1

ExploringtheNatureof“TradingIntuition”∗

AntoineJBruguier1,StevenRQuartz1andPeterLBossaerts1,2

1CaliforniaInstituteofTechnology,Pasadena,CA91125,USA

2EPFL,CH‐1015Lausanne,Switzerland

Thisversion:28July2008

Abstract

TheEfficientMarketsHypothesis(EMH)andtheRationalExpectations

Equilibrium(REE)bothassumethatuninformedtraderscancorrectlyinfer

informationfromthetradingprocess.Experimentalevidencestartinginthemid

80shasconsistentlyconfirmedtheabilityofuninformedtraders,evennovices,

todoso.Here,wehypothesizethatthisabilityrelatestoaninnatehumanskill,

namely,TheoryofMind(ToM).WithToM,humansarecapableofdiscerning

maliciousorbenevolentintentintheirenvironment.Weconfirmourhypothesis

inevidencethatparticipationinmarketswithinsidersengagesthe(evolutionary

relativenew)brainregionsthatspecializefunctionallyinToM,andinevidence

thatskillinpredictingpricechangeswhenthereareinsidersiscorrelatedwith

scoresontwotraditionalToMtests.SinceToMisgenerallyunderstoodtorelyon

patternrecognition(whichrecentlyhasbeenconfirmedformallyinthecontext

ofstrategicgames),wesearchedforfeaturesinthedatawithwhichonecould

identifythepresenceofinsiders.WediscoveredthatGARCH‐likepersistencein

absolutepricechangesincalendartimecharacterizesmarketswithinsiders.

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I.Introduction

Thispaperreportsresultsfromexperimentsmeanttoexplorehowuninformed

tradersmanagetoreadinformationfromtransactionpricesandorderflowin

financialmarketswithinsiders.SincetheseminalexperimentsofCharlesPlott

andShyamSunderintheearly1980s[PlottandSunder(1988)],ithasbeen

repeatedlyconfirmed(andwewilldosoheretoo)thatuniformedtradersare

quitecapableofquicklyinferringthesignalsthatinformedtraders(insiders)

receiveaboutfuturedividends,despitetheanonymityofthetradingprocess,

despitelackofstructuralknowledgeofthesituation,anddespiteoftheabsence

oflonghistoriesofpastoccurrencesofthesamesituationfromwhichtheycould

havelearnedthestatisticalregularities.

Itisstrikingthatsolittleisunderstoodabouttheabilityoftheuninformedto

inferthesignalsofothers.Thisabilityconstitutesthebasisoftheefficient

marketshypothesisEMH[Fama(1991)],whichstatesthatpricesfullyreflectall

availableinformation.UnderlyingEMHistheideathattheuninformedwilltrade

onthesignalstheymanagetoinfer,andthat,throughtheordersofthe

uninformed,thesesignalsareeffectivelyamplifiedinthepriceformation.Inthe

extreme,priceswillfullyreflectallavailableinformation.Withoutabetter

understandingofhowuninformedpracticallymanagetoreadinformationin

prices,EMHremainsahypothesiswithoutawell‐understoodfoundation.

Thefeedbackfromtradingbasedoninferredinformationtopriceformationhas

beenformalizedintheconceptoftherationalexpectationsequilibrium(REE)

[Green(1973),Radner(1979)].Foreconomists,REEformsthetheoretical

justificationofEMH.Butagain,REEtakestheabilityoftheuninformedto

correctlyreadinformationfrompricesasgiven,ratherthanexplainingit.As

such,likeEMH,REElacksawell‐articulatedfoundation.

Thegoaloftheexperimentsthatwereportonherecanbeexpressedinamore

mundaneway,asanattempttobetterdefinewhatismeantwith“trading

intuition,”andtounderstandwhysometradersarebetterthanothers.Books

havebeenwrittentoelucidatetradingintuition[Fenton‐O'Creevy,Nicholson,

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SoaneandWillman(2005)]butattemptsatformalizingthephenomenonhaveso

farfailed.

Whatdistinguishesmarketswithinsidersisthepresenceofawinner’scurse:

salesareoftensuccessfulonlybecausepriceshappentobetoolow(relativeto

theinformationoftheinsiders),whilepurchasesmayoccuronlyatinflated

prices.Eitherway,theuninformedtraderishurt.Whilethewinner’scurseis

usuallyassociatedwithstrategic,single‐sidedauctions,italsoappliesto

competitive,double‐sidedmarkets,andindeed,thewinners’curseisnotonly

implicitinthetheoryofREEbutalsoverymuchofconcerninreal‐worldstock

markets[Biais,BossaertsandSpatt(2008)]

Fromthepointofviewoftheuninformedtrader,thewinner’scurseconjuresup

animageofpotentialmalevolenceinthetradingprocess.Humansareactually

uniquelyendowedwiththecapacitytorecognizemalevolence(aswellas

benevolence)intheirenvironment,acapacitythatpsychologistsrefertoas

TheoryofMind[GallagherandFrith(2003)].TheoryofMindisthecapacityto

readintentionorgoal‐directnessinpatterns,throughmereobservationofeye

expression[Baron‐Cohen,Jolliffe,MortimoreandRobertson(1997)],or

movementofgeometricobjects[HeiderandSimmel(1944)],inthemovesofan

opponentinstrategicplay[McCabe,Houser,Ryan,SmithandTrouard(2001),

Gallagher,Jack,RoepstorffandFrith(2002),Hampton,BossaertsandO'Doherty

(2008)],orinactionsthatembarrassothers(“faux‐pas”)[Stone,Baron‐Cohen

andKnight(1998)].TheoryofMindisthustheabilitytoreadbenevolenceor

malevolenceinpatternsinone’ssurroundings.Thiscontrastswithpredictionof

outcomesgeneratedpurelyby,say,physicallaws,whichmayharmorbe

beneficialbutwithoutintention.1

PerhapsthemosttellingexampleofhowTheoryofMindconcernsdetectionof

intentionalityinpatternsconcernsacasewheresimplephysicallawsofmotion

areviolated.Subjectsarefirstshownanobject(say,ablock)attractedtoatarget

(ball)butencountersaphysicalbarrier(awall)thatitovercomesbymoving

aroundit(seeFigure1,top).Subsequently,thebarrierisre‐movedandtwo

situationsareshown.Inthefirstone,theblock,freedoftheobstacle,moves

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alongastraightpathtowardstheoriginaltargetlocation(Figure1,middle);in

thesecondone,theblockcontinuesalongtheoriginaltrajectory(Figure1,

bottom).Thefirstsituationaccordswithstandardphysics;thesecondoneis

unusual(fromaphysicspointofview)andmayalertthesubjectthattheoriginal

patharoundthebarrierwasintentional,i.e.,thatitreflectedgoal‐directed

behavior.Ithasbeenrepeatedlyobservedthathumans(includingone‐yearold

infants[Gergely,Nadasdy,CsibraandBiro(1995)]andsomenon‐human

primates[UllerandNichols(2000)]spendmoretimegazingatthesecond

situationthanthefirstone,despiteitsnovelty(theballtakesadifferentpath),

suggestingthatthesuspectedintentionalitydrawstheirattention.

Thefirstgoalofourstudywas,throughexperiments,todeterminetowhat

extenttradingintuitionandToMarerelated.ToM,asmentionedbefore,isthe

abilitytoreadbenevolenceormalevolenceinpatternsinone’senvironment.So,

itwasreasonabletoconjecturethatitappliedtoorderflowsinfinancialmarkets

withinsidersaswell.Specifically,weaskedwhethertheuninformedengageToM

brainregionswhenshowntheorderflowofamarketwithinsiders,andwhether

ToMskillscorrelatewithsuccessinforecastingmarketpriceswhenthereare

insiders.

Theanswerstobothquestionsareaffirmative.Wefoundthatinsideinformation

engaged(only)functionallyspecificToMregionsinthebrainoftheuninformed,

andwefoundthatabilitytocorrectlyforecastpricechangesinmarketswith

insiderscorrelatedsignificantlywithperformanceinstandardToMtasks.

ThesecondgoalofourstudywastostartformalizingtheconceptofToMtothe

extentthatitappliedtofinancialmarketswithinsiders.ToMisaboutpattern

recognition–whichisintuitivelyclearfromtheexampleinFigure1,andwas

recentlyconfirmedformallyforplayinstrategicgames[Hampton,Bossaertsand

O'Doherty(2008)].Formarkets,however,itisnotevenknownwhetherthere

areanyfeaturesatallinthedatathatwouldallowonetomerelyidentifythe

presenceofinsiders(inanalogywiththeviolationofphysicallawsinthebottom

panelofFigure1thatpromptsmanytoconcludethattheremaybe

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intentionality).Existenceofsuchfeaturesisanimportantcomponentwhen

arguingthatToMmayapply.

Here,wereportresultsfromastatisticalinvestigationoftradeflowsinour

experimentalfinancialmarketsthroughwhichthepresenceofinsiderscouldbe

discriminated.WefindthatGARCH‐likefeaturesemergewhenthereareinsiders.

Specifically,autocorrelationcoefficientsofabsolutepricechangesincalendar

timearesignificantlymoresizeable.

ItseemstousthatthelinkbetweenGARCH‐likefeaturesandinsidertradingisa

majorfindingthatdeservesfurtherinvestigationirrespectiveofitsimportfor

theplausibilityofToMinthecontextoffinancialmarkets.

Remainderisorganizedasfollows.SectionIIdescribestheexperimentsand

discussestheresults.SectionIIIpresentsthefindingsfromstatisticalcontrasts

oftradeflowsinsessionsinourexperimentswhenthereareinsidersandwhen

therearenone.FurtherdiscussionisprovidedinSectionIV.

II.DescriptionOfTheExperimentsAndTheResults

Here,weprovidebriefexplanationsoftheexperimentalset‐up(afulldiscussion

canbefoundintheAppendix)andwepresentthemainempiricalresults.

Wefirstranamarketsexperimentforthesolepurposeofgeneratingorderand

tradeflowinacontrolledsetting,tobeusedinthemainexperiments.Thelatter

consistedof:(i)abrainimagingexperiment,meanttodiscernhowsubjects

attemptedtointerpretthedatabylocalizingareasofthebrainthatareactive

duringre‐playofthemarkets;(ii)abehavioralexperiment,wherewetestedfor

subjects’abilitytopredicttransactionprices,andtoascertaintheirgenericToM

skills(wealsoranatestoflogicalandmathematicalthinking,forareasontobe

discussedlater).

II.A.Step1:TradingDataCollectionExperiment

Twenty(20)subjectsparticipatedinaparameter‐controlledmarketexperiment

that used an anonymous, electronic exchange platform (jMarkets; see

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http://jmarkets.ssel.caltech.edu/).Thefollowingsituationwasreplicatedseveral

times;eachreplicationwillbereferredtoasasession.Subjectswereendowed

with notes, cash, and two risky securities, all ofwhich expired at the end of a

session. The two risky securities (“stocks”) paid complementary dividends

between 0 and 50¢: if the first security, called stock X, paid x cents, then the

secondsecurity,calledstockZ,wouldpay50‐xcents.Thenotesalwayspaid50¢.

Allocationofthesecuritiesandcashvariedacrosssubjects,butthetotalsupplies

of the risky securities were equal; hence, there was no aggregate risk, and,

theoreticallyaswellasbasedonobservations inpriorexperiments [Bossaerts,

Plott and Zame (2007)], prices should converge to levels that equal expected

payoffs; that is, risk‐neutral pricing should arise. Subjects could trade their

holdings for cash in an anonymous, continuous open‐book exchange system.

Subjects were not allowed to trade security Z, however. Consequently, risk

aversesubjectsthatheldmoreofXthanofZwouldwanttosellatrisk‐neutral

prices; the presence of an equal number of subjectswithmore of Z than of X

allowedmarketstoclear,inprinciple.Inmostofthesessions,tobereferredtoas

testsessions,anumberofsubjects(the“insiders”)weregivenanestimateofthe

dividendintheformofa(common)signalwithin$0.10oftheactualdividend.All

subjectswere informedwhentherewere insiders;only the insidersknewhow

many insiders there were. Subjects were paid in cash according to their

performance and made $55 on average. More details can be found in the

appendix.

Figure2displaystheevolutionoftransactionpricesthroughouttheexperiment.

Trading was brisk, independent of the type of session; on average, traders

entered or cancelled an offer every 0.7s and one transaction took place every

3.2s. During test sessions, the uneven distribution of information evidently

skewedthetransactionprices.Overall,theevolutionofpricesisconsistentwith

priorexperiments[whichdidnotcontrolforaggregaterisk,however;Plottand

Sunder(1988)].

As mentioned before, the sole purpose of the markets experiment was to

generateorder flowand transactiondata frommarketswith tightcontrolover

endowments,informationandexchangeplatform.Theresultingdataformedthe

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inputforthebrainimagingandbehavioralexperiments.Forthisreason,wewill

notelaborateonthemarketsexperiment.Wewillcomebacktorelevantfeatures

ofthetradingflowinthenextsection,however.

II.B.Step2:fRMIExperiment

Eighteen(18)newsubjectswereshownareplayofthe13previouslyrecorded

marketsessionsinrandomorderwhilebeingscannedwithfMRI.Thesesubjects

played the role of outsiders who did not trade. Subjects were given the

instructions of themarkets experiment, so that theywere equally informedas

theoutsidersinthatexperiment.Subjectsfirstchosewhethertheywouldbeton

stock X or Z, after being told whether there were insiders in the upcoming

sessionornot. Subsequently, theorder flowand transactionhistoryof stockX

was replayed in a visually intuitive way (see Figure 3 and Video 1). During

replay, subjects were asked to push a button each time they saw a trade,

indicatedbya500ms(millisecond)changeincolorofthecirclecorrespondingto

thebestbidorask.

Ourdesignhad threemainadvantages.First, the subjectsdidnot tradeduring

thereplay(theydidhavetotakepositionsbeforethereplay).Whilethequestion

ofhowthehumanbrainmakesfinancialdecisionsisinteresting,weneededfirst

to understand how humans perceive a stock market. By not introducing

decision‐making,weavoidedaconfoundingfactor.Second,theperiodswithout

insiders were perfect controls. Since the trading data acquisition method, the

display screens, and the number of traders were the same, the two types of

sessionswere identical in every respect except for the presence or absence of

insiders. Third, by adding a blind bet, we elicited a feeling of “randomness.”

Indeed,ifwehadforcedsubjectstochoosestockXforeverysession,thepayoff

wouldhavebeenthesamefixednumberforeverysubject.Moreover,wecould

nothaveseparatedanincreaseinstockpricefromahigherexpectedreward,as

thesetwosignalswouldhavebeenperfectlycorrelated.Instead,byintroducinga

blindbet,weorthogonalizedexpectedrewardandstockprice.

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Toidentifyareasofsignificantbrainactivationintheinsidersessionsrelativeto

the control sessions, we used a standard approach as implemented in the

packageBrainVoyager(BrainInnovation,Maastricht,TheNetherlands).Wefita

General LinearModel (GLM) to the (filtered,motion‐corrected) activationdata

for each “voxel” (a cubic volume element of 27mm3) which included several

auxiliary predictors (to capture motion and visual effects) as well as the

expectedrewardforthesubjectandfourtask‐relevantpredictors(Figure4).The

task‐relevant predictors were as follows. First, we constructed a parametric

regressor that would quantify the effect of the insiders (if present) on stock

prices.Weusedtheabsolutevalueofthedifferencebetweenthestock’strading

price and 25¢. Separate parametric predictors were thus computed for the

sessions with insiders and without insiders. This way, the sessions without

insiderscouldbeusedascontrols,againstwhichthesessionswithinsiderscould

becompared.Second,weaddedblockregressors(dummyvariables),toidentify

sessionswithandwithoutinsiders.

All predictors were convolved with the standard “hemodynamic response

function,”inordertoaccountforthelagbetweenactivationattheneuronallevel

and the fMRI signal. Areas of significant brain activation “contrast”were then

recovered as those areas where the difference (across insider and no‐insider

sessions)intheslopecoefficientsofthepredictorsweredeemedtobesignificant

usingstandardstatisticaltests.

Our way of modeling brain activation had several advantages. First, as

mentionedabove,westrippedouttheeffectofdecision‐makinginthebrainand

focusedon theperceptionof themarket. Second, thepredictorswebuiltwere

orthogonaltoexpectedrewardasweusedtheabsolutevalueofthedistanceto

25¢ratherthanthe(signed)differencewith25¢.Third,bycontrastingsessions

with and without insiders and making sure that these two types of sessions

displayednoobviousdifferencesintradingactivity,wecontrolledfordifferences

invisualactivationandisolatedtheeffectof insidersonsubjects’perceptionof

themarket.

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Wefoundasignificantcontrastfortheparametricregressorsinonelargeregion

ofparacingulatecortex(PCC;Figure5‐aandTableI).Wealsofoundsignificant

activationsinasmallerregioninthefrontalpartoftheanteriorcingulatecortex

(‐14; 23; 39; 5 voxels; Figure 5‐a and Table I). Finally, we found strong

differentialactivationsinrightamygdala(21;‐10;‐12;5voxels;Figure5‐band

TableI)andleftinsula(‐30;‐7;11;5voxels;Figure5‐candTableI).

Significantcontrastsfortheblockpredictorsshowedupinalargeareaoflingual

gyrus (‐9; ‐65; ‐6; 25 voxels; Figure 6 andTable II), aswell as a small area of

cerebellum(‐13; ‐58; ‐30;9voxels;Figure6andTableII).Nootherareaswith

fiveormorevoxelsexhibitedsignificantcontrasts.

Ourresultsprovidesupport for thehypothesis thatTheoryofMind is involved

when subjects are facingmarketswith insiders.We found that the samebrain

areasareactivatedasduring traditionalToMtasks.PCC(paracingulatecortex)

activationisstandardintasksinvolvingToM[GallagherandFrith(2003)],andin

strategic games in particular [Gallagher, Jack, Roepstorff and Frith (2002)],

[McCabe,Houser,Ryan,SmithandTrouard(2001)].Similaractivationwasalso

reported in choice vs. belief game theory experiments [Bhatt and Camerer

(2005)]. The PCC has also been observed in tasks that involve attribution of

mental states to dynamic visual images, such as intentionally moving shapes

[Castelli,Happe,FrithandFrith(2000)].

Wealso foundthatactivation intherightamygdalaandthe leftanterior insula

increased as transaction prices deviated from the uninformed payoff. While

some studies have reported the involvement of these structures in ToM tasks

[Baron‐Cohen, Ring,Wheelwright andBullmore (1999), Critchley,Mathias and

Dolan (2001)], they are more typically regarded as involved in processing

affective features of social interaction. Specifically, the amygdala is a critical

structure in the recognition of facial emotional expressions of others [Phillips,

Young, Scott, Calder, Andrew, Giampietro, Williams, Bullmore, Brammer and

Gray (1999), Phan, Wager, Taylor and Liberzon (2002), Morris, Ohman and

Dolan(1998)]whiletheanteriorinsulaisthoughttoplayacriticalrolebothin

subjective emotional experience [Bechara and Damasio (2005)] and in the

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perception/empathetic response to the emotional state of others [Singer,

Seymour, O'Doherty, Kaube, Dolan and Frith (2004)]. A complementary

interpretation of these activations is that they may also reflect subjects’ own

emotionalresponsestomarketactivity,whichisconsistentwithrecentpsycho‐

physiological evidence that financial market participation engages somatic

marker(emotional)circuitryduringheightenedmarketvolatility[LoandRepin

(2002)].Futureresearchshouldshedmore lightonthispotential linkbetween

marketparticipationandemotions.

We also found activations in the frontal part of the ACC (anterior cingulate

cortex). Our activation is in a slightlymore posterior and dorsal location than

when ToM is used in strategic and non‐anonymous, simple two‐person games

[Gallagher,Jack,RoepstorffandFrith(2002), McCabe,Houser,Ryan,Smithand

Trouard(2001)].

The increased activation of lingual gyrus in the presence of insiders provides

further support for the role of ToM in market perception. For example, the

lingual gyrus is involved in the perception of biologicalmotion, a key cue for

mentalizing [Servos, Osu, Santi and Kawato (2002)]. However, increased

activation of lingual gyrus may also be related to recent accounts that this

structureisinvolvedincomplexvisualtaskswheresubjectsareaskedtoextract

global meaning despite local distractors [Fink, Halligan, Marshall, Frith,

Frackowiak and Dolan (1996), Fink, Halligan, Marshall, Frith, Frackowiak and

Dolan(1997)].Whentherearenoinsiders,subjectscanconcentrateonthetask

we imposed, namely, to track trades. In our display, transactionswere a local

feature, indicatedby changes in color of circles in themiddle of the screen. In

contrast, when there are insiders, the entire list of orders may reflect

informationwithwhich tore‐evaluate the likelypayoffon thesecuritiesbutat

the same time, subjects are still asked to report all transactions, which now

amounts to a local distraction.Our interpretationof lingual gyrus activation is

inconsistent with theories [Easley and O'Hara (1992), Glosten and Milgrom

(1985)] thatpredict thatonly the tradepricesarerelevant toupdatebeliefs. If

thesetheorieswereright,otherfeaturesofthedisplayneednotbewatched,and

simultaneously keeping track of transactions is not a distraction. Rather, our

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finding is consistent with experimental evidence that insiders do not exploit

theirsuperiorinformationbyexclusivelysubmittingmarketorders[Barner,Feri

andPlott(2005)].Futureresearchshoulddeterminetowhatextentlingualgyrus

activation reflects ToM (through motion of objects) or the proverbial conflict

betweenthe“forest”(insiderinformation)andthe“trees”(trades).

We did not observe any significant activation in brain areas related to formal

mathematical reasoning. In particular, there was no evidence of estimation of

probabilities [Parsons and Osherson (2001)] or arithmetic computation

[Dehaene,Spelke,Pinel,StanescuandTsivkin(1999)].Wealsodidnotobserve

any significant activation in brain areas related more generally to problem‐

solving or analytical thought [Newman, Carpenter, Varma and Just (2003)] or

reasoning [Acuna,Eliassen,DonoghueandSanes (2002)].This findinghasalso

beenhighlightedinarecentstudyofToMinstrategicgames[CoricelliandNagel

(2008)].WeshallelaborateinthenextSection.

ItisimportanttonotethatengagementofToMbrainstructureswasnotsimply

inresponsetoacomplexgraphicalrepresentationofthemarket,asbothcontrol

andtestsessionsgeneratedapproximatelyequivalentmarketactivity.Similarly,

in both conditions the market activity was the result of human interactions.

Hence,itwasnotmerelythepresenceofhumanactivitythatresultedinToM,as

this was equivalent in both conditions. Rather, the salient difference between

session type was the fact that, during sessions with insiders, trading activity

providedinformationthatcouldbeextractedwiththeappropriateinferences.

II.C.Step3:BehavioralExperiment

The behavioral experiment was meant to correlate subjects’ ability to predict

tradepricesinmarketswithinsidersandtheirgeneralToMskillasreflectedin

traditional ToM tests. We added a test for mathematical and logical thinking,

promptedbytheabsenceofactivationinregionsofthebrainusuallyassociated

withformalmathematicalandprobabilisticreasoninginourtask.

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Forty‐three (43) new subjects were given a series of four tasks that were

administeredinrandomorder.ThefirsttaskwasaFinancialMarketPrediction

(FMP)taskinwhichthetradingactivitywasreplayedtothesubjectsatoriginal

speedandpausedevery5seconds.Duringhalfofthepauses,weaskedsubjects

to predict whether the next trade was going to occur at a higher, lower, or

identicalpriceastheprevioustradethathadhappened.Fortheotherhalfofthe

pauses,we reminded subjects of their predictions and informed them of their

success. The second task was a ToM task based on eye gaze [Baron‐Cohen,

Jolliffe,MortimoreandRobertson(1997)].ThethirdtaskwasaToMtaskbased

on displays of geometric shapes whose movement imitated social interaction

[HeiderandSimmel(1944)].AswiththeFMPtask,wepausedthemovieevery

fivesecondsandaskedsubjectstopredictwhethertwooftheshapeswouldget

closer,farther,orstayatthesamedistance.Fortheotherhalfofthepauses,we

reported the outcomes and the subjects’ predictions. The fourth task (the M

task) involved a number of standard mathematics and probability theory

questions[andfrequentlyusedinWallStreetjobinterviews–seeCrack(2004)].

ThebehavioralexperimentconfirmedtheuseofToM.Weobservedasignificant

correlation(p=0.048andp=0.023)betweentheFMPtaskandbothToMtasks

(Figure7,toppanels)butnosignificantcorrelation(p=0.22)betweentheFMP

andtheMtasks(Figure7,bottomleft).Surprisingly,wedidnotobserveany

correlationbetweenthetwoToMtests(Figure7,bottomright).Self‐reports

duringthebehavioralexperimentdidnotshowanyevidenceofpersonalization.

Wedidnotobserveanysignificantgenderdifferences.

Our behavioral experiments corroborate the relationship between trading

successandToMthatourfMRIresultssuggest.Thecorrelationbetweenthetwo

ToMtestsandtheabilitytopredictpricechangesinafinancialmarketconfirms

thatsuccessfultradersuseToM.Wealsofoundthatthesubjectscoresonthetwo

ToMtestswerenotcorrelated(Figure7‐D).ThisfindingsuggeststhatToMisa

multi‐dimensionalsetofabilities,apossibilitythathasnotbeenraisedyetinthe

ToMliterature:eachtestrepresentsonedimensionofToMabilities,butfinancial

abilitiescorrelatewithbothdimensions.

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Lackof(significant)correlationbetweenthescoresonthetwoToMtests

providesindirectconfirmationthatgeneralintelligenceorstateofattentiveness

cannotexplainthesignificantcorrelationsbetweenscoresontheFMPandToM

tests.

IV.TheoryofMindinMarketswithInsiders:WhatPatternsToAttendto?

Formally,ToMremainsaratherelusiveconcept.Itisoftendefinedonlyvaguely,

andmostlyintermsofspecifictasks[GallagherandFrith(2003)],orintermsof

activationofparticularbrainregions[McCabe,Houser,Ryan,SmithandTrouard

(2001),Gallagher,Jack,RoepstorffandFrith(2002)].Itisgenerallyaccepted,

however,thatToMconcernspatternrecognition,butonlyinsimpleexamplesis

itimmediatelyobviouswhatpatternsareinvolved.Figure1(bottompanel)

providesanexample:themotionofanobjectviolatesphysicallawsandhenceis

readilyrecognizedasrevealingintention.

Inthecontextofstrategicgames,however,onerecentstudyhassuccessfully

identifiedthepatternsinthemovesofone’sopponentonwhichToMbuilds.

Thus,incollaborationwithAlanHamptonandJohnO’Doherty[Hampton,

BossaertsandO'Doherty(2008)],oneofusestablishedthat,whenasubjectis

engagedinplayingtheinspectiongame,brainactivationinToMregionsofthe

humanbrainreflecttheencodingofanerrorinpredictinghowone’sopponent

changesmovesasaresultofone’sownactions.2

TheimportofthisfindingisthatToMingameplaycanbeconcretizedintermsof

precisemathematicalquantitiesthatcharacterizeanopponent’sactualplay.As

such,ToMconcernsconcrete,“online”learningofgameplay.Thisisconsistent

withthepropositionthatToMinvolvespatternrecognition–detectionofthe

natureofintentionalityinone’senvironment.

ItdeservesemphasisthatToMthereforecontrastswithNashreasoning,where

playerswouldsimplyhypothesizethatopponentschooseNashequilibrium

strategiesandthattheywouldsticktothem.UnlikeToM,Nashreasoningis

“offline:”itworksevenifoneneverseesanymoveofone’sopponent;itisalso

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abstract:itconcernswhattheopponentcouldrationallydoandhowtooptimally

respond.ConsistentwiththeideathatToMandNashthinkingarenotrelated,

brainregionsthatareknowntobeengagedinabstractlogicandformal

mathematics[Dehaene,Spelke,Pinel,StanescuandTsivkin(1999),Newman,

Carpenter,VarmaandJust(2003),Acuna,Eliassen,DonoghueandSanes(2002)],

donotdisplaysignificantactivationduringgameplay[CoricelliandNagel

(2008)].

Inthecontextofourmarketswithinsiders,itisbyfarclearonwhichpatterns

ToMcouldbuild.Thisisbecauseithasnotevenbeenestablishedwhetherthere

areanypatternsthatdistinguishmarketswithandwithoutinsiders.Butour

findingthatsubjectsengageinToMtocomprehendinsidertradingandthe

generallyacceptedviewthatToMconcernspatternrecognitionsuggeststhat

theyexist.

Consequently,wesetouttodeterminewhethertherearefeaturesofthedata

thatdifferentiatedmarketswithinsiders.Inthephysicalmovementofobjects,

violationofphysicallawssignalsthepresenceofintentionality(seeFigure1).In

markets,wehopedtoidentifystatisticalpropertiesofthedatathatarenot

presentwhentherearenoinsiders.Wefocusedonanexaminationofthetrade

flow.

Welookedatahostoftimeseriespropertiesofthetradeflowsinthemarkets

experimentthatformedthebasisofourstudy,suchasdurationbetweentrades

orskewnessintransactionpricechanges.Intheend,itwaspersistenceinthe

sizeoftransactionpricechangesovercalendartimeintervalsthatprovidedthe

onlystatisticallysignificantdiscrimination.Assuch,GARCH‐likefeaturesappear

todistinguishmarketswithandwithoutinsiders.

Specifically,wecomputedtransactionpricechangesoverintervalsof2s(as

mentionedbefore,thereisatradeevery3.7sonaverage,socalendartimetick

sizewaschosentobeslightlyshorterthanaveragedurationbetweentrades).

Wefollowedstandardpracticeandtookthelasttradedpriceineach2sinterval

asthenewprice,andiftherewasnotradeduringaninterval,weusedthe

transactionpricefromthepreviousinterval.

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Wethencomputedthefirstfiveautocorrelationsinthesize(absolutevalue)3of

transactionpricechanges.Figure8‐aplotstheresultsfortwoadjacentperiods,

Periods7and8.AscanbeinferredfromFigure2,therewere14insiders(outof

20subjects)inPeriod7,whiletherewerenoneinPeriod8.Thepatternsinthe

autocorrelationsoftheabsolutepricechangesinthetwoperiodsarevery

different.ThereissubstantialautocorrelationatalllagsforPeriod7(whenthere

areinsiders)whilethereisnoneforPeriod8(whentherearenoinsiders).

Figure8‐bshowsthatthisisageneralphenomenon.Plottedisthesumofthe

absolutevaluesofthefirstfiveautocorrelationcoefficientsagainstthenumberof

insiders.Werefertotheformeras“GARCHintensity”becauseitmeasuresthe

extenttowhichthereispersistenceinthesizeofpricechanges.GARCHintensity

increaseswiththenumberofinsiders;theslopeissignificantatthe5%leveland

theR‐squared,at0.32,isreasonablyhighgiventhenoiseinthedata.

Consequently,itappearsthatGARCH‐likefeaturesintransactionpricechanges

provideonewaytorecognizethepresenceofinsiders,andhence,afoundation

onwhichToMinmarketswithinsiderscouldbuild.Assuch,wehaveshownthat

thereindeedexistpatternsinthedatathatreflectintentionality,agenerally

acceptedconditionforToMtoapply.Fromthisperspective,ourfindingsthat

participationinmarketswithinsidersengagesToMbrainregionsandthatToM

skillsandpriceforecastingperformancearecorrelatedmakesense.

WehavenotidentifiedyetwhataspectoftheseGARCH‐likefeaturessubjectsare

exploitingtoinferinsideinformation,butourresultsopenupmanypromising

avenuesforfutureresearch.Ourapproachofcombiningmarketsexperiments

withbrainimagingandindividualbehavioraltestingmaythuseventuallyleadto

aformalunderstandingofhowhumansmanagetocomprehendasocial

institutionascomplexasafinancialmarket.

V.FurtherDiscussion

Ourimagingresultsformarketswithinsidershaveatleastonemoreaspectin

commonwithrecentneurobiologicalstudiesofToMinstrategicgames,namely,

theabsenceofactivationinregionsofthebraininvolvedinformalmathematical

16

reasoning.Theresultssuggestthatabstractreasoningskillsareunrelatedto

performanceineitherdomain.Withrespecttostrategicgames,itisnotknown

whetherperformanceiscorrelatedwithmathematicalskill.Withrespectto

marketswithinsiders,wesetouttoinvestigatetheissue.Specifically,aspartof

thethird,behavioralexperiment,wetestedoursubjectsontheirabilitytosolve

mathematicsandlogicproblemsandcorrelatedtheirscoreswithperformance

onthemarketpredictiontest.Wefocusedonasetofformalproblemsthathave

becomepopularinrecruitmentinthefinancialindustry[Crack(2004)].Figure6

(BottomLeftPanel)showsthat,whilethecorrelationwaspositive,itwas

insignificant.Thebehavioralresultsarethereforeinlinewiththeimaging

results.

Our study is not only relevant to finance. It contains at least two major

contributions for psychology and neuroscience. We are the first to report

activationinToMbrainregionsduringtheperceptionofanonymousmulti‐agent

systems, significantly extending the scope of ToM. Moreover, along with

Hampton, Bossaerts andO'Doherty (2008) and Coricelli andNagel (2008),we

arethefirsttoquantifyToM.Inparticular,whentherewereinsiders, themore

transaction prices deviated from the uninformed payoff of 25¢, the more

evidence outsiders had that there was important information to be inferred,

makingmentalizingincreasinglyimportant.

Personalization(oranthropomorphization)isoftensuggestedasanexplanation

whyToMsometimesapplieseveninsituationsthatdonotdirectlyinvolve

personalcontactwithanotherhumanbeing,suchasintheHeidermovieusedin

oneofourToMtests[HeiderandSimmel(1944)].Inthecontextoffinancial

markets,personalizationemergesattimesinspeech,whenmarketsare

describedasbeing“exuberant,”“jittery,”or“anxious”[Oberlechner(2004)].

Answersontheexitsurveyfollowingourbehavioralexperiment,however,do

notrevealanyevidenceofpersonalization.

Hence,itappearsthatthepersonalcomponentisnotimportant.Intentionality

thatcanbeinferredfrompattersinone’senvironmentis,however.Thisshould

17

explainwhyToMalsoappliestolarge‐scaleanonymoussocialinteraction(such

asourfinancialmarkets).

Theimportanceofintentionalityalsoclarifiesrecentevidence[McCabe,Houser,

Ryan,SmithandTrouard(2001),Gallagher,Jack,RoepstorffandFrith(2002)]

thatToMbrainregionsareactivatedwhenplayingstrategicgameswithhumans

andnotwhenplayingagainstapre‐programmedcomputer.Theevidenceshould

beinterpretednotasindicatingthatthehumancomponentpersewasimportant,

butassuggestingthatpotentialmalevolencewascrucial.Indeed,thecomputers

werepre‐programmedinawaythatwascompletelytransparenttosubjects,and

didnotinvolveanyintentiontoharmorexploit;theyfollowedspecific“laws”

justliketheobjectinFigure1,middlepanel,obeyedphysicallaws.

Ourfindingshaveimmediateimplicationsforhiringpracticeinfinance.They

suggestthatthefinancialindustryshouldtestcandidatetradersonsocialskills,

especiallythoseinvolvingToM,suchastheabilitytorecognizeintentinother

people’seyes,orrecognizemalevolenceinthemovementofgeometricobjects,

and,becauseithasrecentlybeenshowntoalsoinvolveToM,skillinplaying

strategicgames.Ouradviceisfarmorespecificthantheonetocomeoutofa

recentanalysisofoveronehundredprofessionaltraders,whichrevealedthat

tradercompensation(aratherindirectmeasureoftradingsuccess)correlated

positivelywithexperienceandrank(perhapsnotsurprisingly)andnegatively

withpsychologicalmeasuresofemotionality,mostofwhomarerelevantfor

generaleverydayproblemsolvingratherthanbeingspecifictofinancialmarket

trading[Fenton‐O'Creevy,Nicholson,SoaneandWillman(2005)].

Ourfindingsshouldalsohelpimprovevisualrepresentationoforderandtrade

flow.Sincehumansoftenarebestinrecognizingthenatureofintentionin

moving(animateorinanimate)objects[CastelliCastelli,Happe,FrithandFrith

(2000),HeiderandSimmel(1944)],wesuggestthattradersmaybemorelikely

tosuccessfullydetectinsidertradingwhenorderandtradeflowsarepresented

inamovingdisplay,asopposedtothepurelynumericallistingscommonlyfound

intheindustry.Infact,onemaywonderwhetherthesuccessofour(untrained)

subjectsinpredictingpricechangesinmarketswithinsidersmaybeattributable

18

toourusingagraphicalinterfacewhereorderandtradeflowaretranslatedinto

movementofcirclesofvarioussizesandcolors.

Inthesamevain,onemayconjecturethatToMisbehindthesuccessof

continuousdoubleauctionsoverone‐shotcallclearingsystemsinfacilitating

equilibration[PlottandVernon(1978)].Intheformermechanism,the

continuousflowofordersmayinduceToM,thusenhancingtrustthatthereisno

insideinformation.Inacallmarket,absentorderflowinformation,assessment

ofthesituationcannotrelyonToMandhencemustinvoketraders’abilitiesto

maketherightconjecturesaboutendowments,preferencesandinformationof

others.Thepracticalsuperiorityofthecontinuousauctionsystemoverthecall

marketsextendstosituationswherethereareinsiders[PlottandSunder

(1988)],evenifthelattermayintheorybebetter[Madhavan(1992)].

19

AppendixIn thisappendix,wedescribe indetail the threeexperimentsof thispaper.We

used college students or college‐educated subjects for every experiment. Both

CaltechandUCLAethicsboardsapprovedtheexperiments.

A.1.PriorMarketsExperiment

Wecollected tradingdatawithamarketsexperiment.Weasked20subjects to

tradewiththehelpofananonymouscomputerizedtradingsystem.Theytraded

for13independentsessions.Attheendoftheexperiment,wepaidthesubjects

withcashaccordingtotheirperformance.

Subjectsownedtwotypesofstocks.Theycouldbuyandsellthefirsttype(“stock

X”)forapricebetween0¢and50¢.Attheendofeachsession,thisstockpaidan

amount of money that we drew randomly between 0¢ and 50¢ (uniformly

distributed).We called this amount ofmoney “dividend.” The subjects learned

thevalueofthedividendonlyattheendofeachsession.Subjectscouldnottrade

thesecondtypeofstock(“stockZ”).Itpaidadividendthatwascomplementary

tothedividendofstockX(thetwodividendsaddedupto50¢).Forexample, if

werevealedattheendofasessionthatthedividendofstockXwas38¢,thenthe

dividendofstockZwas12¢.

For each session, the payment was determined as followed. Before trading

started,weendowedeach subjectwith adifferentmixof stockX, stockZ, and

cash.Duringtrading,subjectscouldexchangestockXforcashastheysawfit.As

aresult,attheendoftrading,asubjectgenerallyownedadifferentcombination

ofstockX,stockZandcash.Aftermarketsclosed,werevealedthevalueof the

dividend, and subjects learned the amount of their payoff for the session. For

example,ifatraderowned10unitsofstockX,5unitsofstockZ,andhad87¢in

cash,whenwerevealedthatthedividendforstockXwas38¢,thetraderlearned

thatherpayoffwas10×38¢+5×(50¢‐38¢)+87¢=$5.27.Weadded$5.27tothe

trader’searnings,andthenwerestartedanewtradingsessionindependently.

20

Sincethesubjectsdidnotknowthedividenduntilthetradingsessionwasover,

the expected payoff of one unit of a stock was 25¢. In addition, risk‐averse

subjects could neutralize risk by balancing their holdings of the

(complementary) stocks X and Z. Since the total endowment of stock X and Z

acrossallsubjectswasthesame,everyonecouldintheorybalanceholdings.Asa

result of this absence of aggregate risk, risk‐neutral pricing should obtain.

Consequently, without insider information, the predicted equilibrium price is

25¢.

Weexplainedindetailthepayoffschedulebutdidnottellthesubjectsthatthe

equilibriumpriceof the stockwas25¢.During the trading, thepricemovedas

predicted by the theory, confirming earlier experiments [Bossaerts, Plott and

Zame (2007)]. Essentially, when the price was below 25¢, subjects tended to

purchasethestock.Indeed,ifastockthatpaysoffonaverage25¢weretrading

at, say, 17¢, a subject that would purchase it would earn on average 8¢. The

purchase would push the price of the stock higher, until it reached the

equilibrium,at25¢.Similarly,traderswouldsellastocktradingat,say,33¢until

thepricewentdownto25¢.

The setup described above constituted the two control sessions of our

experiments. For the 11 other sessions (test sessions), we introduced an

additionalfactor.

For these test sessions,wesplit the traders into tworandomlychosengroups:

the “insiders” and the “outsiders.” At the beginning of each session, we gave

additionalinformationtotheinsidersintheformofa“signal.”Thesignalwasa

number chosen at random within 10¢ of the actual dividend of X (uniformly

distributed).Forexample,ifwetoldtheinsidersthatthesignalwasat14¢,they

knewforsurethatattheendofthetradingsessionwewouldrevealadividend

between4¢and24¢.Wedidnotgiveanyinformationtotheoutsidersexceptthe

factthattherewereinsidersinthemarket.

Theunevendistributionofinformationskewedthetrading.Atthebeginningof

eachsession,thetwogroupsattacheddifferentvaluestothestocks.Forexample,

ifwetoldtheinsidersthatthesignalwas14¢,thentheywouldvaluestockXat

21

14¢. The outsiders did not have this additional information and could only

estimate the value of stock X to be 25¢. Insiders and outsiders had to act

carefully. Insiders could use their information to make additional profits. For

example,ifthesignalwasat14¢,theycouldsellastocktoanoutsiderwhowas

willing topay25¢.The insiderwouldhavereceived25¢ forastock thatwould

havepaidatmost24¢,andonaverage14¢(i.e.hemadeanaverageprofitof11¢).

However,byselling, insiderswould lower thepriceof thestock,and thus they

wouldrevealtotheoutsiderstheirknowledgeofthesignal.Theoutsiders,who

knew that there was a signal but did not know its value, had to observe the

marketcarefullyandattempttoinferthesignalfromthetradingactivity. Ifthe

outsiders were successful at estimating the signal from the trade, they would

makeextraprofits.Vice‐versa,theinsidershadtotradeasdiscreetlyaspossible

toavoidrevealingtheirknowledgeofthesignaltotheoutsiders.Theanonymity

of the trading interface helped conceal their information. At the same time,

however, insiders had to trade before the other insiders in order to make

additionalprofits.

The dynamics of such markets are extremely complicated. While researchers

haveattempted tomodel them[Admati (1985),GrossmanandStiglitz (1980)],

there is no exact description of how the traders (insiders or outsiders) do

behave.Thus,weusedfMRItoimproveourunderstandingofsuchmarkets.We

used the periodswithout insiders as control and the periodswith insiders as

test.

A.2.StimulusSetforfMRIExperiment

We used 18 new subjects and replayed the order and trade flow while we

recordedbrainactivity.First,weexplainedtothesubjectshowwehaveacquired

thedataandmadesurethattheyunderstoodtheexperimentbyadministeringa

quiz.We also reminded the subjects that they were not going to trade in the

market but that they would only observe the replay of a previously recorded

market.Still,theyhadaninterestinpayingattentionastheirpayoffsdepended

22

onwhat happened in themarket (in a way that we describe below).We also

instructedthemthattheterm“insider”didnotrefertoillegal“insidertrading.”

Wedisplayedeachofthe13sessionsinadifferentrandomorderforeachsubject

(Figure3andVideo1).Eachsessionbeganwitha“blindbet:”weaskedsubjects

to choose between the stock X and the (complementary) stock Z. After the

subjects had made a choice, we replayed the market activity for stock X,

regardlessoftheirchoice,atdoublethespeed(2minutesand30secondsinstead

of5minutes).Finally,weinformedthesubjectsofhowmuchtheyearnedduring

thatsession.

Foreachsession,thepaymentwasdeterminedasfollows.Whensubjectsplaced

ablindbet,weendowedthemwith10unitsofthestocktheychose.Aftertheend

ofthetradingreplay,wepaidthemaccordingtothedividendofthestockthey

had chosen. For example, if a subject had placed a bet on stock X before the

tradingreplayandifwerevealedafterthetradingreplaythatthedividendwas

45¢,weadded10×45¢=$4.50tothesubject’searnings.Ifthesubjecthadchosen

to bet on stock Z, he would have received 10×(50¢ ‐ 45¢)=$0.50. Thus, the

subjectsforthefMRIexperimentsplayedtheroleofoutsiderswhodidnottrade.

Theywereoutsidersbecausetheydidnotknowthesignalandtheydidnottrade

becausetheyonlysawareplayoftradesthathadoccurredinthepast.

Thestockpricewasanindicatoroftheexpectedrewardforthesubjectsonlyin

the case of a sessionwith insiders. For example, an increasing price indicated

thattheinsidersmayhaveskewedthemarketbecausethesignalwashigh.Thus,

if a subject had placed a blind bet on stock X, she could have expected her

earningsfortheperiodtobehigh. IfshehadplacedablindbetonstockZ,she

could have expected her earnings for the period to be low. If there were no

insiders,thestockpricedidnotcontainanyinformationontheexpectedearning

for the period.We illustrated this computation of the expected reward on the

thirdrowofFigure4.

Thisdesignhad threemainadvantages.First, thesubjectsdidnot trade.While

thequestionofhowthehumanbrainmakesfinancialdecisionsisinteresting,we

needed first to understand how humans perceive a stock market. By not

23

introducing decision‐making, we avoided a confounding factor. Second, the

periodswithoutinsiderswereperfectcontrols.Sincethetradingdataacquisition

method,thedisplayscreens,andthenumberoftraderswerethesame,thetwo

types of sessions were identical in every respect except for the presence or

absence of insiders. Third, by adding a blind bet, we elicited a feeling of

“randomness.” Indeed, if we had forced subjects to choose stock X for every

session, the payoffwould have been the same fixed number for every subject.

Moreover, we could not have teased apart an increase in stock price with a

higher expected reward, as these two signals would have been perfectly

correlated. Instead, by introducing a blind bet, we orthogonalized expected

rewardandstockprice.

We replayed the market activity (section (iii) of Figure 3) with a simplified

interface(Video1).Werepresentedthepricelevelsfortheofferstobuyandsell

(“bids”and“asks”)withacircle.Anumberinsideeachcircleindicatedtheprice

incentsandthediameterofthecirclerepresentedthenumberofunitsoffered.

Bluecircles represented thebidsandredcircles represented theasks.Whena

tradeoccurredatacertainprice,we turned thecorrespondingcirclegreen for

500ms.We rearranged the circles dynamically to reflect the changes in prices

andtrades.Thelocomotionbetweensessionswithandwithoutinsidersdidnot

displayanyobviousdifferences.Finally,inordertomonitorattention,weasked

subjectstopressakeyeverytimeatradeoccurred.

Despitethehighlysalientandvividnatureofourgraphicaldisplayoftheorder

andtradeflow,itshouldbeunderscoredthatitisnotwhatcausedtheToMbrain

activation that we report. This is because we contrast brain activation in a

treatment with and without insiders using the same interface. Likewise, the

humanfactorbehindthemarket in itselfcannotbe thecauseof theToMbrain

activations,becausethereisanequalamountofhumaninteractioninthecontrol

treatment.

A.3.Constructionofpredictors

24

ToanalyzethefMRIdata,weconstructedfourpredictors(Figure4).Wewanted

tousethesessionswithoutinsiders(secondandfourthcolumnsofFigure4)as

controlsandcomparethemwiththesessionswithinsiders(othercolumns).We

constructedtwoblockpredictors(lasttworows)andtwoparametricpredictors

(fourthandfifthrows).

As described above,we could compute the expected reward of one sessionby

takingintoaccountthestockprice,thepresenceorabsenceofinsiders,andthe

blind‐bet (second row of Figure 4). Indeed, during sessions without insiders,

neithertheblindbetnorstockpricescarriedinformation;theexpectedreward

wasthemeanvalueofthedividend,namely25¢.Ifinsiderswerepresent,thena

higherstockpriceforstockXindicatedthatthedividendwaslikelytobehigher.

Thus, ifasubjecthadplacedablindbetonstockX,shewouldhaveexpecteda

higher return. Conversely, if she had placed a bet on stock Z, shewould have

expectedalowerreturn.

We quantified the insiders’ activity using the absolute value of the difference

between the trading price and 25¢ (Figure 4, third row). Indeed the more

insiders skewed the market, the further the price would go from 25¢. We

computed this value and built two parametric predictors. One parametric

predictor modeled this effect during sessions with insiders (fourth row). To

control for other effects, we built a similar predictor for the sessionswithout

insiders(fifthrow).Bycontrastingthesetwoparametricpredictors,weisolated

theeffectofinsidersonsubjects’perceptionofthemarket.Wealsocreatedtwo

block predictors. They captured themeanbrain activation during the sessions

withorwithoutinsiders.

Thismodelinghadthreeadvantages.First,asmentionedabove,westrippedout

theeffectofdecision‐making in thebrainand focusedon theperceptionof the

market.Second,thepredictorswebuiltwereorthogonaltoexpectedrewardas

weusedtheabsolutevalueofthedistanceto25¢andratherthanthedistanceto

25¢.Similarly,ourpredictorswereorthogonaltorisk,measuredbythebid‐ask

spread [Glosten andMilgrom (1985)]. Third, by contrasting sessionswith and

withoutinsidersandmakingsurethatthesetwotypesofsessionsdisplayedno

25

obvious differences in trading activity, we controlled for differences in visual

activationaswell.

A.4.BehavioralExperiment

This experiment is necessary to confirm the fMRI results becauseToM‐related

brainareasmayactivateduringnon‐ToMsituations.

Theexperimentconsistedoffourtasksthatweadministeredinarandomorder

to43newsubjects.Duringthefirsttask,wereplayedthetradingactivityforfour

sessionswith insiders.Weused the same interfaceas for the fMRIexperiment

except that we played the market at the original speed (5 minutes) and we

paused the replay of themarket every 5s. During these pauses,we alternated

predictionsandoutcomes.Specifically,forhalfofthepauses,weaskedsubjects

to predict whether the next trade was going to occur at a higher, lower, or

identicalpriceastheprevioustradethathadhappened.Fortheotherhalfofthe

pauses, we reminded subjects of their prediction and informed them of the

outcome.Werewardedsubjectsforcorrectpredictionsbutdidnotpunishthem

for incorrect ones. However, we only gave subjects 5 seconds to make a

predictionandpenalizedthemforindecision.Thus,guessingwasalwaysbetter

thannotanswering.

ThesecondtaskwasaToMtest.Usingacomputerizedinterface,werecordedthe

scoresonaneye test [Baron‐Cohen, Jolliffe,MortimoreandRobertson(1997)].

While several advanced tests were available, such as the faux‐pas test [Stone,

Baron‐CohenandKnight(1998)],wedecidedtousethisparticularonebecause

itprovidedacontinuousscaleofToMabilitiesandwasdifficultenoughtoreveal

differencesinabilitiesbetweenhealthyadults.Inaddition,thefaux‐pastestmay

not be appropriate as social codes are culturally dependent. We also time‐

constrainedtheeyetest,andguessingwasbetterthannotanswering.

ThethirdtaskwasalsoaToMtestbasedondisplaysofmovinggeometricshapes

[Heider and Simmel (1944)].We played two “Heidermovies” and paused the

replayevery5s.Forhalfofthepauses,weaskedsubjectstopredictwhethertwo

26

oftheshapeswouldgetcloser,farther,orstayatthesamedistance.Fortheother

halfofthepauses,wereportedtheoutcomesandthesubjects’predictions.The

better the subjectsunderstood the social interactionsof the shapes, thebetter

theywereatpredictingmovements.

Weusedthefourthtasktomeasuremathematicalabilities.Withacomputerized

interface, we asked subjects to solve seven mathematical puzzles (Table III)

under time constraints and without the use of paper. Subjects typed their

answers on the keyboard, and guessing was better than not answering.

27

Figure1.Top:Object(magneticblockatright)attractedtotarget(ballatleft),flowingoverwall

in themiddle;Middle:wall is removed and blockmoves straight to target, as expected under

physicallaws;Bottom:Samesituation,butnowblockcontinuestomakeacurveevenifattracted

totarget,suggestingintention(tocurve).(Adaptedfrom:UllerandNichols(2000).)

28

Figure2.Evolutionoftransactionprices inthemarketofstockX.Sessionsaredelineatedwith

solid vertical separators; dotted vertical separators indicated end‐of‐trading. Sessions with

insiders aremarked “ins.” Signal levels are indicatedwith green horizontal line segments; red

line segments denote final dividend (of X) for the session. “i” denotes number of insiders (all

insiders receive the same signal); “K#” indicateswhether all subjects (“All”) know howmany

insiderstherewere,ornone(“0”),oronlytheinsiders(“Ins”).Allsubjectsalwaysknewwhether

therewereinsiders.

29

Figure3.fMRIexperiment.(i)Atthestartofeachsession,subjectswereinformedofwhetheror

not thesessioncontained insidersandwere instructed tomakeachoice(ablindbet)between

stockXandstockZ.Theywerethenendowedwith10unitsofthestocktheychose.(ii)Ablank

screenwas thenpresented for 10 seconds, (iii) amarket sessionwas then replayed at double

speed,(iv) followedbya10secondblankscreenafterwhich(v)subjectsare informedof their

paymentforthatsession(10Xtheirchosenstock’sdividend).

10s 2 min 30s 10s 3s 13s

repeated 13 times

blank (iv) blank blank (ITI)

There are insidersChoose X or Z?

The stockyoupicked paid $0.45

(i) choice (iii)replay (v) outcome

(ii) blank

10s

30

Figure 4. Construction of predictors in the GLM used in the analysis of brain activation data.

Columns 1‐5 represent five fictive periods of different combinations of presence/absence of

insidersandwhetherthesubjectchosestockXorZ.A)Theevolutionofthechosenstockpriceis

displayed.B)Thefirstpredictorwastheexpectedreward(ER),computedfromthestockprice,

thepresence/absenceofinsiders,andtheblindbet.Duringsessionswithoutinsiders(2ndand4th

sessions), neither the blind bet nor the stock prices carried any information and the expected

reward was the mean value of the dividend, namely 25¢. During sessions with insiders

(remainingsessions)ahigherpriceforstockXwastakentoindicatethatthedividendwaslikely

tobehigher, resulting in ahigherexpected reward in the caseof ablindbeton stockXanda

lowerexpectedrewardonstockZ.C) Insideractivitywasproxiedby theabsolutevalueof the

differencebetweenthetradingpriceand25¢.Fromthisproxy,twoparametricpredictorswere

constructed.D)First,aparametricpredictormodeledthiseffectduringsessionwithinsiders.E)

Second,asimilarpredictorwasconstructedforsessionswithoutinsiders.Inaddition,weadded

thefollowingpredictors:F)Blockpredictorcapturingmeanbrainactivationduringsessionswith

insiders;G)Blockpredictorcapturingmeanbrainactivationduringsessionswithoutinsiders.

31

Figure5.Locationofsignificantcontrastbetweenslopecoefficientstotheparametricregressor

betweeninsiderandno‐insidersessions(p<0.001,uncorrected,randomeffects).(a)Sagittalview

oftheactivationinparacingulatecortex(Talairachcoordinates‐9;41;36;Brodmannareas9/32;

extends for 22 voxels). (b) Amygdala activation in coronal view (‐14; 23; 39; extends for 5

voxels).(c)Activationoftheleftinsulainaxialview(‐30;‐7;11;extendsfor5voxels).

32

Figure 6. Location of significant contrast between slope coefficients to the block regressor

between insider and no‐insider sessions.We use the threshold p<0.001 (uncorrected, random

effect).Weobservetwoclustersofvoxelsactivated:thelingualgyrusandcerebellum.

33

Figure7.Toppanels:CorrelationofthescoresontheFinancialMarketPrediction(FMP)andtwo

ToMtests(Left:EyeTest;Right:HeiderTest).Sincebothmeasuresarenoisy,wecouldnotusea

linearregressionandinsteadwecomputedthecorrelationanditsp‐value.Wealsocomputedthe

mean line with the help of the correlation coefficient. We observe that there is a significant

correlation (EyeTest:p=0.048;HeiderTest:p=0.023)between thescoreson the tests.Bottom

Left:Correlationof thescoreson theFinancialMarketPrediction(FMP)andMathematical (M)

tests.Whilepositive,thecorrelationisnotsigificant(p>0.200).BottomRight:Wecomparehere

theperformanceontheEyetestandtheHeidertests.Thecorrelationisinsignificant.

34

a

b

Figure8.(a)Autocorrelationcoefficients(lags1to5)ofabsolutetransactionpricechangesover

2s intervals intheMarketsExperiment(seeFigure2),Periods7(insiders)and8(no insiders).

Autocorrelation is more sizeable in Period 7. (b) Sum of absolute values of first five

autocorrelation coefficients of absolute price changes (“GARCH intensity”) for all periods in

Markets Experiments, arranged by number of insiders; Fitted line is significant at p=0.05;

R2=0.32.

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35

Availableat:http://www.bruguier.com/pub/stockvideo.html

Incaseofdifficultyplayingthemovie,wesuggestusingamulti‐platform

(Windows,Linux,MacOSX)program:http://www.videolan.org/vlc/

Video1.Displayofthetradingactivity.Eachcirclerepresentsanoffertobuy(bid,bluecircle)or

tosell(ask,redcircle)atacertainpriceindicatedbythenumberinsidethecircle.Thediameter

ofthecircleindicatesthenumberofunitsofthestockoffered.Thisnumberistheaggregateofall

theoffersatthisprice.Weorderedthecirclesbyincreasingvalue,alongonediagonal,chosenat

random.Theotherdiagonaldoesnotcarryanyinformationandweuseittospaceoutthecircles.

The circles move, grow, and shrink with the incoming orders. Every time a trade occurs, the

correspondingcircle(bidoraskquotethatisinvolvedinthetransaction)turnsgreenfor500ms,

shrinksby thenumberof stocks traded, and then returns to itsoriginal color (unlessnomore

stocksremaintobetraded,inwhichcaseitdisappears).

36

x y z clustersize t17 Area

‐30 ‐7 11 5 4.476 leftinsula

‐14 23 39 5 4.688 frontalpartoftheanteriorcingulate

cortex

‐9 41 36 22 5.380 paracingulatecortex

‐9 32 45 6 4.290 frontalpartofanteriorcingulatecortex

17 36 43 6 6.322 frontalpartoftheanteriorcingulate

cortex

21 ‐10 ‐12 5 5.160 rightamygdala

TableI.Areaswithsignificantdifferenceinslopecoefficientstoparametricregressors(insiders

vs.no‐insider).Standardcoordinates(Talairachx,y,z)areused.Wereportregionswith5ormore

voxels of 27mm3 each activated at p<0.001 (uncorrected) for a random effect GLM. The

parametric regressor is theabsolutedifferencebetween the last tradedpriceand the25¢.The

clustersizeisspecifiedinnumberofcontiguousvoxels.

37

x Y z clustersize t17 Area

‐13 ‐58 ‐30 9 4.485 Cerebellum

‐9 ‐65 ‐6 25 4.440 lingualgyrus

TableII.Areaswithsignificantdifferenceinslopecoefficientsforblockregressors(insidersvs.

no‐insider). Standard coordinates (Talairach x,y,z) are used. Random effects, thresholded at

p<0.001(uncorrected).

38

Question Answer

Consideragameplayedwithadeckofthreecards:spades,clubs,andhearts.Yourgoalistoidentifythe

hearts.

Thecardsareshuffledanddisplayedinarow,facedown.Youmakeyourchoice.Thedealerthenturns

overoneofthetworemainingcards,provideditisnothearts.Hethenoffersyouthepossibilitytochange

yourchoiceandswitchtotheothercardthatisleftfacedown.Whatisthebeststrategy?

Shouldyouswitch,stay,ordoesitnotmatter?

Answerbelow"switch","stay"or"either".

switch

Consideradeckoffourcards:spades,clubs,hearts,anddiamonds.Thecardsareshuffledanddisplayedin

arow,facedown.

Youchooseonecardatrandomanditisdiscarded.Thenthedealerturnsovertwocards,chosenat

random,butprovidedtheyarenothearts.Nowthereisonlyonecardleftunturned.

Ifthetwocardsthedealerturnsoverarediamondsandclubs,istheprobabilitythattheremainingoneis

heartsmorethan,lessthan,orequalto0.5?

Answerbelow"more","less"or"same".

Less

Thereare8marblesthatweighthesame,and1marblethatisheavier.Themarblesarealluniforminsize,

appearance,andshape.

Youhaveabalancewith2trays.Youareaskedtoidentifytheheaviermarbleinatmost2(two)

weightings.

Howmanymarblesdoyouinitiallyhavetoplaceoneachtray?

Inputanumberbelow.

3

Divide100by1/2.Istheresultmore,lessthanorequalto100?

Answerbelow"more","less",or"same".

More

JennhashalftheBeanieBabiesthatMolliehas.Allisonhas3timesasmanyasJenn.Togethertheyhave72.

DoesMolliehavemorethan,lessthan,orequalto,20BeanieBabies?

Answerbelow"more","less"or"same".

More

Johnny’smotherhadthreechildren.ThefirstchildwasnamedApril.ThesecondchildwasnamedMay.

Whatwasthethirdchild'sname?

Typethenamebelow.

Johnny

ThepoliceroundedupJim,BudandSamyesterday,becauseoneofthemwassuspectedofhavingrobbed

thelocalbank.Thethreesuspectsmadethefollowingstatementsunderintensivequestioning.

Jim:I'minnocent.

Bud:I'minnocent.

Sam:Budistheguiltyone.

Ifonlyoneofthesestatementsturnsouttobetrue,whorobbedthebank?

Typethenameoftherobberbelow.

Jim

TableIII.TheMathematical(M)test.Wepresentedsubjectswithsevenquestions inarandom

order.Subjectshad30secondstotypetheanswer.Weignoredaccounttypos.

39

ReferencesAcuna,B.,J.Eliassen,J.Donoghue,andJ.Sanes,2002,Frontalandparietallobe

activationduringtransitiveinferenceinhumans,CerebralCortex12,1312‐1321.

Admati,A.R.,1985,ANoisyRationalExpectationsEquilibriumforMulti‐AssetSecuritiesMarkets,Econometrica53,629‐657.

Barner,M.,F.Feri,andC.R.Plott,2005,Onthemicrostructureofpricedeterminationandinformationaggregationwithsequentialandasymmetricinformationarrivalinanexperimentalassetmarket,AnnalsofFinance1,73.

Baron‐Cohen,S.,T.Jolliffe,C.Mortimore,andM.Robertson,1997,Anotheradvancedtestoftheoryofmind:evidencefromveryhighfunctioningadultswithautismorAspergerSyndrome,JournalofChildPsychologyandPsychiatry38,813‐822.

Baron‐Cohen,S.,H.A.Ring,S.Wheelwright,andE.T.Bullmore,1999,Socialintelligenceinthenormalandautisticbrain:anfMRIstudy,TheEuropeanjournalofneuroscience11,1891‐1898.

Bechara,A.,andA.R.Damasio,2005,Thesomaticmarkerhypothesis:Aneuraltheoryofeconomicdecision,GamesandEconomicBehavior52,336‐372.

Bhatt,M.,andC.Camerer,2005,Self‐referentialThinkingandEquilibriumasStatesofMindinGames:fMRIEvidence,GamesandEconomicBehavior52,424‐459.

Biais,Bruno,PeterBossaerts,andChesterS.Spatt,2008,EquilibriumAssetPricingUnderHeterogeneousInformation,ReviewofFinancialStudiesForthcoming.

Bossaerts,P.,C.Plott,andW.Zame,2007,PricesandPortfolioChoicesinFinancialMarkets:Theory,Econometrics,Experiment,Econometrica75,993‐1038.

Bossaerts,Peter,CharlesPlott,andWilliamZame,2007,PricesandPortfolioChoicesinFinancialMarkets:Theory,Econometrics,Experiments,Econometrica75,993‐1038.

Camerer,ColinF.,Teck‐HuaHo,andJuin‐KuanChong,2002,SophisticatedExperience‐WeightedAttractionLearningandStrategicTeachinginRepeatedGames,JournalofEconomicTheory104,137‐188.

Castelli,F.,F.Happe,U.Frith,andC.Frith,2000,Movementandmind:afunctionalimagingstudyofperceptionandinterpretationofcomplexintentionalmovementpatterns,NeuroImage12,314‐325.

Coricelli,G.,andR.Nagel,2008,BeautyContestintheBrain;aNeuralBasisofStrategicThinking,Underreview.

Crack,T.F.,2004.HeardontheStreet:QuantitativeQuestionsfromWallStreetJobInterviews(TimothyCrack,Dunedin,NewZealand).

Critchley,H.D.,C.J.Mathias,andR.J.Dolan,2001,Neuralactivityinthehumanbrainrelatingtouncertaintyandarousalduringanticipation,Neuron29,537.

Dehaene,S.,E.Spelke,P.Pinel,R.Stanescu,andS.Tsivkin,1999,SourcesofMathematicalThinking:BehavioralandBrain‐ImagingEvidence,Science284,970‐974.

Easley,D.,andM.O'Hara,1992,TimeandtheProcessofSecurityPriceAdjustment,TheJournaloffinance47,577‐605.

40

Fama,EugeneF.,1991,EfficientCapitalMarkets:II,TheJournalofFinance46,1575‐1617.

Fenton‐O'Creevy,Mark,NigelNicholson,EmmaSoane,andPaulWillman,2005.Traders:Risks,Decisions,andManagementinFinancialMarkets(OxfordUniversityPress).

Fink,G.R.,P.W.Halligan,J.C.Marshall,C.D.Frith,R.S.Frackowiak,andR.J.Dolan,1996,Whereinthebraindoesvisualattentionselecttheforestandthetrees?,Nature382,626.

Fink,G.R.,P.W.Halligan,J.C.Marshall,C.D.Frith,R.S.Frackowiak,andR.J.Dolan,1997,Neuralmechanismsinvolvedintheprocessingofglobalandlocalaspectsofhierarchicallyorganizedvisualstimuli,Brain120,1779‐1791.

Gallagher,H.L.,andC.D.Frith,2003,Functionalimagingof'theoryofmind',TrendsinCognitiveSciences7,77‐83.

Gallagher,H.L.,A.I.Jack,A.Roepstorff,andC.D.Frith,2002,Imagingtheintentionalstanceinacompetitivegame,NeuroImage16,814‐821.

Gergely,G.,Z.Nadasdy,G.Csibra,andS.Biro,1995,Takingtheintentionalstanceat12monthsofage,Cognition56,165‐193.

Glosten,L.,andP.Milgrom,1985,Bid,askandtransactionpricesinaspecialistmarketwithheterogeneouslyinformedtraders,Journaloffinancialeconomics14,71‐100.

Green,Jerry,1973,Information,EfficiencyandEquilibrium,HarvardInstituteofEconomicResearchDiscussionPaper.

Grossman,SanfordJ.,andJosephE.Stiglitz,1980,OntheImpossibilityofInformationallyEfficientMarkets,TheAmericanEconomicReview70,393‐408.

Hampton,AlanN.,PeterBossaerts,andJohnP.O'Doherty,2008,Neuralcorrelatesofmentalizing‐relatedcomputationsduringstrategicinteractionsinhumans,ProceedingsoftheNationalAcademyofSciences105,6741‐6746.

Heider,F.,andM.Simmel,1944,Anexperimentalstudyofapparentbehavior,AmericanJournalofPsychology57,243‐249.

Heider,F.,andM.Simmel,1944,Anexperimentalstudyofapparentbehaviour,AmericanJournalofPsychology57,243‐259.

Lo,A.W.,andD.V.Repin,2002,ThePsychophysiologyofReal‐TimeFinancialRiskProcessing,JournalofCognitiveNeuroscience14,323‐339.

Madhavan,Ananth,1992,TradingMechanismsinSecuritiesMarkets,TheJournalofFinance47,607‐641.

McCabe,K.,D.Houser,L.Ryan,V.Smith,andT.Trouard,2001,Afunctionalimagingstudyofcooperationintwo‐personreciprocalexchange,ProceedingsoftheNationalAcademyofSciences98,11832‐11835.

Morris,J.S.,A.Ohman,andR.J.Dolan,1998,Consciousandunconsciousemotionallearninginthehumanamygdala,Nature393,467‐470.

Newman,S.,P.Carpenter,S.Varma,andM.Just,2003,FrontalandparietalparticipationinproblemsolvingintheTowerofLondon:fMRIandcomputationalmodelingofplanningandhigh‐levelperception,Neuropsychologia41,1668‐1682.

Oberlechner,T.,2004,UnderstandingtheForeignExchangeMarketthroughMetaphors,BritishJournalofSocialPsychology43,133‐156.

41

Parsons,L.,andD.Osherson,2001,Newevidencefordistinctrightandleftbrainsystemsfordeductiveversusprobabilisticreasoning,CerebralCortex11,954‐965.

Phan,K.L.,T.D.Wager,S.F.Taylor,andI.Liberzon,2002,FunctionalNeuroanatomyofEmotion:aMeta‐AnalysisofEmotionActivationStudiesinPETandfMRI,NeuroImage16,331‐348.

Phillips,M.L.,A.W.Young,S.K.Scott,A.J.Calder,C.Andrew,V.Giampietro,S.C.Williams,E.T.Bullmore,M.Brammer,andJ.A.Gray,1999,Neuralresponsestofacialandvocalexpressionsoffearanddisgust,ProceedingsofRoyalSocietyofLondon.265,1809‐1817.

Plott,C.R.,andS.Sunder,1988,RationalExpectationsandtheAggregationofDiverseInformationinLaboratorySecurityMarkets,Econometrica56,1085‐1118.

Plott,CharlesR.,andL.SmithVernon,1978,AnExperimentalExaminationofTwoExchangeInstitutions,TheReviewofeconomicstudies45,133‐153.

Radner,Roy,1979,RationalExpectationsEquilibrium:GenericExistenceandtheInformationRevealedbyPrices,Econometrica47,655‐678.

Servos,P.,R.Osu,A.Santi,andM.Kawato,2002,Theneuralsubstratesofbiologicalmotionperception:anfMRIstudy,CerebralCortex12,772‐782.

Singer,T.,B.Seymour,J.O'Doherty,H.Kaube,R.J.Dolan,andC.D.Frith,2004,EmpathyforPainInvolvestheAffectivebutnotSensoryComponentsofPain,Science303,1157‐1162.

Stahl,DaleO.,2000,RuleLearninginSymmetricNormal‐FormGames:TheoryandEvidence,GamesandEconomicBehavior32,105‐138.

Stone,V.E.,S.Baron‐Cohen,andR.T.Knight,1998,Frontallobecontributionstotheoryofmind.,JournalofCognitiveNeuroscience10,640‐656.

Uller,Claudia,andShaunNichols,2000,Goalattributioninchimpanzees,Cognition76,B27‐B34.

Yoshida,W.,R.J.Dolan,andK.J.Friston,2008,GameTheoryofmind,Underreview.

Zhuanxin,Ding,W.J.GrangerClive,andF.EngleRobert,2001,Alongmemorypropertyofstockmarketreturnsandanewmodel,inEssaysineconometrics:collectedpapersofCliveW.J.Granger(HarvardUniversityPress).

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∗Acknowledgements:ThisworkwassupportedbytheNSFthroughgrantSES‐0527491toCaltechandbytheSwissFinanceInstitute.CommentsfromRalphAdolphs,ColinCamerer,FulviaCastelli,JohnDickhaut,JohnLedyard,CharlesPlott,theEditor,anAssociateEditorandthereferees,andseminarparticipantsatBI(Oslo),EPFL,HEC(Paris),NorthwesternUniversity(Kellogg),theNationalUniversityofSingapore,OkinawaInstituteofScienceandTechnology,RiceUniversity,theUniversityofZurich,UniversityofLouvain,UniversityofTexas‐AustinandDallas,the2007Caltech‐TamagawaNeuroscienceSymposium,the2007JapanNeuroscienceSocietymeetings,the2008meetingsoftheSwissFinanceInstitute,the2008WesternFinanceAssociationmeetings(especiallythediscussant,HeatherTookes),the2008InternationalMeetingsoftheEconomicScienceAssociation,aregratefullyacknowledged.1OneofthewaysthatweknowthatTheoryofMindisratheruniquelyhuman(orsharedonlywithhighernonhumanprimates)isthattaskssuchasrecognizingintentinanopponent’seyesengagesbrainstructuresthatareevolutionarylatedevelopments(andpresentonlyinafewotherprimates),suchasparacingulatecortex,themostfrontalandmedialpartofthecortex.

2Assuch,ToMactuallyinvolvesanaspectoflearningtoplaygamesthathasbarelycometotheattentionofgametheorists[exceptionsincludeStahl,DaleO.,2000,RuleLearninginSymmetricNormal‐FormGames:TheoryandEvidence,GamesandEconomicBehavior32,105‐138.,Camerer,ColinF.,Teck‐HuaHo,andJuin‐KuanChong,2002,SophisticatedExperience‐WeightedAttractionLearningandStrategicTeachinginRepeatedGames,JournalofEconomicTheory104,137‐188.],namely,strategicsophistication.Strategicsophisticationisthelevelofcognitivehierarchythataplayerreaches.E.g.,second‐levelthinkinginvolvesoptimallyrespondingtomyopponent’sreactiontohis/herconjectureastohowIwouldplaygiventhehistoryofplay.BuildingonHampton,AlanN.,PeterBossaerts,andJohnP.O'Doherty,2008,Neuralcorrelatesofmentalizing‐relatedcomputationsduringstrategicinteractionsinhumans,ProceedingsoftheNationalAcademyofSciences105,6741‐6746.,Yoshida,W.,R.J.Dolan,andK.J.Friston,2008,GameTheoryofmind,Underreview.haverecentlysuggestedthatToMisnotjustaboutimprovingthepredictionofhowone’sopponentchangesstrategyasaresultofone’sownactions,butactuallyismeanttoestimatetheopponent’sdegreeofstrategicsophistication.AlsoconsistentwiththeideathatToMingameplayconcernsstrategicsophistication,activationinparacingulatecortexinthebeautycontesthasrecentlybeenshowntocorrelatewithstrategicsophistication[Coricelli,G.,andR.Nagel,2008,BeautyContestintheBrain;aNeuralBasisofStrategicThinking,Underreview.].3Wefocusedonautocorrelationsofabsolutevaluesofpricechangesbecause,infieldmarkets,persistenceisknowntobehigherforabsolutevaluesinsteadofthemorewidelyinvestigatedsquaredpricechanges.SeeZhuanxin,Ding,W.J.GrangerClive,andF.EngleRobert,2001,Alongmemorypropertyofstock

43

marketreturnsandanewmodel,inEssaysineconometrics:collectedpapersofCliveW.J.Granger(HarvardUniversityPress).