Journal of Economic Interaction and Coordination

, Volume 2, Issue 2, pp 195–210 | Cite as

Self-organization of R&D search in complex technology spaces

  • Gerald Silverberg
  • Bart Verspagen
Open Access


We extend an earlier model of innovation dynamics based on percolation by adding endogenous R&D search by economically motivated firms. The {0, 1} seeding of the technology lattice is now replaced by draws from a lognormal distribution for technology ‘difficulty’. Firms are rewarded for successful innovations by increases in their R&D budget. We compare two regimes. In the first, firms are fixed in a region of technology space. In the second, they can change their location by myopically comparing progress in their local neighborhoods and probabilistically moving to the region with the highest recent progress. We call this the moving or self-organizational regime (SO). The SO regime always outperforms the fixed one, but its performance is a complex function of the ‘rationality’ of firm search (in terms of search radius and speed of movement). The clustering of firms in the SO regime grows rapidly and then fluctuates in a complex way around a high value that increases with the search radius. We also investigate the size distributions of the innovations generated in each regime. In the fixed one, the distribution is approximately lognormal and certainly not fat tailed. In the SO regime, the distributions are radically different. They are much more highly right skewed and show scaling over at least 2 decades with a slope around one, for a wide range of parameter settings. Thus we argue that firm self-organization leads to self-organized criticality.


Innovation Percolation Search Technological change R&D Clustering Self-organized criticality 

JEL Classification

C15 C63 D83 O31 


  1. Brock WA, Hommes CH (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. J Econ Dyn Control 22:1235–1274CrossRefGoogle Scholar
  2. Dosi G (1982) Technological paradigms and technological trajectories. Res Policy 11:147162CrossRefGoogle Scholar
  3. Foray D, Grübler A (1990) Morphological analysis, diffusion and lock-out of technologies: ferrous casting in France and the FRG. Res Policy 19:535–550CrossRefGoogle Scholar
  4. Frenken K, Leydesdorff L (2000) Scaling trajectories in civil aircraft 1913–1997. Res Policy 29:331–348CrossRefGoogle Scholar
  5. Harhoff D, Narin F, Scherer FM, Vopel K (1999) Citation frequency and the value of patented inventions. Rev Econ Stat 81:511–515CrossRefGoogle Scholar
  6. Harhoff D, Scherer FM, Vopel K (2003) Exploring the tail of patented value distribution. In: Grandstrand O (ed) Economics, law and intellectual property. Kluwer, Boston/Dordrecht/LondonGoogle Scholar
  7. Hausman J, Hall BH, Griliches Z (1984) Econometric models for count data with an application to the patents-R&D relationship. Econometrica 52:909–938CrossRefGoogle Scholar
  8. Hill BM (1975) A simple general approach to inference about the tails of a distribution. Ann Stat 3:1163–1174Google Scholar
  9. Nelson RR, Winter SG (1977) In search of a useful theory of innovation. Res Policy 6:36–76CrossRefGoogle Scholar
  10. Resnick S (2004) Modeling data networks. In: Finkenstaedt B, Rootzen H (eds) Extreme values in finance, telecommunications, and the environment. Chapman& Hall, LondonGoogle Scholar
  11. Sahal D (1981) Patterns of technological innovation. Addison-Wesley, New YorkGoogle Scholar
  12. Saviotti PP (1996) Technological evolution, variety and the economy. Edward Elgar, Cheltenham and BrookfieldGoogle Scholar
  13. Scherer FM (1998) The size distribution of profits from innovation. Ann Econ Stat 49/50:495–516Google Scholar
  14. Scherer FM, Harhoff D (2000) Technology policy for a world of skew-distribution outcomes. Res Policy 29:559–566CrossRefGoogle Scholar
  15. Scherer FM, Harhoff D, Kukies J (2000) Uncertainty and the size distribution of rewards from innovation. J Evol Econ 10:175–200CrossRefGoogle Scholar
  16. Schumpeter JA (1939) Business cycles: a theoretical, historical and statistical analysis of the capitalist process. McGraw-Hill, New York (page numbers quoted in the text refer to the abridged version reprinted in 1989 by Porcupine Press, Philadelphia)Google Scholar
  17. Silverberg G (2002) The discrete charm of the bourgeoisie: quantum and continuous perspectives on innovation and growth. Res Policy 31:1275–1289CrossRefGoogle Scholar
  18. Silverberg G, Lehnert D (1996). Evolutionary chaos: growth fluctuations in a Schumpeterian model of creative destruction. In: Barnett WA, Kirman A, Salmon M (eds) Nonlinear dynamics in economics. Cambridge University Press, CambridgeGoogle Scholar
  19. Silverberg G, Verspagen B (2003a) Brewing the future: Stylized facts about innovation and their confrontation with a percolation model. Eindhoven: ECIS Working Paper 80. Working%20Papers/eciswp80.pdfGoogle Scholar
  20. Silverberg G, Verspagen B (2003b) Breaking the waves: a Poisson regression approach to schumpeterian clustering of basic innovations. Camb J Econ 27:671–693CrossRefGoogle Scholar
  21. Silverberg G, Verspagen, B (2004) The size distribution of innovations revisited: an application of extreme value statistics to citation and returns measures of patent significance. Maastricht: MERIT Research Memorandum 2004–021., forthcoming in J EconGoogle Scholar
  22. Silverberg G, Verspagen B (2005) A percolation model of innovation in complex technology spaces. J Econ Dyn Control 29:225–244CrossRefGoogle Scholar
  23. Sneppen K (1992) Self-organized pinning and interface growth in a random medium. Phys Rev Lett 69:3539–3542CrossRefGoogle Scholar
  24. Trajtenberg M (1990) A penny for your quotes: patent citations and the value of innovations. Rand J Econ 21:172–187CrossRefGoogle Scholar
  25. Winter SG (1984) Schumpeterian competition in alternative technological regimes. J Econ Behav Org 5:287–320CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.MERITMaastrichtThe Netherlands
  2. 2.ECISTechnical University of EindhovenEindhovenThe Netherlands
  3. 3.IIASALaxenburgAustria

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