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.
