Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Locally noisy autonomous agents improve global human coordination in network experiments


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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: Results of sessions involving only human players.
Figure 2: Survival curves of sessions, by noisiness and location of bots.
Figure 3: Results of the survival analysis by bot and network characteristics.
Figure 4: Effect of bots on the behaviour of human players.


  1. Hardin, G. The tragedy of the commons. The population problem has no technical solution; it requires a fundamental extension in morality. Science 162, 1243–1248 (1968)

    Article  CAS  ADS  Google Scholar 

  2. Dawes, R. M. Social deilemmas. Annu. Rev. Psychol. 31, 169–193 (1980)

    Article  Google Scholar 

  3. Tavoni, A., Dannenberg, A., Kallis, G. & Löschel, A. Inequality, communication, and the avoidance of disastrous climate change in a public goods game. Proc. Natl Acad. Sci. USA 108, 11825–11829 (2011)

    Article  CAS  ADS  Google Scholar 

  4. Calvert, R. Leadership and its basis in problems of social coordination. Int. Polit. Sci. Rev. 13, 7–24 (1992)

    Article  Google Scholar 

  5. Dyer, J. R. G., Johansson, A., Helbing, D., Couzin, I. D. & Krause, J. Leadership, consensus decision making and collective behaviour in humans. Phil. Trans. R. Soc. Lond. B 364, 781–789 (2009)

    Article  Google Scholar 

  6. Van Huyck, J. B., Battalio, R. C. & Beil, R. O. Tacit coordination games, strategic uncertainty, and coordination failure. Am. Econ. Rev. 80, 234–248 (1990)

    MATH  Google Scholar 

  7. Nowak, M. Stochastic strategies in the prisoner’s dilemma. Theor. Popul. Biol. 38, 93–112 (1990)

    Article  MathSciNet  Google Scholar 

  8. Kandori, M., Mailath, G. J. & Rob, R. Learning, mutation, and long run equilibria in games. Econometrica 61, 29–56 (1993)

    Article  MathSciNet  Google Scholar 

  9. Young, H. P. Learning by trial and error. Games Econ. Behav. 65, 626–643 (2009)

    Article  MathSciNet  Google Scholar 

  10. Kearns, M., Suri, S. & Montfort, N. An experimental study of the coloring problem on human subject networks. Science 313, 824–827 (2006)

    Article  CAS  ADS  Google Scholar 

  11. Axelrod, R. The Evolution of Cooperation (Basic Books, 1984)

  12. Rand, D. G. & Nowak, M. A. Human cooperation. Trends Cogn. Sci. 17, 413–425 (2013)

    Article  Google Scholar 

  13. Jiang, J.-J., Huang, Z.-G., Huang, L., Liu, H. & Lai, Y.-C. Directed dynamical influence is more detectable with noise. Sci. Rep. 6, 24088 (2016)

    Article  CAS  ADS  Google Scholar 

  14. Eldar, A. & Elowitz, M. B. Functional roles for noise in genetic circuits. Nature 467, 167–173 (2010)

    Article  CAS  ADS  Google Scholar 

  15. Couzin, I. D. et al. Uninformed individuals promote democratic consensus in animal groups. Science 334, 1578–1580 (2011)

    Article  CAS  ADS  Google Scholar 

  16. Gao, J., Barzel, B. & Barabási, A.-L. Universal resilience patterns in complex networks. Nature 530, 307–312 (2016)

    Article  CAS  ADS  Google Scholar 

  17. Sniegowski, P. D., Gerrish, P. J. & Lenski, R. E. Evolution of high mutation rates in experimental populations of E. coli. Nature 387, 703–705 (1997)

    Article  CAS  ADS  Google Scholar 

  18. Kirkpatrick, S., Gelatt, C. D. Jr & Vecchi, M. P. Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  CAS  ADS  MathSciNet  Google Scholar 

  19. Kadri, U., Brümmer, F. & Kadri, A. Random patterns in fish schooling enhance alertness: a hydrodynamic perspective. EPL 116, 1–6 (2016)

    Article  Google Scholar 

  20. Traulsen, A., Semmann, D., Sommerfeld, R. D., Krambeck, H. J. & Milinski, M. Human strategy updating in evolutionary games. Proc. Natl Acad. Sci. USA 107, 2962–2966 (2010)

    Article  CAS  ADS  Google Scholar 

  21. Helbing, D. & Yu, W. The outbreak of cooperation among success-driven individuals under noisy conditions. Proc. Natl Acad. Sci. USA 106, 3680–3685 (2009)

    Article  CAS  ADS  Google Scholar 

  22. Couzin, I. D., Krause, J., Franks, N. R. & Levin, S. A. Effective leadership and decision-making in animal groups on the move. Nature 433, 513–516 (2005)

    Article  CAS  ADS  Google Scholar 

  23. Liu, Y.-Y., Slotine, J.-J. & Barabási, A. L. Controllability of complex networks. Nature 473, 167–173 (2011)

    Article  CAS  ADS  Google Scholar 

  24. Barabási, A. L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  25. Kesting, A., Treiber, M., Schönhof, M. & Helbing, D. Adaptive cruise control design for active congestion avoidance. Transp. Res., Part C Emerg. Technol. 16, 668–683 (2008)

    Article  Google Scholar 

  26. Rand, D. G., Arbesman, S. & Christakis, N. A. Dynamic social networks promote cooperation in experiments with humans. Proc. Natl Acad. Sci. USA 108, 19193–19198 (2011)

    Article  CAS  ADS  Google Scholar 

  27. Shirado, H., Fu, F., Fowler, J. H. & Christakis, N. A. Quality versus quantity of social ties in experimental cooperative networks. Nat. Commun. 4, 2814 (2013)

    Article  ADS  Google Scholar 

  28. Sørensen, J. J. W. H. et al. Exploring the quantum speed limit with computer games. Nature 532, 210–213 (2016)

    Article  ADS  Google Scholar 

  29. Cooper, S. et al. Predicting protein structures with a multiplayer online game. Nature 466, 756–760 (2010)

    Article  CAS  ADS  Google Scholar 

  30. Munger, K. Tweetment effects on the tweeted: experimentally reducing racist harassment. Polit. Behav. (2016)

Download references


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).

Author information

Authors and Affiliations



H.S. and N.A.C. designed the project. H.S. collected the data and performed the statistical calculations. H.S. and N.A.C. analysed the results. H.S. and N.A.C. wrote the manuscript. N.A.C. obtained funding.

Corresponding author

Correspondence to Nicholas A. Christakis.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

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.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Extended Data Figure 3 Impact of bots on colour conflicts over the entire network.

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).

Extended Data Figure 5 Survival curves for sessions by bot visibility.

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.

Related audio

Supplementary information

Supplementary Information

This file contains Supplementary Methods and additional references. (PDF 1770 kb)

An example of the colour coordination game with all human subjects

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)

PowerPoint slides

Source data

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shirado, H., Christakis, N. Locally noisy autonomous agents improve global human coordination in network experiments. Nature 545, 370–374 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing