Coordination and Competitive Innovation Spreading in Social Networks

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


Competition is one of the most fundamental phenomena in physics, biology and economics. Recent studies of the competition between innovations have highlighted the influence of switching costs and interaction networks, but the problem is still puzzling. We introduce a model that reveals a novel multi-percolation process, which governs the struggle of innovations trying to penetrate a market. We find that innovations thrive as long as they percolate in a population, and one becomes dominant when it is the only one that percolates. Besides offering a theoretical framework to understand the diffusion of competing innovations in social networks, our results are also relevant to model other problems such as opinion formation, political polarization, survival of languages and the spread of health behavior.


Switching Cost Percolation Threshold Percolation Process Coordination Game Asymptotic Density 
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.



C. P. R. and D. H. were partially supported by the Future and Emerging Technologies programme FP7-COSI-ICT of the European Commission through project QLectives (grant no. 231200).


  1. 1.
    M. Sahimi, Applications of Percolation Theory (Taylor & Francis, PA, 1994)Google Scholar
  2. 2.
    J. Shao, S. Havlin, H.E. Stanley, Dynamic opinion model and invasion percolation. Phys. Rev. Lett. 103, 018701 (2009)Google Scholar
  3. 3.
    J. Goldenberg, B. Libai, S. Solomon, N. Jan, D. Stauffer, Maketing percolation. Physica A 284, 335–347 (2000)Google Scholar
  4. 4.
    D. Stauffer, A. Aharony, Introduction to Percolation Theory, second edn. (Taylor & Francis, Philadelphia, 1991)Google Scholar
  5. 5.
    J. Chalupa, P.L. Leath, G.R. Reich, Bootstrap percolation on a bethe lattice. J. Phys. C: Solid State Phys. 12, L31–L35 (1979)Google Scholar
  6. 6.
    S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, k-core organization of complex networks. Phys. Rev. Lett. 96, 040601 (2006)Google Scholar
  7. 7.
    W.B. Arthur, Competing technologies, increasing returns, and lock-in by historical events. Econ. J. 99, 116–131 (1989)Google Scholar
  8. 8.
    E.M. Rogers, Diffusion of Innovations, 5th edn. (Simon and Schuster, NY, 2003)Google Scholar
  9. 9.
    H. Amini, M. Draief, M. Lelarge, Marketing in a random network. Network Contr. Optim. LNCS 5425, 17–25 (2009)Google Scholar
  10. 10.
    P. Klemperer, Competition when consumers have switching costs: An overview with applications to industrial organization, macroeconomics, and international trade. Rev. Econ. Stud. 62, 515–539 (1995)Google Scholar
  11. 11.
    M.S. Granovetter, Threshold models of collective behavior. Am. J. Sociol. 83, 1420–1443 (1978)Google Scholar
  12. 12.
    R.B. Myerson, Game Theory: Analysis of Conflict (Harvard University Press, Cambridge, 1991)Google Scholar
  13. 13.
    B. Skyrms, The Stag Hunt and the Evolution of Social Structure (Cambridge University Press, Cambridge, 2003)Google Scholar
  14. 14.
    M.A. Nowak, R.M. May, Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)Google Scholar
  15. 15.
    H. Gintis, Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction, 2nd edn. (Princeton University Press, Princeton, 2009)Google Scholar
  16. 16.
    J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998)Google Scholar
  17. 17.
    D. Helbing, A mathematical model for behavioral changes through pair interactions, in Economic Evolution and Demographic Change ed. by G. Hagg, U. Mueller, K.G. Troitzsch (Springer, Berlin, 1992), pp. 330–348Google Scholar
  18. 18.
    S. Wasserman, K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, 1994)Google Scholar
  19. 19.
    F. Vega-Redondo, Complex Social Networks (Cambridge University Press, Cambridge, 2007)Google Scholar
  20. 20.
    M. Nakamaru, S.A. Levin, Spread of two linked social norms on complex interaction networks. J. Theor. Biol. 230, 57–64 (2004)Google Scholar
  21. 21.
    A. Galeotti, S. Goyal, M.O. Jackson, F. Vega-Redondo, L. Yariv, Network games. Rev. Econ. Studies 77, 218–244 (2010)Google Scholar
  22. 22.
    M.E.J. Newman, D.J. Watts, S.H. Strogatz, Random graph models of social networks. Proc. Natl. Acad. Sci. U.S.A. 99, 2566–2572 (2002)Google Scholar
  23. 23.
    C.P. Roca, J.A. Cuesta, A. Sánchez, Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics. Phys. Life Rev. 6, 208–249 (2009)Google Scholar
  24. 24.
    G. Szabó, G. Fáth, Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)Google Scholar
  25. 25.
    G. Grimmett, Percolation, 2nd edn. (Springer, Berlin, 1999)Google Scholar
  26. 26.
    D. Achlioptas, R.M. D’Souza, J. Spencer, Explosive percolation in random networks. Science 323, 1453–1455 (2009)Google Scholar
  27. 27.
    D. McFadden, Conditional logit analysis of qualitative choice behavior, in Frontiers of Econometrics, ed. by P. Zarembka (Academic Press, New York, 1974), pp. 105–142Google Scholar
  28. 28.
    J.K. Goeree, C.A. Holt, Stochastic game theory: For playing games, not just for doing theory. Proc. Natl. Acad. Sci. U.S.A. 96, 10564–10567 (1999)Google Scholar
  29. 29.
    L.E. Blume, The statistical mechanics of strategic interaction. Games Econ. Behav. 5, 387–424 (1993)Google Scholar
  30. 30.
    A. Traulsen, M.A. Nowak, J.M. Pacheco, Stochastic dynamics of invasion and fixation. Phys. Rev. E 74, 011909 (2006)Google Scholar
  31. 31.
    D. Centola, The spread of behavior in an online social network experiment. Science 329, 1194–1197 (2010)Google Scholar
  32. 32.
    K.P. Smith, N.A. Christakis, Social networks and health. Annu. Rev. Sociol. 34, 405–429 (2008)Google Scholar
  33. 33.
    A. Traulsen, D. Semmann, R.D. Sommerfeld, H.-J. Krambeck, M. Milinski, Human strategy updating in evolutionary games. Proc. Natl. Acad. Sci. U.S.A. 107, 2962–2966 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

Personalised recommendations