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A Percolation Model of Innovation in Complex Technology

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  • Silverberg,Gerald
  • Verspagen,Bart

    (MERIT)

Abstract

Innovations are known to arrive more highly clustered than if they werepurely random, and their rate of arrival has been increasing nearlyexponentially for several centuries. Their distribution of importance ishighly skewed and appears to obey a power law or lognormal distribution.Technological change has been seen by many scholars as followingtechnological trajectories and being subject to ‘paradigm’ shifts fromtime to time. To address these empirical observations, we introduce acomplex technology space based on percolation theory. This space issearched randomly in local neighborhoods of the current best-practicefrontier. Numerical simulations demonstrate that with increasing radiusof search, the probability of becoming deadlocked declines and the meanrate of innovation increases until a plateau is reached. Thedistribution of innovation sizes is highly skewed and heavy tailed. Forpercolation probabilities near the critical value, it seems to resemblean infinite-variance Pareto distribution in the tails. For highervalues, the lognormal appears to be preferred.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT) in its series Research Memorandum with number 032.

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Date of creation: 2002
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Handle: RePEc:unm:umamer:2002032

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Keywords: microeconomics ;

References

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  1. Gerald Silverberg & Bart Verspagen, 2003. "Breaking the waves: a Poisson regression approach to Schumpeterian clustering of basic innovations," Cambridge Journal of Economics, Oxford University Press, vol. 27(5), pages 671-693, September.
  2. Dosi, Giovanni, 1993. "Technological paradigms and technological trajectories : A suggested interpretation of the determinants and directions of technical change," Research Policy, Elsevier, vol. 22(2), pages 102-103, April.
  3. Zhi-Feng Huang, 2000. "Self-organized model for information spread in financial markets," Papers cond-mat/0004314, arXiv.org.
  4. Scherer, F. M. & Harhoff, Dietmar, 2000. "Technology policy for a world of skew-distributed outcomes," Research Policy, Elsevier, vol. 29(4-5), pages 559-566, April.
  5. Manuel Trajtenberg, 1990. "A Penny for Your Quotes: Patent Citations and the Value of Innovations," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 172-187, Spring.
  6. Grassberger, Peter & Yi-Cheng Zhang,, 1996. "“Self-organized” formulation of standard percolation phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(1), pages 169-179.
  7. F. M. Scherer, 1998. "The Size Distribution of Profits from Innovation," Annales d'Economie et de Statistique, ENSAE, issue 49-50, pages 495-516.
  8. Nelson, Richard R. & Winter, Sidney G., 1977. "In search of useful theory of innovation," Research Policy, Elsevier, vol. 6(1), pages 36-76, January.
  9. F. M. Scherer & Dietmar Harhoff & J, rg Kukies, 2000. "Uncertainty and the size distribution of rewards from innovation," Journal of Evolutionary Economics, Springer, vol. 10(1), pages 175-200.
  10. Vega-Redondo, Fernando, 1994. "Technological Change and Path Dependence: A Co-evolutionary Model on a Directed Graph," Journal of Evolutionary Economics, Springer, vol. 4(1), pages 59-80, March.
  11. Silverberg, Gerald & Lehnert, Doris, 1993. "Long waves and 'evolutionary chaos' in a simple Schumpeterian model of embodied technical change," Structural Change and Economic Dynamics, Elsevier, vol. 4(1), pages 9-37, June.
  12. Goldenberg, J & Libai, B & Solomon, S & Jan, N & Stauffer, D, 2000. "Marketing percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 335-347.
  13. Dietmar Harhoff & Francis Narin & F. M. Scherer & Katrin Vopel, 1999. "Citation Frequency And The Value Of Patented Inventions," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 511-515, August.
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