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An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange

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  • Bruce M. Boghosian
  • Merek Johnson
  • Jeremy Marcq

Abstract

In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single individual. In this work, we prove that conjecture by demonstrating that the Gini coefficient, a measure of inequality commonly used by economists, is an $H$ function of both the Boltzmann and Fokker-Planck equations for the model.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1412.7227
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    File URL: http://arxiv.org/pdf/1412.7227
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    Cited by:

    1. 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.

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