Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 1007–1019 | Cite as

How Fear of Future Outcomes Affects Social Dynamics

  • Boris Podobnik
  • Marko Jusup
  • Zhen Wang
  • H. Eugene Stanley


Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a “carrot and stick” approach towards symbionts with a stabilizing effect on their symbiosis. In open human societies, a mutualistic relationship arises when a native insider population attracts outsiders with benevolent incentives in hope that the additional labor will improve the standard of all. A lingering question, however, is the extent to which insiders are willing to tolerate outsiders before mutualism slips into antagonism. To test the assertion by Karl Popper that unlimited tolerance leads to the demise of tolerance, we model a society under a growing incursion from the outside. Guided by their traditions of maintaining the social fabric and prizing tolerance, the insiders reduce their benevolence toward the growing subpopulation of outsiders but do not invoke punishment. This reduction of benevolence intensifies as less tolerant insiders (e.g., “radicals”) openly renounce benevolence. Although more tolerant insiders maintain some level of benevolence, they may also tacitly support radicals out of fear for the future. If radicals and their tacit supporters achieve a critical majority, herd behavior ensues and the relation between the insider and outsider subpopulations turns antagonistic. To control the risk of unwanted social dynamics, we map the parameter space within which the tolerance of insiders is in balance with the assimilation of outsiders, the tolerant insiders maintain a sustainable majority, and any reduction in benevolence occurs smoothly. We also identify the circumstances that cause the relations between insiders and outsiders to collapse or that lead to the dominance of the outsiders.


Game theory Complex networks Social thermodynamics Open systems Tolerance Herd behavior 



We are grateful to Robert Axelrod, Robin Dunbar, Yoh Iwasa, Jürgen Kurths, and Tomislav Lipić for helpful suggestions. B.P. and H.E.S. received support from the National Science Foundation (NSF) Grant CMMI 1125290. B.P. also received support from the University of Rijeka. M.J. was partly supported by the Japan Science and Technology Agency (JST) Program to Disseminate Tenure Tracking System. Z.W. was supported by the National Natural Science Foundation of China, Grant No. 61201321 and 61471300.

Supplementary material

10955_2016_1649_MOESM1_ESM.pdf (410 kb)
Supplementary material 1 (pdf 409 KB)


  1. 1.
    Popper, K.: The Open Society and Its Enemies. With a Foreword by A. Ryan and an essay by E.H. Gombrich. Princeton University Press, Princeton (2013)Google Scholar
  2. 2.
    Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)MATHGoogle Scholar
  3. 3.
    Riolo, R.L., Cohen, M.D., Axelrod, R.: Evolution of cooperation without reciprocity. Nature 414, 441–443 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Nowak, M.A.: Tides of tolerance. Nature 414, 403–404 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    Uchida, S., Sigmund, K.: The competition of assessment rules for indirect reciprocity. J. Theor. Biol. 263, 13–19 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hauser, O.P., Rand, D.G., Peysakhovich, N.M.A.: Cooperation with the future. Nature 511, 213–220 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    Jusup, M., Matsuo, T., Iwasa, Y.: Barriers to cooperation aid ideological rigidity and threaten societal collapse. PLoS Comput. Biol. 10, e1003618 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    Axelrod, R., Hamilton, W.D.: The evolution of cooperation. Science 211, 1390–1396 (1981)ADSMathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Nowak, M.A.: Generosity: a winner’s advice. Nature 456, 579 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)ADSCrossRefGoogle Scholar
  11. 11.
    Nowak, M.A., Sigmund, K.: Evolution of indirect reciprocity by image scoring. Nature 393, 573–577 (1998)ADSCrossRefGoogle Scholar
  12. 12.
    Ohtsuki, H., Hauert, C., Lieberman, E., Nowak, M.A.: A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    Bshary, R., Oliveira, R.F.: Cooperation in animals: toward a game theory within the framework of social competence. Curr. Opin. Behav. Sci. 3, 31–37 (2015)CrossRefGoogle Scholar
  14. 14.
    Huang, W., Hauert, C., Traulsen, A.: Stochastic game dynamics under demographic fluctuations. Proc. Natl. Acad. Sci. USA 112, 9064–9069 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    Durlauf, S.N.: How can statistical mechanics contribute to social science? Proc. Natl. Acad. Sci. USA 96, 10582–10584 (1999)ADSMathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Hidalgo, C.A., Klinger, B., Barabási, A.L., Hausmann, R.: The product space conditions the development of nations. Science 317, 482–487 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    Tacchella, A., Cristelli, M., Caldarelli, G., Gabrielli, A., Pietronero, L.: Economic complexity: conceptual grounding of a new metrics for global competitiveness. J. Econ. Dyn. Control 37, 1683–1691 (2013)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Dunbar, R.I.: Neocortex size as a constraint on group size in primates. J. Hum. Evol. 22, 469–493 (1992)CrossRefGoogle Scholar
  19. 19.
    Hill, R.A., Dunbar, R.I.: Social network size in humans. Hum. Nat. 14, 53–72 (2003)CrossRefGoogle Scholar
  20. 20.
    Barra, A., Contucci, P., Sandel, R., Vernia, C.: An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action. Sci. Rep. 4, 4174 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Agliari, E., Barra, A., Contucci, P., Sandell, R., Vernia, C.: A stochastic approach for quantifying immigrant integration: the Spanish test case. New J. Phys. 16, 103034 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    Agliari, E., Barra, A., Galluzzi, A., Javarone, M.A., Pizzoferrato, A., Tantari, D.: Emerging heterogeneities in Italian customs and comparison with nearby countries. PLoS ONE 10, e0144643 (2015)CrossRefGoogle Scholar
  23. 23.
    Barra, A., Galluzzi, A., Tantari, D., Agliari, E., Requena-Silvente, F.: Assessing the role of migration as trade-facilitator using the statistical mechanics of cooperative systems. Palgrave Commun. 2, 16021 (2016)CrossRefGoogle Scholar
  24. 24.
    Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1, 143–186 (1971)MATHCrossRefGoogle Scholar
  25. 25.
    Watts, D.J.: A simple model of global cascades on random networks. Proc. Natl. Acad. Sci. USA 99, 5766–5771 (2001)ADSMathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Lee, J.-H., Jusup, M., Podobnik, B., Iwasa, Y.: Agent-based mapping of credit risk for sustainable microfinance. PLoS ONE 10, e0126447 (2015)CrossRefGoogle Scholar
  27. 27.
    Helbing, D. (ed.): Social Self-Organization. Agent-based Simulations and Experiments to Study Emergent Social Behavior. Springer, Berlin (2012)Google Scholar
  28. 28.
    Ramos, M., Shao, J., Reis, S.D.S., Anteneodo, C., Andrade, J.S., Havlin, S., Makse, H.A.: How does public opinion become extreme? Sci. Rep. 5, 10032 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Hohhman, M., Yoeli, E., Nowak, M.A.: Cooperate without looking: why we care what people think and not just what they do. Proc. Natl. Acad. Sci. USA 112, 1727–1732 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    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)ADSCrossRefGoogle Scholar
  31. 31.
    Helbing, D., Wenjian, Y.: The future of social experimenting. Proc. Natl. Acad. Sci. USA 107, 5265–5266 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    Galam, S., Javarone, M.A.: Modeling radicalization phenomena in heterogeneous populations. PLoS ONE 11, e0155407 (2016)CrossRefGoogle Scholar
  33. 33.
    Aguiar, F., Parravano, A.: Tolerating the intolerant homophily, intolerance, and segregation in social balanced networks. J. Confl. Resolut. 59, 29–50 (2015)CrossRefGoogle Scholar
  34. 34.
  35. 35.
  36. 36.
    Betz, H.G.: The new politics of resentment: radical right-wing populist parties in Western Europe. Comp. Polit. 25, 413–427 (1993)CrossRefGoogle Scholar
  37. 37.
    Lim, M., Metzler, R., Bar-Yam, Y.: Global pattern formation and ethnic/cultural violence. Science 317, 1540–1544 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    Krueger, A.B., Maleckova, J.: Attitudes and action: public opinion and occurrence of international terrorism. Science 325, 1534–1536 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    Dancygier, R.M.: Immigration and Conflict in Europe. Cambridge University Press, Cambridge (2013)Google Scholar
  40. 40.
    McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: homophily in social networks. Annu. Rev. Sociol. 27, 415–444 (2001)CrossRefGoogle Scholar
  41. 41.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)ADSMathSciNetMATHCrossRefGoogle Scholar
  42. 42.
    Jusup, M., Iwami, S., Podobnik, B., Stanley, H.E.: Dynamically rich, yet parameter-sparse models for spatial epidemiology: Comment on “Coupled disease-behavior dynamics on complex networks: A review” by Z. Wang et al. Phys. Life Rev. 15, 43–46 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    Esteban, J., Mayoral, L., Ray, D.: Ethnicity and conflict: theory and facts. Science 336, 858–865 (2012)ADSCrossRefGoogle Scholar
  44. 44.
    Kiers, E.T., Rousseau, R.A., West, S.A., Denison, R.F.: Host sanctions and the legume-rhizobium mutualism. Nature 425, 78–81 (2003)ADSCrossRefGoogle Scholar
  45. 45.
    Wang, R.W., Sun, B.F., Zheng, Q., Shi, L., Zhu, L.: Asymmetric interaction and indeterminate fitness correlation between cooperative partners in the fig-fig wasp mutualism. J. R. Soc. Interface 8, 1487–1496 (2011)CrossRefGoogle Scholar
  46. 46.
    Clutton-Brock, T.H., Parker, G.A.: Punishment in animal societies. Nature 373, 209–216 (1995)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA
  2. 2.Faculty of Civil EngineeringUniversity of RijekaRijekaCroatia
  3. 3.Zagreb School of Economics and ManagementZagrebCroatia
  4. 4.Center of Mathematics for Social CreativityHokkaido UniversitySapporoJapan
  5. 5.Interdisciplinary Graduate School of Engineering SciencesKyushu UniversityFukuokaJapan

Personalised recommendations