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arXiv · 2602.00988

Wealth exchange under ceiling and flooring constraints: a modified Bennati-Dragulescu-Yakovenko model

Fei Cao·Sebastien Motsch·Wendy Garcia Umbarita
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Abstract

We investigate the classical Bennati-Dragulescu-Yakovenko (BDY) dollar exchange model introduced in \cite{dragulescu_statistical_2000} where the effects of wealth ceiling and wealth flooring are explored. In our model, $N$ identical economical agents involved in the BDY game are also subjected to certain policies issued by a (artificial) government, which prevent agents whose wealth exceeds some prescribed threshold value (denoted by $b \in \mathbb N_+$) from receiving money and which prohibit agents whose wealth falls below certain threshold value (denoted by $a \in \mathbb N$) from giving out their money. We derive a mean-field system of coupled nonlinear ordinary differential equations (ODEs) governing the evolution of the distribution of money as the number of agents $N$ tends to infinity and study the large time behavior of the resulting ODE system. The impact of a wealth cap and a wealth floor on economic inequality (measured by the Gini index) will also be explored numerically.

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Fei Cao, Sebastien Motsch, Wendy Garcia Umbarita. 2026-02-01. Wealth exchange under ceiling and flooring constraints: a modified Bennati-Dragulescu-Yakovenko model. https://arxiv.org/abs/2602.00988

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