Abstract
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.
This chapter has been prepared by C. Roca, Moez Draief, and D. Helbing under the project title “Percolate or die: Multi-percolation decides the struggle between competing innovations”.
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References
M. Sahimi, Applications of Percolation Theory (Taylor & Francis, PA, 1994)
J. Shao, S. Havlin, H.E. Stanley, Dynamic opinion model and invasion percolation. Phys. Rev. Lett. 103, 018701 (2009)
J. Goldenberg, B. Libai, S. Solomon, N. Jan, D. Stauffer, Maketing percolation. Physica A 284, 335–347 (2000)
D. Stauffer, A. Aharony, Introduction to Percolation Theory, second edn. (Taylor & Francis, Philadelphia, 1991)
J. Chalupa, P.L. Leath, G.R. Reich, Bootstrap percolation on a bethe lattice. J. Phys. C: Solid State Phys. 12, L31–L35 (1979)
S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, k-core organization of complex networks. Phys. Rev. Lett. 96, 040601 (2006)
W.B. Arthur, Competing technologies, increasing returns, and lock-in by historical events. Econ. J. 99, 116–131 (1989)
E.M. Rogers, Diffusion of Innovations, 5th edn. (Simon and Schuster, NY, 2003)
H. Amini, M. Draief, M. Lelarge, Marketing in a random network. Network Contr. Optim. LNCS 5425, 17–25 (2009)
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)
M.S. Granovetter, Threshold models of collective behavior. Am. J. Sociol. 83, 1420–1443 (1978)
R.B. Myerson, Game Theory: Analysis of Conflict (Harvard University Press, Cambridge, 1991)
B. Skyrms, The Stag Hunt and the Evolution of Social Structure (Cambridge University Press, Cambridge, 2003)
M.A. Nowak, R.M. May, Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)
H. Gintis, Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction, 2nd edn. (Princeton University Press, Princeton, 2009)
J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998)
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. 330–348
S. Wasserman, K. Faust, Social Network Analysis: Methods and Applications (Cambridge University Press, Cambridge, 1994)
F. Vega-Redondo, Complex Social Networks (Cambridge University Press, Cambridge, 2007)
M. Nakamaru, S.A. Levin, Spread of two linked social norms on complex interaction networks. J. Theor. Biol. 230, 57–64 (2004)
A. Galeotti, S. Goyal, M.O. Jackson, F. Vega-Redondo, L. Yariv, Network games. Rev. Econ. Studies 77, 218–244 (2010)
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)
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)
G. Szabó, G. Fáth, Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)
G. Grimmett, Percolation, 2nd edn. (Springer, Berlin, 1999)
D. Achlioptas, R.M. D’Souza, J. Spencer, Explosive percolation in random networks. Science 323, 1453–1455 (2009)
D. McFadden, Conditional logit analysis of qualitative choice behavior, in Frontiers of Econometrics, ed. by P. Zarembka (Academic Press, New York, 1974), pp. 105–142
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)
L.E. Blume, The statistical mechanics of strategic interaction. Games Econ. Behav. 5, 387–424 (1993)
A. Traulsen, M.A. Nowak, J.M. Pacheco, Stochastic dynamics of invasion and fixation. Phys. Rev. E 74, 011909 (2006)
D. Centola, The spread of behavior in an online social network experiment. Science 329, 1194–1197 (2010)
K.P. Smith, N.A. Christakis, Social networks and health. Annu. Rev. Sociol. 34, 405–429 (2008)
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)
Acknowledgements
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).
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Helbing, D. (2012). Coordination and Competitive Innovation Spreading in Social Networks. In: Helbing, D. (eds) Social Self-Organization. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24004-1_9
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