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Duality in an asset exchange model for wealth distribution

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  • Li, Jie
  • Boghosian, Bruce M.

Abstract

Asset exchange models are agent-based economic models with binary transactions. Previous investigations have augmented these models with mechanisms for wealth redistribution, quantified by a parameter χ, and for trading bias favoring wealthier agents, quantified by a parameter ζ. By deriving and analyzing a Fokker–Planck equation for a particular asset exchange model thus augmented, it has been shown that it exhibits a second-order phase transition at ζ∕χ=1, between regimes with and without partial wealth condensation. In the “subcritical” regime with ζ∕χ<1, all of the wealth is classically distributed; in the “supercritical” regime with ζ∕χ>1, a fraction 1−χ∕ζ of the wealth is condensed. Intuitively, one may associate the supercritical, wealth-condensed regime as reflecting the presence of “oligarchy,” by which we mean that an infinitesimal fraction of the total agents hold a finite fraction of the total wealth in the continuum limit.

Suggested Citation

  • Li, Jie & Boghosian, Bruce M., 2018. "Duality in an asset exchange model for wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 154-165.
    • Handle: RePEc:eee:phsmap:v:497:y:2018:i:c:p:154-165
    DOI: 10.1016/j.physa.2017.12.068
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    References listed on IDEAS

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    1. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    2. Bruce M. Boghosian & Adrian Devitt-Lee & Hongyan Wang, 2016. "The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange: A Logistic Equation for Wealth Condensation," Papers 1608.05851, arXiv.org.
    3. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
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    6. Boghosian, Bruce M. & Devitt-Lee, Adrian & Johnson, Merek & Li, Jie & Marcq, Jeremy A. & Wang, Hongyan, 2017. "Oligarchy as a phase transition: The effect of wealth-attained advantage in a Fokker–Planck description of asset exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 15-37.
    7. S. Ispolatov & P.L. Krapivsky & S. Redner, 1998. "Wealth distributions in asset exchange models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 2(2), pages 267-276, March.
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    Cited by:

    1. Lima, Hugo & Vieira, Allan R. & Anteneodo, Celia, 2022. "Nonlinear redistribution of wealth from a stochastic approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Li, Jie & Boghosian, Bruce M. & Li, Chengli, 2019. "The Affine Wealth Model: An agent-based model of asset exchange that allows for negative-wealth agents and its empirical validation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 423-442.

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