Abstract.
We propose a simple stochastic exchange game mimicking taxation and redistribution. There are g agents and n coins; taxation is modeled by randomly extracting some coins; then, these coins are redistributed to agents following Polya's scheme. The individual wealth equilibrium distribution for the resulting Markov chain is the multivariate symmetric Polya distribution. In the continuum limit, the wealth distribution converges to a Gamma distribution, whose form factor is just the initial redistribution weight. The relationship between this taxation-and-redistribution scheme and other simple conservative stochastic exchange games (such as the BDY game) is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Boltzmann, Wissenschaftliche Abhandlungen, edited by Hasenöhrl (1909), Vol. 1, pp. 49–96
E. Parzen, Modern Probability Theory and Its Applications (Wiley, 1960)
L. Boltzmann, Wissenschaftliche Abhandlungen, edited by Hasenöhrl (1909), Vol. 2., pp. 164–223
A. Bach, Arch. Ex. Sci. 41, 1 (1990)
A. Chatterjee, S. Yarlagadda, B.K. Chakrabarti, Econophysics of Wealth Distributions (Springer, Berlin, 2005)
M. Gallegati, S. Keen, T. Lux, P. Ormerod, Physica A 370, 1 (2006)
R. Axtell, J.M. Epstein, H.P. Young, The Emergence of Classes in a Multi-Agent Bargaining Model, Working Paper No. 9, Center on Social and Economic Dynamics, February 2000
E. Scalas, U. Garibaldi, S. Donadio, Eur. Phys. J. B 53, 267 (2006)
M. Aoki, H. Yoshikawa, Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes (Cambridge University Press, Cambridge, UK, 2006)
E. Bennati, Riv. Int. Sci. Econom. Comme. 35, 735 (1988)
A. Dragulescu, V.M. Yakovenko, Eur. Phys. J. B 17, 723 (2000)
V.M. Yakovenko, Statistical Mechanics Approach to Econophysics, Springer Encyclopedia of Complexity and System Science http://refworks.springer.com/complexity/
D. Costantini, U. Garibaldi, Found. Phys. 30, 81 (2000)
http://en.wikipedia.org/wiki/Gini_coefficient
L. March, J. Soc. Stat. Paris 193, 241 (1898)
L. Amoroso, Ann. Mat. Pura Appl. 21, 123 (1925)
A.B. Salem, T.D. Mount, Econometrica 42, 1115 (1974)
R. D'Addario, Giorn. Econ. Ann. Econ. 8, 91 (1949)
J. Angle, Physica A 367, 388 (2006)
U. Garibaldi, D. Costantini, S. Donadio, P. Viarengo, Physica A 355, 224 (2005)
U. Garibaldi, D. Costantini, S. Donadio, P. Viarengo, Comput. Econ. 27, 115 (2006)
S. Keen, working paper, 2007
A. Chakraborti, B.K. Chakrabarti, Eur. Phys. J. B 17, 167 (2000)
T. Di Matteo, T. Aste, S.T. Hyde, in The Physics of Complex Systems, edited by F. Mallamace, H.E. Stanley, Proceedings of International School of Physics “Enrico Fermi” (IOS Press, Amsterdam, 2004), pp. 435–442
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Garibaldi, U., Scalas, E. & Viarengo, P. Statistical equilibrium in simple exchange games II. The redistribution game. Eur. Phys. J. B 60, 241–246 (2007). https://doi.org/10.1140/epjb/e2007-00338-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2007-00338-5