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Rapid Innovation Diffusion in Social Networks

  • H Peyton Young
  • Gabriel E. Kreindler

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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File URL: http://www.economics.ox.ac.uk/materials/papers/12437/paper626.pdf
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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
Contact details of provider: Postal: Manor Rd. Building, Oxford, OX1 3UQ
Web page: http://www.economics.ox.ac.uk/
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  1. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
  2. William H. Sandholm, 2001. "Almost global convergence to p-dominant equilibrium," International Journal of Game Theory, Springer, vol. 30(1), pages 107-116.
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  5. Lawrence E. Blume, 1994. "How Noise Matters," Game Theory and Information 9407002, EconWPA, revised 27 Jul 1994.
  6. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
  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. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  9. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  10. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  11. R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
  12. 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.
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