# A two-group kinetic wealth model with wealth-gap drift and non-Maxwellian kernels

## TL;DR

This paper uses statistical mechanics to study how wealth is distributed between two groups of agents through interactions influenced by market risk and trading rates.

## Contribution

The novelty lies in using non-Maxwellian kernels and wealth-gap drift to model wealth distribution dynamics between two groups.

## Key findings

- Reducing market risk and increasing wealth replacement and trading rates promote wealth equalization.
- A high proportion of steady-state wealth in one group reduces disparities there but increases them in the other group.
- Numerical experiments confirm the theoretical conclusions about wealth distribution dynamics.

## Abstract

This paper applies statistical mechanics to investigate wealth distribution in binary interactions between two groups of agents. Using an exchange rule with non-zero expected random variables and non-Maxwellian collision kernels, we consider the case that wealth distribution is affected by the wealth replacement rate, trading rate, market risk and the proportion of steady-state wealth distributions of two groups of agents. The decrease of market risk and the increase of the wealth replacement rate and trading rate are conducive to the equalization of wealth distribution, and high proportion of steady-state wealth distributions of two groups of agents narrows disparities in group 1 but worsens them in group 2 under certain conditions. We verify our conclusions by numerical experiments.