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Rapid Innovation Diffusion in Social Networks

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  • H Peyton Young
  • Gabriel E. Kreindler
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    Abstract

    The diffusion of an innovation can be represented by a process in which agents choose perturbed best responses to what their neighbors are currently doing.� Diffusion is said to be fast if the expected waiting time until the innovation spreads widely is bounded above independently of the size of the network.� Previous work has identified specific topological properties of networks that guarantee fast diffusion.� Here we apply martingale theory to derive topology-free bounds such that diffusion is fast whenever the payoff gain from the innovation is sufficiently high and the response function is sufficiently noisy.� We also provide a simple method for computing an upper bound on the expected waiting time that holds for all networks.� For the logit response function, it takes on average less than 80 revisions per capita for the innovation to diffuse widely in any network, when the error rate is at least 5% and the payoff gain (relative to the status quo) is at least 150%.� Qualitatively similar results hold for other smoothed best response functions and populations that experience heterogeneous payoff shocks.

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    Bibliographic Info

    Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 626.

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    Date of creation: 02 Oct 2012
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    Handle: RePEc:oxf:wpaper:626

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    Related research

    Keywords: Innovation diffusion; Convergence time; Local interaction;

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    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
    3. R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
    4. Duncan J. Watts & Peter Sheridan Dodds, 2007. "Influentials, Networks, and Public Opinion Formation," Journal of Consumer Research, University of Chicago Press, vol. 34(4), pages 441-458, 05.
    5. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 0. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.
    6. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
    7. William H. Sandholm, 2001. "Almost global convergence to p-dominant equilibrium," International Journal of Game Theory, Springer, vol. 30(1), pages 107-116.
    8. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
    9. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
    10. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406, October.
    11. H Peyton Young & Gabriel E. Kreindler, 2011. "Fast Convergence in Evolutionary Equilibrium Selection," Economics Series Working Papers 569, University of Oxford, Department of Economics.
    12. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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