Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 385 Accesses

  • 4 Citations


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.


  1. Brock WA, Hommes CH (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. J Econ Dyn Control 22:1235–1274

  2. Dosi G (1982) Technological paradigms and technological trajectories. Res Policy 11:147162

  3. Foray D, Grübler A (1990) Morphological analysis, diffusion and lock-out of technologies: ferrous casting in France and the FRG. Res Policy 19:535–550

  4. Frenken K, Leydesdorff L (2000) Scaling trajectories in civil aircraft 1913–1997. Res Policy 29:331–348

  5. Harhoff D, Narin F, Scherer FM, Vopel K (1999) Citation frequency and the value of patented inventions. Rev Econ Stat 81:511–515

  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/London

  7. Hausman J, Hall BH, Griliches Z (1984) Econometric models for count data with an application to the patents-R&D relationship. Econometrica 52:909–938

  8. Hill BM (1975) A simple general approach to inference about the tails of a distribution. Ann Stat 3:1163–1174

  9. Nelson RR, Winter SG (1977) In search of a useful theory of innovation. Res Policy 6:36–76

  10. Resnick S (2004) Modeling data networks. In: Finkenstaedt B, Rootzen H (eds) Extreme values in finance, telecommunications, and the environment. Chapman& Hall, London

  11. Sahal D (1981) Patterns of technological innovation. Addison-Wesley, New York

  12. Saviotti PP (1996) Technological evolution, variety and the economy. Edward Elgar, Cheltenham and Brookfield

  13. Scherer FM (1998) The size distribution of profits from innovation. Ann Econ Stat 49/50:495–516

  14. Scherer FM, Harhoff D (2000) Technology policy for a world of skew-distribution outcomes. Res Policy 29:559–566

  15. Scherer FM, Harhoff D, Kukies J (2000) Uncertainty and the size distribution of rewards from innovation. J Evol Econ 10:175–200

  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)

  17. Silverberg G (2002) The discrete charm of the bourgeoisie: quantum and continuous perspectives on innovation and growth. Res Policy 31:1275–1289

  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, Cambridge

  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. http://www.tm.tue.nl/ecis/ Working%20Papers/eciswp80.pdf

  20. Silverberg G, Verspagen B (2003b) Breaking the waves: a Poisson regression approach to schumpeterian clustering of basic innovations. Camb J Econ 27:671–693

  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. http://www.merit.unimaas.nl/publications/rmpdf/2004/rm2004-021.pdf, forthcoming in J Econ

  22. Silverberg G, Verspagen B (2005) A percolation model of innovation in complex technology spaces. J Econ Dyn Control 29:225–244

  23. Sneppen K (1992) Self-organized pinning and interface growth in a random medium. Phys Rev Lett 69:3539–3542

  24. Trajtenberg M (1990) A penny for your quotes: patent citations and the value of innovations. Rand J Econ 21:172–187

  25. Winter SG (1984) Schumpeterian competition in alternative technological regimes. J Econ Behav Org 5:287–320

Download references

Author information

Correspondence to Gerald Silverberg.

Additional information

The online version of the original article can be found under doi:10.1007/s11403-006-0008-5.

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Cite this article

Silverberg, G., Verspagen, B. Self-organization of R&D search in complex technology spaces. J Econ Interac Coord 2, 195–210 (2007). https://doi.org/10.1007/s11403-007-0023-1

Download citation


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

JEL Classification

  • C15
  • C63
  • D83
  • O31