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The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process

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  • Nicolas Bouleau

    (CIRED - centre international de recherche sur l'environnement et le développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Chorro

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we consider some elementary and fair zero-sum games of chance to study the impact of random effects on the wealth distribution of N interacting players. Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties. From a mathematical perspective, we interestingly recover for small and high-frequency transactions some diffusion limits extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms.

Suggested Citation

  • Nicolas Bouleau & Christophe Chorro, 2017. "The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01138383, HAL.
    • Handle: RePEc:hal:cesptp:hal-01138383
    DOI: 10.1016/j.physa.2017.03.017
    Note: View the original document on HAL open archive server: https://hal.science/hal-01138383v2
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Francisco Cardoso, Ben-Hur & Gonçalves, Sebastián & Iglesias, José Roberto, 2023. "Why equal opportunities lead to maximum inequality? The wealth condensation paradox generally solved," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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