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arXiv · 1412.7227

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

Bruce M. Boghosian·Merek Johnson·Jeremy Marcq
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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.

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Bruce M. Boghosian, Merek Johnson, Jeremy Marcq. 2014-12-23. An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange. https://doi.org/10.1007/s10955-015-1316-8

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