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Wealth distribution and collective knowledge. A Boltzmann approach

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  • Lorenzo Pareschi
  • Giuseppe Toscani

Abstract

We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi, Toscani, J. Stat. Phys. 2005. The trades, which include both saving propensity and the risks of the market, are here modified in the risk and saving parameters, which now are assumed to depend on the personal degree of knowledge. The numerical simulations show that the presence of knowledge has the potential to produce a class of wealthy agents and to account for a larger proportion of wealth inequality.

Suggested Citation

  • Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    • Handle: RePEc:arx:papers:1401.4550
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Cui, Lijie & Lin, Chuandong, 2021. "A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    3. Brugna, Carlo & Toscani, Giuseppe, 2018. "Kinetic models for goods exchange in a multi-agent market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 362-375.
    4. J. Franceschi & L. Pareschi & M. Zanella, 2022. "From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-26, December.
    5. Max Greenberg & H. Oliver Gao, 2024. "Twenty-five years of random asset exchange modeling," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-27, June.
    6. Zanella, Mattia, 2020. "Structure preserving stochastic Galerkin methods for Fokker–Planck equations with background interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 28-47.
    7. Hongjing Chen & Chong Lai & Hanlei Hu, 2024. "Kinetic Models for the Exchange of Production Factors in a Multi-agent Market," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2559-2584, June.
    8. Xia Zhou & Shaoyong Lai, 2023. "The mutual influence of knowledge and individual wealth growth," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-22, June.
    9. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.
    10. Giuseppe Toscani & Andrea Tosin & Mattia Zanella, 2019. "Multiple-interaction kinetic modelling of a virtual-item gambling economy," Papers 1904.07660, arXiv.org.
    11. 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.
    12. Wang, Lingling & Lai, Shaoyong & Sun, Rongmei, 2022. "Optimal control about multi-agent wealth exchange and decision-making competence," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    13. G. Dimarco & L. Pareschi & G. Toscani & M. Zanella, 2020. "Wealth distribution under the spread of infectious diseases," Papers 2004.13620, arXiv.org.
    14. Pareschi, Lorenzo & Vellucci, Pierluigi & Zanella, Mattia, 2017. "Kinetic models of collective decision-making in the presence of equality bias," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 201-217.
    15. Marco Torregrossa & Giuseppe Toscani, 2017. "Wealth distribution in presence of debts. A Fokker--Planck description," Papers 1709.09858, arXiv.org.

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