefailstoincreasechannelef?ciency.Moreover,theframingofthe?xedfeedoesmakeadifference:anopaqueframeasquantitydiscountsachieveshigherchannelef?ciencythanasalientframeasatwo-parttariff,althoughthesetwocontractualformatsaretheoreticallyequivalent.Toaccountfortheseanomalies,wegeneralizethestandardeconomicmodelbyallowingtheretailer’sutilitiestobereferencedependentsothattheup-front?xedfeepaymentisperceivedasalossandthesubsequentretailpro?tsasagain.Weembedthisreference-dependentutilityfunctioninaquantalresponseequilibriumframeworkwheretheretailerisallowedtomakedecisionmistakesduetocomputationalcomplexity.Thekeypredictionofthisbehavioralmodelisthatchannelef?ciencydecreaseswithlossaversionforsuf?cientlyNash-rationalretailers.Consistentwiththisprediction,theestimatedloss-aversioncoef?cientis1.37inthetwo-parttariffcondition,signi?cantlyhigherthan1.27inthequantitydiscountcondition.Atthesametime,http://wendang.chazidian.comstly,weconductafollow-upexperimenttocon?rmthecentralroleoflossaversionasabehavioraldriver.Inonecondition,theretailerbecomeslesslossaversewhenwetemporallycompressthe?xedfeepaymentandtherealizationofretailpro?ts,whichsupportsthelossaversiontheory.Intheothercondition,theretailer’scontractacceptanceratedoesnotdeclinewhenwerewardthemanufacturerahighercashpaymentforeachexperimentalpointearned,whichrulesoutthecompetinghypothesisthattheretailerrejectscontractoffersduetofairnessconcerns.

Keywords:?xedfee;two-parttariffs;quantitydiscounts;distributionchannels;lossaversion;behavioraleconomics;experimentaleconomicsHistory:AcceptedbyDetlofvonWintefeldt,decisionanalysis;receivedNovember8,2004.Thispaperwaswiththeauthors2yearsand3monthsfor1revision.PublishedonlineinArticlesinAdvanceMarch12,2008.1.Inanymarkettransaction,asellermustdetermineawaytochargeabuyer.Thistransferofpaymentcantakevariousformats.Some?rmssimplyadoptalinearpricingrule,wherecustomerspayaconstantpriceforeachunitbought.Inothersettings,typicallybusiness-to-businesscontexts,thepricingformatcanbemorecomplex.Wecanclassifypricingcontractsbywhethertheystipulatea?xedfeepayment,andbythenumberofdifferentmarginalprices(i.e.,thepriceforanadditionalunit)theycharge.Figure1presentsthistwo-by-twotaxonomy:Alinear-pricecontractdoesnotimposea?xedfee,andchargesasinglemarginal

686Introductionpriceindependentofthesalesvolume.Atwo-parttar-iffrequiresa?xedfeeinadditiontochargingasinglemarginalprice.Inotherwords,thebuyermust?rstincura?xedfeewhenenteringthepurchaseagree-ment,andwhenthetransactionmaterializes,payaconstantpriceforeachunitbought.Ablocktariffdoesnotimposea?xedfee,butsetsmultiplemarginalprices,http://wendang.chazidian.comstly,athree-parttariffconsistsofa?xedfeeandchargesmultiplemarginalprices.Inthispaper,westudyhowtheuseofthe?xedfeeinpricingcon-tractsaffectsmarketoutcomes.Toisolatetheroleof

Designing Pricing Contracts for Boundedly

HoManagementandZhang:ScienceFraming54(4),pp.ofthe686–700,Fixed©Fee

2008INFORMS

Figure1ATaxonomyofPricingContracts

Fixed fee not charged

Fixed fee chargedNumber of marginalprices = 1

Linear-price contract

Two-part tariff(Quantity discount)Number of marginalprices >1

Block tariff

Three-part tariff

thecontracts—ones?xed,wefocusthatonchargetheasimplestsinglemarginalclassofpricingprice.1

payment.Therearedifferentwaystoframethesame?xedfeetariffessaryscheme,Onewhereframetheisthe?xedaforementionedfeeistwo-partnatively,entrypaymentforagreeingtolabeledpurchase.astheAlter-nec-aperquantitythisdiscountsameschedule,pricingcontractwherecanbeframedastheunitdecreaseswiththequantitythesoldaveragebecausepriceofsearchspreadthequestionofthe?xedfeeovermoreunits.Ourre-outcomes;introductionisofthusthetwofold:?xedfee?rstly,weaskhowwhetherframing.

thesecondlyeffectsofandthemore?xedimportantly,affectsthefeearesensitivewemarketasktomanufacturer-retailerWechoosetoanswerthetheoriesInyieldsharppredictionsdyadwhereresearchstandardquestioneconomicinatailer,thissetting,amanufacturersellsonmarketaproductoutcomes.toaofwhichgoesonandsellstheproducttoagroupre-determineendconsumers.pro?t.apricingBothcontract?rmstomustmaximizeindependentlypricingItisassumedthattheretaileradoptstheiralinearownpricingrule.wpro?tperunit,ruleIfandtheitcanchargesmanufacturerbeshownauniformalsoemploysalinearthatthewholesaletotalpricethemizetwoislessthanthatofanintegratedchannelchannelwhereindependenttheir?rmsjointsetpro?t.theirThispricesinef?ciencycooperativelytomaxi-accountthepriceother’sthepro?t.externalitychannelbecauseneither?rmoccurstakesinintoanConsequently,itspricingbothdecisionchargeimposesahigheronThislemprice(Spengleristhanknowniftheywerepartoftheintegratedchannel.1950),asthenamed“double-marginalization”forthefactthatprob-duemargins.

tofacingthestackingtheendofconsumersmanufacturerissuboptimallytheretailandretailerpro?thightheAnumberofsolutionshavebeenfordouble-marginalizationfacturerasummary).Theyproblemproposed(seeTiroletosolve1988thatinducesemployingtheretaileramoretypicallytocomplexinvolvechargethepricingtheretailschedulemanu-priceof

1

numberLimandofHoblocks(2007)in?uencesstudyblockmarkettariffsoutcomes.

andinvestigatehowthe687

theMoorthyintegratedwould1987).channelIntroducing(e.g.,Jeulanda?xedandShugan1983,ufacturerintheoryacanadopteliminatetheinef?ciency.fee,forTheexample,man-ing?xedtotalaconstantfeeonwholesaletheretaileratwo-partprice(F)tariffbyimposing(inw)additionforeachtounit.charg-qrevenuetomanufactureristhenF+w·q,whereThemarginaldenotesufacture’scosttheoftotalproduction,quantitysold.Ifwequalsthechargemanufacturerthepro?tretailmargin,priceofthethewhichintegratedretailerremoveswouldthechannel.wantman-Thetonelcanthendividethismaximizedchan-feepro?tgainingF,takingbetweenintothetwo?rmsbychoosinga?xedeconomistspower.Theaccountquantitythediscountretailer’sisadvocatedrelativebar-byef?ciency.whichConsiderasanequivalentaquantitywaydiscounttorestoreschedulechannelin Fq/q??+thewforretailerischargedaunitpricegivenbytractsthetwo-partasalestariffquantityq.NotethatforthesameIninfact,conferidenticalandrevenuesthequantitytothediscountmanufacturer.con-marketaverage-costthelatterterms.issimplyEconomicareframingtheoriesoftheformeringbetweenof?xedoutcomesfeesgivenshouldbeinvarianttothispredictrefram-thatsharpInsummary,thetwostandardpricingthemathematicalequivalenceeconomiccontracts.

theoriesmakenelthatpredictionsconsistsofforthemarketoutcomesofachan-twoef?ciency1.Theintroductionamanufacturer-retailerthe2.Channeltotheofthe?xedfeerestoresdyad:

channeloutcomeslevelofaretheinvariantintegratedtochannel.

theframingoftity?xedWhetherdiscountfee.Speci?cally,achievetheatwo-parttariffandaquan-icalpreferquestion.thetwohypothesessameholdchannelisanoutcomes.openempir-paymenttheclassIfoftheypricinghold,contractsthemanufacturerwithashoulditandwillbeandimportantshouldignoreitsframing.Ifthey?xedfail,feeoutcomes.

whichwayoftoframingknowwhichyieldthepricingbestcontractmarkettheTheassigntwostudyhypotheses.containsInthethe?rstexperimentaltestofspondingsubjectstracts:tothreeintotypesthreetreatmentlaboratory,conditionswerandomlycorre-theasquantitythelinear-priceofmanufacturerpricingcon-discount.contract,thetwo-parttariff,andrespondingeithermanufacturersInoreachretailerscondition,andplaysubjectsthecor-actmonetarypricinggame,motivatedbysubstantialexperimentalincentivestomakeoptimaldecisions.Thepredictions:improvetheresultsintroductioncontradictofthethestandard?xedfeetheories’doesnotachieveschanneloutcomes,andthequantitydiscounttariff.

higherchannelef?ciencythanthetwo-part

Designing Pricing Contracts for Boundedly

688

havioralToaccountdent.paidInmodelforitstwo-partinthesewhichanomalies,wedevelopabe-tariffutilitiesframing,arereferencethe?xeddepen-feeisearnsup-frontpaymenttheretailbeforemargin.salesConsequently,materialize,andthetheretailerratedferentsothatandthetheretailretailermarginaretemporally?xedsepa-feecomparedmentalmayregisterthemindif-ingtotheaccountsretailer’s(Thalerstatus1980).quoInbeforeparticular,reach-canthepurchaseagreement,theup-front?xedfeeceedsregisterbeagain.asThesealosstwoandthesubsequentretailpro-thegiventheloss-aversiondifferentmentalaccountsmaythuscoef?cient.utilityweights,asmeasuredbycounts,?xedfeeisframedinOntermstheotherofquantityhand,whenstagegrateofthe?xedretailerfeepayment,doesnotexperienceaseparatedis-andinthesamementalaccountandisproceedsmorelikelyfromtointe-way,itsdichotomythetotalquantitypaymentsdiscounttoframethemanufacturer.Insalesthischologicalmoreopaque.Ifthisismakesthecase,thegain-lossthepsy-severeufacturerwithlosstheattachedtwo-parttotarifftheframe,?xedfeewillbemoreraiseef?ciency.

thewholesaletolowertheprice?xedtothefeedetrimentand,forcingtocompensate,theman-ofchannelsionApartfromlossaversion,thereisacountsalongthemaywhichdiffer:two-partcontracttariffsandsecondquantitydimen-dis-theeffectstalreference-dependentofcontractcomplexity,complexity.TocaptureutilitywefurtherembedPalfreyresponse“Nash1995),equilibriumfunctionintoaquan-whichallowsframework(McKelveyanddecisionrational”theretailertobelessneststaskandmakemoremistakeswhentheandthestandardismoreeconomiccomplex.2modelThisbehavioralasamodelaversionallowscomes.anduscontracttoassesstherelativeimpactspecialofcase,lossexperimentalWeestimatecomplexityonchannelout-?cientdata.thebehavioralmodelusingthetariffaddition,frameisindeedTheestimatedloss-aversioncoef-thansigni?cantlyinthequantityhigherdiscountintheframe.two-partInsioninlossaversiondominatescomplexityaver-aversionWeconductexplainingresults,astheafollow-upthedata.

experimenttocon?rmlossnativeandtoruleprimaryoutfairnessdriverofconcerntheexperimentalasanofposes.theexplanation.two-parttariffWecontractcreatetwotoadditionalalter-achievevariantspationInthe?xeddecisionthe?rstfeeregisters,stagevariant,whenweeliminatethethesepartici-pur-andaskthethelossretailerperceivedtosimply

from2

advancesThisapproach2003andinHobehavioralsharesthesamespiritwithanumberofrecentetal.2006).

economics(forasurvey,seeCamereretal.ManagementHoScienceand54(4),Zhang:pp.686–700,Framing©of2008theINFORMS

FixedFee

choosetheingoptionaretailtoprice.Theretailer,however,stillretainsByamaximalturnretaildownpricethethatcontractresultsofferbycharg-realizationcombiningretailerstages,thethispurchaseagreementinzeroanddemand.thesalesproceedstoincludethe?xedcontractfeevariantpaymentencouragesandthesalesthenelshouldoutcomesinonearecommonindeeddrivenmentalbyaccount.Ifchan-variantondexceptvariantthanseeaisinlowerloss-aversioncoef?cientlossaversion,inthisweidenticalthetwo-parttothetarifforiginalcondition.two-partThesec-thement,experimentalthatwechangecurrencytheandconversiontarifftheratebetweentojectsthemakingmanufacturereachexperimentaleventualcashpay-thanpointworthmoretocareaboutfairness,wetowouldtheretailer.expectShouldtheretailersub-inbeaversionthismorenewpronecondition,torejectalthoughthemanufacturer’sofferresultsloss-aversionsupportshouldournotbein?uenced.theThedegreeexperimentaloflossvarianttheandcoef?cientbehavioralisindeedmodel:lowertheinestimatedthe?rsttheretailerdoesremainsnottherejectsameoffersinthemoresecondvariant;fairnesssecondvariant,contrarytothepredictionfrequentlyoftheinSectionTheresthypothesis.

formulates2outlinesofthisthepaperstandardisorganizedeconomicasfollows.theSectiondesigntheandmainimplementationhypotheses.Sectionmodelandof3describesdevelops4theareportsbehavioraltheexperimentaltheexperiment.modelresults.Section5ondexperimentalhypothesisstudydesigneddata.Sectionand6estimatespresentstheitusingsec-petingandtoassesstoexplicitlyfairnesstestconcerntheloss-aversionasadiscussesexplanation.futureresearchSectiondirections.

7concludesthepapercom-and2.TheInandHypotheses

StandardEconomicModel

model,thiscontractswhichsectionillustrateswepresenthowthethestandarduseofeconomicchannel,restoresandcancausehowtheinef?cienciesintroductioninofanindependentlinear-pricechannelchanneldardoutcomeef?ciency.hypothesesWethenformallythe?xedstatethefeesistsWeeconomicconsideramodel.

derivedfromthestan-simpledistributionchannelthatmanufacturer,ofaone-manufacturer-one-retailerdyad.con-Theproductanupstreammonopolist,producesaufactureratretailerextendsaconstantatake-it-or-leave-itmarginalcostcoffer.Theman-Theconsumerretailer,thatandmarket.inspeci?esturn,auniformwholesalepricetothew.Itincursisamonopolistnoadditionalsellerintheendsumerchargesmarketaretailisassumedpricepto.Demandbecommoninthesellingknowledge,

endcosts,con-

Designing Pricing Contracts for Boundedly

HoManagementandZhang:ScienceFraming54(4),pp.ofthe686–700,Fixed©Fee

2008INFORMS

andthegreatermaximumtakesthelinearformofq=d?p,wheredishence,thancpossible.3Theproductdemandhasandnoisassumedsalvagetobetofromendtheconsumersretaileriswillequalensuretothethatthequantityvalue;soldturerIfthethemanufacturer.

quantitypurchasedjointandchanneltheisintegrated(i.e.,themanufac-maximizepro?t), pthearetailerretailpricecooperatepshouldtomaximizebechosentheirtoequals?c?? d?p??.Ittotalfollowschannelthatpro?tthisgivenby?? p??= dThe?c??/ d+c??/2,yieldinganoptimalef?cientsalesretailquantitypriceofamanufacturer2andamaximizedandchannelpro?tof d?c??2/4.them.

transferpricewtodividetheretailerthechannelcanthenpro?tnegotiatebetweentheIftively,retailerthechannelchooseisindependent,theirownprices,themanufacturerwandp,andufacturertomaximizethemoves?rsttheirandindividualoffersawholesalepro?ts.priceTherespec-man- pretaileracceptsthisoffer,itspro?twillbe??w.IfR p??=imizes?w?? danticipatingthe?p??retailer’s.Thebest-responsepro?tis dretailpricethatmax-would wthe?c?? dchoosethe? daretailer’s+ww??/to2maximizeresponse,+w??/2.Rationally??intheitspro?tthemanufacturerof??M w??=inducingequilibriumwholesaleprice?rstequalsplace. d+Therefore,c??/2>c,thanlowsthethatef?cientaretailthemanufacturerpricepriceofofan 3d+c??/4,whichishigherearnsintegratedapro?tchannel.of d?Itc??2fol-andrealizedtheretailerearns d?c??2/16.Thetotalpro?t/8,3channel d?c??2/in16,thisrepresentingindependentonlychannel75%isreducedtonalityother’seachpro?t.?rm’sThispricinginef?ciencydecisionstemsoftheintegratedimposesfromtheexter-externalitypro?t.ainWhenanindependentthe?rmsfailonthechannel,tointernalizebothsuchprice,higherretailerasthanaresultoptimalofstackingpricemargin.theThe?nalchooseretailinef?ciencymargins,tractsproblemishigherassociatedthanthemanufacturerandwithef?cientlinear-pricelevel.Thisproblem.

isthusknownasthedouble-marginalizationcon-izationAwell-knowncally,problemissolutiontointroducetothisa?xeddouble-marginal-fee.Speci?-imposesthemanufacturercanofferatwo-parttariffthatingretaileraconstanta?xedmarginal“franchisewholesalefee”Finpriceadditionw.tocharg-tedoftopayingentersthethispurchaseamountofagreement,?xeditisOncecommit-theitincurstherealizedatotalsales.costIfofthewqretailer+F,buysfeeandthusaindependentquantityearnsqa

,3

Villas-BoasReyandTirole(1986),Desaiandofdemand(2003)uncertainty.

explorethechannelSrinivasanequilibrium(1995),intheIyerpresenceand689

pro?tretail dpriceof??Requals p??= p d?+w?? dw??/?2,p??and?Fthe.Theretailer’sbest-responsepro?tisoption?w??2/4?F.Iftheretailerdoesnothavethemanufacturer(whichisthecancaseanoutsidechargeinathe?xedexperimentfeeof d?setting),w??2andtheappropriatetheentirechannel/4,maxmanufacturer’soptimizationproblempro?t.Therefore,becomeslibrium,w??M= w?c?? d? d+w??/2??+ d?w??2/4.Inequi- dIn+c??/2w=c,inducinganef?cientretailpriceofef?ciencyessence,andaanef?cientchannelpro?tof d?c??2/4.andreliesloweringbytwo-parteliminatingtariffcontractrestoreschanneltheretailthemanufacturer’smargintwo-partEconomicsonthe?xedfeeasprice.itssourceThemanufacturerofpro?t.

thenequivalent.tariffliteratureoftenjuxtaposestheaboveaverageConsidercontractthewithitsquantitydiscountareunitpriceof F/q??contract+w,thatwherespeci?esFandetermine,nonnegativeretailer.andconstantsqistheamountthemanufacturerneedsandtowbecauseThismoretheretailercontractlowersrepresentspurchasedbytheitsaveragequantitydiscountsalentunits.bothtotheThistwo-partquantitydiscountschemecostbyisbuyingequiv-enuecontractsaccordthetariffmanufacturerinthat,fortheasamegivenq,restoreFtariffchannel+wq.Therefore,rev-ef?ciencyainquantitydiscountwouldthedoes:themanufacturerthechargessamewayw=ac,two-partinducesextractsretailerappropriately.

thetomaximizedchargethechannelef?cientpro?tprice,byandsettingthenFtwoInformallysharpsummary,statedpredictionsthestandardasfollows:

abouteconomicthechannelmodeloutcomes,yieldsintroductionHypothesisof1.(TheEf?ciencyHypothesis).Thetariff(a)(TPT)TheStrongthe?xedrestoresEf?ciencyfeeimprovesfullchannelHypothesischannelef?ciency.

.ef?ciency.Atwo-part??TPT=

d?c??2

M

+??R

TPT??wheretariff(b)Mstandsformanufacturer,andRstandsforretailer.(LP)contract.

generatesTheWeakahigherEf?ciencychannelHypothesispro?tthana.Alinear-pricetwo-part??MTPT+??RTPT>??MLP+??R

LPsis)Hypothesis?xed.Channeloutcomes2.(TheareFrameinvariantInvarianceHypothe-?xed(a)fee.

totheframingofthe

Totalchannelpro?tisinvarianttothe(QD)fee.areThatrevenueis,aequivalent.

two-parttariffandaquantityframingdiscountofthe??M

TPT+??R

TPT=??M

QD+??R

QD=K??

0≤K≤ d?c??2

??

Designing Pricing Contracts for Boundedly

690

Figure2

TheEf?ciencyandFrameInvarianceHypotheses

16

14

12

t

ifor10

p rerut8

acfunaM6

4

2

Retailer profit

invariant(b)Themanufacturer’sshareoftariffandtothethequantityframingdiscountofthe?xedarefee.thedivisionThatchannelequivalent.

is,thetwo-partpro?tis??MTPT

QD=??M

0≤??≤1??

MR??M+??R

=????assumeFigureneld2=10illustratesandc=the2soabovethatthehypotheses.ef?cientWepairspro?tshouldobtainedequalswhen16.Themanufacturer-retailerchan-pro?tesispassesholds,fallonandlineshouldAusingifthethetwo-parttariffcontractfallstrongnortheastef?ciencyhypoth-linear-pricepointsiscontract) 4??8??(i.e.,thepro?tpairwhenoflineusingBthattheallthepro?tholds.pairsIftheobtainedframeiftheinvarianceweakef?ciencyhypothe-usingthetwo-parthypothesistariffholds,toorigin.A,quantityandshoulddiscountfallonshouldalinethatfallpassesonalinethroughparallelandhypothesesThetwo-partontarifftostandardholdeconomicmodelpredictsboththeandsothatallpro?tpairsundertheassumethesameevendivisionpoint—forthequantityoftheexample,discountchannelpointpro?t.

should8??8??iffallwe3.TheExperiment

3.1.WetestinggiveExperimentalthestandardDesign

economicmodelitsbestshotbyratoryemulatesenvironment.itstwohypothesesinawell-controlledlabo-wethecleanestIfatheoryfailsinthelab,whichtheshould?eld.Wequestionrecruithumanhowpossiblewellsubjectsthemarkettheoryenvironment,whoassumeappliesthe

inManagementHoScienceand54(4),Zhang:pp.686–700,Framing©of2008theINFORMS

FixedFee

Table1PredictionsoftheStandardEconomicModel

Treatmentconditions

Variables

LPTPTQDWholesaleFixedpriceRetailfee—6162Manufacturerprice

8162Retailer8166Channelpro?tpro?t0166Channelpro?t

124Manufactureref?ciencypro?t(%)

share(%)

7566??7

10016100

100160100

Note.Assumeq=10?p,c=2,andretailerreservationutilityequals0.

rolethepaymentscorrespondingofeitherthemanufacturerpricingdecisions,ortheretailer,makerandomlybasedtions:assignedontheandreceivecashtopro?tstheymake.SubjectsaredetermineLP,TPT,andQD,onewhereofthreethechanneltreatmentcontractcondi-andchannelaquantityisalinear-pricediscount,respectively.contract,atwo-parttoThetariff,tion,theistheoreticalwithsettingq=isidenticaltothatinthetheorylaboratorysec-predictions10?pandforc=the2.Table1summarizesofpredictedwithawholesalepricethreeof6,conditions.aretailpriceLPon8,oftheandotheratotalhand,channelpro?tof12.TPTandQD,Because2,aretailpricepredictof6,andtheasamechannelwholesalepricethe16inmanufacturertheretailerbothTPTandishaspredictednooutsideoptionspro?tintheoflab,16.QDconditions.

tochargea?xedfeeof3.2.Wetion,ranExperimentalundergraduate4for10experimentalProcedures

TPT,sessions,2fortheLPcondi-participatedstudentsand4foratQD.aWestOneCoasthundreduniversitytwenty12sionsubjects,inandtheallexperiment.4sessionsconsistedMostsessionsofhadtimes.rounds,ofThisdesignsothatiseachmeantsubjecttoincreaseplayedthe11thegamedeci-number11ingobservationsandtocaptureanypotentiallearn-beMatchingmatchedeffects.Thewithdesignadifferentalsopartnerrequiredinasubjecttosameboardssessionwassatanonymous.incubiclesSubjectsenrolledeachround.5intheners.tionbetweenActionsanddidnotknowtheseparatedidentityofbytheirpartitionpart-subjects.weretakenThetogoalpreventofunrepeatedcommunica-and

4

industrialItisacommoninorganizationpracticetheoriestouse(seeundergraduateHolt1995).studentstotestingprinciple,groupsprofessionalsbereplicatedTheresultscould,(seePlottandwithmanagers.Severalstudiescompar-1987,studentsBalland?ndCechlittle1996).

differencebetweenthetwo5playInsessionstothegamewhereonly11subjectsshowedup,wehadeachsubjectsubjectsensureparticipated,unrepeated10times,eachmatching.withonesubjectInsubjectsittingstillineachroundstillsessionsplayedwhereonly11moretimes.

than12