Coordination in groups faces a sub-optimization problem1,2,3,4,5,6 and theory suggests that some randomness may help to achieve global optima7,8,9. Here we performed experiments involving a networked colour coordination game10 in which groups of humans interacted with autonomous software agents (known as bots). Subjects (n = 4,000) were embedded in networks (n = 230) of 20 nodes, to which we sometimes added 3 bots. The bots were programmed with varying levels of behavioural randomness and different geodesic locations. We show that bots acting with small levels of random noise and placed in central locations meaningfully improve the collective performance of human groups, accelerating the median solution time by 55.6%. This is especially the case when the coordination problem is hard. Behavioural randomness worked not only by making the task of humans to whom the bots were connected easier, but also by affecting the gameplay of the humans among themselves and hence creating further cascades of benefit in global coordination in these heterogeneous systems.
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We thank P. Allison, F. Fu, M. Kearns, G. Kraft-Todd, A. Oswald, D. Rand and D. Spielman for comments. M. McKnight provided technical support and programming for our Breadboard platform. Support for this research was provided by grants from the Robert Wood Johnson Foundation, the National Institute of Social Sciences, and the National Institutes of Health (P30-AG034420).
The authors declare no competing financial interests.
Reviewer Information Nature thanks C. A. Hidalgo, I. D. Couzin, C. F. Camerer and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
Extended Data Figure 1 Histogram of the response time of humans in the colour-matching test (n = 142).
In the colour-matching test in our preliminary experiments, subjects were asked three times to click the same colour button as a picture on the screen with five options: green, orange, purple, pink and yellow. This histogram shows the response time (from when a colour in question showed up on screen to when a subject clicked a button) for 142 pilot subjects. Most subjects clicked the correct button in 1.0–2.0 s (median time = 1.59 s).
Extended Data Figure 2 Relationship between different measures of the structure-based complexity of the graph colouring sessions.
The correlation coefficient after logarithmic transformation is −0.990 (P < 0.001; n = 230). The solution set (x axis), known as the chromatic polynomial, is the number of possible colour combinations that satisfy the task of colouring the network. The average number of steps to reach a solution (y axis) involves computing the following statistic: a node is randomly selected and changes its colour to one that is different from its random neighbour and this is repeated until a solution is reached; the number of steps is then measured. This linear probability algorithm offers the advantage of allowing us to evaluate the landscape of the solution space starting from an arbitrary initial value. The mean convergence steps statistic was calculated for 100 iterations of each experimental network given the same initial colouring.
The error bars are s.e.m. (n = 30 for the no-bots sessions; n = 20 for all the bot-treated sessions). When placed in the centre, bots with 0% behavioural noise reduce the number of conflicts but increase the duration of unresolvable conflicts; bots with 30% noise decrease the duration of unresolvable conflicts but increase the overall conflicts; and bots with 10% noise decrease both the number of conflicts and the duration of unresolvable conflicts, compared with results of only human players. In contrast to central placement, when bots are placed in the periphery, conflict status does not vary with behavioural noise (data points are overlapping).
Extended Data Figure 4 Effect of bots’ behavioural noise on players’ satisfaction with their neighbours.
After each session was completed, subjects rated their satisfaction with the actions of their neighbours on a five-point scale: very satisfied, satisfied, neither, dissatisfied, and very dissatisfied (the specific question asked was: “How satisfied were you with the actions of your neighbours you were connected with?”). These coefficients show the effect of number of bots among neighbours on subjects’ satisfaction with their neighbours, estimated by a proportional odds logistic regression, incorporating number of neighbours and whether the session was solved. The error bars are s.e.m. (n = 3,035).
The curves show the percentage of sessions unsolved at a given time. Dark blue lines show the n = 20 sessions (involving n = 340 additional subjects) where human players were informed of which nodes were played by bots (visible-bots condition; n = 20), and light blue lines show the sessions where humans were not informed (invisible-bots condition; n = 20). The difference of the survival curves is not statistically significant (P = 0.435, log-rank test).
Extended Data Figure 6 Effect of bot visibility on players’ unresolvable conflicts for each geodesic location.
The dark purple line shows results for the sessions where human players were informed of which nodes were played by the bots (visible-bots condition; n = 20), the dark blue line shows results from the sessions where humans were not informed (invisible-bots condition; n = 20). In both conditions, the bots were located at high-degree nodes with 10% noise. The light blue line shows results for the sessions with all human players as a control (n = 30). The error bars are s.e.m. by session. Except for the addition of the dark purple line (the results of the visible-bots condition), this figure is the same as Fig. 4e. Pertinently, the dark purple and dark blue lines are not statistically distinguishable, suggesting that making the bots visible has a similar effect throughout the network on players’ behaviour compared to keeping them invisible.
This file contains Supplementary Methods and additional references. (PDF 1770 kb)
Each node’s colour shows the colour choice made by assigned human subjects at the time. Wide red edges show that the connected players are in the same colour (“colour conflicts”). Figure 1a shows the structure snapshots of the session. (MP4 13969 kb)
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Shirado, H., Christakis, N. Locally noisy autonomous agents improve global human coordination in network experiments. Nature 545, 370–374 (2017). https://doi.org/10.1038/nature22332