Abstract
Cooperative interactions profoundly shape individual and collective behaviors of social animals. Successful cooperation requires coordinated efforts by cooperators toward collective goals. However, the underlying behavioral dynamics and neuronal mechanisms within and between cooperating brains remain largely unknown. We recorded intracranial electrophysiological signals from human pairs engaged in a cooperation game. We show that teammate coordination and goal pursuit make distinct contributions to the behavioral cooperation dynamics. Increases and decreases in high-gamma activity in the temporoparietal junction (TPJ) and amygdala distinguish between establishing and maintaining cooperation and forecast transitions between these two states. High-gamma activity from distinct neuronal populations encodes teammate coordination and goal pursuit motives, with populations of TPJ neurons preferentially tracking dominant motives of different cooperation states. Across cooperating brains, high-gamma activity in the TPJ and amygdala synchronizes in a state-dependent manner that predicts how well cooperators coordinate. These findings provide fine-grained understandings of human cooperation dynamics as a state-dependent process with distinctive neurocognitive profiles of each state.
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Data availability
The raw MRI and iEEG data containing personal information of the participants are protected and not available because of data privacy laws. Processed MRI and iEEG data are available with restricted access for ethical and privacy reasons. Access can be obtained from the corresponding author upon request. Supporting data are available online (https://osf.io/cjv9k/). The ICBM template brain (2009c) for channel visualization is publicly available online (https://nist.mni.mcgill.ca/icbm-152-nonlinear-atlases-2009/).
Code availability
The custom codes for the main analysis written in MATLAB are available online (https://osf.io/cjv9k/).
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (projects 32125019 and 32430041 to Y.M.), STI-2030 Major Projects (2022ZD0211000 to Y.M.) and the Fundamental Research Funds for the Central Universities (2233300002 to Y.M.). We thank D. Wang and C. Hao for their assistance in data collection.
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Y.M. conceptualized the project and designed the experiments. F.M., C.X., Y.Z., K.L., C.H., Y.G., X.Y., X.Z., J.N., H.T. and J.Y. performed the experiments and collected data. J.W. and Z.L. analyzed the data under the supervision of Y.M. J.W. and Y.M. wrote the original and final versions of the manuscript. All authors approved the final version of the manuscript for submission.
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Extended data
Extended Data Fig. 1 The impact of behavioral variables on trial outcome.
Linear mixed effect models are used for analysis. The response variable (trial outcome) was code as a categorical variable (1 for win and 0 for loss). Each behavioral variable (as a predictor) was z-scored across trials before model fitting. a, Impact of maintenance state (indicated by the percentage of time in the maintenance state in a trial) on trial outcome against different duration criteria for defining maintenance state. For example, under a 1-s criterion, maintenance state referred to time windows when teammate avatars maintained connected for at least 1 s. Larger beta weights indicate a stronger predictive effect on trial success. Maintenance state is defined as teammate avatars maintaining connected for at least 2 s due to the observed dramatic decrease in beta values after this 2-s criterion (dashed line), and sufficient duration to investigate behavioral dynamics. b, Impact of initiation state (indicated by the percentage of time in the initiation state in a trial) on trial outcome against different duration criteria used to exclude connected time-points within the remaining trial time after defining maintenance state based on the 2-s criterion. For example, under a 1-s criterion, we removed all time-points in which avatars are connected equal or less than 1 s within the remaining trial time to define initiation state. Smaller beta weights indicate stronger predictive effect on trial failure. Therefore, initiation state is defined as the time periods apart from the maintenance state in a trial (no further removal of connected time points). The p values associated with each beta value are FWE-corrected for multiple time criteria and show significance across all criteria (a, b, pFWE < 0.001). c, Impact of behavioral variables of interest on trial win/lose. Logistic mixed-effect models were constructed to quantify the impact of each behavioral variable on cooperation by using trial outcome as the binary response variable and each behavioral index as an independent predictor. Behavioral predictors include: i) percentage of time spent in maintenance state, ii) percentage of time spent in initiation state, iii) the number of resets, iv) velocity-based coordination \({v}_{C}\), v) velocity-based collective goal pursuit \({v}_{G}\), vi) differences in \({v}_{C}\) between teammate avatars, and vii) differences in \({v}_{G}\) between teammate avatars. Additionally, we explored other variables that may contribute to cooperation by calculating avatar acceleration using second-order derivation of the position vector with respect to time, xiii) acceleration-based coordination, and ix) acceleration-based collective goal pursuit. We also calculated x) magnitudes of velocity at team center and xi) magnitudes of acceleration at team center. We aggregated trials from all patient dyads and calculated the above behavioral indices for each trial (n = 270). For time series variables such as velocity and acceleration, we averaged the value across all time points in each trial. We then normalized for each behavioral variable across trials as a fixed-effect variable and treated dyad and its interaction with trial number as two random-effect variables. We built individual models for each behavioral variable to estimate their independent impact on cooperation outcome while correcting for multiple comparisons using FWE to adjust p values. We showed that longer time spent in maintenance state increased the likelihood of winning the trial (t268 = 8.359, pFWE = 3.831 × 10-14, Radj2 = 0.728, 95% CI: 1.692, 2.734), while longer time spent in initiation state decreased it (t268 = -8.027, pFWE = 3.478 × 10-13, Radj2 = 0.533, 95% CI: -2.018, -1.223). A higher number of reset events in a trial may lead to losing it (t268 = -5.159, pFWE = 5.330 × 10-6, Radj2 = 0.222, 95% CI: -2.453, -1.098). Larger velocity toward the team center (\({v}_{C}\)) negatively predicted trial outcome (t268 = -4.656, pFWE = 5.595 × 10-5, Radj2 = 0.215, 95% CI: -1.101, -0.447), whereas larger velocity toward the finish line (\({v}_{G}\)) positively predicted trial outcome (t268 = 4.476, pFWE = 1.240 × 10-4, Radj2 = 0.196, 95% CI: 0.404, 1.039), indicating that excessive focus on coordination could hinder reaching the finish line. Higher between-teammate movement synchrony toward the finish line predicted trial outcome (collective goal difference: t168 = -4.327, pFWE = 2.353 × 10-4, Radj2 = 0.138, 95% CI: -0.960, -0.359). Additionally, we found a relatively weak positive impact of acceleration toward the team on trial outcome (t268 = 3.005, pFWE = 0.032, Radj2 = 0.086, 95% CI: 0.145, 0.695). Data are mean ± 95% CI. Statistical tests are two-sided. Asterisks denote a significant difference (*p < 0.05, ***p < 0.001, FWE-corrected for multiple comparisons).
Extended Data Fig. 2 Higher behavioral synchrony during cooperation maintenance.
a, b, Comparisons of teammate coordination between initiation and maintenance states, averaged across the entire task session (a) and for each time-point of 2-s epochs (b). \({v}_{C}\) differences were smaller in maintenance than initiation states (a, t14 = -3.968, p = 5.715 × 10-4, Cohen’s d = 0.862, 95% CI: -1.052, -0.332, paired t-test), particularly during 280-850 ms time-window (b, pcorr < 0.05), suggesting that teammates exhibited better synchrony in moving towards teammate during cooperation maintenance. c,d, Same as (a) and (b), for collective goal pursuit. \({v}_{G}\) differences were comparable in initiation and maintenance states (c, t24 = -1.362, p = 0.186, Cohen’s d = 0.356, 95% CI: -0.408, 0.084, paired t-test; d, pcorr < 0.05), indicating a state-independent synchrony in pursuit of collective goals. Additionally, we observed poor synchrony in both movement towards teammate (b, \({v}_{C}\) differences from onset to 190 ms) and the finish line (d, \({v}_{G}\) differences from onset to 310 ms) at an early time-window of the maintenance state, possibly due to an initiation-to-maintenance transition effect. Given that there were more maintenance epochs than initiation ones, we randomly choose a number-matched subset of initiation epochs for statistical analysis in b and d. For visualization (b) and (d), behavioral time series were smoothed using a moving average window of 200 ms and averaged across epochs, with black horizontal lines indicating significant temporal clusters in two-sided permutation tests, corrected for multiple comparisons at the cluster level (pcorr < 0.05, n = 10000). Data are mean ± 95% CI. Overlaid dots represent session dyads (n = 25). Statistical tests are two-sided. ***p < 0.001.
Extended Data Fig. 3 Behavioral control analysis.
a, Orthogonal decomposition of \({v}_{C}\) and \({v}_{G}.\) To quantify team coordination and collective goal pursuit, we employed an alternative approach of decomposing velocity onto the x axis and y axis to define \({v}_{C}\) and \({v}_{G}\). We define the positive direction of x as pointing towards the finish line, and the positive direction of y as pointing towards the teammate’s side. This decomposition method enables orthogonalization of \({v}_{C}\) and \({v}_{G}\). b, By applying the decomposition method as described in (a), we have identified a significant interaction between Velocity and State (F1,24 = 316.448, p = 2.511 × 10-15, ηp2 = 0.930, 90% CI: 0.870, 0.950, ANOVA of repeated-measurement), with \({v}_{C}\) dominating the initiation state (\({v}_{C}\) > \({v}_{G}\): t24 = 8.266, p = 1.760 × 10-8, Cohen’s d = 2.068, 95% CI: 0.764, 1.273, paired t-test) and \({v}_{G}\) dominating the maintenance state (\({v}_{C}\) < \({v}_{G}\): t24 = -16.893, p = 7.947 × 10-15, Cohen’s d = 4.445, 95% CI: -2.022, -1.582). c, We used linear interpolation and shape-preserving Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) to interpolate the original trajectories (time series of x and y positions). The PCHIP method ensures continuity of velocity data while also preventing overshoots of data at flat regions. Shown here are examples of velocity temporal traces using both linear and PCHIP methods. d, Similarly, using the PCHIP method, we again observed the significant Velocity × State interaction (F1,24 = 283.466, p = 8.561 × 10-15, ηp2 = 0.922, 90% CI: 0.856, 0.945, ANOVA of repeated-measurement). During the initiation state, \({v}_{C}\) dominated (\({v}_{C}\) > \({v}_{G}\): t24 = 7.696, p = 6.221 × 10-8, Cohen’s d = 1.957, 95% CI: 0.710, 1.231, paired t-test), while during the maintenance state, \({v}_{G}\) was dominant (\({v}_{C}\) < \({v}_{G}\): t24 = -16.757, p = 9.514 × 10-15, Cohen’s d = 4.412, 95% CI: -2.009, -1.568). Data are mean ± 95% CI. Overlaid dots represent session dyads (n = 25). Statistical tests are two-sided. ***p < 0.001.
Extended Data Fig. 4 The time-frequency spectrograms of oscillatory power.
a-f, Time-frequency spectrograms (t-value maps) across 4-150 Hz for initiation state (a, b), maintenance state (c, d), between-state contrast (e, f) in the amygdala/TPJ. Initiation state exhibited increased power, covering broad gamma and high-gamma bands, in both the amygdala (a, from initiation onset and lasted up to 1290 ms, between 24-150 Hz) and TPJ (b, one significant cluster between onset and 1170 ms, 30-150 Hz; another 1380-2000 ms and 41-120 Hz). In addition, we found decreased power in the low frequency band (4-30 Hz) between 940 ms to 1820 ms in the TPJ. Maintenance state was featured with significant power decreases across a broad frequency range (c, amygdala: beginning 110 ms after the maintenance onset, between 10-150 Hz; d, TPJ: from 450 ms after the maintenance onset above 30 Hz and extending the whole maintenance epoch below 30 Hz). A positive cluster was also found in TPJ from 40 ms to 390 ms and between 58-150 Hz, possibly due to the transition effect. Direct comparisons of high-frequency power between initiation and maintenance states revealed significant clusters covering a broad frequency band in the amygdala (e, a cluster extending the whole epoch between 12-150 Hz) and in the TPJ (f, a cluster from epoch onset to 1270 ms at a lower frequency band of 4-24 Hz, another cluster from 310 ms to 2000 ms at the high frequency band of 26-150 Hz). g-j, Time-frequency spectrograms across 4-150 Hz of 2 s around state transition points of reset (g, h) and connection (i, j) for the amygdala/TPJ. During maintenance-to-initiation transition, we observed activity changes from decreased to increased power within gamma and high-gamma bands in the amygdala (g, negative power clusters lasted up to 320 ms before reset points, between 33-150 Hz; a positive power cluster occurring 310 ms after reset points, between 28-134 Hz) and TPJ (h, a negative cluster lasted up to 90 ms before reset points, between 52-150 Hz; a positive power cluster occurring 230 ms after reset points, between 34-146 Hz). In addition, a negative cluster was observed from 650 ms prior to reset points to 910 ms after reset points in across a lower frequency band of 4-54 Hz. During initiation-to-maintenance transition, we observed an opposite pattern of activity, which changed from increased to decreased power within gamma and high-gamma bands in the amygdala (i, positive clusters from 1000 to 140 ms prior to connection points, between 30-100 Hz; a negative cluster from 200 ms to 1000 ms after connection points, between 28-150 Hz) and the TPJ (j, positive clusters from 1000 prior to connection points to 480 ms after connection points, between 49-150 Hz; a negative cluster from 510 ms to 1000 ms after connection points, at high-gamma band of 105-150 Hz). We also found decreased power at the lower frequency band before and after transition in TPJ (a cluster from 1000 prior to connection points to 180 ms after connection points, between 6-46 Hz; another from 530 ms to 2000 ms after connection points, between 4-52 Hz). For display purposes, heat maps were smoothed by convolving power time series with a moving Gaussian window of 250 ms for each frequency bin. Black contours delimit significant clusters after two-sided cluster-based permutation tests (pcorr < 0.05, n = 10000).
Extended Data Fig. 5 Control analyses confirmed inter-brain neural correlations.
We conducted a series of control analyses to validate the findings of inter-brain neural correlations (Supplementary Note 3). a-d, Circular shifted control. The t value of actual inter-brain correlations (in 30-150 Hz) for each state were compared against null distributions of t statistics created from the correlations of circularly shifted data between cooperators. We found increased inter-brain neural correlation of the actual data compared to that of circularly shifted data for both the amygdala (especially in the initiation state: p = 0.012, a; similar increasing trend in the maintenance state, p = 0.149, c) and TPJ (initiation: p = 0.027, b; maintenance: p < 2 × 10-4, d). e-h, Competition dyad as a control condition. We calculated the inter-brain correlation between competitors and compared it with that of cooperators. We found higher inter-brain correlations between cooperators than competition dyads during both the initiation (e, amygdala: t64 = 2.477, p = 0.016, Cohen’s d = 0.403, 95% CI: 0.003, 0.032; f, TPJ: t95 = 1.910, p = 0.059, Cohen’s d = 0.258, 95% CI: -2.803 × 10-4, 0.015) and maintenance states (g, amygdala: t65 = 2.040, p = 0.045, Cohen’s d = 0.347, 95% CI: 1.529 × 10-4, 0.014; h, TPJ: t92 = 3.322, p = 0.001, Cohen’s d = 0.435, 95% CI: 0.005, 0.190). Probability distributions of correlation coefficients for each channel (amygdala: n = 67, TPJ: n = 97) are shown as violin plots with black dots representing the mean and error bars representing 95% CI. Correlation coefficients were Fisher-transformed, and coefficient outliers (mean ± 3 s.d.) were excluded prior to statistical tests. Two-sided paired t-tests were used. i-n, Pseudo dyad control. The t value of real-interacting cooperators’ inter-brain correlations (in 30-150 Hz) for each state and state difference were compared against null distributions of t statistics calculated from neural correlations between pseudo dyads. The significant inter-brain neural correlations in the amygdala and TPJ were replicated during both initiation (i, amygdala: p < 2 × 10-4; j, TPJ: p = 0.005) and maintenance states (k, amygdala: p = 0.063; l, TPJ: p < 2 × 10-4). Moreover, the inter-brain neural correlations in the amygdala showed a significant increase during initiation than maintenance states (m, amygdala: p < 2 × 10-4), while TPJ showed an opposite pattern with larger correlation in the maintenance state than initiation state (n, TPJ: p < 2 × 10-4). In a-d and i-n, vertical solid lines and dashed lines indicate observed inter-brain correlations and the upper/lower 95% CI of the null distributions (one-sided non-parametric permutation tests). Asterisks denote a significant difference (†p < 0.10, *p < 0.05, **p < 0.01, uncorrected).
Extended Data Fig. 6 The time-frequency spectrograms (t-value maps) of inter-brain neural correlations.
a-f, Inter-brain neural correlation spectrograms are calculated across 4-150 Hz using sliding window method with a 500 ms sliding window and incremental steps of 10 ms (Supplementary Note 3) for the initiation state (a, b), maintenance state (c, d), and state contrast (e, f) for the amygdala/TPJ. During the initiation state, we observed clusters exhibiting a significant increase in inter-brain neural correlation within high-gamma bands (a, a cluster from epoch onset to 990 ms, ranging between 60 Hz to 94 Hz; another cluster from 30 ms to 890 ms, ranging between 123 Hz to 150 Hz) and within alpha and beta frequencies (from onset to 1160 ms, ranging between 4 Hz to 26 Hz) in the amygdala. A significant cluster at beta and lower gamma band were found in TPJ (b, from 280 ms to 1680 ms, ranging between 17 Hz to 38 Hz). During the cooperation maintenance state, we observed clusters with significantly increased inter-brain neural correlation in the gamma band in the amygdala (c, an early cluster from epoch onset to 1000 ms, ranging between 61 Hz to 109 Hz) and in TPJ (d, a cluster from 850 ms to 1830 ms, between 81 Hz to 97 Hz, another cluster from 990 ms to 2000 ms, between 27 Hz to 79 Hz). The comparison of spectro-temporal maps between the initiation and maintenance states revealed positive clusters in the high-gamma band in the amygdala (e, stronger inter-brain correlation during initiation, occurring between 80 ms to 840 ms at a frequency range of 124 Hz to 150 Hz, and between 940 ms to 1730 ms at a frequency range of between 98 Hz to 111 Hz) but negative clusters at the lower high-gamma band in TPJ (f, higher inter-brain neural correlation during maintenance state occurring between 1020 ms and 2000 ms at a frequency range of between 33 Hz to 69 Hz). Our results showed that the state-dependent inter-brain correlations were reliably observed at millisecond timescales, but exhibited region-specific patterns with opposite trends in the amygdala and TPJ. g-j, Inter-brain neural correlation spectrograms across 4-150 Hz of 2 s around state transition points of reset (g, h) and connection (i, j) for the amygdala/TPJ. During transition from maintenance state to initiation state, we observed clusters exhibiting significant inter-brain neural correlation within gamma and high-gamma bands in the amygdala (g, from 650 ms prior to reset points to 1000 ms after reset points, between 45 Hz and 91 Hz) and TPJ (h, a cluster from 1000 ms before reset points to 60 ms after reset points, between 35 Hz to 49 Hz; another cluster from 320 ms before reset points to 1000 ms after reset points, between 92 Hz to 117 Hz). A cluster extending the whole transition period was also found within alpha and beta bands in TPJ (from 6 Hz to 25 Hz). During transition from initiation state to maintenance state, we observed positive clusters of inter-brain neural correlation within the high-gamma band (i, from 1000 ms prior to connection points to 630 ms after connection points, between 64 Hz and 95 Hz) and the lower frequency band (90 ms to 890 ms after connection points, between 13 Hz and 38 Hz) in the amygdala. Results also revealed positive clusters of inter-brain neural correlation in the gamma band (j, from 190 ms prior to connection points to 730 ms after connection points, between 60 Hz and 87 Hz) and across alpha and beta bands (from 50 ms prior to connection points to 1000 ms after connection points, between 8 Hz and 26 Hz) in the TPJ. Our results suggested co-fluctuation of increased or decreased neural activity between cooperators during state transitions, prominently at the high-frequency band. The significant inter-brain correlation occurred temporally early than the transition points, suggesting that activities were also synchronized in predicting the upcoming transition events. During state transitions, inter-brain correlation might play an important role in updating and exchanging social information about the upcoming transition between cooperators. In e and f, significant clusters were identified from the observed data through two statistical comparisons84. First, we compared time-frequency maps of inter-brain correlation against zero for initiation and maintenance states separately, and extracted significant clusters with positive t-values under a single condition. Then, we compared time-frequency maps of inter-brain correlation between initiation and maintenance states and extracted significant clusters under condition contrast. New clusters were obtained by calculating the intersection of significant clusters from both comparisons, which were further statistically compared with the null distribution from the second comparison to obtain corrected p-values for each cluster. These procedures ensured that significant between-state differences in inter-brain correlations were also reliably larger than zero in each state. For display purposes, heat maps were smoothed by convolving inter-brain correlation time series with a moving Gaussian window of 250 ms for each frequency bin. Black contours delimit significant clusters after cluster-based permutation tests (n = 10000). In a-d and g-j, we used one-sided test with a threshold of pcorr < 0.05. In e and f, we used two-sided test with a threshold pcorr < 0.05.
Extended Data Fig. 7 The behavioral results of the 4-person team, non-competitive cooperative running game.
a, A schematic representation of the virtual cooperative running game. In this task, there is only one 4-person team, aiming to cross the finish line together but without any competitive pressure. The four avatars in this game are of different shapes and colors (blue triangle, orange rectangle, purple diamond, and green pentagon), allowing participants to easily identify themselves. The initial positions of these avatars are predetermined and remained unchanged throughout gameplay. For illustration purpose, the avatars are depicted as colored circles. Despite some modifications of game settings, this game inherited the fundamental principles of the ‘three-legged’ analogy. Prior to entering the running zone during each trial, avatars had to establish a connection with the other teammates when the distances between any two teammates are all below a preset safe distance (that is, dij < 250, where dij ∈ {d12, d13, d14, d23, d24, d34}). Note that we have slightly relaxed the safe distance threshold due to the increased challenge of maintaining connected among 4 participants. All other aspects of the game interface and procedures remain identical to those of the three-legged racing game. They proceed through the running zone towards the finish line while maintaining their connection, striving to move as fast as possible. However, if the connection is lost within the running zone, a reset event occurs and avatars must restart from the preparation zone. To illustrate this occurrence, we have used a dashed red line and an ‘explosion’ symbol to indicate where the connection is broken; these elements were not present in actual gameplay. b, c, We quantified team coordination (b, \({v}_{C}\) averaged across four teammates) and collective goal pursuit (c, \({v}_{G}\) averaged across four teammates) by decomposing avatars’ velocity and projecting it onto the team center and the finish line, respectively. Specifically, velocities from all four teammate avatars were used to calculate \({v}_{C}\) and \({v}_{G}\). Behavioral synchrony variables were calculated between each two teammates and averaged across pairs. Schematic illustration of \({v}_{C1}\) and \({v}_{G1}\) were shown in the panels as an example. d, Initiation and maintenance states were dominated by \({v}_{C}\) and \({v}_{G}\), respectively. Teammate coordination dominated the initiation state (\({v}_{C}\) > \({v}_{G}\): t14 = 7.657, p = 2.273 × 10-6, Cohen’s d = 2.808, 95% CI: 0.514, 0.914, paired t-test). In contrast, moving toward the finish line dominated the maintenance state (\({v}_{C}\) < \({v}_{G}\): t14 = -15.681, p = 2.825 × 10-10, Cohen’s d = 4.912, 95% CI: -1.492, -1.133). A significant Velocity × State interaction (F1,14 = 164.739, p = 3.926 × 10-9, ηp2 = 0.922, 90% CI: 0.817, 0.948, ANOVA of repeated-measurement) further confirmed this opposite pattern. e, f, Temporal profiles of \({v}_{C}\) and \({v}_{G}\), as well as their contrast across the 2-s maintenance epochs (e) and initiation epochs (f), respectively. In the maintenance state, \({v}_{G}\) was significantly larger than \({v}_{C}\) for a long time period from 300 ms after onset (pcorr < 0.05). In the initiation state, \({v}_{G}\) was lower than \({v}_{C}\) especially in an early time window of 230-1030 ms (cluster-based permutation tests, pcorr < 0.05, n = 10000). g-j, Decreasing \({v}_{C}\) (g, h) and increasing \({v}_{G}\) (i, j) accounted for state transition from maintenance to initiation. We observed significant decreases in \({v}_{C}\) (g, t14 = -10.626, p = 4.379 × 10-8, Cohen’s d = 2.594, 95% CI: -0.789, -0.524, one-sample t-test) and significant increases in \({v}_{G}\) (i, t14 = 4.912, p = 2.290 × 10-4, Cohen’s d = 1.120, 95% CI: 0.420, 1.072, one-sample t-test) occurring 500 ms prior to the reset points, and covering the last 500-ms time window before transitions from maintenance to initiation states (relative to other stable maintenance periods, h, j, pcorr < 0.05). k-n, Increasing \({v}_{C}\) (k, l) with unchanged \({v}_{G}\) (m, n) contributed to state transition from initiation to maintenance. We found significant increases in \({v}_{C}\) (k, t14 = 4.780, p = 2.935 × 10-4, Cohen’s d = 1.167, 95% CI: 0.441, 1.158, one-sample t-test), covering the entire 500 ms before the connection point (l, pcorr < 0.05), without significant changes in \({v}_{G}\) (m, t14 = 1.496, p = 0.157, Cohen’s d = 0.365, 95% CI: -0.061, 0.341, one-sample t-test; n, pcorr < 0.05). o-r, Comparisons of teammate coordination (o, p) and collective goal pursuit (q, r) between initiation and maintenance states, averaged across the entire task session (o, q) and for each time point of 2-s epochs (p, r). Results showed smaller \({v}_{C}\) differences (o, t14 = -11.841, p = 1.110 × 10-8, Cohen’s d = 4.111, 95% CI: -2.992, -2.074, paired t-test) from 350 ms after epoch onset (p, pcorr < 0.05), and also smaller \({v}_{G}\) differences (q, t14 = -6.243, p = 2.151 × 10-5, Cohen’s d = 2.120, 95% CI: -1.555, -0.760, paired t-test) during the time window of 400 ms to 2000 ms (r, pcorr < 0.05) in the maintenance than the initiation states. We balanced the numbers of non-transition epochs and state-transition epochs in h, j, l and n, and also the numbers of initiation epochs and maintenance epochs in P and R for plotting and statistical testing (Methods). Data are mean ± 95% CI. Overlaid dots represent 4-person teams (n = 15). Statistical tests are two-sided. For visualization of behavioral temporal profiles, time series (e, f, h, j, l, n, p and r) were smoothed with a 200-ms moving average window, with horizontal colored bars indicating significant temporal clusters in permutation tests corrected for multiple comparisons at the cluster level (pcorr < 0.05, n = 10000). ***p < 0.001, n.s. not significant.
Extended Data Fig. 8 The neural results of the 4-person team, non-competitive cooperative running game.
a, b, Normalized power in the amygdala (a, n = 103 channels) and TPJ (b, n = 162 channels) during cooperation initiation and maintenance states plotted as a function of frequency. We replicated that initiation and maintenance states were differentiated by a significant difference in power in the 30 Hz to 150 Hz high-frequency band. This power difference was further confirmed by a significant power increase in the initiation state but a significant power decrease in the maintenance state within the 30-150 Hz frequency band. Horizontal orange, blue, and black bars indicate the significant frequency bands for the initiation state, maintenance state, and between-state contrast (cluster-based permutation tests, pcorr < 0.05, n = 10000). c, d, Normalized high-frequency power averaged between 30-150 Hz during initiation and maintenance states in the amygdala (c, n = 23 patients) and TPJ (d, n = 18 patients). The state-dependent high-frequency activity pattern was strikingly consistent across sessions in both amygdala (c, initiation vs. maintenance: t22 = 8.160, p = 4.240 × 10-8, Cohen’s d = 2.724, 95% CI: 0.082, 0.137, paired t-test, consistent in 100% teams) and TPJ (d, initiation vs. maintenance: t17 = 8.380, p = 1.929 × 10-7, Cohen’s d = 2.858, 95% CI: 0.056, 0.094, paired t-test, consistent in 94% teams). Specifically, we found significant power increases in the initiation state (amygdala: t22 = 6.310, p = 2.380 × 10-6, Cohen’s d = 1.270, 95% CI: 0.045, 0.089; TPJ: t17 = 6.337, p = 7.444 × 10-6, Cohen’s d = 1.426, 95% CI: 0.033, 0.066, one-sample t-tests) but power decreases in the maintenance state (amygdala: t22 = -10.228, p = 7.995 × 10-10, Cohen’s d = 2.059, 95% CI: -0.051, -0.034; TPJ: t17 = -8.210, p = 2.558 × 10-7, Cohen’s d = 1.848, 95% CI: -0.033, -0.019). Overlaid dots represent session participants. e-j, Time-frequency spectrograms (t-value maps) of epochs from initiation state (e, f), maintenance state (g, h), and between-state contrast (i,j) in the amygdala/TPJ. In the initiation state, we found clusters exhibiting power increases covering a broad frequency range of 30-150 Hz, in both the amygdala (e, significant clusters emerged at initiation onset and lasted up to 1440 ms) and TPJ (f, a significant cluster covering the entire 2000 ms epoch). In the cooperation maintenance state, there were significant power decreases across a broad frequency range of 30-150 Hz in both the amygdala (g, beginning 260 ms after the maintenance onset) and TPJ (h, from 300 ms after the maintenance onset). Direct comparisons of high-frequency power between initiation and maintenance states revealed significant clusters in amygdala (i, one cluster between onset and lasted up to 1690 ms, 30-150 Hz; another covering 1830-2000 ms and 39-142 Hz), and in TPJ (j, covering the entire 2000 ms epoch). For display purposes, power heat maps were smoothed by convolving power time series with a moving Gaussian window of 250 ms for each frequency bin. Black contours delimit significant clusters after two-sided cluster-based permutation tests (pcorr < 0.05, n = 10000). k,l, Inter-brain neural correlation (Pearson correlation coefficients) in 30-150 Hz between two interacting brains across all channel pairs in the amygdala (k, n = 286) and TPJ (l, n = 555), during initiation and maintenance states. The results replicated the findings in the three-legged racing game that the amygdala high-frequency power of the cooperating teammates was significantly correlated in the initiation state (t282 = 8.656, p = 1.904 × 10-16, Cohen’s d = 0.513, lower 95% CI: 0.023, one-sided one-sample t-test) and the maintenance state (t280 = 2.096, p = 0.018, Cohen’s d = 0.125, lower 95% CI: 0.001). The TPJ power in the 30-150 Hz band of two teammates was significantly correlated during both the initiation (t553 = 5.858, p = 4.027 × 10-9, Cohen’s d = 0.249, lower 95% CI: 0.008) and maintenance states (t550 = 5.017, p = 3.554 × 10-7, Cohen’s d = 0.213, lower 95% CI: 0.003). Inter-brain neural correlation also exhibited state-dependency, however, with stronger correlation during initiation than maintenance states in both amygdala (t277 = -7.174, p = 6.655 × 10-12, Cohen’s d = 0.591, 95% CI: -0.032, -0.018, paired t-test) and TPJ (t549 = -3.501, p = 5.005 × 10-4, Cohen’s d = 0.201, 95% CI: -0.011, -0.003). Correlation coefficients were Fisher-transformed. Data are mean ± 95% CI. In k and l, violin plots depict the probability distributions of inter-brain neural correlation across channel pairs, with black dots represent the mean. Prior to statistical tests, any correlation coefficient outliers (mean ± 3 s.d.) were excluded. Statistical tests are two-sided unless otherwise stated. *p < 0.05, ***p < 0.001.
Extended Data Fig. 9 Behavioral and neural profiles between win and loss trials.
To examine whether the behavioral and neural profiles differed between win and loss trials, we performed ANOVAs on the behavioral and neural data, including the trial outcome as a within-subject independent variable. For the behavioral analysis, we conducted a three-way ANOVA of repeated measurement including Velocity, State, and Outcome as within-dyads variables. For the intra- and inter-brain analysis, we averaged high-frequency power (30-150 Hz), and calculated inter-brain correlation across win and loss trials respectively. We conducted two-way ANOVAs of repeated measurement for power and inter-brain correlation including State and Outcome as within-dyads variables. a, b, Behavioral results revealed a significant Velocity × State × Outcome three-way interaction, indicating stronger Velocity × State interaction for win trials than loss trials (F1,22 = 13.897, p = 0.001, ηp2 = 0.387, 90% CI: 0.120, 0.564, ANOVA of repeated-measurement). Further decomposing the three-way interaction, we conducted ANOVA separately for each cooperation state and found significant Velocity × Outcome interaction in both initiation (F1,22 = 10.526, p = 0.004, ηp2 = 0.324, 90% CI: 0.074, 0.514) and maintenance (F1,22 = 5.117, p = 0.034, ηp2 = 0.189, 90% CI: 0.008, 0.397) states. Specifically, for initiation state (a), we found wining trials are featured by increased \({v}_{C}\) (t22 = 2.711, p = 0.013, Cohen’s d = 0.657, 95% CI: 0.117, 0.882) and decreased \({v}_{G}\) (t22 = -3.128, p = 0.005, Cohen’s d = 0.536, 95% CI: -0.345, -0.070), suggesting that during cooperation initiation, more focus on coordination and stronger suppression of collective goal pursuit contributed to wining the trial. For maintenance state (b), lower level of \({v}_{C}\) (t22 = -4.509, p = 1.738×10-4, Cohen’s d = 0.536, 95% CI: -0.345, -0.070) and a trend of higher \({v}_{G}\) (t22 = 1.848, p = 0.078, Cohen’s d = 0.313, 95% CI: -0.022, 0.383) were found in win trials compared to loss trials, indicating less concentration on teammate coordination and more effort exerted toward collective goal during cooperation maintenance facilitates winning the trial. These behavioral findings once again highlight the important role of teammate coordination in the success of cooperation. More engagement in interpersonal coordination during cooperation establishment, and less during cooperation maintenance enable cooperators to achieve cooperation more efficiently. c, Contrast of power between win and lose trials showed a significant State × Outcome interaction only in amygdala (F1,156 = 15.069, p = 1.526×10-4, ηp2 = 0.088, 90% CI: 0.030, 0.164), but not in TPJ (F1,229 = 0.348, p = 0.556, ηp2 = 0.002, 90% CI: 0.000, 0.021). We found that high-frequency band neural activity increased in initiation state (t156 = 2.495, p = 0.014, Cohen’s d = 0.296, 95% CI: 0.004, 0.036) and decreased in maintenance state (t156 = -2.470, p = 0.015, Cohen’s d = 0.249, 95% CI: -0.018, -0.002) for win trials compared with loss trials. d, For inter-brain correlation, we found a significant State × Outcome interaction only in TPJ (F1,457 = 9.381, p = 0.002, ηp2 = 0.020, 90% CI: 0.004, 0.046), but not in amygdala (F1,246 = 1.106, p = 0.294, ηp2 = 0.004, 90% CI: 0.000, 0.028). This interaction was mainly attributed to a significant larger inter-brain correlation at high-frequency band in maintenance state in win trials than loss trials (t458 = 3.506, p = 5.002×10-4, Cohen’s d = 0.228, 95% CI: 0.005, 0.019). The result indicates that more synchronized TPJ activities between teammates during well-maintained cooperation contributed to higher efficiency and a satisfactory outcome. Together, these results suggested that the significant behavioral and neural patterns might facilitate efficient cooperation since these patterns were more prominent in winning trials than losing trials. In a and b, overlaid dots represent session dyads with both win and loss trials (n = 23). In c and d, violin plots depict the probability distributions of power or inter-brain neural correlation across channel (c, amygdala: n = 157) or channel pairs (d, TPJ, n = 479). Correlation coefficients were Fisher-transformed, and coefficient outliers (mean ± 3 s.d.) were excluded prior to statistical tests. ANOVA of repeated-measurement are used for multi-factor analyses. Paired t-tests are used for pair-wise comparisons. Data are mean ± 95% CI. Statistical tests are two-sided unless otherwise stated. †p < 0.05, *p < 0.05, **p < 0.01, ***p < 0.001, n.s. not significant.
Supplementary information
Supplementary Information
Supplementary Notes 1–4 and Tables 1–6.
Supplementary Video 1
Video of an example trial of the three-legged racing task. Real-time recording of the screen display of a participant with epilepsy (indicated as the blue triangle) while performing one trial of the three-legged racing task.
Supplementary Video 2
Video of an example trial of the cooperative running task. Real-time recording of the screen display of a four-person team while performing one trial of the cooperative running task.
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Wang, J., Meng, F., Xu, C. et al. Simultaneous intracranial recordings of interacting brains reveal neurocognitive dynamics of human cooperation. Nat Neurosci 28, 161–173 (2025). https://doi.org/10.1038/s41593-024-01824-y
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DOI: https://doi.org/10.1038/s41593-024-01824-y
