Cognitive mechanisms for human flocking dynamics

Abstract

Low-level “adaptive” and higher-level “sophisticated” human reasoning processes have been proposed to play opposing roles in the emergence of unpredictable collective behaviors such as crowd panics, traffic jams, and market bubbles. While adaptive processes are widely recognized drivers of emergent social complexity, complementary theories of sophistication predict that incentives, education, and other inducements to rationality will suppress it. We show in a series of multiplayer laboratory experiments that, rather than suppressing complex social dynamics, sophisticated reasoning processes can drive them. Our experiments elicit an endogenous collective behavior and show that it is driven by the human ability to recursively anticipate the reasoning of others. We identify this behavior, “sophisticated flocking”, across three games, the Beauty Contest and the “Mod Game” and “Runway Game”. In supporting our argument, we also present evidence for mental models and social norms constraining how players express their higher-level reasoning abilities. By implicating sophisticated recursive reasoning in the kind of complex dynamic that it has been predicted to suppress, we support interdisciplinary perspectives that emergent complexity is typical of even the most intelligent populations and carefully designed social systems.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. 1.

    Bikhchandani, S., Hirshleifer, D., & Welch, I. (1998). Learning from the behavior of others: Conformity, fads, and informational cascades. Journal of Economic Perspectives, 12, 151–170.

    Article  Google Scholar 

  2. 2.

    Schelling, T. C. (1978). Micromotives and macrobehavior. New York: W. W. Norton & Company.

    Google Scholar 

  3. 3.

    Castellano, C., Fortunato, S., & Loreto, V. (2009). Statistical physics of social dynamics. Reviews of Modern Physics, 81, 591–646. https://doi.org/10.1103/revmodphys.81.591.

    Article  Google Scholar 

  4. 4.

    Dyer, J., Ioannou, C., Morrell, L., et al. (2008). Consensus decision making in human crowds. Animal Behaviour, 75, 461–470.

    Article  Google Scholar 

  5. 5.

    Raafat, R. M., Chater, N., & Frith, C. (2009). Herding in humans. Trends in Cognitive Sciences, 13, 420–428. https://doi.org/10.1016/j.tics.2009.08.002.

    Article  Google Scholar 

  6. 6.

    Fowler, J. H., & Christakis, N. A. (2010). Cooperative behavior cascades in human social networks. Proceedings of the National Academy of Sciences, 107, 5334–5338. https://doi.org/10.1073/pnas.0913149107.

    Article  Google Scholar 

  7. 7.

    Lux, T. (1999). Scaling and criticality in a stochastic multi-agent model of a financial market. Nature, 397, 498–500.

    Article  Google Scholar 

  8. 8.

    Helbing, D., Farkas, I., & Vicsek, T. (2000). Simulating dynamical features of escape panic. Nature, 407, 487–490.

    Article  Google Scholar 

  9. 9.

    Kerr, B., Riley, M. A., Feldman, M. W., & Bohannan, B. J. M. (2002). Local dispersal and interactions promote coexistence in a real-life game of rock–paper–scissors. Nature, 418, 171–174.

    Article  Google Scholar 

  10. 10.

    Semmann, D., Krambeck, H. J., & Milinski, M. (2003). Volunteering leads to rock–paper–scissors dynamics in a public goods game. Nature, 425, 390–393.

    Article  Google Scholar 

  11. 11.

    Kirkup, B. C., & Riley, M. A. (2004). Antibiotic-mediated antagonism leads to a bacterial game of rock–paper–scissors in vivo. Nature, 428, 412–414.

    Article  Google Scholar 

  12. 12.

    Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314, 1560–1563. https://doi.org/10.1126/science.1133755.

    Article  Google Scholar 

  13. 13.

    Sato, Y., Akiyama, E., & Crutchfield, J. P. (2005). Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena, 210, 21–57. https://doi.org/10.1016/j.physd.2005.06.031.

    Article  Google Scholar 

  14. 14.

    Barnett, V. (2015). Keynes and the psychology of economic behavior: From stout and sully to the general theory. History of Political Economy, 47, 307–334.

    Article  Google Scholar 

  15. 15.

    Koppl, R. (1991). Retrospectives: Animal spirits. The Journal of Economic Perspectives, 5, 203–210. https://doi.org/10.1257/jep.5.3.203.

    Article  Google Scholar 

  16. 16.

    Selten, R. (1991). Anticipatory learning in two-person games. In R. Selten (Ed.), Game equilibrium models: Evolution and game dynamics (p. 98). Berlin: Springer.

    Chapter  Google Scholar 

  17. 17.

    Bloomfield, R. (1994). Learning a mixed strategy equilibrium in the laboratory. Journal of Economic Behavior and Organization, 25, 411–436.

    Article  Google Scholar 

  18. 18.

    Stahl, D. O. (2000). Rule learning in symmetric normal-form games: Theory and evidence. Games and Economic Behavior, 32, 105–138.

    Article  Google Scholar 

  19. 19.

    Tang, F. F. (2001). Anticipatory learning in two-person games: Some experimental results. Journal of Economic Behavior and Organization, 44, 221–232.

    Article  Google Scholar 

  20. 20.

    Camerer, C. F. (2003). Chapter 6: Learning. Behavioral game theory: Experiments in strategic interaction (pp. 265–335). Princeton: Princeton University Press.

    Google Scholar 

  21. 21.

    Camerer, C. F., & Fehr, E. (2006). When does “Economic Man” dominate social behavior? Science, 311, 47–52. https://doi.org/10.1126/science.1110600.

    Article  Google Scholar 

  22. 22.

    Lee, R., Wolpert, D. H., Bono, J., et al. (2013). Counter-factual reinforcement learning: How to model decision-makers that anticipate the future. Decision making and imperfection (pp. 101–128). Berlin Heidelberg: Springer.

    Chapter  Google Scholar 

  23. 23.

    Fujiwara-Greve, T., & Nielsen, C. (1999). Learning with forward looking players. Keio Economic Society Discussion Paper.

  24. 24.

    de Weerd, H., Verbrugge, R., & Verheij, B. (2014). Theory of mind in the Mod game: An agent-based model of strategic reasoning. ECSI.

  25. 25.

    Sato, Y., Akiyama, E., & Farmer, J. D. (2002). Chaos in learning a simple two-person game. Proceedings of the National Academy of Sciences, 99, 4748–4751.

    Article  Google Scholar 

  26. 26.

    Sato, Y., & Crutchfield, J. P. (2003). Coupled replicator equations for the dynamics of learning in multiagent systems. Physical Review E, 67, 015206.

    Article  Google Scholar 

  27. 27.

    Kleinberg, R., Ligett, K., Piliouras, G., & Tardos, É. (2011). Beyond the Nash equilibrium barrier. Symposium on Innovations in Computer Science (ICS).

  28. 28.

    Galla, T., & Farmer, J. D. (2013). Complex dynamics in learning complicated games. PNAS, 110, 1232–1236. https://doi.org/10.1073/pnas.1109672110.

    Article  Google Scholar 

  29. 29.

    Frey, S., & Goldstone, R. L. (2013). Cyclic game dynamics driven by iterated reasoning. PLoS ONE. https://doi.org/10.1371/journal.pone.0056416.

    Google Scholar 

  30. 30.

    Frith, C. D., & Frith, U. (2008). Implicit and explicit processes in social cognition. Neuron, 60, 503–510. https://doi.org/10.1016/j.neuron.2008.10.032.

    Article  Google Scholar 

  31. 31.

    Helbing, D., & Molnár, P. (1995). Social force model for pedestrian dynamics. Physical Review E, 51, 4282–4286. https://doi.org/10.1103/physreve.51.4282.

    Article  Google Scholar 

  32. 32.

    Goldstone, R. L., Wisdom, T. N., Roberts, M. E., & Frey, S. (2013). Learning along with others. Psychology of learning and motivation (pp. 1–45). Amsterdam: Elsevier.

    Google Scholar 

  33. 33.

    Goldstone, R. L., Roberts, M., Mason, W., & Gureckis, T. (2010). Collective search in concrete and abstract spaces. In T. Kugler, J. C. Smith, T. Connolly, & Y. Son (Eds.), Decision modeling and behavior in complex and uncertain environments (pp. 277–308). New York: Springer.

    Google Scholar 

  34. 34.

    Sumpter, D. J. T. (2010). Collective animal behavior. Princeton: Princeton University Press.

    Book  Google Scholar 

  35. 35.

    Couzin, I. D., & Krause, J. (2003). Self-organization and collective behavior in vertebrates. Advances in the Study of Behavior, 32, 1–75.

    Article  Google Scholar 

  36. 36.

    Nagel, R. (1995). Unraveling in guessing games: An experimental study. American Economic Review, 85, 1313–1326.

    Google Scholar 

  37. 37.

    Ho, T.-H., Camerer, C. F., & Weigelt, K. (1998). Iterated dominance and iterated best response in experimental “p-beauty contests”. American Economic Review, 88, 947–969.

    Google Scholar 

  38. 38.

    Coricelli, G., & Nagel, R. (2009). Neural correlates of depth of strategic reasoning in medial prefrontal cortex. Proceedings of the National Academy of Sciences, 106, 9163.

    Article  Google Scholar 

  39. 39.

    Arad, A., & Rubinstein, A. (2012). The 11–20 money request game: A level-k reasoning study. American Economic Review, 102, 3561–3573. https://doi.org/10.1257/aer.102.7.3561.

    Article  Google Scholar 

  40. 40.

    Camerer, C. F., Ho, T.-H., & Chong, J.-K. (2002). A cognitive hierarchy theory of one-shot games. UCLA Department of Economics Working Paper (pp. 1–38).

  41. 41.

    Duffy, J., & Nagel, R. (1997). On the robustness of behaviour in experimental beauty contest games. The Economic Journal, 107, 1684–1700.

    Article  Google Scholar 

  42. 42.

    Frey, S., & Goldstone, R. L. (2011). Going with the group in a competitive game of iterated reasoning. Cognitive Science Society, 33, 6.

    Google Scholar 

  43. 43.

    Robinson, D., & Goforth, D. (2005). The topology of the 2 × 2 games. London: Routledge.

    Google Scholar 

  44. 44.

    Crawford, V. P., & Iriberri, N. (2007). Fatal attraction: Salience, naivete, and sophistication in experimental “Hide-and-Seek” games. American Economic Review, 97, 1731–1750.

    Article  Google Scholar 

  45. 45.

    Heap, S. H., Arjona, D. R., & Sugden, R. (2014). How portable is level-0 behavior? A test of level-k theory in games with non-neutral frames. Econometrica, 82, 1133–1151.

    Article  Google Scholar 

  46. 46.

    Crawford, V. P. (2014). A comment on “How portable is level-0 behavior? A test of level-k theory in games with non-neutral frames” by Heap, Rojo-Arjona, and Sugden. Unpublished Manuscript. Available at http://econweb.ucsd.edu/~vcrawfor/HeapComment.pdf.

  47. 47.

    Camerer, C. F., Ho, T.-H., & Chong, J. (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119, 861–898.

    Article  Google Scholar 

  48. 48.

    Friedman, J. W. (1971). A non-cooperative equilibrium for supergames. The Review of Economic Studies, 38, 1–12. https://doi.org/10.2307/2296617.

    Article  Google Scholar 

  49. 49.

    Rubinstein, A. (1979). Equilibrium in supergames with the overtaking criterion. Journal of Economic Theory, 21, 1–9. https://doi.org/10.1016/0022-0531(79)90002-4.

    Article  Google Scholar 

  50. 50.

    Aumann, R. J., & Shapley, L. S. (1994). Long-term competition—A game-theoretic analysis. Essays in game theory (pp. 1–15). New York, NY: Springer.

    Google Scholar 

  51. 51.

    Fudenberg, D., & Maskin, E. (1986). The folk theorem in repeated games with discounting or with incomplete information. Econometrica, 54, 533. https://doi.org/10.2307/1911307.

    Article  Google Scholar 

  52. 52.

    Benoit, J.-P., & Krishna, V. (1985). Finitely repeated games. Econometrica, 53, 905. https://doi.org/10.2307/1912660.

    Article  Google Scholar 

  53. 53.

    Abreu, D., Dutta, P. K., & Smith, L. (1994). The folk theorem for repeated games: A NEU condition. Econometrica, 62, 939. https://doi.org/10.2307/2951739.

    Article  Google Scholar 

  54. 54.

    Denzau, A. T., & North, D. C. (1994). Shared mental models: Ideologies and institutions. Kyklos, 47, 3–31. https://doi.org/10.1111/j.1467-6435.1994.tb02246.x.

    Article  Google Scholar 

  55. 55.

    Richards, D. (2001). Coordination and shared mental models. American Journal of Political Science, 45, 259–276.

    Article  Google Scholar 

  56. 56.

    Nagel, R., Bühren, C., & Frank, B. (2017). Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game. Mathematical Social Sciences, 90, 191–207.

    Article  Google Scholar 

  57. 57.

    Palacios-Huerta, I., & Volij, O. (2009). Field centipedes. American Economic Review, 99, 1619–1635. https://doi.org/10.1257/aer.99.4.1619.

    Article  Google Scholar 

  58. 58.

    Stahl, D. O., & Wilson, P. W. (1994). Experimental evidence on players’ models of other players. Journal of Economic Behavior and Organization, 25, 309–327.

    Article  Google Scholar 

  59. 59.

    Heinrich, T., & Wolff, I. (2012). Strategic reasoning in hide-and-seek games: A note. Thurgau Research Paper Series.

  60. 60.

    Agranov, M., Potamites, E., Schotter, A., & Tergiman, C. (2012). Beliefs and endogenous cognitive levels: An experimental study. Games and Economic Behavior, 75, 449–463. https://doi.org/10.1016/j.geb.2012.02.002.

    Article  Google Scholar 

  61. 61.

    Frey, S. (2013). Complex collective dynamics in human higher-level reasoning (Doctoral dissertation, pp. 1–324). Retrieved from Proquest (3599175).

  62. 62.

    Kocher, M., Sutter, M., & Wakolbinger, F. (2014). Social learning in beauty-contest games. Southern Economic Journal, 80, 586–613.

    Article  Google Scholar 

  63. 63.

    Alaoui, L., & Penta, A. (2016). Endogenous depth of reasoning. Review of Economic Studies, 83, 1297–1333. https://doi.org/10.1093/restud/rdv052.

    Article  Google Scholar 

Download references

Acknowledgements

The data are available upon request. The authors would like to thank Yuzuru Sato, Harmen De Weerd, Tatsuya Kameda, Max Kleiman-Weber, Arlington Williams, and James Walker. This work was supported in part by NSF REESE Grant 0910218; NSF/IGERT 0903495; NASA/INSGC Space Grant NNX10AK66H. This work is based on the dissertation of author SF (http://gradworks.umi.com/35/99/3599175.html). All experiments were approved by the Indiana University IRB.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Seth Frey.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 3360 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Frey, S., Goldstone, R.L. Cognitive mechanisms for human flocking dynamics. J Comput Soc Sc 1, 349–375 (2018). https://doi.org/10.1007/s42001-018-0017-x

Download citation

Keywords

  • Complex game dynamics
  • Human collective behavior
  • Behavioral game theory
  • Cognitive game theory
  • Iterated reasoning
  • Adaptive learning