Wealth exchange under ceiling and flooring constraints: a modified Bennati-Dragulescu-Yakovenko model
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| Format: | Preprint |
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2026
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| author | Cao, Fei Motsch, Sebastien Umbarita, Wendy Garcia |
| author_facet | Cao, Fei Motsch, Sebastien Umbarita, Wendy Garcia |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_00988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wealth exchange under ceiling and flooring constraints: a modified Bennati-Dragulescu-Yakovenko model Cao, Fei Motsch, Sebastien Umbarita, Wendy Garcia Probability 91B70, 91B80, 82C31, 35Q84 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. |
| title | Wealth exchange under ceiling and flooring constraints: a modified Bennati-Dragulescu-Yakovenko model |
| topic | Probability 91B70, 91B80, 82C31, 35Q84 |
| url | https://arxiv.org/abs/2602.00988 |