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Research Report

Impaired strategic decision making in schizophrenia

Hyojin Kima, Daeyeol Leeb, Young-Min Shinc, Jeanyung Cheya,⁎aDepartment of Psychology, Seoul National University, San 56-1 Shillim-dong Kwanak-gu, Seoul 151-742, Republic of KoreabDepartment of Neurobiology, Yale University School of Medicine, 333 Cedar Street, New Haven, CT 06510, USAcDepartment of Psychiatry, Seoul Medical Center, 171-1 Samsung-dong Kangnam-gu, Seoul 135-740, Republic of Korea

A R T I C L E I N F O

⁎ Corresponding author. Fax: +82 2 880 6428.E-mail address: jychey@snu.ac.kr (Jeanyu

0006-8993/$ – see front matter © 2007 Elsevidoi:10.1016/j.brainres.2007.08.049

A B S T R A C T

Article history:Accepted 22 August 2007Available online 28 August 2007

Adaptive decision making in dynamic social settings requires frequent re-evaluation ofchoice outcomes and revision of strategies. This requires an array of multiple cognitiveabilities, such as working memory and response inhibition. Thus, the disruption of suchabilities in schizophrenia can have significant implications for social dysfunctions inaffected patients. In the present study, 20 schizophrenia patients and 20 control subjectscompleted two computerized binary decision-making tasks. In the first task, the participantsplayed a competitive zero-sum game against a computer in which the predictable choicebehavior was penalized and the optimal strategy was to choose the two targetsstochastically. In the second task, the expected payoffs of the two targets were fixed andunaffected by the subject's choices, so the optimal strategy was to choose the target with thehigher expected payoff exclusively. The schizophrenia patients earned significantly lessmoney during the first task, even though their overall choice probabilities were notsignificantly different from the control subjects. This was mostly because patients wereimpaired in integrating the outcomes of their previous choices appropriately in order tomaintain the optimal strategy. During the second task, the choices of patients and controlsubjects displayed more similar patterns. This study elucidated the specific components instrategic decision making that are impaired in schizophrenia. The deficit, which can becharacterized as strategic stiffness, may have implications for the poor social adjustment inschizophrenia patients.

© 2007 Elsevier B.V. All rights reserved.

Keywords:Decision makingGame theoryMixed strategyRandom responsePrefrontal cortexSocial dysfunctionExecutive function

1. Introduction

Schizophrenia is a debilitating disorder characterized by avariety of cognitive impairments and poor social functioning,which often result in a decline in the socioeconomic status ofthe patients suffering the illness (American Psychiatric Asso-ciation, 1994; Carson, 1984; Hollingshead and Redlich, 1958). Inparticular, the process of adaptive decision making might beimpaired in schizophrenia (Ernst and Paulus, 2005; Ludewig et

ng Chey).

er B.V. All rights reserved

al., 2003; Ritter et al., 2004; Shurman et al., 2005; Waltz andGold, 2007). During the process of decision making, the prosand cons of available options are evaluated, and a particularoption is selected, often in the context of uncertainty (Tverskyand Kahneman, 1981). This is necessary for everyday tasksranging from making personal choices of grooming to main-taining interpersonal relationships and meeting occupationalresponsibilities. Two related lines of evidence suggest thatschizophrenia patients may be impaired in their ability to

.

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make decisions adaptively. First, schizophrenia patients haveshown impairments in various executive functions related todecision making, such as working memory, planning ability,cognitive–behavioral flexibility, and self-monitoring abilities(Heinrichs and Zakzanis, 1998; Weinberger and Berman, 1996).Second, dysfunction of the prefrontal functions in schizo-phrenia has been relatively well established (Gold and Harvey,1993; Weinberger et al., 1986), and decision making engages anumber of executive functions that are often thought tolocalize in the prefrontal cortex, such asworkingmemory andoutcome evaluation (Krawczyk, 2002).

Nevertheless, it is only recent that investigators have begunexamining the decision-making process of schizophreniapatients systematically. Paulus and his colleagues (Ludewiget al., 2003; Paulus et al., 1999a, 1999b, 2002) were among thefirst to study the choice behavior of schizophrenia patientsusing a binary choice paradigm. For example, they found thatdecision-making behavior in schizophrenia patients displayedstronger correlation among their choices than control subjects(Paulus et al., 1999a). More recent studies utilizing the IowaGambling task have demonstrated that patients with schizo-phrenia tend to make choices with high risk more frequently,eventually reducing their payoffs (Ritter et al., 2004; Shurmanet al., 2005). These previous studies have used a task in whichthe probability of obtaining a desirable outcome from aparticular choice was fixed irrespective of the previous choicepattern of the subject. In real life, however, outcomes ofdecisions are not always stationary. Rather, outcomes areoften determined through social interaction: your decisionaffects the outcome of someone else's decision, and decisionsof others affected by your decisions once again affect yourdecision making (Sally, 2003). In such dynamic contexts ofmulti-agent environment, strategic approaches are oftenessential, and game theory provides a rigorous frame work toanalyze such interactive decision making (von Neumann andMorgenstern, 1944).

In game theory, a game is defined by a number of decisionmakers or players, a list of choices or actions available for eachplayer, and the rule that describes the payoff for each playeraccording to the combination of the choices of all players. Incompetitive games in which the payoff of one player isdiametrically opposed to that of another player, it is oftennecessary to choose different actions randomly. During a two-player zero-sum game known as the matching pennies, forexample, one of the players receives a fixed amount of moneywhen the two players choose the same side of a coin andotherwise loses money. Any deterministic strategy, such aschoosing always one side of the coin, is clearly not optimal,since itwouldbe exploitedby theopponent. In fact, theoptimalstrategy during the matching-pennies game with a symme-trical payoff is to choose the two choices with equal prob-abilities. This kind of strictly competitive game occurs ineveryday life with examples ranging from sporting contests topolitical campaigns (Colman, 1995). In game theory, choosing aparticular choice exclusively is referred to as a pure strategy,whereas choosingmultiple choices stochastically is referred toas amixed strategy. An optimal strategymay be pure ormixed.A game in which the optimal strategy is a mixed strategy isreferred to as a mixed-strategy game. A mixed-strategy gamerequires decisionmakers to update their strategies continually

so that these strategies cannot be easily predicted by theopponents. Up to now, however, decision-making behavior ofschizophrenia patients in such interactive and competitivesettings has not been investigated.

There is some evidence that strategic behavior necessary ina mixed-strategy game might involve the dorsolateral pre-frontal cortex (DLPFC). For example, the activity of someneurons in the DLPFC changes when the animal chooses itstargets during a competitive game, compared to when theanimal's choice is instructed by a visual cue during a searchtask (Barraclough et al., 2004; Seo et al., 2007). Given thesignificant amount of accumulated evidence for DLPFC pathol-ogy in schizophrenia from structural (Shenton et al., 2001) andfunctional (Barch et al., 2001; Weinberger et al., 1986) imaging,neuropathological (Pierri et al., 1999; Selemon et al., 1995;Selemon and Goldman-Rakic, 1999) to neurocognitive studies(GoldandHarvey, 1993;Goldman-Rakic andSelemon, 1997),wespeculated that thedecision-makingbehaviorof schizophreniapatients may be more impaired during a competitive game inwhich theyneed to choose their actions stochastically than inanon-competitive setting. To test this hypothesis, the presentstudy characterized the strategic decision-making behavior inschizophreniausinga computerizedcompetitive game, similarto the one used previously in non-human primates (Barra-clough et al., 2004; Lee et al., 2004). The payoffs during thematching pennies task, a mixed strategy game, used in thepresent study were different for the two alternative choicesavailable to the participants. As a result, the optimal strategyduring this task was to choose the two targets with unequalprobabilities. The subjects then performed a pure-strategycontrol task in which the choice outcomes were determinedindependently of the subject's choice patterns and the optimalstrategy was to choose one of the targets exclusively.

2. Results

2.1. Overall performance

Twenty schizophrenia patients and 20 control subjects madebinary choices in a card game modeled after a matchingpennies game (1500 trials) and this was followed by a two-armed bandit task (500 trials; Fig. 1). The transition to the two-armed bandit task was not explained to the subjects. In eachtrial, the subject chose the face or the back of a card. The face ofa card (“risky target”) resulted in the gain ofW——450 or the loss ofW——350,whereas the back of a card (“safe target”) resulted in thegain of W——150 or the loss of W——50. The optimal strategy thatwould maximize the expected income for the subject wasdifferent for these two tasks. During the matching penniesgame, the optimal strategy was to choose the risky target with0.2 probability, whereas during the two-armed bandit task, itwas to choose the risky target exclusively (see Experimentalprocedures). The overall probability that the subjects wouldchoose the risky target during thematching pennies game taskwas relatively close to the optimal value of 20% in bothschizophrenia patients and the normal controls, and thedifference between the two groups was not statisticallysignificant (Table 1). However, the probability of risky choicegradually approached this value during the course of the

Fig. 1 – Layout of the decision-making task. The task of the subject was to predict whether the computer opponent wouldchoose the front or the back of a card and to press a designated letter in a computer keyboard accordingly. After the subject'sresponse, the sides chosen by the subject and the computer were revealed simultaneously. The subject won or lost a certainamount of money depending on whether the two sides matched and which side was chosen by the subject.

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matching pennies game task (Fig. 2). During the first 500 trials,for example, the patients and the controls selected the riskytargetwith 0.236 and 0.224 probabilities, respectively, and bothof these values were significantly different from 0.2, t-test,p<.0001. By contrast, during the last 500 trials of the matching

Table 1 – Performance on decision-making tasks

Measure Matching pennies game task

Schizophrenia Normal control T

Money earned 48,020 (13,818) 69,575 (11,324) −P (risky target) .220 (.018) .211 (.010)P (win) .581 (.065) .600 (.066)P (win–risky target) .245 (.076) .317 (.098) −P (win–safe target) .678 (.106) .678 (.110)P (WSLS) .633 (.054) .612 (.064)P (WS) .759 (.030) .736 (.025)P (LS) .469 (.088) .436 (.086)P (WS–risky target) .291 (.104) .228 (.064)P (WS–safe target) .808 (.028) .802 (.015)P (LS–risky target) .778 (.075) .776 (.034)P (LS–safe target) .266 (.084) .231 (.034)Choice MI .013 (.018) .005 (.005)Choice–outcome MI .034 (.014) .015 (.010)

Data are reported as means (SD) unless otherwise indicated.P (risky target), probability of risky choice. P (win), probability of winninchoice. P (win–safe target), probability of winning with safe choice. P (WSLwin–stay strategy. P (LS), probability of lose–switch strategy. P (WS–riskytarget), probability of win–stay strategy after safe choice. P(LS–risky targtarget), probability of lose–switch strategy after safe choice. Choice MI,successive trials and the choice in the next trial. Choice–outcome MI, musuccessive trials and the subject's choice in the next trial.∗p<.05. ∗∗p<.01. ∗∗∗p<.001.

pennies game task, neither group displayed any significantdeviation from the equilibrium. We also tested a linearregression model that includes the block number as theindependent variable and the probability of choosing therisky target in each block as the dependent variable. The

Two-armed bandit task

score Schizophrenia Normal control T score

5.40∗∗∗ 61,900 (15,941) 65,950 (12,265) − .9011.852 .575 (.177) .641 (.128) −1.346− .923 .537 (.064) .553 (.049) − .9012.584∗ .694 (.015) .685 (.009) 2.1859∗.005 .327 (.018) .318 (.019) 1.415

1.114 .666 (.110) .640 (.077) .8422.657∗ .805 (.109) .757 (.112) 1.3721.195 .505 (.139) .485 (.078) .5562.342∗ .773 (.235) .765 (.159) .128.837 .727 (.210) .645 (.179) 1.325.100 .583 (.188) .430 (.166) 2.741∗∗

1.747 .527 (.188) .584 (.131) −1.1232.089∗ .078 (.053) .075 (.088) .1545.081∗∗∗ .212 (.099) .151 (.094) 1.986

g on average. P (win–risky target), probability of winning with riskyS), probability of win–stay–lose–switch strategy. P (WS), probability oftarget), probability of win–stay strategy after risky choice. P (WS–safeet), probability of lose–switch strategy after risky choice. P (LS–safemutual information between the subject's choice sequence in threetual information between the choice sequence of two players in two

Fig. 2 – Probability of choosing the risky target for individualsubjects in each block of 500 trials. The dotted horizontallines indicate the optimal strategy during the matchingpennies game task (blocks 1–3) or the probability that thecomputer would chose the risky target during the two-armedbandit task (block 4). Error bars: SEM.

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slope of this regressionmodel was significantly different fromzero (t-test, p<0.05) for both patient (−0.012) and control(−0.008) groups.

Following the introduction of the two-armed bandit task,the probability of selecting the risky target drasticallyincreased to 0.575 and 0.641 for the schizophrenia patientand the control groups, respectively (Table 1). Clearly, neithergroup of subjects behaved optimally during the two-armedbandit task, since the optimal strategy for this task was tochoose the risky target exclusively. Instead, the probability ofchoosing the risky target was relatively close to the probabilitythat such a choice would be rewarded, which is known asprobability matching (Estes, 1962).

If both players are playing optimally during the matchingpennies game task, namely, if they are at the Nash equili-brium, the expected value of income for the subject wouldbe W——50/trial. Therefore, for a subject playing optimally, theexpected total income would be W——75,000 for the matchingpennies game task. The average amount of money earnedduring the matching pennies game task was W——48,020 andW——69,575 for the patients and control subjects, respectively.Thus, although the overall probability of choosing the riskytarget did not differ significantly for the two groups, theschizophrenia patients on average earned significantly lessmoney during the matching pennies game task (Table 1).Interestingly, the overall probability of winning did not differsignificantly for the two groups during this task. However, theprobability of winning for the risky choice was significantlylower in the patient group. This suggests that the patientsmaybe impaired in organizing the temporal sequence of theirchoices appropriately, since the computer exploited thepredictability in the choice sequence of each subject duringthe matching pennies game task.

As in the matching pennies game task, the overallprobability of winning during the two-armed bandit task did

not differ for schizophrenia patients and normal controls.Further, there was no significant difference in the amount ofmoney earned between the groups. Nevertheless, schizophre-nia patients won more frequently with the risky choice thanthe control subjects (Table 1). Although this difference wasstatistically significant, this reflects a greater rate of coin-cidental hits in schizophrenia patients (i.e., type I error).

2.2. Randomness and serial correlation in choices

The fact that schizophrenia patients earned significantly lessmoney than the control subjects without a large difference inthe overall choice probability during the matching penniesgame task raises the possibility that patients might beimpaired in their ability to make their choices randomly. Forthe choice sequence in the matching pennies game task, theruns test rejected the null hypothesis for 7 out of 20schizophrenia patients as opposed to only 1 out of 20 nor-mal controls. This difference was statistically significant(χ2=5.625, p<.05), indicating that during the matching pen-nies game task, the choices of schizophrenia patients wereindeed less random compared to the control subjects. Incontrast, for the two-armed bandit task, the number ofsubjects for whom the null hypothesis was rejected increaseddrastically to 15 in schizophrenia patients and 17 in normalcontrols. This difference between the two groups was notsignificant (χ2= .625, p>.05). Thus, subjects in both groupsdisplayed less random behavior during the two-armed bandittask.

To measure more quantitatively the difference in predict-ability the subject's choice based on his/her recent choices, wecalculated mutual information between the subject's choicesequence in three successive trials and his/her choice in thenext trial. This choice mutual information was significantlyhigher for the schizophrenia patients than for the normalcontrol subjects (Table 1), indicating that compared to thecontrol subjects, the choices of schizophrenia patients couldbepredicted more reliably from their own previous responses. Inthe two-armed bandit task, the choice mutual informationincreased drastically in both groups and the differencesbetween two groups disappeared (Table 1).

It is a common strategy used in many decision-makingtasks to choose the same action when it was successful and toswitch to adifferent actionwhen itwasunsuccessful. Frequentuse of this so-called win–stay–lose–switch strategy would bedetrimental during a competitive game, since it can beexploited by the opponent. During the matching penniesgame task, the schizophrenia patients did not differ signifi-cantly from the control subjects in the overall probability ofwin–stay–lose–switch strategy (Table 1). However, the prob-ability of win–stay strategy was significantly higher in theschizophrenia group during the matching pennies game task(Table 1). Furthermore, theprobability ofwin–stay strategywashigher in the schizophrenia patients than the control subjectsonly after winning with the risky choice, but not after winningwith the safe target (Table 1). The patients on average selectedthe risky target again in 29.1% of the trials after choosing therisky target and winning, whereas the corresponding prob-ability in the control subject was 22.8% (Table 1). For theschizophreniapatients, this reduced theprobability ofwinning

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with a risky choice, since the repeated choice of the risky targetwould be predicted and exploited by the computer opponent.During the two-armed bandit task, the group difference in theprobability of win–stay strategy after the risky choice was notsignificant. Instead, the probability of lose–switch strategyafter the risky choice was significantly higher in the schizo-phrenia patients than in control subjects (Table 1).

We also quantified the difference in the extent to which thesubject's choices were influenced by the outcomes of theirprevious choices using the choice–outcome mutual informa-tion (see Experimental procedures). Consistent with thepattern of win–stay–lose–switch strategy described above,the choice–outcome mutual information was significantlyhigher for schizophrenia patients than normal controls duringthematching pennies game task (Table 1). This difference wasnot significant in the two-armed bandit task.

2.3. Cumulative effects of previous choices and theiroutcomes

We applied a logistic regression analysis to investigatewhether the choice in a given trial was influenced by thesubject's choices and their outcomes in previous trials. For theregression coefficients related to the subject's previous choicesin the matching pennies game task, a 2 (group)×10 (trial lag)ANOVA yielded significant main effects of group, F(1,38)=18.519, p<.001, and trial lag, F(9,38)=2.907, p<.05, but not asignificant interaction between group×trial lag, F(9,38)= .977,p>.05. The coefficients in the schizophrenia group were largerthan those of the control subjects in all the trial lags (Fig. 3, topleft), showing significant differences in trial lags 3 through 7.These results indicate that during thematching pennies game

Fig. 3 – Logistic regression coefficients related to thesubject's choices (top) and computer's choices (bottom) in thelogistic regressionmodel in the matching pennies game taskand the two-armed bandit task. Error bars: SEM. ∗p<0.05.

task, the schizophrenia patients tended to choose the sametarget as in theprevious trialsmore frequently than the controlsubjects. By contrast, the regression coefficients related to thesubject's previous choices in the two-armedbandit taskdidnotshow any significant main effects or interaction betweengroup×trial lag.

The regression coefficients related to the computer'schoices in the matching pennies game task did not show asignificantmain effect of group, but showed a significantmaineffect of trial lag, F(9,38)=12.243, p<.001, and a significantgroup×trial lag interaction, F(9,38)=6.339, p<.001. Unlike theresults from the control subjects, the regression coefficient inthe schizophrenia patients was maximal in trial lag 1 andbecamesmaller precipitously for trial lags greater than 2 (Fig. 3,bottom left), suggesting that compared to the control subjects,choices of the schizophrenia patients were more stronglyinfluenced by the most recent choice of the computeropponent and less influenced by more remote previouschoices of the computer. The regression coefficients relatedto the computer's choices in the two-armed bandit taskdisplayed a similar pattern. They showed a significant maineffect of trial lag, F(9,38)=43.561, p<.001, and a significantgroup×trial lag interaction, F(9,38)=3.242, p<.05. In sharpcontrast to the results in the matching pennies game task,the coefficient wasmaximal for trial lag 1 in both groups. As inthematchingpennies game task, the coefficient for trial lag 1 inthe schizophrenia patientswas significantly larger than that ofthe normal controls, suggesting that the choice of the schizo-phrenia patients tended to be more influenced by the mostrecent choice of the computer opponent, regardless ofwhetherchoices are made in a competitive setting or not.

2.4. Task performance and clinical symptoms

To test whether any of the decision-making strategiesexamined in our study was related to the negative symptomsin schizophrenia, we evaluated the clinical symptoms of thepatients with the Positive and Negative Syndrome Scale(PANSS; Kay et al., 1987). Correlation coefficient was calculatedbetween the PANSS Negative scores and each of the 14behavioral measures described above, and also between thePANSS Positive scores and each behavioral measure. The twoPANSS scores reflect the severity of negative symptoms (e.g.,blunted affect, social withdrawal) and positive symptoms (e.g.,hallucination, delusions), respectively. The only significantcorrelation was found between the negative symptom scoresand the choice mutual information in the matching penniesgame task (r=.484, p<.05). This significance, however, did notsurvive a Bonferroni correction for multiple comparisons. Inthe two-armed bandit task, none of the measures on thedecision-making task was correlated with either of the PANSSscore.

3. Discussion

3.1. Impaired decision making in schizophrenia

We found that schizophrenia patients showed impairmentsin their abilities to make decisions optimally in a competitive

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context. Compared to the normal control subjects, theschizophrenia patients earned less money during the match-ing pennies game task. Detailed analyses revealed that thechoices of the schizophrenia patients could be predictedmore reliably from their previous choices. In addition, theirchoices were more strongly influenced by the outcomes oftheir most recent choices. Both of these tendencies wereexploited by the computer opponent, and therefore weredetrimental to the performance of the patients. To ourknowledge, these results provide the first evidence thatschizophrenia patients are impaired in producing unpredict-able responses required in a competitive setting. The schizo-phrenia patients, however, did not display a general deficit indecision making, since they did not differ from the controlsubjects in their overall choice probabilities. The performanceof the schizophrenia patients during the two-armed bandittask was also comparable to that of normal control subjects,indicating that they successfully revised their decision-mak-ing strategies when the statistical properties of their environ-ment changed.

Our results suggest that during thematching pennies gametask, the schizophrenia patients were impaired in suppressingthe win–stay strategy sufficiently as required by the optimalstrategy. In addition, during the two-armed bandit task, theschizophrenia switched to the safe target more frequentlyafter losing money from the risky target compared to thecontrol subjects. Since both of these results point to a reducedability to suppress the default win–stay–lose–switch strategy,we can refer to it as strategic stiffness. However, it should beemphasized that schizophrenia patients did not always usethe win–stay or lose–switch strategies more frequently thanthe control subjects. Rather, schizophrenia patients wereparticularly impaired in their abilities to suppress the tendencytomake their choices according to such default strategies afterwinning or losing a large amount of money from the riskytarget. Therefore, impaired decision-making abilities of schi-zophrenia patients observed in the present study cannot befully accounted for by defective inhibitorymechanism that hasbeen proposed by studies examining executive dysfunction(Kiehl et al., 2000; Perlstein et al., 2003), anti-saccade dysfunc-tion (Manoachet al., 2002), andnegativeprimingdeficit (Park etal., 2002) in schizophrenia. Deficits of schizophrenia patientswere reflectednot only in the increased tendency to choose thesame target as in the previous trial according to the win–staystrategy, but also in the increased tendency to switch to theother target according to the lose–switch strategy. In addition,the patients were able to switch to a different strategy, whenthe contingencies changed in the two-armed bandit task.Therefore, it is difficult to attribute the deficits found in thisstudy to the set-switching problem that schizophreniapatients show in neuropsychological tests, such as theWisconsin Card Sorting Task (Pantelis et al., 1999). We alsofound that the randomness of choices in the schizophreniapatients was reduced compared to the control subjects, butonly in the matching pennies game task and therefore whensuch biaseswere indeed exploited by the opponent. Therefore,the schizophrenia patients were particularly impaired whenthey had to control their default strategies dynamicallyaccording to complex changes in the environmental contin-gencies, as is common in social interactions.

Previous studies have found that compared to the choicesof control subjects, the choices of schizophrenia patients weremore predictable based on the combined information of theprevious choices and their outcomes (Paulus et al., 2002, 2003).The present study provides two important additional findings.First, the schizophrenia patients displayed stronger depen-dence only on the choice of the computer opponent in theimmediately preceding trial and weaker dependence in theprevious trials. This suggests that the schizophrenia patientswere impaired in integrating the outcomes of choices over arelatively long period of time (Kennerley et al., 2006). Second,the schizophrenia patients demonstrated certain abilities ofadaptive decision making, when they were required tosuppress their dependency on the previous outcomes as inthe matching pennies game task, compared to when this wasnot necessary as in the two-armed bandit task. Generatingrandom behavior has been found to be difficult even fornormal adults (Bar-Hillel and Wagenaar, 1991; Tune, 1964a,b;Wagenaar, 1972). In addition, there is some evidence that thegeneration of random responses requires capacity-limitedcognitive resources (Baddeley et al., 1998; Rapoport andBudescu, 1997). Therefore, increased predictability in thetwo-armed bandit task suggests that schizophrenia patientsaswell as normal controls displayed cost-effective behavior bywithdrawing resources necessary to generate random beha-viors when they are not needed.

The results in the present study suggest that strategicstiffness of schizophrenia patients would make it difficult todiscover an optimal decision-making strategy, evenwhen theyare faced with important financial decisions. Combined withtheir tendency to make predictable choices that can beexploited by their competitors, this is likely to reduce theirabilities to gain profits and desirable social status. In additionto the cognitive deficits and psychotic symptoms that wouldhinder an individual with schizophrenia to hold a competitivejob, we propose that strategic stiffness and predictable choicesin competitive situationswould also contribute to the patient'ssocial maladjustment and low socioeconomic status (Amer-ican Psychiatric Association, 1994; Carson, 1984; Davidsonet al., 1999; Hollingshead and Redlich, 1958). The present studyrelied on the comparison of two simple computerized deci-sion-making tasks. In real life, however, the process of sociallyinteractive decision making is likely to rely on a variety ofperceptual cues, such as facial expressions, and to interactwith other cognitive processes, such as theory of mind (Lee,2006). Therefore, impaired abilities of decision making ob-served in the present studymight be exacerbated in real life tothe extent that these additional perceptual and cognitivecapacities are also compromised in schizophrenia (Brune,2005; Kee et al., 2003).

3.2. Implications for prefrontal dysfunctions inschizophrenia

The process of decision making relies on a broad network ofcortical and subcortical regions (see Lee, 2006), including theprefrontal cortex (Barraclough et al., 2004; Bechara et al., 2000)and the posterior parietal cortex (Paulus et al., 2001, 2002;Sugrue et al., 2004). Although the altered pattern of choicesfound in the schizophrenia patients might result from

Table 2 – Descriptive statistics of the participants

Schizophreniapatients

Normalcontrols

Sample size 20 20AgeMean 36.10 (9.41) 39.05 (11.87)Range 17–52 18–55

Gender (male : female) 8:12 7:13Education (years) 12.05 (2.89) 11.60 (2.94)K-WAIS Informationsubscale scorea

10.37 (1.98) 9.60 (2.35)

K-WAIS Vocabularysubscale scoreb

11.28 (2.32) 10.10 (2.79)

K-WAIS Block Designsubscale scorec

9.47 (2.43) 10.20 (3.04)

Data are reported as means (SD) unless otherwise indicated. Thescores of the K-WAIS subtests were all age-appropriate stan-dardized scores.aData were missing for 1 patient (N=19).bData were missing for 2 patients (N=18).cData were missing for 3 patients (N=17).

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disruptions in multiple areas, the dorsolateral prefrontalcortex (DLPFC) might play an important role in adaptivedecision making. First, evidence from several PET and TMSstudies has suggested that the DLPFC contributes to thegeneration of random responses by suppressing dominant,but inappropriate responses (Brown et al., 1998; Jahanshahi etal., 1998, 2000). Second, neurophysiological recordings fromthe DLPFC of monkeys making choices in a competitive gamedemonstrated that some neurons in the DLPFC displayedmodulations in their activity according to a specific combina-tion of the animal's choice and its outcome in the previoustrial, providing key information necessary to control a win–stay–lose–switch strategy (Barraclough et al., 2004; Seo et al.,2007). Third, DLPFC pathology and dysfunction observed inschizophrenia (Bunney and Bunney, 2000; Gold and Harvey,1993; Goldman-Rakic and Selemon, 1997; Pierri et al., 1999;Selemon and Goldman-Rakic, 1999; Shenton et al., 2001) alsolay down the grounds for future studies to investigate the roleof DLPFC in strategic decision-making impairment. Forexample, the strong dependence on the most recent outcomeof the choice in the schizophrenia patientsmight be due to thereduced working memory capacity.

It should be noted that there are some limitations in thepresent study. First, since all our patients were stabilized onatypical antipsychotic drugs, the relatively normal perfor-mance of schizophrenia patients in some aspects of thedecision-making task observed in our study may be due tothe ameliorating effects of these drugs on cognitive functions,such as executive functions andworkingmemory (Bilder et al.,2002; Kasper and Resinger, 2003). Second, the size of thesample was relatively small, andmay have also contributed tonegative findings on some of the comparisons. Future studieswith larger sample size and with patients on typical anti-psychotic medication or medication-free patients would benecessary to test these possibilities.

4. Experimental procedures

4.1. Participants

Twenty schizophrenia patients and 20 normal control subjectsparticipated in the study. Table 2 shows the characteristics ofthe two groups. Informed consents were obtained from allparticipants prior to their participation in the study, and smallhonorarium were paid. The patients were recruited frompublic hospitals located in Seoul, Korea, where they werehospitalized. The diagnosis of schizophrenia was establishedusing the Structured Clinical Interview for DSM-IV (SCID-IP;First et al., 1997) and a comprehensive review of medicalrecords. Patients were excluded if they had current diagnosesor histories of mood disorders or substance abuse disorders.Nineteen patients were taking stable dosages of atypicalantipsychotics, such as clozapine, amisulpride, olanzapine,zotepine, quetiapine, risperidone and aripiprazole, and onepatient was taking a typical antipsychotic medication, halo-peridol, in addition to an atypical medication.

All 20 patientswere administered the Positive andNegativeSyndrome Scale (PANSS; Kay et al., 1987) to assess theirpsychiatric symptoms in terms of the positive symptoms

(e.g., hallucination, conceptual disorganization, delusion) andthe negative symptoms (e.g., blunted affect, social withdrawal,catatonia or stereotyped behavior). The mean total PANSSscore for the schizophrenia group was 78.05 (SD=17.98). Themean subscale scores were 22.75 (SD=9.71) for the positivescale, 17.6 (SD=8.79) for the negative scale, and 37.7 (SD=8.22)for the general psychopathology scale. The average duration ofthe illness for these patients was 11.55 years (SD=7.74).

The control subjects were recruited from the local commu-nity. Their demographic information, current status andhistory of psychiatric and other medical illnesses, and familyhistory of psychiatric illnesses were obtained by an interviewusing the Study Participant's Information Sheet that isroutinely used in the Clinical Neuroscience Lab at SeoulNational University. The exclusion criteria for the controlsubjects were: (1) a current diagnosis or a history of Axis Ipsychiatric disorder; (2) a current diagnosis or a history of aneurological condition including a head injurywith significantloss of consciousness (more than 5 min); (3) debilitatingmedical condition that could compromise the cognitiveperformance; and (4) a family history (first degree) of Axis Ipsychiatric disorder.

The control subjects did not differ significantly from thepatients in terms of age, t(38)=− .871, p>.05, gender, χ2(1)=.107, p>.05, years of education completed, t(38)= .488, p>.05,or intelligence as measured with the Korean version of theWechsler Adult Intelligence Scale–Revised (K-WAIS; Yeomet al., 1992; Wechsler, 1981) using the short form consistingof two verbal subscales and one performance subscale, theInformation, t(37)=1.102, p>.05, the Vocabulary, t(36)=1.406,p>.05, and the Block Design, t(35)=− .797, p>.05.

4.2. Stimuli and tasks

The experimental protocol began with the administration ofthe clinical interviews, the SCID and the PANSS, for theschizophrenia patients. After a break, they performed the

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decision-making tasks, which were followed by the adminis-tration of the short-form of the Korean-Wechsler AdultIntelligence Scale (K-WAIS; Yeom et al., 1992; Wechsler,1981). For the control subjects, we first conducted a screeninginterview using the Study Participant's Information Sheet.Patients and control subjects followed the same procedures toperform the decision-making tasks described below.

4.2.1. Stochastic decision-making taskSubjects were instructed to play a card game (Fig. 1) against acomputer, and to try to win as much money as possible. Eachsubject completed a total of 2000 trials. During the first 1500trials, subjects played a matching pennies game, whereasduring the remaining 500 trials, they performed a control taskreferred to as the two-armed bandit task. In analogy to a one-armed bandit, a two-armed bandit refers to the problem ofchoosing between two actions that are rewarded indepen-dently with two different probabilities. At the beginning of theexperiment, the faces of two ace cards were shown along themidline on a computer screen. The top card would subse-quently correspond to the choice of the computer opponentand the bottom card would correspond to the subject's choice.Subjects were told to predict whether the computer wouldchoose the face or the back of the card in each trial with a keypress. Subjects won money if they correctly predicted thecomputer's choice, and lost money otherwise. Subjects werealso told that the computer opponent would not choose atarget according to a predetermined schedule, but ratherwould attempt to predict the choice of the subject and choosethe opposite target as a human opponent would in acompetitive game. If the subject selected the face of the card,theywouldeitherwinW——450 (approximatelyUS50 cents) or loseW——350 depending on whether their choice matched thecomputer's or not. By contrast, if the subject selected theback of the card, they could either winW——150 or loseW——50, againdepending on whether the choice matched the computer's ornot. The payoffs of the two available choices were described tothe subjects before the experiment, and remained displayedthroughout the experiment, with the face and back of the cardshown on the left and right of the computer screen, respec-tively (Fig. 1). The face of the card is referred to as a “risky”target, and the back a “safe” target, since choosing the face canresult in a larger gain or larger loss compared to choosing theback.

At the beginning of the experiment, each subject startedwith a balance of W——10,000 (approximately US $10) and wasinformed that he or she would receive 10% of the entirebalance in cash at the end of the experiment. Immediatelyafter the subject responded, the two targets chosen by thesubject and computer were shown simultaneously along themidline either with a fanfare sound for a correct prediction orwith a pinging sound for an incorrect prediction. Thecumulative amount of money earned was shown at thebottom of the computer screen (Fig. 1). The display for thenext trial appeared one second after the subject's response inthe previous trial. The subjects responded at their own pace,and the response time was not measured. A break of tenseconds was given after every 100 trials, and a mandatorybreak of 5 min was given after every 500 trials, but thesubjects were allowed to take longer breaks if necessary.

Depending on the duration of the breaks taken by thesubjects, the entire experiment lasted approximately between60 and 135 min.

During the first 1500 trials, in which the computersimulated the matching pennies game, the computerexploited any systematic biases in the subject's choice andpayoff sequence in order to predict the subject's next choiceand minimize the subject's payoff (Barraclough et al., 2004;Lee et al., 2004). This implies that choosing one of the twooptions exclusively during this task is not an optimal strategy.How often the subjects should choose each target in order tomaximize their payoffs is determined by the specific payoffsassociated with different options. Formally, a set of strategiesfor all the players is defined as the Nash equilibrium, whennone of the players can increase his or her payoff by adoptingany other strategy (Nash, 1950). For the matching penniesgame used in the present study, the Nash equilibriumcorresponds to the subject choosing the risky and safe targetswith 20% and 80% probabilities, respectively, and the compu-ter choosing the two targets with equal probabilities. Denotingthe probability that the subject chooses the risky target as p,the expected payoff for the computer is [−450p+50(1−p)] if itchooses the risky target, and [350p−150(1−p)] if it chooses thesafe target. These two values become identical for p=0.2.Therefore, if the subject chose the risky target more fre-quently than 20% probability, the computer would maximizeits payoff by choosing the safe target exclusively, and thiswould reduce the payoff for the subject. Similarly, if thesubject chose the safe target more frequently than 80%probability, the computer would always choose the riskytarget. Similar reasoning shows that when the subject chosethe risky target with 20% probability, the computer shouldchoose the two targets with equal probabilities to maximizeits payoff, because any other strategy of the computer couldbe exploited by the subject.

To determine whether the subject's choice behaviordeviated from this equilibrium prediction, the computersaved the entire choice and payoff history of each subject. Atthe beginning of each trial, the computer then used thisinformation to test a series of null hypotheses that the subjectwould select the risky targetwith the conditional probability of0.2, given his/her choices and payoffs during the previous Ntrials (N=0 to 4). If none of these null hypotheses were rejected(binomial test, p<0.05), it was assumed that the subject wasplaying optimally, and the computer selected the two targetswith equal probabilities. If one or more null hypotheses wererejected, then the computer made its choice by exploiting thesubject according to the conditional probability that wassignificantly different and maximally deviated from theoptimal strategy. For example, if the value of this conditionalprobability indicated that the subject would choose the riskytarget more frequently than a 0.2 probability, then thecomputer would choose the safe target.

During the last 500 trials, the computer selected the riskyand the safe target randomly with 70% and 30% probabilities,regardless of the choices made by the subject previously.Therefore, stochastic responses required in the matchingpennies game task were no longer necessary. Instead, theoptimal strategy for the subject in this two-armed bandit taskwas to choose the risky target exclusively. The subjects were

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not informed of the transition from the matching penniesgame task to the two-armed bandit task.

4.2.2. Behavioral measuresThe following variables were recorded during the decision-making task: (1) the target selected by the subject; (2) the targetselected by the computer; and (3) the outcome of the subject'schoice (win or lose). As described in the Results, there was alarge and significant difference in the total amount of moneyearned between the patient and control groups. Therefore, toinvestigate the source of this difference, in addition to (1) thetotal money earned, we examined the following behavioralmeasures: (2) the probability of choosing the risky target; (3)the overall probability of winning; (4) the probability ofwinning with the risky target; and (5) the probability ofwinning with the safe target. We also measured the extentto which the subject's choice depended on the outcome of hisor her previous choice by calculating (6) the probability ofusing the win–stay–lose–switch strategy, i.e., choosing thesame target chosen by the computer in the previous trial. Inaddition, we also measured (7) the probability of using thewin–stay strategy, namely choosing the same target againafter winning the money in the previous trial; (8) theprobability of using the lose–switch strategy, namely switch-ing to the other target after losing the money in the previoustrial; (9) the probability of using win–stay strategy after a riskychoice; (10) the probability of using win–stay strategy after asafe choice; (11) the probability of using lose–switch strategyafter a risky choice; and (12) the probability of using lose–switch strategy after a safe choice.

To quantify the randomness in the subject's choicesequence, two additional measures based on informationtheory (Cover and Thomas, 1991) were obtained. In informa-tion theory, statistical dependence between two randomvariables is quantified by mutual information. For two binaryrandom variables that are equally likely to take the twoalternative values, mutual information would be 0 bit, if theyare completely independent, and 1 bit if the twoare completelycorrelated. To quantify the extent towhich the subject's choicein a given trial dependedonhis or her previous choices,we firstestimated (13) the mutual information between the subject'schoice sequence in three successive trials and the choice in thenext trial. We refer to this as choice mutual information.Second, we also measured (14) the mutual informationbetween the choice sequence of the two players in twosuccessive trials and the subject's choice in the next trial.This measures the extent to which the subject's choice in agiven trial depends on his or her previous choices and theiroutcomes (Lee et al., 2004). Therefore, we refer to this aschoice–outcome mutual information. Estimates of mutualinformation are biased when they are calculated from alimited amount of data, and this bias was corrected as in theprevious study (Lee et al., 2004; Miller, 1955).

4.2.3. Statistical analysisThe statistical significance of the difference in each of themeasures from (1) to (14) mentioned above between theschizophrenia and the normal control groups was determinedwith a t-test. The runs test (Bradley, 1968) was also performedto test the hypothesis that each player made their choices

randomly. The statistical significance of the differencebetween the two groups in the number of subjects for whomthe null hypothesis was rejected was determined with a χ2-test. The possibility that the subject's choice in a given trialmight be influenced by his or her own choices or thecomputer's choices in the previous ten trials was tested witha logistic regression model (Lee et al., 2004). In this analysis, apositive regression coefficient for a given trial lag quantifiesthe extent to which the subject is more likely to choose thesame target selected by himself/herself or the computer acertain number of trials before the current trial. One of theregression coefficients related to a patient's choice in the two-armedbandit taskhadanunusually largenegative value in onepatient (−31.5), and therefore was removed from the analysisas an outlier, and treated as a missing value in the remaininganalyses. A 2 (group)×10 (trial lag) repeated-measures ANOVAwas performed to test whether the interaction between thesetwo factors was significant, namely, whether the differencebetween the two groups varies with the trial lag. To determinewhether specific impairments in decision making werecorrelated with the positive or negative scores of the PANSSin the schizophrenia patients, correlation coefficients werecalculated between the subscale scores of the PANSS and eachof the 14 behavioral measures described above. The statisticalanalyses were carried out with the SPSS 11.5 (SPSS Inc., IL) andthe Matlab 7.0 (MathWorks Inc., MA).

Acknowledgments

We would like to express our gratitude to the two anonymousreviewerswhogavehelpful suggestions, Drs. Sohee Park, GillianO'Driscoll, and Cheongtag Kim, and Jongan Choi for theirconstructive discussions, and toHanaKim, Jungmi Lee, SooyeonSa, and Yukyung Lee for their assistance in collecting the data.This research was supported by a grant (#M103KV010021-03K2201-02130) from the Brain Research Center of the 21stCentury Frontier Research Program funded by the Ministry ofScience and Technology of Republic of Korea.

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