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Statistical equilibrium in simple exchange games II. The redistribution game

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  • U. Garibaldi
  • E. Scalas
  • P. Viarengo

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • U. Garibaldi & E. Scalas & P. Viarengo, 2007. "Statistical equilibrium in simple exchange games II. The redistribution game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 241-246, November.
    • Handle: RePEc:spr:eurphb:v:60:y:2007:i:2:p:241-246
    DOI: 10.1140/epjb/e2007-00338-5
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    References listed on IDEAS

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    1. Axtell, R. & Epstein, J.M. & Young, H.P., 2000. "The Emergence of Classes in a Multi-Agent Bargaining Model," Papers 9, Brookings Institution - Working Papers.
    2. Aoki,Masanao & Yoshikawa,Hiroshi, 2011. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9781107634206.
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    Cited by:

    1. Enrico Scalas & Tijana Radivojević & Ubaldo Garibaldi, 2015. "Wealth distribution and the Lorenz curve: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 79-89, April.
    2. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    3. G. Dimarco & L. Pareschi & G. Toscani & M. Zanella, 2020. "Wealth distribution under the spread of infectious diseases," Papers 2004.13620, arXiv.org.
    4. Giacomo Dimarco & Giuseppe Toscani & Mattia Zanella, 2024. "A multi-agent description of the influence of higher education on social stratification," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 19(3), pages 493-521, July.
    5. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    6. Düring, Bertram & Matthes, Daniel & Toscani, Giuseppe, 2008. "A Boltzmann-type approach to the formation of wealth distribution curves," CoFE Discussion Papers 08/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    7. Hu, Chunhua & Feng, Huarong, 2024. "Kinetic model for asset allocation with strategy switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 636(C).
    8. Gualandi, Stefano & Toscani, Giuseppe, 2018. "Pareto tails in socio-economic phenomena: A kinetic description," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-17.

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