I A I N S T I T U T E O F T E C H N O L O G Y C A LI F O R N

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1 DIVISION OF THE HUMANITIES AND SOCIAL SCIENCES CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA, CALIFORNIA MENTAL PROCESSES AND STRATEGIC EQUILIBRATION: AN FMRI STUDY OF SELLING STRATEGIES IN SECOND PRICE AUCTIONS Dvid M. Grether Cliforni Institute of Technology Chrles R. Plott Cliforni Institute of Technology Dniel B. Rowe Medicl College of Wisconsin Mrtin Sereno University of Cliforni Sn Diego John M. Allmn Cliforni Institute of Technology I A I N S T I T U T E O F T E C H N O L O G Y 1891 C A LI F O R N SOCIAL SCIENCE WORKING PAPER 1189R Februry 2004 Revised June 2004

2 Mentl Processes nd Strtegic Equilibrtion: An fmri Study of Selling Strtegies in Second Price Auctions Dvid M. Grether Chrles R. Plott Dniel B. Rowe Mrtin Sereno John M. Allmn Abstrct This study is the first to ttempt to isolte reltionship between cognitive ctivity nd equilibrtion to Nsh Equilibrium. Subjects, while undergoing fmri scns of brin ctivity, prticipted in second price uctions ginst single competitor following predetermined strtegy tht ws unknown to the subject. For this uction there is unique strtegy tht will mximize the subjects' ernings, which is lso Nsh equilibrium of the ssocited gme theoretic model of the uction. As is the cse with ll gmes, the bidding strtegies of subjects prticipting in second price uctions most often do not reflect the equilibrium bidding strtegy t first but with experience, typiclly exhibit process of equilibrtion, or convergence towrd the equilibrium. This reserch is focused on the process of convergence. In the dt reported here subjects prticipted in sixteen uctions, fter which ll subjects were told the strtegy tht will mximize their revenues, the theoreticl equilibrium. Following tht nnouncement, sixteen more uctions were performed. The question posed by the reserch concerns the mentl ctivity tht might ccompny equilibrtion s it is observed in the bidding behvior. Does brin ctivtion differ between equilibrted nd non-equilibrted in the sense of bidding strtegy? If so, re their differences in the loction of ctivtion during nd fter equilibrtion? We found significnt ctivtion in the frontl pole especilly in Brodmnn's re 10, the nterior cingulte cortex, the mygdl nd the bsl forebrin. There ws significntly more ctivtion in the bsl forebrin nd the nterior cingulte cortex during the first sixteen uctions thn in the second sixteen. The ctivity in the mygdl shifted from the right side to the left fter the solution ws given. JEL clssifiction numbers: C91, D83, C23 Key words: uctions, strtegy, imging

3 Mentl Processes nd Strtegic Equilibrtion: An fmri Study of Selling Strtegies in Second Price Auctions 4 Dvid M. Grether, Chrles R.Plott, Dniel B. Rowe, Mrtin Sereno, nd John M. Allmn 1. INTRODUCTION The development of tools to mesure rections ssocited with mentl ctivity opens the possibilities of fruitful interctions between economists nd biologists, especilly neuroscientists. This study is the first to join tht interfce with focus on equilibrtion. Economic theory is typiclly theory of equilibrium nd equilibrtion for individuls, mrkets or, more generlly, systems. While both mrket models nd gme theory models hve both equilibrium nd equilibrtion defined in terms of observble vribles, the theory itself, when pplied to the individul, is often developed in terms of the unobservble beliefs nd objectives tht the individul might hold. Thus, the theory is often developed from ssumptions bout unobservble sttes of mind long with the use of "s if" ssumptions, to which theorists often resort when confronted by unobservbles. The ppliction of the resulting "s if" methodology is widespred, well understood nd remrkbly successful in developing models for the behvior of both individuls nd complex systems of individuls. Included re postultes of optimizing behvior nd strtegy, s well s postultes bout the consequences of strtegies tht others might employ. Intentions, ttributions of intentions nd strtegic thinking, none of which cn be observed, ply role in the theory. At the bse of the success of the theory, in spite of the lck of observbility of key vribles, rests theory of equilibrium nd equilibrtion. It is tht prticulr feture of this complex tht we focus on here. Cn we observe mentl ctivities tht cn be interpreted s equilibrtion tht tke plce when observed choices would lso be so interpreted? Developments in the use of lbortory techniques in experimentl economics together with the technologicl dvncements of fmri mke possible collbortion between economics nd neuroscience (Glimcher 2003, McCbe 2001) tht might nrrow the scope for specultion bout wht is tking plce in the mind s economic decisions re mde. Distinguishing between equilibrium behvior nd out of equilibrium behvior could hve importnt implictions for the study of economics. First, economic theory hs little to sy bout behvior out of equilibrium. Thus, observing behvior of individuls who re not equilibrted does not provide vlid test of the theory. Knowing which dt represent equilibrium behvior nd which do not would be significnt brekthrough. The implictions of commonly observed behvior tht ppers inconsistent with economic theory (Cmerer, 1995), re quite different if the behvior is equilibrium behvior s opposed to confused responses of subjects serching for solution (Plott, 1996). 4 The reserch support of the Cltech Lbortory for Experimentl Economics nd the Ntionl Science Foundtion re grtefully cknowledged. 2

4 In this pper, we report the results of experiments conducted while subjects were inside MRI scnner. Subjects prticipted in series of uctions in which the optionl response is to ccurtely revel preferences, which seem obvious once understood. Indeed, with trining which sometimes includes explining the optiml strtegy, subjects typiclly dopt the strtegy nd in some cses do so only fter few trils. In the experiments conducted, optiml nd non-optiml strtegies re esily observed nd then cn be used to distinguish between equilibrium nd disequilibrium behvior. Such decisions re mde while the subject is undergoing fmri so the differences in mentl process during nd fter equilibrtion cn be observed 2. EXPERIMENTAL PROCEDURES The Tsk The subject is given coupon with fce vlue stted in the experimentl currency clled frncs. Frncs were converted to dollrs t the end of the experiment t fixed known exchnge rte (300f= $1). The subject my keep the coupon nd redeem it for csh t the end of the experiment or sell it nd ern the sles price insted. The subject s tsk is to stte reservtion price, i.e. the lowest price t which the subject is willing to sell the coupon. Tht price will be compred with bid rndomly generted independently of the subject s price. If the rndom bid is bove the reservtion price, the subject sells the coupon t the higher price. Otherwise the subject keeps the coupon. The experimentl tsk is bsed upon the method developed by Becker, De Groot nd Mrshk (1964) for determining subjects vlutions of objects. We refer to this procedure s BDM. We used frncs rther thn direct csh vlues so tht if we lter the design nd chnge the number of tsks in session the exchnge rte cn be djusted to keep subjects ernings t resonble level. In prctice, subjects erned bout $70 for the session, which rn bout n hour nd hlf. If one wnts to mximize rewrds, the optiml strtegy is to be "truthful" in the sense of bidding exctly the mount of the coupon. Thus, if the subjects nme n mount less thn the vlue to them of the coupon, they risk selling it for less thn the vlue. On the other hnd, if they nme n mount tht is more thn the coupon is worth to them, there is the possibility of rejecting bids tht they would prefer to hving the coupon. By nming ny mount other thn the true vlue of the coupon they cnnot gin nything, but my lose something. Regrdless of the simplicity, mjor elements of this problem re present in lmost every economic decision. First, is notion of independence between subjects bids nd the bids to which theirs will be compred. If the bids re somehow relted, then subjects would hve n incentive to plce bids with n objective of influencing the future bids used by the experimenter. Secondly, there is notion of optimizing behvior from the point of view of the subject, s opposed to the set of ll bidders. A subject who is concerned bout being "fir" or concerned bout ppernce could behve much differently from theoreticl predictions. Third, is the recognition tht one strtegy is dominnt: it is optiml regrdless of the outcome of the rndomness. Recognition of dominnce is n exercise in bstrct logic tht leds to the conclusion of the type of strtegy tht is optiml. Such interctions mong motive, understnding, logic, beliefs nd strtegy hve lwys been chllenge to economists, who trditionlly hve only observed behviors s dt. 3

5 Subjects mke sixteen bidding decisions nd fter ech re informed of the mount of money they ccumulte s result. After the first sixteen uctions, subjects were told the correct strtegy, tht is, the strtegy tht will ensure them the lrgest mount of money. Instructions re ttched in the Appendix. These were red prior to ny decision or experience in the mchine. Once in the mchine, the screens they sw re typicl of the exmple in Figure 1. The Instructions bout the optionl strtegy, which ws fter the first sixteen uctions, re ttched t the end of the generl instructions. The objective of the reserch reported here is to study the subjects while mentl ctivity is tking plce both before nd fter the instruction bout strtegy is given to them. Presumbly, if the decisions of the subject re not equilibrted before the instruction is given to them, they would be so fterwrd. The reserch questions we ddress re twofold. Wht loctions in the brin show ctivtion in the tsk? Are there systemtic differences in brin ctivtion before nd fter subjects hve found the solution to the problem? Session Procedures Subjects were recruited primrily from the upper level, undergrdute student popultion of University of Cliforni t Sn Diego. However, the subjects did include grdute students, postdoctorl fellow nd working dult. Ech subject ws first given sfety orienttion nd, if willing, signed the consent form. Next the subject red the Keypd Instructions for operting the specilly designed non-metllic fiber optic BRU nd then prcticed with the BRU while seted in front of lptop with the keypd to the right of the computer. There re no metl prts tht could cuse interference. The unit hs four buttons tht cn be used to correspond to ny four keys on the keybord. In these experimentl sessions, the buttons on the BRU corresponded to: Left, Right, Up nd Down. Numbers were displyed on the screen s four digit numbers with ll columns initilized t zero. The Right (Left) button cused the cursor to move one column to the right (left) with wrp round to the fr left (right) if the cursor ws lredy in the rightmost (leftmost) column. The Up (Down) button incresed (decresed) the digit in the ctive column by one. All buttons hd nlogous wrp round fetures. When the subject ws comfortble with the BRU the subject ws given the selling instructions. At this point, ny questions bout the procedures were nswered. The subject ws then positioned in the scnner with the BRU tped to the right side nd the right rm tped on the BRU to llevite the need to hold the rm still. The projected output from the lptop ws ligned on screen so tht the subjects cn see the informtion on the experimentl tsks projected into the scnner. Once the subject ws properly plced in the scnner nd ble to red informtion displyed the subject is given second prctice session prctice with the BRU under the new condition of lying down in the scnner. As the positioning in the scnner tkes severl minutes nd could be distrcting, the instructions for the bidding tsk re summrized on screen projected into the scnner (See Appendix instructions). At this point, the experiment, which consists of four scnning session is conducted. Imging ws performed on 1.5T Siemens mgnet t the Thornton Hospitl of UCSD. The functionl imges consisted of 24 xil plnes ech 64 by 64. Individul voxels were 45 cubic mm mesuring 3 by 3 in plne nd 5mm thick. A custom progrm ws written tht lterntely displyed Bidding Tsk nd blnk screen. The progrm lso reds the subject s input from the BRU nd records ech keystroke, the time elpsed, 4

6 the bids nd ernings. The progrm includes disply clibrtion screen to lign the projector nd Rw Disply Progrm, which reds nd displys the Rw Dt (Supporting mteril). 3. THE STATISTICAL MODEL The dt re pnel dt with the unit of observtion being x (i, t), the hemodynmic response of voxel i t time t. The bsic model is (Rowe 2001, 2003): (1) x(i,t) = (i) + b(i)*t + c(i,1)*s(1,t) c(i,k)*s(k,t) + ε(i,t). In the eqution, the S (k, t) re the vlues of k possibly unobserved stimuli often clled reference functions tht the voxels re responding to. Ech voxel hs its own intercept nd trend s well s coefficients for contributions from the k responses to the stimuli or reference functions. We tke the disturbnces, ε (i, t) to be mtrix norml with contemporneous covrince mtrix Ψ nd uncorrelted over time. If the reference functions re unobserved, the model is similr to fctor nlysis model. In fctor nlysis it is usully ssumed tht the fctors (reference functions in this ppliction) re orthogonl. We do not impose tht condition here, so the model is perhps better described s ltent vrible model. We proceed in Byesin fshion, nd quntify vilble knowledge in the form of priors for the models prmeters. The regression coefficients re tken to be jointly norml with covrince mtrix Ψ, nd men mtrix C 0. The reference functions re tken to be mtrix norml with prior men S 0, the columns of which re the ssumed to be boxcr functions representing the experimentl tretments, nd covrince mtrix R. Usul prctice is to estimte differences in response by introducing the boxcr functions (so-clled due to their shpe) tking the vlue 1 during tretment nd -1 or 0 when the tretment is not on, shifting them to llow for the hemo-dynmic lg nd smoothing or tpering them to reduce discontinuities. The Byesin pproch llows the dt to determine the shpe of the reference functions. For fuller discussion, see Rowe (2000, 2001). For n elementry but elegnt discussion of Byesin inference see Edwrds, Lindmn nd Svge (1963). The vrince covrince mtrices, Ψ nd R, re tken to hve inverted Wishrt distributions with prmeters (ν, Q) nd (η, V) respectively. The number of components ws initilly tken to be one. Lter we considered the possibility of two reference functions nd ssumed tht ech of the two possible vlues of k (the number of functions) hd prior probbility of one hlf. We use n empiricl Byes pproch nd tke the prior mens for the coefficients of the reference functions to be the estimted coefficients of the voxels ctivtions on boxcr. We obtin the conditionl densities of the prmeters given the vlues of the other prmeters nd the hyper prmeters. We estimte the mode of the posterior distribution by the method of iterted conditionl modes (see Lindley nd Smith (1972) nd Rowe (2001) for detils), nd we obtin our estimtes of the reference function (s) from the posterior mode. We proceed conditionl upon the reference functions tht we estimted from the mode of the posterior distribution. Tht is, we look t the reltionship between the hemodynmic responses in voxels nd the sttisticlly determined Byesin reference functions, using the Byesin reference functions in plce of the boxcr functions. The procedures for clculting the sttisticl significnce of the ctivtion were bsed on the AFNI progrm nd relted softwre. For ech scn, we computed the 5

7 histogrm of the t sttistics for the full brin nd picked the vlue tht corresponded to fixed percentile of the distribution (typiclly 95 %). We defined regions of interest (ROIs) prior to the nlysis, nd only used regions we could identify without reference to ctivtion mps. For the frontl pole, for exmple, we took to ll of the brin forwrd of minus 55 (Tlirch) on the y-xis. We identified ll clusters of voxels in ROIs such tht t ech voxel in the cluster the t sttistic ws t lest s lrge s the cut off level. Voxels were defined s being in the sme cluster if their centers were no more thn 5.7mm prt. We clculted the bndwidths of the Gussin filter corresponding to the sptil correltions in the dt using the progrm 3dFWHM. We simulted the clusters in the ROIs using res of roughly the sme configurtions s the ROIs. In the simultions smples of independent stndrd norml vribles re generted nd smoothed with the Gussin filter estimted from the dt. Ech simultion ws preformed 10,000 times nd the number of clusters tbulted by size of cluster. Rther thn perform seprte simultions for ech scn, we performed the simultions using the mximl bndwidths from the four scns for ech subject. As lrger bndwidths led to more clusters this procedure is conservtive. The procedures for clculting the differences in ctivtion were similr. The time series for scns one nd two were dded nd the series for scns three nd four subtrcted from them. The sttisticl model ws then fit using the verge overll subjects nd scns of the Byesin components s the functions in eqution (1). Once these clcultions were performed, the methods were the sme s those described. 4. RESULTS The results re prtitioned into two subsections. The first is found in the dily behvior s viewed from the point of view of economics. The second subsection is relted to mentl ctivity s rendered from the fmri. Bidding Results The tsk is one tht we believed subjects would spend some time trying to find the correct strtegy nd, then, would spend the rest of the trils using the optiml strtegy. Previous experiments suggested the tsk we chose. The purpose ws to observe ctivity during non-equilibrted period nd subsequent equilibrted period. The first result of this section demonstrtes tht equilibrtion processes, s seen by economic theory, were observed on verge. Tble 1 shows the time structure of bsolute difference between bid nd the vlue of the ticket for ech subject. Compred re the first sixteen uctions with the lst sixteen. Equilibrtion occurs when the difference is zero. For no subject is the medin lower in the first sixteen nd for most it is higher. The dt cn be viewed different wy in Figure 2. Shown there re the eight bids for ech subject during ech of the four sessions plotted ginst the vlue of the ticket for which the subject ws bidding. Equilibrium theory predicts tht ll bids should lie on the 45 degree line. Subjects were told the equilibrium strtegy t the strt of the third series of eight. The equilibrtion tendencies re obvious in the dt. RESULT 1: Overll, subjects exhibited convergence to the equilibrium strtegy with more rpid convergence exhibited fter the domintion fetures of the equilibrium strtegy were explined. 6

8 SUPPORT. Ech of the 17 subjects prticipted in 32 uctions, producing totl of 544 bids. Of these, 241 were exctly equl to the vlue of the coupon. There were 75 bids equl to coupon vlue in the first 16 trils nd 166 during the second 16 trils. All coupon vlues nd the predetermined bids were in multiples of ten (subjects were not told this). Thus, ny bid within 10 of the coupon vlue erned the sme mount s bidding the vlue exctly. More bids, minly from the second 16 trils (203 compred to 108) stisfied this criterion. The mgnitudes of the differences were not lrge in generl. Averging over ll subjects, the verge differences were 42.3 points for the first eight trils nd 47.9 for the second eight trils. The differences for the second hlf of the session were much smller: 0.5 points for the lst eight trils nd 9.1 for the third eight (ignoring one outlier t 9000). The figure illustrtes the existence of vribility cross subjects. One concern ws tht the tsk would be so obvious to the subjects tht they would see the solution immeditely nd indeed for some subjects tht ws the cse s is summrized by the next result nd support. RESULT 2: Convergence properties differ cross the behvior of individuls. SUPPORT. Of the seventeen subjects who prticipted in scns, four nerly lwys used the dominnt strtegy from the very beginning (subjects 2, 4, 6 nd 11). An dditionl three subjects (subjects 3, 9 nd 14) converged to the dominnt strtegy without being told for totl of seven subjects tht consistently used the dominnt strtegy without being given the solution. In ddition, seven subjects followed the correct strtegy fter being given the solution. Even fter being given the solution, subjects frequently experimented bit before dopting the dominnt strtegy. All but three subjects dopted the dominnt strtegy by the end of the experiment (two consistently priced over the vlue nd one priced below). Initil behvior, however, ws heterogeneous. Six subjects begn by pricing over the vlue, three consistently set prices below the vlue, four gve prices both over nd under the vlue nd four used the dominnt strtegy from the beginning. The source of the observed vriblity differs from individul to individul nd during the first phses ppers to be relted to strtegic behvior bsed on misunderstndings or confusion bout the full impliction of vrious strtegies. The misguided strtegy seems to come in two forms. Some individuls plce higher bid believing they will receive higher price not relizing tht in second price uction they re exposed to n opportunity for loss. Other subjects offer t low prices explining the strtegy by sying tht they wnted to mke the sle. Both properties cn be seen in the first pnels of Figure 2. Notice two seprte groupings of dt, one with tendency to be bove the 45 line of the optiml strtegy nd the other much below the line. On verge, there ws greter tendency to over bid with 205 prices set bove coupon vlue nd 95 7

9 set below. 5 Notice tht in the lower pnels the two groups hve merged into one s subjects tended to dopt the optionl strtegy. Those subjects who did not dopt the dominnt strtegy of giving the coupon vlue s their reservtion price seemed to dopt some simple lterntive e.g. rounding up the coupon vlue to the next multiple of 100, or lternting bove nd below. One subject lternted by being over the coupon vlue by 30 points nd by under 70 points. A scnner is hrdly n idel decision mking environment. The subjects re motionless on their bcks nd in tube looking t screen through mirrored glsses. The button response unit (BRU) is tped to them, nd the scnner, when ctive, mkes lot of noise. Given this, the overll performnce is resonble. Pilot experiments with subjects who were not in scnners exhibited similr convergence. Results from fmri: Mentl Activity Mesurements The brin res ctivted in these experiments include the frontl polr cortex, which is known from previous studies to be involved in clcultion, nd group of brin structures tht receive input from the dopminergic neurons in the midbrin tht signl expecttion of rewrd. These structures include the bsl forebrin, the mgdl nd the nterior cingulte cortex. Two dditionl results emerge from the brin scns. The first of these (Result 3) identify the loction in which significnt ctivities were observed. The second (Result 4) summrizes the chnges in mentl ctivity cross the tretments. Ech subject prticipted in four sets of bids ech eight minutes nd thirty-two seconds long. The sequence ws twenty-two seconds during which the vlue of the coupon ws displyed (see supporting mterils for the disply) nd the subject entered their reservtion price, ten seconds for feedbck, followed by thirty-two seconds of blnk screen. For technicl resons we were unble to nlyze the MRI dt from the first 6 subjects; the nlysis is bsed on subject 7 through 17. RESULT 3. Significnt ctivtion occurs in four res: the frontl pole (especilly Brodmnn's Are 10), the mygdl, the nterior cingulte cortex nd the bsl forebrin. SUPPORT. The ctivtions re summrized in Tble 2. The tble gives the estimted significnce levels for the lrgest cluster of voxels in the indicted regions ll of which exceeded predetermined cutoff level. Frequently, there were multiple clusters found which were significnt t conventionl levels of significnce. The significnce levels shown re, therefore, conservtive. As stted bove, the nterior cingulte ctivity ws greter in the first sixteen uctions, which is shown in Figure 3, sgittl view (t x=0) depicting the difference between the intensity over the first 16 rounds minus rounds The right mygdl ws more ctive in the first 16 rounds thn the left (see Figure 4). 5 Explntion of the tendency to over bid involves some controversy. Khnemn, Knitsch nd Thler (1991) interpret this s n inducement effort, on the other hnd Plott nd Zeiler (2003) suggest tht it results from subject s misunderstndings of the tsk. 8

10 RESULT 4. Activtion levels chnged over the course of the tretments. The nterior cingulte ctivity ws greter during the first (during theoreticl equilibrtion) trils s ws the right mygdl. During the second sixteen trils (fter theoreticl equilibrtion), mygdlr ctivity shifted to the left side nd the nterior cingulte ctivity reduced. SUPPORT. The right mygdl ws more ctive in the first 16 rounds thn the left (see Figure 2). In the finl rounds, the mygdlr ctivity shifted to the left side. Tble 3 gives the significnce levels for the differences in the responses between the first two scns (before subjects were given the solution to the problems) nd the lst two scns (fter the solution ws given). Tble 4 contins the sme informtion for the scns immeditely before nd fter subjects were given the solution (scns 2 nd 3). In the tbles we report significnce levels for the lrgest clusters of ech sign ( minus sign indictes the cluster is significnt with negtive sign indicting greter ctivtion in the lter scns) nd the centers of mss of the clusters (weighted by intensity). 5. DISCUSSION The results reported here suggest the existence of correspondence between the phenomenon of equilibrtion in decision rules s it is interpreted by economic theory nd the physiologicl trces of mentl processing. Such correspondence holds potentil for joining two sciences in useful wys. On one hnd, s lredy noted, concept of equilibrium is centrl to much of economic theory. The theory interprets behvior "s if" certin mentl processes were tking plce nd introspection bout those processes often serves to motivte new theory. In the bsences of direct observtions of mentl ctivity, competing interprettions of observed behvior re difficult to resolve. For exmple, n individul who is confused nd exhibits unchnging behvior while resolving decision problem could be interpreted s hving ttined equilibrium. Furthermore, mesurements of behvior tend to be limited to those tht re suggested by the theory, which is itself conditioned on n ssumption tht mentl processes cnnot be observed. Thus, for economics the discovery suggests the possibility of enriching the set of observble vribles tht might be interpreted by theory. Similrly, on the other hnd, the discovery connects neuroscience with new set of behviors nd suggests new interprettions of the res of the brin in which mentl ctivities re tking plce. The tsk ws chosen so tht we expected to imge brin ctivity during nonequilibrted or serching stge nd fter equilibrtion. To this end, the tsk ws not perfect. If subject hppens to dopt the equilibrium strtegy, by ccident or without relizing tht it is indeed correct strtegy, there ws no wy no wy to tell. In our experiment, for exmple, it is possible tht subjects could respond with the fce vlue of the coupon becuse it is slient number nd not becuse they hd determined tht this ws in fct the best possible response. Though few subjects dopted the optiml strtegy without being given the solution, ll subjects were given the optiml strtegy fter the first two scns. We do not know if those subjects using the optiml strtegy before getting the solution ctully understood the tsk rther thn responding with the coupon vlue s focl point. 9

11 With the qulifictions s bove, we conservtively identify observtions from the second two scns s being equilibrted nd those from the first two s being nonequilibrted. In this regrd, we see more ctivtion during the first two scns in the nterior cingulte nd the right mygdl thn during the lter scns. Thus, we interpret the phenomen of disequilibrtion with the nterior cingulte, which dmpens with the process of equilibrtion. The findings nd interprettion re consistent with other findings reported in the literture. The strongest nd most consistent ctivtion ws locted ner the frontl pole, primrily in Brodmnn s re 10 (Tble 5). This re hs been previously been found to be ctive in other tsks involving monetry rewrd nd risk ssessment (Rogers et l., 1999; Ernst et l., 2001). Are 10 is lso ctivted in mentl clcultion (Rickrd, 2000) which the subjects would hve been performing in this tsk. Are 10 is ctivted when n expected finncil rewrd is received (Knutson, et l. 2003). Are 10 is both bsolutely nd reltively much lrger in humns thn in other primtes which suggests tht some of the circuitry relted to economic decision-mking is phylogenetic speciliztion in the humn brin (Allmn et l., 2002; Semendeferi et l., 2001). The nterior cingulte cortex, bsl forebrin, nd mygdl ll receive strong dopminergic input from the midbrin, which signls the expecttion of rewrd (Schultz, 2002). The nterior cingulte ws ctive during the first 16 uctions before the subjects were told the optiml bidding strtegy nd less ctive during the second 16 uctions. The nterior cingulte cortex is ctive in difficult tsks involving considerble uncertinty (Critchley, et l. 2001). The nterior cingulte cortex is lso ctive in tsks the require novel s opposed to routine solutions (Richle et l, 1994). The nterior cingulte cortex is the source of n EEG signl ssocited with finncil loss in gmbling (Gehring nd Willoughby, 2002), which would presumbly not occur with the ppliction of the optiml bidding strtegy. More brodly speking, the nterior cingulte cortex is involved in mintining physiologicl homeostsis through the regultion of wide vriety of mechnisms necessry for life including hunger nd thirst. (Liotti, et l. 2001). This broder view of homeosttic role for nterior cingulte is consistent with the lck of ctivtion in these structures during economic decision mking during equilibrium conditions. The bsl forebrin contins mny rewrd-relted neurons (Schultz, 2000). Activity in the ventrl stritl component of the bsl forebrin is specificlly relted to cumultive finncil rewrd during series of gmbles (Elliott et l., 2003). The mygdl is strongly ssocited with fer (Ledoux, 1995) nd it is possible tht the initil ctivtion on the right side during the disequilibrium phse my hve risen from the subjects fer of finncil loss. However, the ctivtion of the left mygdl during the second sixteen uctions fter the subjects hd been informed of the optiml strtegy my be ssocited with their incresed certitude of receiving finncil rewrd. There is incresing evidence tht mygdl is involved in positive rewrd ssessment s well s its more fmilir role in fer (Bxter nd Murry, 2002; Schultz, 2002). Recently, Fried et l., (2001) hve shown through micro dilysis tht the dopminergic input to the mygdl in humn subjects increses during cognitive tsks not involving fer. The fct tht the loction of neurl ctivity chnges s equilibrtion tkes plce mens tht in imging studies, equilibrtion nd time must be considered in ddition to fetures of the tsk. Clerly there is much to be done. In pilot studies, we included control tsks, simple clcultions requiring response on the BRU, nd found tht subjects 10

12 were distrcted by the second tsk, forgetting their experience in the erlier uctions. Thus, we did not include control tsks becuse of the expected interference in subjects finding the optiml strtegy in the selling tsk. A nturl extension would be to bring subjects bck fter few dys to redo the tsk. Assuming tht they then understnd the tsk, we could use these extr trils to compre their now (presumed to be) equilibrted behvior with the scns from the erlier sessions. At this time it should be ble to introduce other control tsks. The tsk studied involves numericl responses. While this is true of mny economic decisions, it is by no mens true of ll. Choices from non-numericlly vlued lterntives re bsic to economics, nd could lso be studied. The tsk studied hs single individul cting lone with lterntive bids predetermined by computer. Brgining, or ny type of other regrding behvior is not included in the sitution studied. A nturl extension would be to hve subjects buying nd selling in mrkets with other prticipnts. 11

13 REFERENCES Allmn, J.M., Wtson, K, nd Hkeem, A. (2002) Two phylogenetic speciliztions in the humn brin, Neuroscientist 8: Bxter, Mrk G., nd Murry, E.A. (2002) The mygdl nd rewrd, Nture Reviews, Neuroscience 3: Critchley, HD, Mthis CJ, Doln RJ. (2001) Neurl ctivity in the humn brin relting to uncertinty nd rousl during nticiption, Neuron Feb;29(2): Dishbrow, E.A. et l. (2000) Functionl MRI t 1.5 tesl: A comprison of the blood oxygention level-dependent signl nd electrophysiology: Proceedings of the Ntionl Acdemy of Sciences, 97: Edwrds, W., Lindmn H. nd Svge L.J. Byesin sttisticl inference for psychologicl reserch, Psychologicl Review 70: Elliott, R., Friston, K., nd Doln, R., (2000) Dissocible neurl responses in humn rewrd systems, Journl of Neuroscience 20: Elliott, R, Newmn, J. Longe, O. nd J. Dekin (2003) Instrumentl responding for rewrds is ssocited with enhnced neuronl response in subcorticl rewrd systems, Neuroimge Mr;21(3): Ellsberg. Dniel (1961) Risk, mbiguity, nd the Svge xions, Qurterly Journl of Economics 75: Ernst, M et l. (2001) Decision-mking in risk-tking tsk: PET study, Neuropsychophrmcology 26: Fried, Itzhk et l. (2001) Incresed dopmine relese in the humn mygdl during performnce of cognitive tsks, Nture Neuroscience Gehring, W.J. nd Willoughby A.R. (2002) The Medil Frontl Cortex nd the Rpid Processing of Monetry Gins nd Losses, Science 295: Glimcher, Pul W. (2003) Decisions, Uncertinty nd the Brin: The Science of Neuroeconomics, MIT Press. Khnemn, D., Knetsch, J.L.,Thler, R.H., (1990) Experimentl Tests of the Endowment Effect nd the Corse Theorem, The Journl of Politicl Economy, 98: Khnemn, Dniel nd Amos Tversky (1979) Prospect Theory: An nlysis of Decision under Risk, Econometric 47: Knutson B., Fong GW, Bennett S.M., Adms C.M., Hommer D., (2003) A region of mesil prefrontl cortex trcks monetrily rewrding outcomes: chrcteriztion with rpid event-relted fmri, Neuroimge Feb;18(2): LeDoux, Joseph (1996) The Emotionl Brin Simon & Schuster, New York. Lindley, D.V. nd A.F.M. Smith (1972) Byes estimtes for the liner model, Journl of the Royl Sttisticl Society 34:1-19. Liotti, M., Brnnn, S., Egn, G., Shde R., Mdden L., Abplnlp, B., Robillrd, R., Lncster, J., Zmrrip, F., Fox, O., nd Denton, D. (2001) Brin responses ssocited 12

14 with consciousness of brethlessness (ir hunger), Proceeding of the Ntionl Acdemy of Sciences 98: McCbe, K., Houser, D., Ryn, L., Smith, V., Tromrd, T. (2001) A functionl Imging Study of Coopertion in Two-Person Reciprocl Exchnge, Proceedings of the Ntionl Acdemy of Sciences 98 (20): Mygkov, Mikil nd Chrles R. Plott (1997) Exchnge Economies nd Loss Exposure: Experiments Exploring Prospect Theory nd Competitive Equilibrium in Mrket Environments, Americn Economic Review 87: Pltt, M.L. nd P.W. Glimcher (1999) Neurl correltes of decision vribles in prietl cortex, Nture 400: Plott, C.R. (1996), "Rtionl Individul Behvior in Mrkets nd Socil Choice Processes: The Discovered Preference Hypothesis", The Rtionl Foundtions of Economic Behvior, K.J. Arrow, E. Colombtto, M. Perlmn nd C. Schmidt (Editors). Plott, C.R. nd K. Zeiler (2003), The Willingness to Py/Willingness to Accept Gp, the Endowment Effect, Subject Misconceptions nd Experimentl Procedures for Eliciting Vlutions, Americn Economic Review (submitted). Richle, M., J.A. Feiz, T.O. Videen, A.M. McLeod, J.V. Prdo, P.T. Fox & S.E. Petersen (1994) Prctice-Relted Chnges in Humn Brin Functionl Antomy During Nonmotor Lerning, Cerebrl Cortex 4:8-26. Rees, G., Friston, K., nd Koch, C. (2000) A direct quntittive reltionship between the functionl properties of humn nd mcque, Nture Neuroscience 3: Rickrd, T., Romero S., Bsso G., Whrton C., Flitmn S., Grfmn J. (2000) The clculting brin: n fmri study, Neuropsychologi 38: Rowe, D.B. (2001) Byesin Source Seprtion for Reference Function Determintion in fmri, Mgnetic Resonnce in Medicine 46: Rowe, D.B (2003) Multivrite Byesin Sttistics: Models for Source Seprtion nd Signl Unmixing, Chpmn nd Hll/CRC Press. Russo, Eugene (2000) Debting the Mening of fmri, The Scientist 14: Schultz. et l. (2000) Rewrd processing in primte orbitl frontl cortex nd bsl gngli, Cerebrl Cortex 10: Schultz, W. (2002) Getting Forml with Dopmine nd Rewrd, Neuron 36: Semendeferi, K., Armstrong, E., Schleicher, A., Zilles, K., nd Vn Hoesen, G. (2001) Prefrontl cortex in humns nd pes: comprtive study of re 10, Americn Journl of Physicl Anthropology 114: Smith, Kip et l. (2002) Neuronl Substrtes for Choice under Ambiguity, Risk, Certinty, Gins nd Losses, Mngement Science 48: Thut, G. et l. (1997) Activtion of the humn brin by monetry rewrd, Neuroreport 8:

15 Figure Smple Disply 14

16 Tble: 1 Absolute Vlue of the Bid minus the Vlue of the Ticket Subject Men Std. Dev. Auctions 1 to 16 Auctions 17 to 32 Medin Number 10 Men Std. Dev. Medin Number Deleting one observtion t 9000 reduces the men nd stndrd devition to 18.7 nd 38.9, respectively. 15

17 Tble 2 Significnce Levels of Responses for the Four Scns Region Frontl Pole Anterior Cingulte Bsl Forebrin Left Right Subject Cortex Amygdl Amygdl 7 c c d c d - b c d d 8 b c b 9 c d b d - 10 c 11 c c c b - - d b b b b b b c c - b - - c - c b - c c c - c c b d c - - d b b - c - b - - b - b d c b c d - d b c c - - b - - c b - b b - c - b b d - c c - c - d - b - - d c c - c - c - c b c - d - c c b b - - cc - - b c c c d b - c d - c - d - - d The letters in ech cell give the significnce levels for the four scns in order. The first row gives significnce levels for the first component, nd the second row gives significnce levels for the second component. Legend: p<.0005; b p<.005; c p<.05; d p<0.1; blnk or - p>.10 16

18 Tble 3 Response Scns 1&2 minus 3& 4 Differences computed for ech voxel First Component Subject Frontl pole Anterior Cingulte Cortex Bsl Forebrin Amygdl 7, - b- c 8 9,- d,- 10, ,- c 13,- b ,- 17,- b Second Component Subject Frontl pole Anterior Cingulte Cortex Bsl Forebrin Amygdl 7,- 8 c 9 c 10,- - 11,- 12,-,- b,- - 13,- 14, c, - Legend: p<.0005; b p<.005; c p<.05; d p<.10 17

19 Tble 4 Response Scn 2 minus Scn 3 Differences computed for ech voxel First Component Subject Frontl pole Anterior Cingulte Cortex Bsl Forebrin Amygdl 7 c 8 9 b,c- d d,- b 10, ,- - 13, , ,- Second Component Subject Frontl pole Anterior Cingulte Cortex Bsl Forebrin Amygdl 7, 8 b,b- 9 10,-,- 11, c- d 14,-,- 15,- 16,- 17 d, - - c- Legend: p<.0005; b p<.005; c p<.05; d p<.10 18

20 Tble 5 Are 10 Significnt Activtion Component 1 Component 2 Scn Subject 7 8, 9 b c, b 12, 13, b 16, 17 b A dot indictes tht prt of Are 10 is contined in cluster tht is significnt t the level indicted bsed on simultions of clusters in the frontl pole. Legend: p<.0005; b p<.005; c p<.05; d p<.10 Multiple letters refer to seprte clusters of voxels 19

21 First 8 bids Second 8 bids bid bid vlue vlue Third 8 Bids Fourth 8 Bids Bid 800 Bid Vlue 0 Vlue 700 Figure 2. Pooled Bids of ll Individuls 20

22 Figure 3 Averge response for the first 16 rounds minus the verge for rounds Note the ctivity in the nterior cingulte cortex is greter in the first 16 rounds. Sgittl view t x=0. Figure 4 Averge response for the first 16 rounds minus the verge for rounds Note the ctivity is greter on the right mygdl in for the first 16 rounds, nd shifts to the left side for rounds Coronl view t y=1. 21

23 991114b Instructions This is n experiment in decision-mking. During the experiment you will be sked to do severl repetitions of selling tsk. The experiment will consist of series of rounds. In ech round, you will perform the tsk once. The mount of money you ern will depend upon the decisions you mke. Our purpose is to study vrious technicl issues involved in decision-mking nd motor tsks. Your purpose should be to simply mke s much money s you cn. Selling Tsk The selling tsk works s follows. You will receive coupon worth money to you. You my keep the coupon nd collect the money or you cn sell the coupon to the experimenter. Your tsk is to choose selling price for the coupon nd enter it with the keypd. Your selling price is compred to n offer price rndomly generted by the computer. The price chosen by the computer is completely unrelted to your coupon vlue or your price. The sle is best described s n uction but it is much different from ny uction you hve seen before. If the computer s rndomly generted offer price is higher thn (or the sme s) your selling price, then you sell the coupon t the computer s offer price. For exmple, if your selling price is 900, nd the computer s offer price is 1000, then the experimenter buys from you t price of If the computer s offer price is below your selling price, then the experimenter does not buy from you. You would keep the coupon nd collect its vlue. 22

24 If the computer s rndom offer price is more thn your vlue of the coupon you would prefer to sell the coupon. If the computer s rndom offer price is less thn your vlue of the coupon you would prefer to keep the coupon. 23

25 Money nd Sequence After you hve completed ech tsk the screen will disply your ernings from the prticulr tsk nd your ccumulted totl ernings. You will be pid of the ccumulted totl ernings. (For technicl resons the numbers used in the experiment re multiple of the ctul money.) After ernings re displyed the screen will go blnk for while nd then the next tsk will be shown. In order to ssure you tht the computer s offer prices re completely unrelted to your offer price or your vlue of the item, the computer s offers hve been previously generted. These offer prices re listed in the envelope you hve been given. If you wnt, fter the experiment you will be ble to verify this independence by compring the list to the offer prices displyed during the experiment. 24

26 *==========================================* Points to remember: 1. You enter the lowest price tht you re willing to offer the coupon for. 2. If your offer is the sme or higher thn the computer's offer, you keep the coupon. If your offer is lower, then you sell it t the higher price. 3. If the computer's offer is higher thn the coupon vlue, you mke more money selling. If it is lower, you re better off keeping the coupon. *==========================================* Summry of instructions show to subjects fter they were positioned in the scnner The wy to mke the most money in the experiment is to set your offer price equl to the vlue of the coupon. If you do this, then you will never sell the coupon for less thn wht it will py t the end of the experiment. Also, you will never reject chnce to sell the coupon for more thn it will py. The progrm will restrt now. Your ernings will be dded to wht you hve erned so fr. 25

27 Messge shown to subjects fter they hd completed the first sixteen uctions. 26