Advertisement

Wealth Distribution in Scale-Free Networks

Conference paper

Abstract

We propose three concepts for multi-agent simulation: These are the characterization of macroscopic systems, the statistical treatment of heterogeneous agents, and the nature of complex networks. We empirically study wealth distributions to characterize macro-economic systems, and show that a high wealth range follows the power law distribution. This fact motivate us to describe an agent’s activities as a stochastic process. Based on the results presented by recent studies on real-world complex networks, we conclude that business networks fall into the small-world category. We also empirically analyze business network topology and raise the possibility that business networks fall into the scale-free category. We construct an interactive stochastic multiplicative process in complex networks to explain wealth distribution and show that complex distribution appear even if an agent trades the wealth under simple rules. Therefore, it is important to take into account network topology even when we consider multi-agent systems.

Keywords

Wealth distribution Stochastic process Complex networks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert R, et al (1999) Diameter of the World-Wide Web. Nature 401:130–131CrossRefGoogle Scholar
  2. Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97zbMATHCrossRefGoogle Scholar
  3. Amaral LAN, et al (2000) Classes of small-world networks. Proc Nat Acad Sci USA 97:11149–11152CrossRefGoogle Scholar
  4. Aoyama H, et al (2000) Pareto’s law for income of individuals and debt of bankrupt companies. Fractals 8:293–300Google Scholar
  5. Barabási AL, et al (1999) Mean-field theory for scale-free random networks. Physica A272:173–187Google Scholar
  6. Barabási AL (2002) Linked: The new science of networks. Perseus Publishing, Cambridge MassachusettsGoogle Scholar
  7. Bouchaud JP, Mézard M (2000) Wealth condensation in a simple model of economy. Physica A282:536–545Google Scholar
  8. DIAMOND INC. (2002) Japanese Company File 2002. Diamond inc, TokyoGoogle Scholar
  9. Drăgulescu A, Yakovenko VM (2000) Statistical mechanics of money. Eur Phys Jour B17:723–729Google Scholar
  10. Drăgulescu A, Yakovenko VM (2001a) Evidence for the exponential distribu tion of income in the USA. Eur Phys Jour B20:585–589Google Scholar
  11. Drăgulescu A, Yakovenko VM (2001b) Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Physica A299:213–221Google Scholar
  12. Forbes (2002) Forbes 400 Richest in America. http://www.forbes.com/lists/
  13. Fujiwara Y, et al (2002) Growth and fluctuations of personal income. to be published in Physica A, arXiv:cond-mat/0208398Google Scholar
  14. Kesten H (1973) Random difference equations and renewal theory for products of random matrices. Acta Math 131:207–248MathSciNetzbMATHCrossRefGoogle Scholar
  15. NIKKEIgoo (2002) http://nikkei.goo.ne.jp/
  16. Sornette D, Cont R (1997) Convergent multiplicative processes repelled from zero: power laws and truncated power laws. J Phys 17:431–444Google Scholar
  17. Souma W (2001a) Universal structure of the personal income distribution. Fractals 9:463–470CrossRefGoogle Scholar
  18. Souma W (2001b) Physics of personal income. In: Takayasu H (ed) Empirical science of financial fluctuations: The advent of econophysics. Springer-Verlag, Tokyo, pp. 343–352Google Scholar
  19. Souma W, et al (2001c) Small-world effects in wealth distribution. arXivxondmat/0108482Google Scholar
  20. Souma W, et al (2002) Complex networks and economics. Proc Int Econ Conf, to be published in Physica AGoogle Scholar
  21. Strogatz SH (2001) Exploring complex networks. Nature 410:268–276CrossRefGoogle Scholar
  22. Takayasu H, et al (1997) Stable infinite variance fluctuations in randomly amplified Langevin systems. Phys Rev Lett 79:966–969zbMATHCrossRefGoogle Scholar
  23. Watts DJ (1999) Small worlds: The dynamics of networks between order and randomness. Princeton University Press, Princeton New JerseyGoogle Scholar
  24. Watts DJ, Strogatz SH (1998) Collective dynamics of’ small-world’ networks Nature 393:440–442CrossRefGoogle Scholar

Copyright information

© Springer Japan 2003

Authors and Affiliations

  1. 1.ATR Human Information Science LaboratoriesKyotoJapan
  2. 2.Faculty of Integrated Human StudiesKyoto UniversityKyotoJapan

Personalised recommendations