Heterogeneous Populations: Coexistence, Integration, or Conflict

  • Dirk Helbing
Part of the Understanding Complex Systems book series (UCS)


Cooperation is of utmost importance to society, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with heterogeneous preferences. Yet, interactions between people with incompatible interests often yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative by another. To understand the outcome of such competitive interactions, we study game-dynamical replicator equations for multiple populations with incompatible preferences and different power to reveal, for example, what mechanisms can foster the evolution of behavioral norms? When does cooperation fail, leading to conflict or even to revolutions? What incentives are needed to reach peaceful agreements? Our quantitative analysis reveals some striking results, significant for society, law, and economics.


Interaction Partner Cooperative Behavior Prefer Behavior Behavioral Norm Strong Population 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank for partial support by the EU Project QLectives and the ETH Competence Center “Coping with Crises in Complex Socio-Economic Systems” (CCSS) through ETH Research Grant CH1-01 08-2. They are grateful to Thomas Chadefaux, Ryan Murphy, Carlos P. Roca, Stefan Bechtold, Sergi Lozano, Heiko Rauhut, Wenjian Yu and further colleagues for valuable comments and to Sergi Lozano for drawing Fig. 10.1. D.H. thanks Thomas Voss for his insightful seminar on social norms.


  1. 1.
    R. Axelrod, The Evolution of Cooperation (Basic Books, New York, 1984)Google Scholar
  2. 2.
    H. Gintis, Game Theory Evolving (Princeton University, Princeton, NJ, 2000)Google Scholar
  3. 3.
    M.A. Nowak, Five rules for the evolution of cooperation. Science 314, 1560–1563 (2006)Google Scholar
  4. 4.
    M. Milinski, D. Semmann, H.J. Krambeck, Reputation helps solve the “tragedy of the commons”. Nature 415, 424–426 (2002)Google Scholar
  5. 5.
    M.A. Nowak, R.M. May, Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)Google Scholar
  6. 6.
    E. Fehr, S. Gächter, Altruistic punishment in humans. Nature 415, 137–140 (2002)Google Scholar
  7. 7.
    C. Hauert, A. Traulsen, H. Brandt, M.A. Nowak, K. Sigmund, Via freedom to coercion: The emergence of costly punishment. Science 316, 1905–1907 (2007)Google Scholar
  8. 8.
    B. Rockenbach, M. Milinski, The efficient interaction of indirect reciprocity and costly punishment. Nature 444, 718–723 (2006)Google Scholar
  9. 9.
    O. Gurerk, B. Irlenbusch, B. Rockenbach, The competitive advantage of sanctioning institutions. Science 312, 108–111 (2006)Google Scholar
  10. 10.
    J. Henrich et al., Costly punishment across human societies. Science 312, 1767–1770 (2006)Google Scholar
  11. 11.
    J.H. Fowler, Altruistic punishment and the origin of cooperation. Proc. Natl. Acad. Sci. USA 102, 7047–7049 (2005)Google Scholar
  12. 12.
    R. Boyd, H. Gintis, S. Bowles, P.J. Richerson, The evolution of altruistic punishment. Proc. Natl. Acad. Sci. USA 100, 3531–3535 (2003)Google Scholar
  13. 13.
    D. Helbing, W. Yu, The outbreak of cooperation among success-driven individuals under noisy conditions. Proc. Natl. Acad. Sci. USA 106(8), 3680–3685 (2009)Google Scholar
  14. 14.
    J.W. Weibull, Evolutionary Game Theory (MIT Press, Cambridge, MA, 1996)Google Scholar
  15. 15.
    D. Helbing, S. Lozano, Phase transitions to cooperation in the prisoner’s dilemma. Phys. Rev. E 81(5), 057102 (2010)Google Scholar
  16. 16.
    H. Ohtsukia, M.A. Nowak, The replicator equation on graphs. J. Theor. Biol. 243, 86–97 (2006)Google Scholar
  17. 17.
    P. Schuster, K. Sigmund, J. Hofbauer, R. Gottlieb, P. Merz, Selfregulation of behaviour in animal societies. III. Games between two populations with selfinteraction. Biol. Cyber. 40, 17–25 (1981)Google Scholar
  18. 18.
    D. Helbing, A mathematical model for behavioral changes by pair interactions, in Economic Evolution and Demographic Change ed. by G. Haag, U. Mueller, K.G. Troitzsch (Springer, Berlin, 1992), pp. 330–348Google Scholar
  19. 19.
    D. Helbing, A. Johansson, Evolutionary dynamics of populations with conflicting interactions: Classification and analytical treatment considering asymmetry and power. Phys. Rev. E 81, 016112 (2010)Google Scholar
  20. 20.
    L. Samuelson, Chap. 5: The Ultimatum Game, in Evolutionary Games and Equilibrium Selection (The MIT Press, Cambridge, 1998)Google Scholar
  21. 21.
    R. Axelrod, An evolutionary approach to norms. Am. Pol. Sci. Rev. 80(4), 1095–1111 (1986)Google Scholar
  22. 22.
    M. Hechter, K.D. Opp (eds.), particularly Chap. 4 Game-theoretical perspectives on the emergence of social norms, in Social Norms, ed. by T. Voss (Russell Sage, New York, 2001), pp. 105–136Google Scholar
  23. 23.
    C. Bicchieri, R. Jeffrey, B. Skyrms (eds.), The Dynamics of Norms (Cambridge University, Cambridge, 2009)Google Scholar
  24. 24.
    J. Bendor, P. Swistak, The evolution of norms. Am. J. Sociol. 106(6), 1493–1545 (2001)Google Scholar
  25. 25.
    F.A.C.C. Chalub, F.C. Santos, J.M. Pacheco, The evolution of norms. J. Theor. Biol. 241, 233–240 (2006)Google Scholar
  26. 26.
    E. Ostrom, Collective action and the evolution of social norms. J. Econ. Perspect. 14(3), 137–158 (2000)Google Scholar
  27. 27.
    P.R. Ehrlich, S.A. Levin, The evolution of norms. PLoS Biol. 3(6), 0943–0948 (2005)Google Scholar
  28. 28.
    K. Keizer, S. Lindenberg, L. Steg, The spreading of disorder. Science 322, 1681–1685 (2008)Google Scholar
  29. 29.
    B. Skyrms, The Stag Hunt and the Evolution of Social Structure (Cambridge University, Cambridge, 2003)Google Scholar
  30. 30.
    K.D. Opp, Theories of Political Protest and Social Movements (Routledge, London, 2009)Google Scholar
  31. 31.
    T.S. Kuhn, The Structure of Scientific Revolutions (University of Chicago, Chicago, 1962)Google Scholar
  32. 32.
    W. Weidlich, H. Huebner, Dynamics of political opinion formation including catastrophe theory. J. Econ. Behav. Organ. 67, 1–26 (2008)Google Scholar
  33. 33.
    E. Fehr, U. Fischbacher, S. Gächter, Strong reciprocity, human cooperation, and the enforcement of social norms. Hum. Nat. 13, 1–25 (2002)Google Scholar
  34. 34.
    A. Whiten, V. Horner, F.B.M. de Waal, Conformity to cultural norms of tool use in chimpanzees. Nature 437, 737–740 (2005)Google Scholar
  35. 35.
    K. Binmore, Natural Justice (Oxford University, New York, 2005)Google Scholar
  36. 36.
    M.A. Nowak, N.L. Komarova, P. Niyogi, Computational and evolutionary aspects of language. Nature 417, 611–617 (2002)Google Scholar
  37. 37.
    V. Loreto, L. Steels, Emergence of language. Nat. Phys. 3, 758–760 (2007)Google Scholar
  38. 38.
    R. Boyd, P.J. Richerson, The Origin and Evolution of Cultures (Oxford University, Oxford, 2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dirk Helbing
    • 1
  1. 1.CLU E1ETH ZurichZurichSwitzerland

Personalised recommendations