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Rapid Innovation Diffusion in Social Networks

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  • H Peyton Young
  • Gabriel E. Kreindler

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.

Suggested Citation

  • H Peyton Young & Gabriel E. Kreindler, 2012. "Rapid Innovation Diffusion in Social Networks," Economics Series Working Papers 626, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:626
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    File URL: http://www.economics.ox.ac.uk/materials/papers/12437/paper626.pdf
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    References listed on IDEAS

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    1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. William H. Sandholm, 2001. "Almost global convergence to p-dominant equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 107-116.
    4. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521857406, December.
    5. Vega-Redondo,Fernando, 2007. "Complex Social Networks," Cambridge Books, Cambridge University Press, number 9780521674096, December.
    6. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    7. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    8. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
    11. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    12. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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    More about this item

    Keywords

    Innovation diffusion; Convergence time; Local interaction;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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