Skip to main content
SpringerLink
Log in

Co-Evolutive Models for Firms Dynamics

  • Chapter
Networks, Topology and Dynamics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 613))

This paper considers the Bak—Sneppen (B&S) Self-Organized Criticality model originally developed for species co-evolution. We focus both on the original application of the model on a lattice, and on scale-free networks. Stylized facts on firms size distribution are also considered for the application of the model to the analysis of firms size dynamics. Thus, the B&S dynamics under the uniform, Normal, lognormal, Pareto, and Weibull distributions is studied. The original model is also extended by introducing weights on links connecting species, and examining the topology of the resulting Minimum Spanning Tree (MST) of the underlying network. In a system of firms a MST may evidence the template of the strongest interactions among firms. Conditions that lead to particular configurations of a MST are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert R, Barabasi AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97

    Article  Google Scholar 

  2. Amaral LAN, Buldyrev SV, Havlin S, Leschhorn H, Maass P, Salinger MA, Stanley HE, Stanley MHR (1997) Scaling behavior in economics: I. Empirical results for company growth.J Phys I 7:621–633

    Article  Google Scholar 

  3. Amaral LAN, Buldyrev SV, Havlin S, Leschhorn H, Maass P, Salinger MA, Stanley HE, Stanley MHR (1997) Scaling behavior in economics: II. Modeling of company growth. J Phys I 7:635–650

    Article  Google Scholar 

  4. Andergassen R, Nardini F, Ricottilli M (2007) The emergence of paradigm setters through firms interaction and network formation (to appear)

    Google Scholar 

  5. Ausloos M, Pekalski A (2007) Model of wealth and goods dynamics in a closed market. Phys-ica A 373:560–568

    Google Scholar 

  6. Ausloos M, Petroni F (2007) Statistical dynamics of religions and adherents. Europhys Lett 77:38002

    Article  Google Scholar 

  7. Ausloos M, Clippe P, Pekalski A (2004) Evolution of economic entities under heterogeneous political/environmental conditions within a Bak—Sneppen-like dynamics. Physica A 332:394–402

    Article  Google Scholar 

  8. Axtell RL (2001) Zipf distribution of u.s. firm sizes. Science 293:1818–1820

    Article  Google Scholar 

  9. Bak P (1996) How nature works. Springer, New York

    Google Scholar 

  10. Bak P, Sneppen K (1993) Punctuated equilibrium and criticality in a simple model of evolution. Phys Rev Lett 71:4083–4086

    Article  Google Scholar 

  11. Cerqueti R, Rotundo G (2007) Processi di rinnovamento nei cluster di imprese. In Garofalo G, Capitalismo distrettuale, localismi d'impresa, globalizzazione. Firenze University Press:129–143

    Google Scholar 

  12. Cuniberti G, Valleriani A, Vega JL (2001) Effects of regulation on a self-organized market.Quantitative Finance 1:332–338

    Google Scholar 

  13. Delli Gatti D, Di Guilmi C, Gaffeo E, Giulioni G, Gallegati M, Palestrini A (2004) Business cycle fluctuations and firms' size distribution dynamics. Adv Complex Syst 7(2):1–18

    Google Scholar 

  14. Delli Gatti D, Di Guilmi C, Gaffeo E, Giulioni G, Gallegati M, Palestrini A (2005) A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility. J Econ Behav Organ 56:489–512

    Article  Google Scholar 

  15. Di Guilmi C, Gaffeo E, Gallegati M (2003) Power law scaling in the world income distribution.Econ Bull 15(6):1–7

    Google Scholar 

  16. Di Guilmi C, Gaffeo E, Gallegati M (2004) Empirical results on the size distribution of business cycle phases. Physica A 333:325–334

    Article  Google Scholar 

  17. Di Guilmi C, Gallegati M, Ormerod P (2004) Scaling invariant distributions of firms exit in OECD countries. Physica A 334:267–273

    Article  Google Scholar 

  18. Dickman R, Muñoz MA, Vespignani A, Zapperi S (2000) Paths to self-organized criticality. Bras J Phys 30:27–41

    Google Scholar 

  19. Dobrin R, Duxbury PM (2001) Minimum spanning trees on random networks. Phys Rev Lett 86(22):5076–5079

    Article  Google Scholar 

  20. Föllmer H, Horst U, Kirman A (2005) Equilibria in financial markets with etherogeneous agents: a prbobabilistic perspective. J Math Econ 41:123–125

    Article  Google Scholar 

  21. Fujiwara Y, Di Guilmi C, Aoyama H, Gallegati M, Souma W (2000) Do Pareto—Zipf and Gibrat laws hold true? An analysis with European firms. Physica A Stat Mech Appl 335 (1–2):197–216

    Google Scholar 

  22. Gaffeo E, Gallegati M, Palestrini A (2003) On the size distribution of firms: additional evidence from the G7 countries. Physica A Stat Mech Appl 324(1–2):117–123

    Article  Google Scholar 

  23. Grassberger P (1995) The Bak—Sneppen model for punctuated evolution. Phys Lett A 200:277–282

    Article  Google Scholar 

  24. Hart PE, Oulton N (1996) Growth and size of firms. Econ J 106:1242–1252

    Article  Google Scholar 

  25. Hart PE, Oulton N (1997) Zipf and the size distribution of firms. Appl Econ Lett 4:205–206

    Article  Google Scholar 

  26. Jensen HJ (1998) Self-organized criticality. Cambridge Lecture Notes in Physics

    Google Scholar 

  27. Kertesz J, Kullmann L, Zawadowski AG, Karadi R, Kaski K (2003) Correlations and response:absence of detailed balance on the stock market. Physica A 324(1):74–80

    Article  Google Scholar 

  28. Kim DH, Noh JD, Jeong H (2004) Scale-free trees: skeleton of complex networks. Phys RevE 70:046126

    Google Scholar 

  29. Kirman A, Teyssiere G (2002) Microeconomic models for long-memory in the volatility of financial time series. Studies in Noninear Dynamics and Econometrics 5:281–302

    Article  Google Scholar 

  30. Kulkarni RV, Almaas E, Stroud D (1999) Evolutionary dynamics in the Bak—Sneppen model on small-world networks. arXiv:cond-mat/9905066 v1 6

    Google Scholar 

  31. Lambiotte R, Ausloos M (2005) Uncovering collective listening habits and music genres in bipartite networks. Phys Rev E 72:066107

    Google Scholar 

  32. Lambiotte R, Ausloos M (2006) Modeling the evolution of coupled networks. In: First World congress on Social Simulation (WCSS 2006), e-Proceedings 1:375–381

    Google Scholar 

  33. Lambiotte R, Ausloos M, Holyst JA (2007) Majority model on a network with communities.Phys Rev E 75

    Google Scholar 

  34. Lee S, Kim Y (2005) Coevolutionary dynamics on scale-free networks. Phys Rev E 71:057102

    Google Scholar 

  35. Lee KE, Hong BH, Lee JW (2005) Universality class of Bak—Sneppen model on scale-free network. arXiv:cond-mat/0510067

    Google Scholar 

  36. Macdonald PJ, Almaas E, Barabasi AL (2005) Minimum spanning trees of weighted scale-free networks. Europhys Lett. 72:308314

    Google Scholar 

  37. Maslov S (1996) Infinite hierarchy of exact equations in the Bak—Sneppen model. Phys RevLett 77:1182

    Google Scholar 

  38. Meester R, Znamenski D (2004) Critical thresholds and the limit distribution in the Bak—Sneppen model. Commun Math Phys 246

    Google Scholar 

  39. Paczuski M, Maslov S, Bak P (1996) Avalanche dynamics in evolution, growth, and depinning models. Phys Rev E 53:414

    Article  Google Scholar 

  40. Palestrini A (2007) Analysis of industrial dynamics: a note on the relationship between firms'size and growth rate. Econ Lett 94(3):367–371

    Article  Google Scholar 

  41. Rotundo G, Ausloos M (2007) Microeconomic co-evolution model for financial technicalanalysis signals. Physica A 373:569–585

    Article  Google Scholar 

  42. Salvemini MT, Simeone B, Succi R (1995) Analisi del possesso integrato nei gruppi di imprese mediante grafi. L'Industria XVI:641–662

    Google Scholar 

  43. Sornette D (2002) Why the stock markets crash. Princeton University Press, Princeton

    Google Scholar 

  44. Stanley MHR, Amaral LAN, Buldyrev SV, Havlin S, Leschhorn H, Maass P, Salinger MA, Stanley HE (1996) Scaling behaviour in the growth of companies. Lett Nature 379:804–806

    Article  Google Scholar 

  45. Stauffer D, Sornette D (1999) Self-organized percolation model for stock market fluctuations.Physica A 271:496

    Article  Google Scholar 

  46. Sutton J (2003) The variance of corporate growth rates. Physica A 324(1):45–48

    Article  Google Scholar 

  47. Szabo GJ, Alava M, Kertesz J (2003) Geometry of minimum spanning trees on scale-free networks. Physica A 330:31–36

    Article  Google Scholar 

  48. Vergeles M (1995) Self-prganization at nonzero temperatures. Phys Rev Lett 75

    Google Scholar 

  49. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:4

    Article  Google Scholar 

  50. Yamano T (2001) Regulation effects on market with Bak—Sneppen model in high dimenzions.Int J Mod Phys C 12:13291333

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics, University of Tuscia, Viterbo, Italy

    Giulia Rotundo

  2. Faculty of Economics, University of Rome “La Sapienza”, Rome, Italy

    Andrea Scozzari

Authors
  1. Giulia Rotundo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Scozzari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipto. Economia Politica, Universià degli Studi di MilanoBicocca, Piazza dell'Ateneo Nuovo, 1, Milano, 20126, Italy

    Ahmad K. Naimzada  & Silvana Stefani  & 

  2. Universià Cattolica del Sarcro Cuore, Largo A. Gemelli, 1, Milano, 20123, Italy

    Anna Torriero

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Rotundo, G., Scozzari, A. (2009). Co-Evolutive Models for Firms Dynamics. In: Naimzada, A.K., Stefani, S., Torriero, A. (eds) Networks, Topology and Dynamics. Lecture Notes in Economics and Mathematical Systems, vol 613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68409-1_7

Download citation

Publish with us

Policies and ethics

Search

Navigation