年纪和决策

1AgingandDcisionMaking:AbroadcomparatistudyofdcisionbhaiorinnurologicallyhalthyldrlyandyoungindiidualsStphaniKoalchika,1,ColinF.Camrrb,DaidM.Grthrb,CharlsR.Plottb,andJohnM.AllmancaCaliforniaInstitutofTchnology,1200E.CaliforniaBld,Pasadna,CA91126bDiisionofthHumanitisandSocialScincs,CaliforniaInstitutofTchnology,Pasadna,CA.cDiisionofBiology,CaliforniaInstitutofTchnology,Pasadna,CA.AbstractWinstigatbhaiorinasrisofconomicdcisionswithtwopopulations,onofhalthyldrlyindiiduals(witharagag82)andonofyoungrstudnts(aragag20).Wxaminconfidnc,gambling,thndowmntffct,andththoryofmind(stratgicthinking).Ourfindingsindicatthattholdradults’dcisionbhaiorissimilartothatofyoungadults,contrarytothnotionthatconomicdcisionmakingisimpairdwithag.Moror,somofthdcisionbhaiorssuggstthatthldrlyindiidualsarlssbiasdthanthyoungrindiiduals.(1)Thrisagratrpralncoforconfidntbhaiorinthyoungrpopulation.(2)Choicorlottrisdonotrflctthagdiffrncspriouslyrportdinthpsychologyandbiologylitratur.(3)Bothpopulationsprformsimilarlyonthbautycontsttask,althoughthrisamodstindicationofahighrincidncofconfusdbhaiorintholdradultsinthistask.(4)Ourrsultsshownosupportforathoryofanndowmntffctinithrpopulation.Kywords:Ag,orconfidnc,ndowmntffct,thoryofmind,gamthory,risktakingClassification:D00,D80,D81AgingandDcisionMaking:Abroadcomparatistudyofdcisionbhaiorinnurologicallyhalthyldrlyandyoungindiiduals1Corrspondingauthor,MSC323CaliforniaInstitutofTchnology,Pasadna,CA91126.stphk@caltch.duRAYLIN2OriwThoughitiswidlyrcognizdthatthpopulationofthUnitdStatsisaging,muchofourcurrntundrstandinginthfildofindiidualdcisionmakingisbasdprimarilyondatafromstudntpopulations.Whilthiscouldbthrsultofsubjctaailability,thnarrowxplorationinthisaramayalsorflctacommonblifamongrsarchrsofdcisionbhaiorthatdcisionmakingabilitydclinswithaging(Ptrs2000).Dspitthprasinss,namongscintists,ofthisiwofaging,itrmainsanunsubstantiatdnotion.Manyoldrindiidualsarproductiandintllctuallyiablthroughoutthirlis.Still,itistruthatothrsarulnrabltodmntiaandnurodgnratiillnsss,suchasAlzhimr'sdisas.Forthsrasons,ourobjctiinthpilotstudywastobgintocharactrizthdcisionbhaiorassociatdwithnormalaging,withanmphasisonconomicchoics.ThrcntbookditdbyStrnandCarstnson(2000)prsntsadancsinundrstandingcognitionofoldrindiidualsandsuggstsanagndaforfuturrsarch.Howwlloldrpoplmakconomicdcisionsisanimportantissuforsocialpolicy.Sincwalthtndstoaccumulatoron’sliftim,alargportionisinthhandsofoldrpopl.Oldrpoplalsoarmorliklytootthanyoungpoplar,sothymayhadisproportionatpoliticalinflunc.Manwhil,bothlongtrmtrnds(incrasdlongity)andshorttrmtrnds(babybooms)manthatincrasingproportionsofthpopulationaroldrandrtird.Itisconciablthatourscintificmodlofconomicdcisionmaking,sohailyrootdinstudisof20yaroldstudnts,isamisladingguidtohowthincrasingsgmntofwalthy,xprincdoldrpoplwillbha.3Thdcisionswchostostudyarafirstcutataddrssingthrobustnssofrgularitisthatarwllstablishdinyoungrpopulations.Thtasksalsowrchosnbcauscommonobsrationsuggstsoldrpoplmaybhadiffrntlyfromyoungpoplonsomofthstasks.Onfaturofwisdom,whichprsumablyisacquirdoraliftim,ismtaknowldg—knowingwhatonknows,andwhatonisgoodat.Wmasurmtaknowldgbyslfrportdconfidncintriiaqustions.Acommonstrotypofoldrpoplisthatthyar“consrati,disliktakingrisk,ar“stinthirways”,andhargularritualsandpracticsthatthyarrluctanttoabandon.Waskifsuchtndncismightmanifstindcisionsundruncrtainty.Wconductxprimntswithchoicsormontarygamblssimilartothosprformdbypsychologistsandbiologists.Whilthsxprimntsarnotthon’sthatarsuggstdbythconomicthoryofrisktakingbhaior,thyarxprimntsthathabnconductdmanytimsandcanthussrasabaslinforfindinglmntsofagdiffrncsinbhaior.Thmontarygamblsincludincompltandcompltinformation(i..,whrprobabilitisarknownxantorunknown).Thfinalgroupofxprimntsxplorspossibldiffrncsinwillingnsstopayandwillingnsstoaccpt.Inthsxprimntsthchoicsinolgamblsforrydayobjcts(acoffmug).Onbodyofthorysuggststhatobsrddiffrncsardutoanasymmtryofprfrncsbtwnlosssandgains,whichmightbxacrbatdbyag.Analtrnatithorysuggststhatthphnomnaardutoxprimntalprocdursandsubjctmisconcptions.Thplanofthpaprisasfollows:sctionsonachofthdcisionswillincludabrifintroduction,adiscussionofmthodology,andaprsntationofthrsults.Wconcludwithagnraldiscussionrgardingourfindings.4SubjctPopulationandGnralExprimntalDsignInourcomparatiinstigation,wprformdintriwswithtwoaggroups:ayoungpopulation(ags1826,51%fmal)andldrlypopulation(ags7095,70%fmal).2Tholdrsubjcts(N=50)srascontrolsforthAlzhimr'sDisasRsarchCntr(ADRC)atthUnirsityofSouthrnCalifornia(USC).Basdonannualcognitiandbhaioraltsting,tholdrindiidualsarconsidrdnurologicallyhalthy,withnohistoryofdmntiaormntalillnss.Thstudntpopulation(N=51)consistdofhalthyundrgraduatsfromajuniorcollgnarCaltch.3Thyoungrpopulation,bingstudntsatacommunitycollg,habtwn12and16yarsofformalducation.Tholdrpopulationishighlyducatdrlatitothiraggroup4—78%hamorthan12yarsofducationand60%ha16ormoryars.Othrpopulationsofoldradultsmaybmordifficulttostudy(.g.indiidualswithParkinsondisasorothralimntsorpoplinassistdliingarrangmnts).Wchosapopulationofhalthyhighfunctioningindiidualsforourfirstattmpttostudydcisionmakinginthldrly.Eachsubjctparticipatinginthstudycompltdanindiiduallyadministrdintriw,inolingawrittnqustionnairandsralintractitasks.Onaragsubjctsofbothpopulationstookfiftyminutstocompltthintriw.Forallarasofthinstigationinolingmontaryrwards,ralcashwasawarddtothsubjcts.This3Thspopulationsarnotrprsntatiofthiraggroups,thoughthyarrasonablywllmatchdonducationll.Rprsntatisamplingwouldbanaturalnxtstpbutwouldrquiramuchmorcomplxdsign.4NotthatcollgducationonlybcamwidspradinthyarsfollowingWorldWarII,risingfrom1.5prcntin1950to5prcntin1980(U.S.Gornmnt(2001),WaltonandRockoff(1998)).Soouroldrsubjcts,whowrbornaround1920onarag,armuchmorliklythanthirprstohagraduatdfromhighschoolorgontocollg.5mthodofcollctingdataisxpnsi.Formanypopulationsofoldradultsliingoutsidofrtirmntcommunitis,indiidualintriwsmaybancssaryburdn.Thsammthodwasusdforallsubjcts(i..,thyoungrsubjctswrintriwdonatatimalso)toaoidconfoundingagwiththmthodofdataacquisition.ConfidncWxamindconfidncusingamtaknowldgtask,whichtststhaccuracyofanindiidual’sassssmntofhisorhrownknowldg.Priousworkinthisarahasshownthatnonxprtindiidualsartypicallyorconfidnt;thyorstimatthqualityofthirownabilitisorknowldg(Snson1981,Winstin1980)andstatxtrmprobabilitismoroftnthanthyshould.Workinconomicthory,particularlywithbusinssrlatdforcasting,hasproiddfurthrsupportforthisbhaioralphnomnon(CamrrandLoallo,1999).Orconfidncisasubjctofintnsdbatamongdcisionthorists(AytonandMcCllland1997).Thrprominntxplanationsoforconfidnchamrgd.Onargumntisthatitisanillusioncratdbyasymmtricallymisladingitmsininstigationmthods(Juslin1994,Gigrnzrtal.1991)Forxampl,onqustionusdwas:whichcityisfarthrnorthRomorNwYork.MostAmricanssmtoblithatthcorrctanswrisNwYork,andarquitconfidnt,nthoughthatanswrisincorrct(butnotbymuch).Somcontndthatorconfidncrsultsfromsubjctsbasingthiranswrsonarasonablprobabilitybutrspondingwithrror,whichbiassthirrportdprobabilitisinthdirctionoforconfidnc(Er1994).OthrsarguthatitisacognitibiasactiatdduringthaluationofinformationRAYLIN6(Kahnman1996),dutoanchoringonanintuitianswrorsnapjudgmnt,andadjustinginsufficintlyforthwaysinwhichthanswrcouldbwrong.Morrcntstudisdsigndtosparatthsxplanationshagnrallyshownthatorconfidncprsistsnwhnqustionsarsampldrandomly(Soll,1996)andrsponssaradjustdforrandomrror(Wallstn1994).Animportantqualificationisthatmanyxprtpopulations.g.wathrforcastrs(Murphy,1984),blackjackdalrsandothrs(Camrr,1995,pp.590592),andhighlyxprincdsubjctsinrpatdgams(Camrr,HoandChong,2002)donotshowthorconfidncthatnormalpopulationsdo.Inthisstudy,winstigatdconfidncbyproidingsubjctswithtwntytriiaqustionsondirssubjcts(sAppndix1).Eachofthsubjctsintriwdwasproiddthsamstoftwntygnralknowldgqustionswithbinaryanswrchoics.Subjctswrinstructdtoslctananswrchoicandthnproidaconfidncassssmnt(100%50%)aboutthirchoic.Oldrsubjctsdidsomwhatbttranswring74.1%ofthqustionscorrctly,whil66.1%ofanswrsginbythyoungrsubjctswrcorrct.Tostudycalibration,forachgroupwcombindallthanswrsinwhichsubjctsgathsamconfidncassssmnt,andcalculatdhowoftnthywrright.Good“calibration”mansthatthfractionofcorrctanswrsinanassssmntcatgoryshouldmatchthatassssmnt(.g.,onqustionswhrsubjctssaidthywr80%right,thyshouldbrightabout80%oftim).Figur1comparsthosconfidncassssmntswiththassociatdaccuracyrats.Nonparamtricmdiananalysisshowsthattholdrsubjcts'assssmntsarsignificantlymoraccuratat60%(p<0.05)and70%(p<0.01)rportddgrsof7confidnc.Tholdrsubjctsdoxhibitorconfidncwhnthrportddgrsofconfidncaratth80%and90%lls(17%ofthirtotalrsponss),butyoungrsubjctsarorconfidntatallthintrmdiatllsofrportdconfidnc(48%ofthirtotalrsponss).Bhaiorbtwngroupsalsodiffrdinthirrsponsdistributions.Thyoungrsubjctsspradoutthirrsponssacrossthconfidnclls:halfofthirslctionswrnlydistributdamongthintrmdiatconfidnclls.Intholdrsubjcts,thmajorityofthrsponsswrginwithithr100%or50%confidnc(incalibrationtrms,thirassssmntshad“highrrsolution”).Whiloldrsubjctsrportdaconfidncof100%significantlymoroftnthanthyoungrsubjcts(p<0.025),thymadsubstantiallyfwrslctionswith60%80%confidnc(p<.05forachgroup).Thprcntagofcorrctrsponsswhnrporting100%confidncwasaboutthsamforthtwogroups(94%corrctfortholdrpopulationand92%forthyoungrsubjcts).Onwaytointrprtthsrsultsisthatoldrsubjctslooklikdomainxprtsoftndo—thymakmorxtrmrsponssof“don’tknow”(50%)or“I’msur”(100%)andthyarnotasorconfidntinmuchofthmiddlrangofrports.Muchasdomainxprtslikwathrforcastrslarntotmprthirorconfidncortim,bymakinghundrdsorthousandsofdailyforcasts,prhapstholdrsubjctshalarndtobcommorxprtoraliftimofmakingassssmnts.DcisionMakingUndrUncrtaintyPsychologistsandbiologistshastudidbhaiorinthcontxtofagamblingparadigm.Bcausthbackgroundrsarchisxtnsiandbcausrsultshabn8intrprtdasrlatdtothphysiologyandhalthofthbrainthnironmntlndsitslftoaninquiryaboutthpossiblffctsofag.Thpsychologyandbiologylitraturrfrtothirworkasrflctingattitudstowardriskbutwwillnotussuchintrprtationsbcausthxprimntalsttingdosnotsupportthintrprtationofriskattitudsasdlopdinththoryofriskasfoundinconomics.Whilthsdiffrncswillbcomclarasthdiscussionprocds,thradrwillsthatthxprimntsarmorfocusdonthpropnsityofsubjctstoxhibitprfrncsthatrspondtothstatisticalproprtisofthlottris.Twogamblingtasksarmployd.ThfirsttaskisamodifidrsionofthcarddckgamblingtaskofBcharatal.(2000)inwhichthrisincompltinformationaboutthprobabilityofprospcts.Inthmodifidgamblingtask,subjctsslctdcardsfromonoftwodckstoarncash.Thcardswrprorganizdsothatondck(A)hadanoralllossof$2.50rytncardsandthothrdck(B)hadanorallgainof$2.50rytncards.AllthcardsindckAgaa$1.00onryturnbutwroccasionallyaccompanidwithhighlosss,$7.50forxampl(forantlossof$6.50).ThothrdckBgaasmallrgainforachcard,+$0.50,buthadsmallroccasionallosss.Subjctsdidnotknowthcompositionofthdcks(gininAppndix2);thyhadtolarnasthywntalong.Subjctswrinstructdthatthyalwayshadtoslctthtopcardofonofthdcks,butthycouldswitchbtwndcksatanytimduringthtask.Eachsubjctslctd50cardsonatatim,butwrnotinformdinadancaboutthtotalnumbrofdraws.InmanarianctrmsdckAisdominatdbydckBbcausithasalowrmanpayoffandagratrarianc.55NotthatchoosingdckBisutilitymaximizingifaprsonissufficintlyriskprfrring,sothathighrariancisprfrrabl(ariskprfrrrwillsacrificmanpayofftogtmorarianc).Th9Bcharatal.conductdthirgamblingtaskwithapopulationofhalthyadultsandapopulationofindiidualswithdamagtothntromdialprfrontalcortx(VM).ThyfoundthatthVMpatints,unlikthhalthyadults,didnotgraduallylarntochoosfromthmoradantagousdckA(withthhighrmanpayoffandlowrarianc).OthrstudismployingBchara’sdsignhafoundthatindiidualswithdamagdorbitofrontalcortxhaanimpairdabilityatadaptingthirdckprfrncstodckAincomparisontocontrolsubjcts(Damasio1994).Dnburgtal.(1999)administrdthistaskwithapopulationofhalthyoldradultsandarguthattholdrindiidualsbhasimilarlytothfrontallobdamagdsubjcts.Thissuggstionthataginfluncsbhaiorinwayssimilartobraindamagladsnaturallytoamorsystmaticinstigationundrawidrrangoftstssuchasthosrportdhr.ConsistntwiththrsultsofthBcharastudy,ourfindingsshowthatsubjctsdcidquicklythatdckBismorprfrrd.Thbginningphasofthtaskisalarningpriodinwhichbothpopulationssamplachdckqually.Byththird10drawintralofslctions,thsubjctsbgintohaaprfrncfordckBandthisprfrncincrassforthfinaltncardsslctd(Fig.2).Intrstingly,tholdrandyoungrsubjctpopulationschoosroughlythsamdcksforthfirstfortycards.Inthfinaltncardsasuggstidiffrncappars.ThyoungrsubjctsshowaslightlymorxtrmprfrncfordckBinthfinal10cards,whichisnotsignificantatconntionallls(p=0.14).Rplicationandmortrialsarnddtodtrminwhthrornotthisdiffrncisarobustproprtyofaginganddcisionmaking.Asacomplmnttothisfirsttask,wconductdascond,gamblingprocdurthatallowdimprssionsaboutrlatiattitudstowardriskbyrmoingthndfornuroscintificlitratur,howr,uniformlytratsthdckBchoicasamistakrathrthananxprssionofriskprfrnc.10subjctstolarnaboutpossiblpayoffs.Inthsxprimnts,unliktharliron,subjctshadcompltinformationaboutthprobabilitisofprospcts.Thirtaskwasagaintoslctonoftwodcks(sAppndix2).UnlikinBchara’sincompltinformationdsign,subjctssawthmonypayoffsfromachofthtncardsinachdckbformakingthirslction.Oncthydciddwhichdckthywantd,thtncardswrshuffldandthsubjctsslctdoncard.Riskydckshadthhighstindiidualgainsandlosss(largrarianc)andanxpctdpayoffthatwaszroorngati.Thlssriskydckshadlowrindiidualgainsandlosss,(andsmallrariancs)andpositixpctdalus.Thusthriskydckhadalowrmanandahighrariancthanthlssriskydck.Atotalofsixchoics,withrshufflingaftrachdraw,wrginto36oftholdrsubjctsand51ofthstudntsubjcts.Incontrasttothgamblingtaskwithincompltinformation,whnsubjctsprdominantlylarndtochoosthdckwiththhighstxpctdrturn,inthiscompltinformationtaskthindiidualsinbothgroupstndtoprfrthhighrriskdcks,withnodiffrncacrossaggroups.Amongoldrsubjcts,58%slctdfourormorriskydcksoutofthsixchoics,whil59%ofthyoungrsubjctsslctfourormorriskydcks(Fig.3)(andthproportionswrsimilaracrossaggroupsforachofthsixdiffrntdckpairs).Anintrstingdiffrncbtwnthgroupsisthatthldrlyindiidualswrmorliklytomixthirchoicsamongriskyandlssriskydcks.Incontrast,youngrsubjctswrmorliklytochoicthriskirdckallsixtims(22%ofyoungrsubjcts,compardto11%ofoldrsubjcts,p=0.10).Allsixlottriswrplaydoutinsqunc,initingatstofapossiblrlationshipbtwnpriouswinsorlosssonfuturchoics(.g.,a“housmony”ffctincrasingrisktakingaftrawin,ora“chasinglosss”ffct,incrasingrisk11takingaftraloss).Rlatitotholdrsubjcts,youngrsubjctshaaslightlystrongrtndncytochosariskydckaftrxprincingalossfromapriousriskydckslction(p=0.25).Oldrsubjctsarslightlymorliklytoslctariskydckaftragainfromapriousriskydckslction(p=0.19).Thsffctsarmodstandcurrntlyinsignificantbutdsrfurthrstudyasclusaboutpotntialdiffrncsinlarningprocsssandadaptationtolossandgain.GndrandDcisionsGinthlargrproportionofwomnintholdrpopulation(dutodiffrntialmortalityofoldrmnandwomn),wconductdananalysisofgndrffctsforthconfidnc,gussinggam,andthdcisionsundruncrtaintyfindings.Basdonnonparamtricanalyss,wdtrmindthatthrwasnosignificantdiffrncbtwnmalandfmalrsponssforthconfidncorgussinggamxprimnts.Gndrwas,howr,highlycorrlatdwithriskbhaiorinthcompltinformationtask.Forthistask,thwomnwrmorriskskingthanthmn(Fig.4).Thistrndisalsoapparntforthlasttwntyrsponssinthriskxprimntwithincompltinformation,butitisawakrcorrlation(paluof0.06forscondtolastand0.13forlastintralofslctions).Whnwdidthsamanalysisforthyoungsubjctsonthcompltinformationtask,wfoundnosignificantdiffrncsbtwnmnandwomnatconntionalsignificanclls.WillingnsstoPayWillingnsstoAccptAsymmtryObsrddiffrncsbtwnstatdwillingnsstopay(WTP)foranitmandwillingnsstoaccptpaymnt(WTA)forthsamitmhabnasubjctofxtnsirsarch.Inpriousinstigationsofthisbhaior,indiidualshabndiiddintoRAYLIN12twogroups:sllrsandbuyrs.Thsllrsarginanitmandtoldthatthyarthownrsofit.Thyarthnaskdtoindicatthminimumthywouldaccpttosllthitm,thWTA.Buyrsarshownthsamitmandaraskdtoindicatthmaximumthywouldbwillingtopayforthitm,thWTP.ArportdtndncyforthWTAtobgratrthanthWTPisthasymmtrythathasattractdattntion.Awidrangofthorticalxplanationsxists.Onthoryisthatthphnomnarflctsanasymmtryofattitudsbtwngainsfroma“rfrncpoint”andaloss.Ththorybasdonarfrncpointrstsonaconcptoflossarsion”7,apossiblasymmtrybtwnattitudstowardsgainsandattitudstowardlosss.Thidaisthatpoplardisproportionatlyarstolosinganamountofmony,compardtohowmuchthylikgainingthsamamount.Thobsrddiffrncsbtwnwillingnsstopayandwillingnsstoaccpthabnlabldan“ndowmntffct”rflctingathorythatthphnomnaisdutolossarsiontothdomainofchoicsorbundlsofgoodsandmony(Thalr,1980;TrskyandKahnman,1991).Ththorticalidaisthatanindiidualwhoownsagoodanticipatsalossfromthsalandthusrquirsahighrpayoffthanthindiidualwouldpaytoacquirthgoodifitwrnotownd(Kahnman1991,Kahnman1990,Kntsch1989,Kntsch1984).Inothrwords,thwillingnsstoaccpt(WTA)xcdsthwillingnsstopay(WTP).Bycontrasttondowmntffctthory,rcntxprimntsproducdatathatsupportaclaimthatthobsrddiffrncsbtwnwillingnsstopayandwillingnsstoaccptisrlatdtoxprimntalprocdursandhasnothingtodowithprfrncasymmtris(PlottandZilr(2003))orisliminatdbytradingxprinc(List,2003).7Rcntrsarchhasproducdidncofsuchanasymmtrythroughbrainimaging(sCamrr,LownstinandPrlc,2003)13Bycarfullydlopdxprimntalprocdursthrsarchrshadmonstratdanabilitytomakthphnomnaapparordisapparbyusingxprimntalprocdursinolingxprincandpracticwiththprfrnclicitationprocdurs.Thclaimofthaltrnatithoryisthatthphnomnonrsultsfromsubjctmisconcptionsandhasnothingtodowithaasymmtryofprfrncsconcrninggainsandlosss.Thprsumptionisthatoldrpoplarmorconsratiorriskaoiding.Ifthisistruthnitwouldsmnaturaltoxpctlossaoidancwouldbstrongrintholdrpopulations.Furthrmor,ifthndowmntffctisinddanxplanationforthasymmtryofWTPandWTAthnonwouldxpctthffcttobmorpronouncdintholdrpopulations.Thus,bytstingforanasymmtrybtwnWTAandWTPusingthcontrolsforsubjctmisconcptionwarabltotstndowmntffctthoryandwaralsoabltotstfordiffrncsbtwnyoungandoldundrcircumstancsthatarliklytoxacrbatthdiffrncsshouldndowmntthorybcorrct.Ourprocdursarasfollow.Thsubjctpopulationswrdiiddintogroups:sllrsorbuyrs.Forachround,sllrsartoldthatthyownthitminfrontofthm(buyrsarshownthitm,butarnottoldthatthyownit).Thsubjctsarthnaskdtorportthiraluforthitm.Sllrsarinstructdtooffrthminimumthywouldaccpttogiupthitm,whilbuyrsarinstructdtooffrthmaximumthywouldbwillingtopayforthitm.Thsubjct’soffristhncompardtoafixdoffr.Thfixdoffrisrandomlydtrmindandnotbasdonthactualaluofthitm(Bckr,DGrootandMarschak(1964)).Forsllrs,ifthsubjct’spricislssthanorqualtothrandomoffr,thywillgiupthiritmandrcithamountofthrandomoffr.Ifthsubjct’spricisgratr,thykpthitm.Forbuyrs,ifthsubjct’soffrisgratrthanorqualtothrandomoffr,thywillpurchasthitmforthamountof14thrandomoffr.Ifthsubjct’soffrislssthanthamountofthrandomoffr,thykpthirmony8.Subjctsarinformdthatthfixdoffrshabndtrmindbyarandommthod,whichwillbraldatthndofthintriw9(PlottandZilr(2003)).Whnachsubjcthasdtrmindthiroffrthywrititonanindxcardandplacitinsidannlop(bothitmsarproidd).Forthactualtask,thsubjctsarinformdthatthintriwrwillnotknowthiroffrorthiroutcom.Thisisdontonsurthatthsubjct’soffrisanonymousandnotinfluncdbythprsncofthintriwr.Thrwratotalofthrroundsinthtask:thfirsttwoarhypothticalandthlastisthactualround.Apnandapicturframarthitmsusdinthhypothticalsituations,andacoffcupisusdforthactualsituation.Onlythactualroundhadaralpayoff,ithrthcuporthcashaluofthfixdoffr.ThdataxhibitnodiffrncsbtwnWTAandWTPinithrgroup.Thusinthsdatandowmntffctthoryisrjctd.Walsoconcludthatthrisnosignificantdiffrncbtwnthyoungandthold.Excludingthdiffrncofrfrncstats,thxprimntaldsignwasidnticalforbothgroups.Thmdiansllrpricisslightlyhighrthanthmdianbuyingpricforachsampl(Fig.5).Inthactualround,thcoffcupround,thmdianoffrpricforthsllrsintholdrpopulationwas$2.50andthmdianbuyrpricwas$2.00.Inthstudntpopulation,8Bothbuyrsandsllrsarinstructdandtraindaboutthoptimalstratgywhnusingthisprfrnclicitationprocss.9Thfixdoffrisdtrmindwitharandomnumbrtabl.Thtablconsistsofmorthanathousandnumbrs.Throwsandcolumnsarnumbrd.Adiisusdtodtrminarowandcolumnposition;acoordinatonthtabl.Bginningatthisposition,thintriwrmostothrightofthrowuntila1ora0israchd.Onca0or1israchd,thatdigitandthfollowingthrdigitsarusdtodtrminafourdigitfixdoffr.Thismthodisdontonsurrandomnss,whilkpingthfixdoffrbtwnzroandtwntydollars.Eachindiidualhasauni