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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.

Suggested Citation

  • Silverberg, Gerald & Verspagen, Bart, 2002. "A Percolation Model of Innovation in Complex Technology," Research Memorandum 032, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    • Handle: RePEc:unm:umamer:2002032
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    File URL: https://www.merit.unu.edu/publications/rmpdf/2002/rm2002-032.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Gerald Silverberg & Bart Verspagen, 2003. "Breaking the waves: a Poisson regression approach to Schumpeterian clustering of basic innovations," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 27(5), pages 671-693, September.
    4. 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.
    5. 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.
    6. 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.
    7. Alfred Kleinknecht, 1987. "Innovation Patterns in Crisis and Prosperity," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-18559-7, December.
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    12. F. M. Scherer, 1998. "The Size Distribution of Profits from Innovation," Annals of Economics and Statistics, GENES, issue 49-50, pages 495-516.
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    15. Zhi-Feng Huang, 2000. "Self-organized model for information spread in financial markets," Papers cond-mat/0004314, arXiv.org.
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    Cited by:

    1. Silverberg, G. & Verspagen, B., 2003. "Brewing the future: stylized facts about innovation and their confrontation with a percolation model," Working Papers 03.06, Eindhoven Center for Innovation Studies.
    2. G. Silverberg, 2007. "Long Waves: Conceptual, Empirical and Modelling Issues," Chapters, in: Horst Hanusch & Andreas Pyka (ed.), Elgar Companion to Neo-Schumpeterian Economics, chapter 50, Edward Elgar Publishing.
    3. Hanappi Hardy, 2014. "Evolutionary Political Economy in Crisis Mode," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 234(2-3), pages 422-440, April.

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