Computing Social Value Conversion in the Human Brain

Choice behavior plot.

We plotted the subjects' choice behavior (Fig. 2A), applying smoothing by Gaussian filter (variance = 10) to the standard value difference (ΔV_S) axis for the choice behavior (right option, 1; left option, 0) of individual subject in each type of trial separately for each condition (for a specific magnitude of either the self/other-bonus, attached to the left or right option). Then, in each case, the mean and SE were calculated across all subjects. Based on the sigmoidal choice curves, we quantified the effects of the bonus on the choices, thus obtaining the extent of behavioral change (Fig. 2B). For each bonus magnitude in the self-bonus and other-bonus trials of each subject, we took the difference in choice probability between each sigmoidal choice curve and that of the corresponding trial with zero magnitude bonus at the point of indifference (ΔV_S = 0). Then, we used Page's test (Page, 1963) (a nonparametric, repeated-measure test for monotonic order) to examine our hypothesis that the extent of behavioral change increases with increasing bonus magnitude (other- and self-bonus in the corresponding trials), wherein the null hypothesis was that there was no monotonic order between the two factors.

Behavior modeling.

Subjects' choice behaviors were modeled as a logit function of decision value (DV, the value difference between the two options). The logit function is given by the following: where q indicates the choice probability. As shown later, this can be rewritten as q = f (Z), where f (Z) ≡ , Z = β × DV, and β is a free parameter often called inverse temperature. Without loss of generality, we write q as the probability of choosing the option on the right side. Note, however, that in many of the fMRI analyses that follow, we often used this function in the alignment of the choice made; in other words, we used the function of choice probability that would correspond to Logit(q) and Logit(1 − q) in the equation above for the right and left option chosen, respectively; it was used to fit the model to behavior by the maximum likelihood approach, and to analyze behavior and the variables in BOLD signals.

DV is modeled in our analysis as follows: Where Δ indicates the difference between options (right minus left option), and V_S, S, and O are variables relating to the standard, self-bonus, and other-bonus, respectively. More precisely, ΔV_S = V_SR − V_SL indicates the standard value difference, where V_SR and V_SL are the standard reward values of the right and left options, respectively. V_SR (or V_SL) was computed as the product of reward magnitude and probability, wherein the probability was allowed to be distorted by risk (Platt and Huettel, 2008). We chose to use the Prelec-2-parameter model (Prelec, 1998), given by p̃ = exp(− δlog^γ p), where the left side is the risk-distorted reward probability, p is a given reward probability, and δ and γ are two free parameters fitted by the logit function (see below). For ΔS and ΔO, note that only one option had an additional deterministic reward in each of the other-bonus and self-bonus trials, so the difference was the magnitude but with a sign (direction), either S_R or −S_L (O_R or −O_L) when it was attached to the right or left option, respectively. Therefore, their respective weights, w_S and w_O, indicated the extents of modifications in the choice behavior by ΔS and ΔO, respectively.

Model fitting and selection.

The maximum likelihood approach was used to fit the models to the behavioral data. For individual subjects, we minimized the sum of the negative log-likelihood of choice probabilities (MATLAB command fminsearch; MATLAB R2012b, The MathWorks) for the options chosen by each subject (i.e., the probabilities q and 1 − q when the right and left options were chosen, respectively). Each minimization was repeated 50 times using randomly generated initial values. Free parameters resulting in a minimal summed negative log-likelihood were then selected, corresponding to the best fit of the model.

To select the best model at the group level while taking into account the different number of free parameters between the models, a paired t test was used to compare differences in the distribution of Akaike's information criterion (AIC) values obtained for the different models (Suzuki et al., 2012). First, to use the expected reward as a probabilistic outcome and include risk parameters (i.e., using rather than p), we examined the fit of our model (V_S = mp̃) for standard trials in comparison with that of four reference models in which V_S was replaced with m, p, p̃, or mp. Among the four reference models, the first three were used to test whether the reward magnitude or probability contributed to the expected reward, whereas the last reference model, mp, was used to test the inclusion of risk parameters. In the group-level comparison, the original model was the best model with statistical significance (Table 1). Therefore, we adopted V_S = mp̃ in our analyses. Second, to further ensure our main model (DV = ΔV_S + w_SΔS + w_OΔO), we compared the fit of our main model to that of three reference models, each of which lacks one of the three variables of the main model: ΔV_S, ΔS, or ΔO. By the group-level comparison of AIC value distributions, we found that the main model was superior to any of the three reference models. These results were also confirmed by using the Bayesian information criterion (BIC) for model selection (Table 1).

We also examined the models' fit to the behavior of each individual subject to ensure that each of the main variables in the behavior model had a considerable effect on the individual behavior. First, for standard trials, the AIC values of the main model (V_S = mp̃) were always the smallest compared with those of the m, p, p̃, and mp models for all individuals, indicating that all individuals used both reward magnitude and probability in their valuation. Second, we compared the fit of the main model with that of the models omitting one of ΔV_S, ΔS, or ΔO for all the trials of each subject. We found that the main model's fit was better for all individuals in comparison with the models omitting ΔV_S or ΔS. However, for the case of ΔO, we found that, for seven subjects, ΔO in the main model had no significantly positive effect compared with the model omitting ΔO and these subjects were excluded in our main analysis of BOLD signals.

We conducted several other verifications of the main model, including interaction terms, offset term, and accumulated payment for other's reward, and also testing the effect of mere presence of a bonus. All of these verifications supported using the main model in this study, and these results are briefly summarized here. A model with an additional interaction term on DV (w_VSSΔV_S × ΔS + w_VSOΔV_S × ΔO) was significantly worse than the main model in fitting the behavior (t₍₄₂₎ = 5.276, p < 0.001 by AIC). A model with an additional constant (offset) was not superior to the main model (t₍₄₂₎ = 1.321, p = 0.192 by AIC), but was significantly worse than the main model (t₍₄₂₎ = 5.522, p < 0.001 by BIC), suggesting that the main model was at least not inferior. A model with a term of accumulated payment, − w_AOA_O × ΔO was significantly worse (t₍₄₂₎ = 3.117, p = 0.003 by AIC, where A_O indicates the accumulated payments for other). We tested this because this term might affect the behavior, decreasing the selection of the option with the other-bonus as the payment accumulated. Investigating whether the mere presence of bonus (i.e., zero magnitude of reward) affects the behavior revealed that, in the trials with additional zero rewards, the main model was better (t₍₄₂₎ = 4.664, p < 0.001, t₍₄₂₎ = 14.805, p < 0.001 by AIC, respectively) than two models with the effect of the mere presence of bonus (adding either the term w_[0]Δ[0] or the term w_[0]SΔ[0]_S + w_[0]oΔ[0]_O to the DV), where Δ[0] = 1 or 0 if the zero reward appeared on the right or left option and the subscripts S and O indicate the self- and other-bonus, respectively.

Signed effective value.

We use signed effective value to indicate the link between an offered bonus value and a final decision for our BOLD analyses. Even for the same offer, the effect of the offered value on the choice (i.e., the amount of change in choice probability due to addition of the offer) may vary depending on the standard value difference (ΔV_S) in the particular trial. This is because of the nonlinearity of the logit function connecting a decision value to choice probability (q). For this reason, the variable signed effective value was defined as a second-stage variable that represents the effective impact of the offer (the first stage) on the choice (the third stage).

First, given a trial with a particular standard value difference (ΔV_S), we assessed the effect of an offered value on choices. This was done using the (choice) effectivity, which is defined as the derivative of the choice probability (q) with respect to ΔV_S and quantifies how the offered value affects the choice as follows: Then, the signed effective other-bonus value is formulated as the product of the signed other-bonus value (signed with respect to choice, e.g., w_OΔO for the other-bonus) and the effectivity as follows: Therefore, the signed effective other-bonus value corresponds to the first-order Taylor expansion term for the variable ΔO at Z = ΔV_S in the logit function. Similar calculations have been used in previous model-based fMRI studies (Bornstein and Daw, 2012, 2013), which also estimated the dependent variables in nonlinear equations by using the first-order Taylor expansion term. Analogous formulations and terminology were also used for the self-bonus value, such as the signed effective self-bonus value as follows:

Further confirmations for similar behaviors in SVO groups.

Even though the two groups of subjects responded differently to the SVO questionnaires, they behaved similarly in our tasks, as indicated by our finding (see Results) that the behavioral weight for the other-bonus was not significantly different between the two groups. For further confirmation, we conducted two additional analyses (Table 2). The first analysis examined the proportion choosing the option with the other-bonus in all other-bonus trials to determine whether the behavior in our task was different between the two groups. This examination was also conducted for smaller subsets of the trials (subsets I and II). Subset I was trials with a conflict between reward gain to the self and others: the trials in which the standard value of the option attached with other-bonus was smaller than that of the option without the other-bonus. Subset II contains the trials in which the two options are similar in nature to those in the SVO questionnaire. These trials were selected as follows: (1) all other-bonus trials in our task and all pairs of options (prosocial vs individualistic option) in the SVO questionnaire were projected onto a 2D map with the self-regarding difference on the x-axis and the other-regarding difference on the y-axis; (2) in this map, a wider range was covered by our task than by the SVO questionnaire, so (3) we selected the other-bonus trials in the range of the SVO questionnaire on both the x- and y-axes.

In the second analysis, we investigated whether the two groups of subjects behaved differently in the responses to the SVO questionnaire using models based on the behavior weights estimated from our task. For this, we set two models that would approximately correspond to two original SVO classifications: an “SVO prosocial” model that used the weights of both w_S and w_O, and an “SVO individualistic” model that used only w_S (setting w_O = 0). Using logistical function analysis, the negative log likelihoods of the fit by each model to the behavior in the prosocial and individualistic group are shown in Table 2.

Data acquisition and preprocessing.

The fMRI images were collected using a 4 T whole-body MRI system (Agilent Technologies) with a transverse electromagnetic volume coil as the transmitter (Takashima Seisakusho) and a 16-array head-shaped coil as the receiver (Nova Medical). For subjects positioned in the scanner, visual input was provided via a fiber-optic goggle system (Avotec) that subtended 25° × 19° of visual angle, and the subject used a button box to make their responses. The BOLD signal was measured using a two-shot T2*-weighted echo planar imaging (EPI) sequence (230 volumes for each block, TR = 2202 ms, TE = 20.5 ms, FA = 64°). Twenty-five axial slices (thickness = 3.0 mm, gap = 1 mm, FOV = 192 × 192 mm, matrix = 64 × 64, thus resulting in voxel size = 3 × 3 × 3 mm) parallel to the AC-PC plane (AC: anterior commissure; PC: posterior commissure) were acquired per volume. The start of an experimental task was synchronized with the first EPI acquisition timing. Before, after, and between the functional runs, a set of high-resolution (1 mm₃) and a set of low-resolution (1.72 mm₃) whole-brain anatomical images were acquired using a T1-weighted 3D MPRAGE pulse sequence (TI = 500 ms, FA = 15°, TR = 9.5 ms, TE = 3.7 ms for the high-resolution scans or 2.5 ms for the low-resolution scans, TR = 7.3 ms). The low-resolution anatomical imaging slices were parallel to the functional imaging slices and were used to aid in coregistering the functional data to the high-resolution anatomical data. A pressure sensor was used to monitor and measure the respiration signal, and a pulse oximeter was used to measure the cardiac signal. The respiratory and cardiac signals were used in postprocessing to remove physiological fluctuations from functional images (Hu et al., 1995).

Functional and anatomical images were mainly analyzed using Brain Voyager QX 2.8 (Brain Innovation; RRID:SCR_013057). Functional images for each subject were preprocessed, which included slice time correction, 3D motion correction, spatial smoothing with a Gaussian kernel (FWHM = 8 mm), and high-pass temporal filtering (three cycles per run length). Anatomical images of each subject were transformed into the standard Talairach space (Talairach and Tournoux, 1988). Functional images were then normalized and resized according to the transformed structural images and thus transformed into the standard Talairach space. Then, images from all scanning sessions were connected.

Generalized linear model analysis.

We used a so-called model-based analysis (O'Doherty et al., 2007) to analyze the BOLD signals in both control and main tasks, using generalized linear model (GLM) regression with two levels of analysis as follows. At the first level, we submitted the BOLD signals of an individual subject into the GLM. When generating the GLM regressors, we used the behavioral weights of our model, which were estimated by fitting to the trials in fMRI experiment of each individual subjects and the estimated behavioral weights were also used as a covariate at the second-level analysis.

Using model-based analysis, we examined computations of social value conversion in three essential stages. The first and third stage correspond to the input and output stages of social value conversion, respectively, whereas the second stage links the two stages. A variable in the first stage, called offered value (e.g., w_O|ΔO|, offered other-bonus value) indicates the value of the possible outcome (|ΔO|) to others before one's choice that would affect the others' outcome. The variable in the second stage is called signed effective value (see “Signed effective value” section). The variable in the third stage is the DV (Eq. 1), which is assumed to determine the choice (or choice probability) given by the value of the chosen option minus the value of the unchosen option.

Therefore, we created subject-specific design matrices containing the following regressors for the GLM. There were 12 regressors for the variables of no interest. Six regressors encoded the average BOLD responses for the onset and period of the DECISION, ISI, and OUTCOME phases, where the DECISION phase was defined as the period from the onset of CUE until the subject responded in the RESPONSE period and the other two phases were defined as shown Figure 1A. Six motion correction parameters to account for motion effects, and the outcome for the standard reward in each trial (1 when rewarded and 0 when not, in the OUTCOME phase) were also included. There were five regressors for the variables of interest, (1) the decision value (DV, on the axis of the chosen minus unchosen option); (2) offered other-bonus value, w_OⁱO, and (3) signed effective other-bonus value, w_Oⁱ(∂q ̸ ∂ΔV_S)ΔO (Eq. 3), only for other-bonus trials; (4) offered self-bonus value, w_SⁱS, and (5) signed effective self-bonus value, only for self-bonus trials. All regressors for the variables of interest were modeled in the DECISION phase. All regressors of interest were mean-corrected, normalized, and convolved with a canonical hemodynamic response function before being entered into GLM analysis.

The estimated effect sizes or their contrasts from the first-level GLM were entered into a whole-brain random-effects analysis to extract significant brain activations for each regressor in group-level statistics (i.e., groupwise one-sample t test). In the random-effects analysis, we also included a covariate for examining relationships with individual variability in the behavioral weights. Specifically, we included w_Oⁱ for offered and signed effective other-bonus values and w_Sⁱ for offered and signed effective self-bonus values. The significance of these covariates was tested by t test (against a null hypothesis of zero estimated effect size). The brain regions with significant effect sizes for each regressor were reported based on corrected p-values (p < 0.05), using familywise error (FWE) correction for multiple comparisons; we first thresholded contrast maps at p < 0.005 (i.e., uncorrected) and then estimated corrected p-values by permutation test (5000 permutations) using PALM software (FMRIB, University of Oxford, https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/PALM) (Winkler et al., 2014). The coordinates reported in Tables 3 and 4 for a given cluster were those of the highest activated voxel within it. To report the coordinates for a given anatomic brain region, such as the rTPJ and ldlPFC, we further used a higher-values-first watershed searching algorithm by BVQX tools (version 0.8d) of Brain Voyager to identify the local maxima peak in the respective brain region (thus, the peaks reported in the text were not necessarily the same as reported in the tables).

Trial-by-trial GLM analysis.

Trial-by-trial GLM analysis (whole-brain) was performed to examine the BOLD signal changes on a trial-by-trial basis for each subject (Fig. 3B) (Gläscher, 2009). This GLM analysis focused on the DECISION phase in each trial; thus, the regressor of interest encodes 1 for the DECISION phase of the trial, whereas any other periods or trials were encoded by 0. To conduct the trial-by-trial GLM analysis for the results shown in main Figure 3B, we used the leave-one-out, cross-validated region of interest (ROI). For each subject, we obtained the cross-validated ROI and then extracted the BOLD signal changes in each trial. For each subject, we used z transformation to normalize the BOLD signal changes across all trials (subtracting the mean and dividing by the SD) and binned them separately for each trial type as low, medium, or high (corresponding to the 33rd, 66th, and 100th percentiles, respectively) to obtain the individual's binwise mean BOLD signal changes. Then, the mean and SEM of the normalized BOLD signal changes in each bin were computed across subjects. We investigated whether the BOLD signal changes increased with the order of the bins by Page's test.

Extraction of ROIs.

The ROIs were extracted as 8-mm-diameter spheres with centers at the local maxima peaks within the clusters of GLM activations. The local maxima peaks were obtained by a higher-values-first watershed searching algorithm in BVQX tools. To extract cross-validated BOLD signals, we used a previously reported leave-one-out procedure (Gläscher et al., 2009) to provide an independent criterion for ROI selection and thus ensure statistical validity (Kriegeskorte et al., 2009). We reestimated our second-level analysis n times (where n equals the number of subjects), leaving out a different subject each time. Starting at the peak voxels for the focal signal, we selected the nearest activated voxels (p < 0.005, uncorrected) in these cross-validation second-level analyses. The selected voxel was defined as a cross-validated ROI.

Analysis of rTPJ and ldlPFC responses while controlling the behavioral effects.

For this reanalysis of the BOLD signals, we controlled the behavioral effect to be comparable between the other-bonus and self-bonus values by selecting a subgroup of subjects and using a subset of the trials. For this purpose, we down-sampled both the pool of self-bonus trials and the pool of subjects to analyze the BOLD signals of self-bonus trials in which the behavioral effect was reasonably comparable to that of other-bonus trials.

First, we took the ratio of behavior weights of the other-bonus relative to that of the self-bonus (i.e., w_O/w_S), and noted that the range of this ratio for all the fMRI subjects (n = 36) was ∼0.5, specifically, from 0.012 to 0.965, mean = 0.426, SD = 0.241. Therefore, we decided to exclude the trials with a self-bonus magnitude equal to 20, which allowed us to control the maximum of the self-bonus and other-bonus as 10 and 20, respectively, and to have their ratio be 0.5. Second, we sorted the subjects in order of their ratio and excluded subjects one by one from the low end of the ratio and monitored the mean of the ratio of the remaining subjects. We stopped excluding subjects when the mean of the ratio first became close to 0.5 (mean = 0.509, SD = 0.205, from 0.224 to 0.965). The number of remaining subjects was 28. Therefore, with the subsampling of the self-bonus trials and the remaining 28 subjects, we performed BOLD signal reanalysis for trials in which the behavioral effect was comparable between the other- and self-bonus.

In the reanalysis, our GLM was in the same form as the original GLM in our main analysis except that the regressors for the self-bonus value were modified to treat the trials having a self-bonus of only 10 or 0 points. Analyzing the corresponding effect sizes in ROIs (generated by the activations in Table 3), we found that activations in the rTPJ remain significant (t₍₂₇₎ = 3.088, p = 0.005) for the other-bonus value, but not for the self-bonus value (t₍₂₇₎ = −0.686, p = 0.498), with a significant difference between the values (t₍₂₇₎ = 3.139, p = 0.004). We also found activation in the left dlPFC remained significant for both the self-bonus and other-bonus values (t₍₂₇₎ = 3.587, p = 0.001, t₍₂₇₎ = 3.047, p = 0.005, respectively) and with no significant difference (t₍₂₇₎ = 0.147, p = 0.884).

Analysis of the effect size covariate with the individuals' behavioral variability.

For the results shown in Figure 3F, we first used the leave-one-out, cross-validated ROI of the right anterior insula (rAI) and extracted the BOLD signal by averaging the signal from all voxels in the ROI from the left-out subject. The effect size was estimated by regressing this BOLD signal in the original GLM. Second, to investigate the group-level variability of the effect sizes in relation to behavior weights (e.g., w_Oⁱ), we calculated Pearson's correlation coefficient between the corresponding variables and tested the corresponding statistical significance by t test.

Psychophysiological interaction (PPI) analysis.

We conducted two types of PPI analyses: ROI PPI and voxelwise PPI (Friston et al., 1997; O'Reilly et al., 2012). In the former, the target brain region was determined based on the activations from the earlier GLM analyses (Table 4). We chose to use both PPIs for clarity because they complement each other. ROI PPI probed the significantly activated regions by using the interaction term to specifically target the relationship of the two activated brain regions obtained from our GLM results with a hypothesized psychological seed. Voxelwise PPI probed the activated regions by using the interaction term for each voxel, allowing us to examine the activation including the regions surrounding the target brain area. We could thus examine the overlap of the significant activations from the voxelwise PPI analysis with the activations from the original GLM.

The PPI regressors were constructed as follows. First, we determined each ROI with respect to a variable of interest based on the group-level activation maps generated from the GLM analysis. We then extracted the averaged BOLD time courses within a given ROI for each subject based on their preprocessed BOLD signals. These extracted signals were used as the signals of the physiological seed. We estimated the signals by deconvolving the time course signals with a canonical hemodynamic response function. Together with a given psychological seed of the variable of interest, we generated the interaction term (i.e., the variable of main interest). We first normalized each of the physiological and psychological terms to [0, 1] and then multiplied them together, further orthogonalizing the product to each of the two first-order terms. Third, the three terms (the interaction and the two first-order terms) were mean-corrected and convolved with a canonical hemodynamic response function. In both PPI analyses, to guard against possible confounding effects, we included not only the first-order terms of the interaction term as usual, but also other regressors, such as the signed effective other-bonus value.

For voxelwise PPI, the maps were analyzed as random effects by t test. The significant activations were determined and reported as p < 0.05, using small volume correction (SVC; the target ROI of the corresponding PPI defined the SVC ROI) and using FWE correction for multiple comparisons by permutation test. For ROI PPI, we determined the target ROI based on the significant brain activations found by the original GLM analysis and then conducted the PPI analysis. The mean and SEM of the effect size in the target ROI was computed across subjects and the statistical significance was tested using a one-sample t test against a null hypothesis of zero mean. The second-level covariates in the original GLM were also included in the both types of PPI analysis.

Dynamic causal modeling analysis.

Dynamic causal modeling (DCM; by SPM12, http://www.fil.ion.ucl.ac.uk/spm/, RRID:SCR_007037) (Friston et al., 2003) was used to analyze the coupling directions and structures over the rTPJ, ldlPFC, rAI, and medial prefrontal cortex (mPFC) signals in relation the three-stage processing revealed by our PPI results. For each subject, we extracted average activation time courses from an 8-mm-radius sphere around the peak of each ROI. By way of example, using cases of Figures 4C and 5, we constructed eight models including a main model based on the three-stage processing and seven models with possible revised directions of connectivity (Fig. 5A). In this DCM analysis (and also all other DCM analyses), we set offered other-bonus value for the rTPJ and ldlPFC signals as driving inputs because we were interested in how the other-bonus value is propagated in social value conversion. Following our PPI results, we set as modulatory inputs the effectivity of other-bonus value for the rTPJ-rAI and ldlPFC-rAI connectivity and the signed effectivity of other-bonus value for the rAI-mPFC connectivity. Second, we performed random-effects Bayesian model comparison to identify which of the eight models best fit our dataset (Stephan et al., 2009). We calculated the exceedance probability for each model relative to the seven other models (Fig. 5B). Third, a model family comparison analysis (also used in Fig. 8) was also conducted similarly using a random-effects Bayesian model selection procedure (Stephan et al., 2009). Further, we also used Bayesian model averaging to examine the estimate of the connection parameters (Penny et al., 2010). The parameters over all models in the model space were averaged using weights corresponding to the posterior model probabilities.

Comparison between prosocial and individualistic subjects.

To explore possible between-group differences, we added the SVO classification variable as another covariate for the brain activations. The effect sizes and statistical tests of the covariate and constant terms are reported for the rAI responses in the prosocial and individualistic groups (Fig. 6B).

To analyze coupling, we examined each of the PPI effects in each SVO group by both voxelwise and ROI analyses (Figs. 7A,B, respectively). Repeated-measures ANOVA was used to identify the between-group difference in SVO, with the seed regions as a within-group factor. Further, to control for the effects of the self-bonus value, we performed a control PPI using [rAI × signed effective self-bonus value] on the mPFC responses (separately for each group) and then explored the effect sizes of the ROI PPI results in the rAI and ldlPFC cases for both other-bonus and self-bonus values on a 2D map (Fig. 7C; details in the following section). DCM analyses were also conducted to examine each SVO group separately (Figs. 7D,E, 8C–E).

Circular statistical analysis for SVO PPI results.

To examine the nature or the relative difference between the other-bonus and self-bonus values between SVO groups in Figure 7C, we defined a vector for each subject, starting from the self-bonus and ending at other-bonus point. We then obtained the mean vector for each group. Using the projection from each vector onto the group mean vector, we assessed the major component (the value of the projection) of each subject's vector and examined the group effect across the subjects in each group, using the t test. The difference between the self-bonus and other-bonus values was significant in the individualistic subjects (t₍₁₁₎ = 2.254, p = 0.046, p = 0.027 by bootstrap test), but not in the prosocial subjects (t₍₂₀₎ = 0.913, p = 0.372, p = 0.352 by bootstrap test) and the difference in differences between the two groups was significant (t₍₃₁₎ = 2.145, p = 0.039, p = 0.017 by bootstrap test). In addition, we traversed the vectors within each group to the origin and examined their vectorial changes; the distribution over the vector directions was examined by the Rayleigh test within each group and compared between the two groups by the Watson–Williams two-sample test. The vector difference in the effect sizes was significantly nonuniformly distributed across the individualistic subjects (z = 3.054 p = 0.044 by Rayleigh test), but not across the prosocial subjects (z = 0.079, p = 0.926). Focusing on angular changes, we also observed that the difference between the two groups was significant (F = 4.255, p = 0.026 by Watson–Williams two-sample test).

Analysis of a larger sample of individualistic subjects.

The number of the individualistic subjects was relatively small (n = 12) in the main experiment, so we conducted two additional analyses and obtained essentially the same results with a larger sample size, both when adding four new individualistic subjects (n = 16, additional sample I, first approach) and when further including the seven originally excluded subjects (n = 23, additional sample II, second approach).

In the first approach, we added four new individualistic subjects for analysis. We scanned seven new, individualistic subjects (four female; all right-handed; age, 20–22 years; range, 21.0 ± 1.00 years) by the same experimental procedure as in the main experiment except that, before the experiment, they were prescreened using the SVO questionnaire to ensure that they were individualistic. Two of them were excluded because we found that the signal-to-noise ratio (SNR) of their fMRI data was significantly lower than the SNR of the data reported in the main experiment (by one-sample t test, p < 0.001). Among the remaining five subjects, one subject's choice behavior was found to be insensitive to the others' reward and therefore this subject was excluded, as was done in the main experiment. Therefore, the remaining four individualistic subjects (three female; age, 20–22 years; 21.3 ± 0.96 years) were added to the original 12 individualistic subjects and we then performed our analyses (additional sample I in Table 5).

In the second approach, we reanalyzed the data by adding some of the originally excluded subjects to the 16 subjects in the first approach (resulting in n = 23, additional sample II). We originally excluded seven subjects in the main experiment and one subject in the additional experiment because their choice behavior was not significantly positively influenced by the other-bonus, despite the intention of this study and our experimental design (our preexperimental procedure). More precisely, among the eight subjects, we found one subject's choice behavior was significantly negatively influenced by the other-bonus, so that subject was excluded in the following. All of the remaining seven subjects were individualistic according to the SVO classification and their behavior was not found to be influenced by the other-bonus in our task. Nevertheless, their social value conversion process may still occur and thus may possibly be detected in BOLD signals. We therefore added the seven subjects to the 16 individualistic subjects in the first approach and conducted our analyses (additional sample II in Table 5).

Bootstrap test.

We used a bootstrap test to further support our statistical examinations, for instance, to guard against potential confounds such as outlier samples, in the analysis of both behavior and brain signals because the bootstrap procedure is distribution independent and thus expected to be less susceptible to different distribution shapes (DiCiccio and Efron, 1996). We primarily used bootstrap tests to estimate the distributions of group means (Efron and Tibshirani, 1993; Adèr et al., 2008). We used the following procedure: resample the original data (with replacement), repeat the resampling to obtain a set of bootstrapped samples of the same size as the original sample, repeat this resampling procedure 10,000 times to obtain 10,000 bootstrapped sets, and then compute their means to obtain the bootstrapped estimated distribution of the means. We used the estimated distribution to perform bootstrap hypothesis testing, finding the probability that the mass differs from zero (in a two-tailed manner). This approach is similarly applied to the case examining the difference between two original samples. For the correlation analysis, similar estimations were applied to the distribution of correlation coefficients.