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Bounding the approach to oligarchy in a variant of the yard-sale model

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  • David W. Cohen
  • Bruce M. Boghosian

Abstract

We present analytical results for the Gini coefficient of economic inequality under the dynamics of a modified Yard-Sale Model of kinetic asset exchange. A variant of the Yard-Sale Model is introduced by modifying the underlying binary transaction of the classical system. It is shown that the Gini coefficient is monotone under the resulting dynamics but the approach to oligarchy, as measured by the Gini index, can be bounded by a first-order differential inequality used in conjunction with the differential Gronwall inequality. This result is in the spirit of entropy -- entropy production inequalities for diffusive PDE. The asymptotics of the modified system, with a redistributive tax, are derived and shown to agree with the original, taxed Yard-Sale Model, which implies the modified system is as suitable for matching real wealth distributions. The Gini -- Gini production inequality is shown to hold for a broader class of models.

Suggested Citation

  • David W. Cohen & Bruce M. Boghosian, 2023. "Bounding the approach to oligarchy in a variant of the yard-sale model," Papers 2310.16098, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2310.16098
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    References listed on IDEAS

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    1. Bruce Boghosian, 2014. "Fokker–Planck description of wealth dynamics and the origin of Pareto's law," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(12), pages 1-8.
    2. Chorro, Christophe, 2016. "A simple probabilistic approach of the Yard-Sale model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 35-40.
    3. 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.
    4. Christophe Chorro, 2016. "A simple probabilistic approach of the Yard-Sale model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01387028, HAL.
    5. Bruce M. Boghosian, 2014. "Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law," Papers 1407.6851, arXiv.org.
    6. Christophe Chorro, 2016. "A simple probabilistic approach of the Yard-Sale model," Post-Print hal-01387028, HAL.
    7. Christoph Borgers & Claude Greengard, 2023. "A new probabilistic analysis of the yard-sale model," Papers 2308.01485, arXiv.org.
    8. Bruce M. Boghosian & Merek Johnson & Jeremy Marcq, 2014. "An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange," Papers 1412.7227, arXiv.org.
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