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The 10 numbers are the choices of either 10 human participants human condition or of one participant and a computer program who chooses uniform randomly 9 numbers from 0 to100 computer condition. The losers got nothing. All this is known to the participants. There were 13 different parameter multipliers. Each multiplier was presented once in each condition in a pseudorandom order.

In a control condition random condition the participants were asked to pronounce a random number between 0 and 100. In the calculation task session 2 subjects were asked to calculate the product between one C1 condition or 2 factors C2 condition times a number, and additionally a random condition. B Game theoretic prediction for M 2 3 If all participants are rational and know that everybody else is rational and so on common knowledge of rationality then everybody should choose 0, because no one should choose 100 2 3 66 weakly dominated choices ; thus all numbers in E 0 are eliminated.

In the reduced game nobody should choose 100 2 3 2 44, thus eliminating E 1and so on until 0 is reached. If M 1 then all players choosing 100 also represents an equilibrium. C Bounded rational model. Cognitive hierarchy for M 2 3 is a cognitively and descriptively more plausible model 17. A random player level 0 L 0 chooses uniformly from 0 to 100 with an average of 50.

A best reply to this is 50 2 3 33 level 1. If everybody chooses 33 then best reply is 50 2 3 2 22 level 2etc. A subject is strategic of degree k if he chooses the number 50 M kcalled level k. Game theory suggests a process of iterated elimination of weakly dominated strategies, which in infinite steps reaches the unique Nash equilibrium in which everybody chooses 0 Fig.

However, the natural way of looking at game situations is not based on circular concepts as for the Nash equilibrium but rather on a step by step reasoning procedure ref. 421which typically results in out-of-equilibrium behavior. This step-reasoning can be some finite steps of the iterated elimination process Fig. 1 B or of the so-called iterated best reply, a cognitive hierarchy of thinking that better describes behavior in our game Fig.

In our game, this means that a naïve player level 0 chooses randomly. A level 1 player thinks of others as level 0 reasoning and chooses 33 2 3 50because 50 is the average of randomly chosen numbers from 0 to 100. A more sophisticated player level 2 supposes that everybody thinks like a level 1 player and therefore he chooses 22 2 3 2 50. And, as Keynes mentioned there might eventually be people reaching the Nash equilibrium of the game and thereby choosing 0.

Choices in many Beauty Contest experimental games 17, 19 21but also in other games 16, 18show limited steps of reasoning, a bounded rational behavior, confirming the relevance of the iterated best-reply model see SI Text SI1. Why do people use different and limited numbers of steps of reasoning. As the number of steps of thinking increases, the decision rule requires more computation, and higher level reasoning indicates more strategic behavior paired with the belief that the other players are also more strategic 16.

One reason for the limited steps of reasoning is that players might be incapable of using high levels of reasoning because of cognitive limitations 22 ; another reason is that a player might believe overconfidently 23 that others will not use as many steps of thinking as he does. Identifying the neural correlates of different levels of reasoning and, more specifically, being able to distinguish between low- versus high-level reasoning people by their brain activity will help to explain the heterogeneity observed in human strategic behavior.

We used functional MRI fMRI to measure brain activity when subjects participated in the Beauty Contest game. We introduced 2 main conditions in an event-related fashion Fig. In the human condition, each participant in a group of 10 was asked to choose an integer between 0 and 100. In the computer condition one participant chose one number between 0 and 100 and a computer algorithm chose uniform randomly and independently of the multiplier parameter 9 numbers between 0 and 100.

The prize for the winner, whose number was closest to M e.M 2 3 times the average of all choices, was 10 euros in both conditions or a split of the prize in the case of a tie. We did not provide any feedback between trials. The computer condition should invoke low levels of reasoning at or near level 1 according to the iterative reply model.

In contrast, in the human condition a greater variety of levels of reasoning should be observed because players might have different ideas about what other players choose. To identify brain activity related to the mental calculation most likely used when deciding in the game, we introduced calculation tasks in which subjects were asked to multiply a given parameter or the square of a parameter with a given integer.

Behavioral Results. Reaction time was quite different in the different conditions of the Beauty Contest. Subjects took longer when choosing a number in the human mean 8. 6 compared with the computer condition mean 7. 6; Wilcoxon signed-rank test, z 2. 03, two-tailed. In both conditions, choosing took more time than in a control condition when they were asked to pick a random number between 0 and 100 mean 2.

07 for both human vs. random and computer vs. random signed-rank tests, z 3. 92, P kwhere k is the number of levels Fig. 1 Cand very seldom by the game theoretic solution 0 for M 1 see SI Text SI2. Most choices in the human condition were between L1 50 M and L3 iq option b M 3only 5 were higher than level 3. We measured the level of reasoning using the quadratic distance between actual choices and the different theoretical values L1, L2, L3, etc. based on the Cognitive Hierarchy model see Methods.

We categorized each player according to 3 categories based on choices in the human condition random behavior and low level level 1 and high level of reasoning level 2 or higher. The subjects classified as low level n 10 behaved similarly against the computer or the humans, at or close to level 1 in both conditions Wilcoxon signed-rank test of the mean quadratic distance between actual choices and theoretical L1 across all trials for each subject in human vs.

computer condition, z 0. The high-level reasoning subjects n 7 differentiated their behavior in the human compared with the computer condition signed-rank test of the mean quadratic distance between actual choices and theoretical L1 across all trials for each subject in human vs. computer condition, z 2. They behaved as level 1 in the computer condition but were classified at a higher level of reasoning level 2 or more when interacting with human counterparts.

Direct comparison between the 2 groups confirms that high reasoners have a significantly smaller quadratic distance between their actual choices and the theoretical level 2 or higher compared with low reasoners Two-sample Wilcoxon rank-sum Mann Whitney test, z 3. 0013 see SI Text SI3. Three subjects behaved in a quite random fashion.

2 A shows the behavior, separately for each condition and for all parameter values, of 2 representative subjects individual behavior of all of the subjects is shown in Fig. In the computer condition, both subjects chose numbers close to or on the level 1 line 50 M, were M is the multiplier parameter. In the human condition, the low-level subject typically chose near the level 1 line, whereas the high-level subject chose near or at the level 2 line 50 M 2 or near or at a higher level.

Patterns of behavior and brain activity for low and high levels of reasoning. A Behavioral results. Here, we present the 26 choices of 2 representative participants for each parameter value M in the human blue dots and computer triangles conditions, separately. Left the choices of one participant representing a so-called low-level type.

In both the computer condition triangles and the human condition blue dots he chose near the theoretical Cognitive Hierarchy Model level 1 line brown line with choices equal to 50 M. Right the choices of one high-level type participant. In the computer condition he chose near the theoretical level 1 line. In the human condition he chose near the theoretical level 2 line blue line with choices equal to 50 M 2.

Below We plot the choice of the 2 participants for the computer and human conditions for M 2 3. In total we classified 10 participants as level 1 low level and 7 as greater than level 1 high level. Three participants played in a random manner. B fMRI results. Group data thresholded at P 0. Choosing a number in the human condition in contrast to the computer condition was associated with relative enhanced activity in the rostral anterior cingulate cortex Left Low level of reasoning subjects, random effect analysis n 10 rACC, MNI coordinates x 9, y 36, z 3 ; and Right high level of reasoning subjects, random effect analysis n 7 activity in the dorsal portion of the medial prefrontal cortex mPFC, MNI coordinates x 3, y 48, z 24 and ventral mPFC relatively less deactivated, MNI coordinates x 3, y 51, z 9.

5 with accuracy number of correct responses in the calculation task; thus it is independent of computation skills. Notably, no other brain region of interest was correlated with strategic IQ. Activity in the dorsal portion of the medial prefrontal cortex related to play against human opponents mPFC, MNI coordinates x 0, y 48, z 24; the mean parameter estimates for each participant were extracted from the functional ROI obtained from the random effect analysis human vs.

computer, n 20 was correlated with a measure of strategic IQ the quadratic distance of choices to the winning numbers using a recombinant estimation method. Values closer to 0 indicate higher strategic IQ. Note red dots and blue dots indicate high and low level of reasoning participants, respectively; participants who played in a random manner are excluded from the figure.

In the experimental Beauty Contest game, levels of reasoning are not induced unlike the tasks used by 26, 43. Therefore, we could detect heterogeneity between subjects based on their own choice of depth of reasoning. We provide a computational account Cognitive Hierarchy Theory; refs. 16 18 of the cognitive processing underlying actual choices in the experimental game, to identify the neural substrates of different levels of strategic thinking.

We found that playing against human opponents versus a computer programmed to play randomly in the Beauty Contest game activated areas commonly associated with theory of mind or mentalizing thinking about other people s minds mPFC, STS, posterior cingulate cortex, and TPJ 3, 5, 6, 24, 25suggesting that these areas encode the complexity underlying human interactive situations. Within this network, the mPFC was the only area that clearly dissociated between subjects with different levels of strategic reasoning.

The mPFC activity peak MNI coordinates, x 0, y 48, z 24 differed in the human versus computer opponent conditions for high reasoning players only Fig. Furthermore, in the human condition, this area was more active for high than low reasoners. Thus, we argue that mPFC implements more strategic thinking about other players thoughts and behavior. We also found that, unlike the mPFC, TPJ and STS mediated activity when playing against humans for both low and high-level reasoners.

This suggests that the TPJ and STS have a more general function in the recognition of social cues or in the ascription of generic features of human-human interaction 44. Strategic IQ and medial prefrontal cortex. An additional insight into the role of the mPFC in social-cognitive processing is provided by the analysis of our measure of Strategic IQ related to winning in the game.

We found a strong correlation between mPFC activity and Strategic IQ. This suggests that the mPFC activity, involved in higher reasoning about others, leads to successful outcomes in our social setting. This is a new finding in the theory of mind literature, thus providing evidence for the fundamental role of the mPFC in successful mentalizing. Notably, the focus of activity in the mPFC peak MNI coordinates, x 0, y 48, z 24; related to higher level of reasoning in our game coincides with the focus of activity related to degree of thinking about how our own behavior can influence others behavior, as reported in a recent study 45.

45 activity in the mPFC was found when contrasting 2 dynamic models of choice in a repeated competitive game. In the study by Hampton et al. One model is based on updating own strategy based on other s past choices and giving best response to the frequency play of actual behavior. A second, more sophisticated model assumes that subjects consider the influence that their own past choices will have on what other players will do next.

The difference is analogous to the difference in the Beauty Contest game between high and low levels of strategic reasoning. Indeed, high-level reasoning in the Beauty Contest game implies thinking about how other players think about the others including your own thinking and behavior, and so on. In other words, high reasoners might assume that their behavior likely affects the behavior of others, thus inducing a process of iterative thinking.

Thus, we argue that mPFC encoding of the effect of our choices on others thoughts and behavior is the neural signature of high-level strategic reasoning level 2 or more. 45 and our study is that in Hampton s study subjects observed others behavior over time and then responded to it, whereas in our study the decisions required that subjects model and predict others choices without knowing other players past choices. The brain does not seem to distinguish between these 2 data sources.

Taken together, the results of these 2 studies represent the first neural evidence of a close link between adaptive learning and levels of reasoning. The pattern of brain activity that is, higher activity for high-reasoning players in the caudolateral orbitofrontal cortex and in the dorsolateral prefrontal cortex, areas commonly associated with complex cognitive processing 33 35together with the mPFC, suggests a substantial jump in complexity beyond the mere calculation required by the decision rule of the Beauty Contest game, as suggested by the fact that there was no activity in these areas related to the mental calculation in the control tasks, C1 and C2 when going from the first to the second level of reasoning.

This might be responsible for the observed limited step-level reasoning, either because subjects are not able to make this jump or because they believe that not everybody else is able to make this jump. Game theory predicts equilibrium play, assuming common knowledge of rationality everybody is rational and thinks that everybody else is rational and so on. However, actual behavior deviates from equilibrium and is heterogeneous given different beliefs about others.

Our work shows that the common tendency for humans to use boundedly rational strategies cognitive hierarchies is reflected in specialized neural substrates, such as the medial prefrontal cortex. The main difference between Hampton et al. Twenty healthy right-handed subjects 11 females were recruited to take part in a study at the Neuroimaging Center of the Insitut des Sciences Cognitives Bron, Lyon, France.

Volunteers gave fully informed consent for the project which was approved by the French National Ethical Committee Comité Consultatif de Protection des Personnes dans la Recherche Biomédicale. Each participant was screened to exclude medication and conditions including psychological or physical illness or history of head injury. Mean age of participants was 26 years 4. Experimental Design and Task.

Each participant underwent fMRI scanning while performing a total of 99 trials of the experimental tasks first session of 26 trials of the Beauty Contest game plus 13 random choices and a second session of 60 trials of a mental calculation task including 12 random choices. During scanning, the subject viewed a projection of a computer screen see Fig. 1 A and gave a spoken response in each trial. The Beauty Contest game session 1 consisted of guessing an integer number between 0 and 100 both limits includedin which the winner is the person whose number is closest to M average of all chosen numbers.

M is the known multiplier parameter in a trial which takes 6 values with M 1 9 8, 6 5, 4 3, 3 2, 5 3, 7 4. We also include M 1, which is a control, whether the thought process started at or 50. However, level 1 and level 2 cannot be distinguished for M 1. The winner received 10 euros. If there was a tie, the 10 euros were split between those who tied. Information about the results of the game was provided at the payment stage see below. The first session consisted of 3 different conditions i human condition, in which a subject knew that he was playing against 9 other subjects who were under exactly the same conditions as himself but at a different scheduled time 13 trials ; ii computer condition, in which the subject was informed that a computer program randomly draws 9 numbers 13 trials ; and iii a random condition, in which the subject was asked to choose a number at random between 0 and 100 13 trials.

Each value of the parameter M was presented twice, once in the human and a second time in the computer condition. The calculation tasks session 2 were of the form N M 24 trials or N M M 24 trialswhere N is a 2 digit number and M is a multiplier from the set mentioned above, excluding M 1. Each product was mentioned twice with the same M but different N.

We also asked for a random number as a control 12 trials. For each correct calculation task a subject received 50 euro cents. A correct answer had to be within a 1 deviation of the up or down rounded result, e. We used an event-related design, mixing the 3 main conditions.a result of 54. 33 produced a winning interval from 53 to 56. The calculation task was always presented after the Beauty Contest game to avoid behavioral biases. The participants were informed and instructed about the calculation task just before it began.

Time Course of the Experimental Tasks. On each trial of the Beauty Contest game session 1 the subject viewed an information screen 2 seconds indicating the type of condition human, computer, or randomthe formula of the target number with the information about the value of the parameter multiplier M with the exception of the random conditionand the question to choose a number between 0 and 100. After pressing the button the subjects had 2 seconds to say a number.

After 2 seconds, the message press the button when ready appeared in the bottom of the screen. There was an intertrial interval of 4 8 s jittered. In the calculation task session 2 the subjects viewed an information screen 2 seconds with the indication of the factor s and the number digit they had to multiply. They were asked to give an answer with a maximum of 10 s.

The message say a number appeared right after they pressed the button, or automatically after the time limit 10 s. Stimuli Presentation. Behavioral responses were logged by means of a desktop computer located outside the scanner running Presentation Neurobehavioral Systems, Inc. stimulus delivery and experimental control software system for neuroscience. At the end of the scanning subjects had to fill in a questionnaire with the following questions.

i Please comment on your first choice. M 2 3 in the human condition. ii Please comment on your choice when M 1 4 in the computer condition. iii Did you have a general rule for the trials in the human condition. iv Did you have a general rule for the trials in the computer condition. Notably, the subjects responses on the questionnaire were very consistent with their pattern of choice see SI Text SI4. Participants were financially motivated. Each subject received a 50 euro show-up fee at the end of the experiment.

Once 10 subjects had been scanned, we sent them an e-mail message with a table of their own choices and the choices of their coplayers preserving anonymity. For each subject, we summed up the winning amount of each trial according to the rules of the game mentioned above. A transfer of the money they won was sent to their bank account. Statistical Analysis of Behavioral Data Behavioral Types.

We categorized each player according to 3 categories based on choices in the human condition random behavior, low level level 1and high-level reasoning level 2 or higher. To measure the level of reasoning of a subject we did the following i we calculated for each trial of the Beauty Contest game the quadratic distance QD between actual choice and the different theoretical level k values L1, L2, L3,according to the Cognitive Hierarchy model Fig.

1 C where x ijM is the choice of participant i in condition j either human or computer in trial with parameter M; k is level k with k 1, 2, 3. ii We determined the minimum distance and the corresponding level k within each trial. For example, a choice of 24 for M 2 3, has is minimum QD for k 2 i.QD1 24 50 2 3 2 87, QD2 24 50 2 3 2 2 4, QD3 24 50 2 3 3 2 84,thus we classified this choice as level 2.

iii Iq option b the human condition, we counted how many times out of 12 M-parameters, thus without M 1, which is not predictive of level of reasoning a player was identified by one of the above-mentioned levels k of reasoning. We categorized a player as high level if at least 7 of 12 cases in the human condition were identified as level 2 or higher.

Players that did not belong to any of these categories were classified as random players. iv We categorized a player as low level if at least 7 of 12 cases in the human condition were identified as level 1. We used the mean quadratic distance between actual choices and one theoretical type e.L1 or L2 across all trials for each subject to test for behavioral differences between conditions human vs.

computer and types high vs. lowas reported in the results section. Strategic IQ. We define strategic IQ as the subject s ability to guess a number that could potentially win against a large population of opponents. We considered all of the possible combinations of 9 choices out of all 19 opponents choices human condition a player can be matched with we followed the recombinant estimation method 46, 47.

For each subject, we calculated i the winning number for each combination of choices including the considered subject s choice per trial; ii the quadratic distance of a subject s choice to the winning number of every combination per trial; iii the average quadratic distance across all of the possible combinations and all trials of a subject plotted in Fig. fMRI Data Acquisition, Preprocessing and Statistical Analysis.

Subjects were scanned using a 1. 5T MRI scanner Siemens Magnetom Sonata with an 8 channel head coil performing the experimental task over 2 sessions. T2-weighted echoplanar images, optimized for blood oxygenation level-dependent BOLD contrast, were acquired. Each volume comprised 26 slices acquired continuously over 2. 5 s TE 60 ms; interleaved acquisition; slice thickness 4 mm; 0.

4 mm noncontiguous; parallel to the subject s anterior posterior axis; in plane resolution 3. 44 mm 2 ; matrix size 64 64allowing for complete brain coverage. Additionally, a T1-weighted image was acquired at the end of each experiment. Head motions were minimized by the use of foam padding. Headphones and ear-plugs were used to dampen the scanner noise. We used an MRI-compatible microphone for recording voice responses.

html on a Matlab platform. Images were initially realigned to correct for motion artifacts. Differences in the timing of images slices across each individual volume were corrected, and each volume was transformed into standard stereotaxic space and smoothed with a Gaussian filter full-width half-maximum 8 mm.

Voxel-wise differences in BOLD contrast within the smoothed normalized images resulting from the different task conditions and trial types were examined using SPM. Standard neuroimaging methods using the general linear model were used with the first level individual subject analyses providing contrasts for group effects analyzed at the second level. Choice-related neural activity at the time of choice was studied during the epoch between trial onset and subject response self-paced button-press before pronouncing a number.

The intertrial intervals were jittered using an optimal signal-to-noise function 48, 49. Choice trials were partitioned according to whether the subject was in the human, computer, or random condition of the Beauty Contest game and in the C1, C2, or random condition in the calculation task. For group analysis of choice-related activity, second-level analyses of contrast for different iq option b of reasoning for different trial types human, computer, and random where computed as ANOVAs with sphericity correction for repeated measures.

Posthoc exploration of individual data is also reported to illustrate specific effects as a function of different trial types. Adjusted activity represents BOLD signal changes proportionally adjusted for the analytic model. Although general threshold significance was set at P 1 To whom correspondence should be addressed. E-mail coricelli isc. Author contributions G.

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