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

Area of Science:

• Statistical mechanics
• Agent-based modeling
• Economic systems analysis

Background:

• Wealth distribution is a complex phenomenon influenced by agent interactions.
• Previous models often simplify exchange rules and agent behaviors.
• Understanding the impact of specific economic parameters on wealth inequality is crucial.

Purpose of the Study:

• To investigate wealth distribution in binary interactions using statistical mechanics.
• To analyze the influence of wealth replacement rate, trading rate, market risk, and steady-state proportions on wealth inequality.
• To model agent interactions with non-Maxwellian collision kernels and non-zero expected random variables.

Main Methods:

• Application of statistical mechanics principles.
• Modeling binary interactions between two agent groups.
• Utilizing an exchange rule with non-zero expected random variables.
• Employing non-Maxwellian collision kernels.
• Verification through numerical experiments.

Main Results:

• Decreased market risk, increased wealth replacement rate, and increased trading rate contribute to wealth distribution equalization.
• High proportions of steady-state wealth distributions narrow wealth disparities in group 1.
• High proportions of steady-state wealth distributions can worsen wealth disparities in group 2 under specific conditions.

Conclusions:

• Economic parameters like market risk, trading rate, and wealth replacement rate significantly impact wealth equalization.
• The proportion of steady-state wealth distributions has a differential effect on wealth inequality between agent groups.
• The study provides insights into wealth dynamics through a statistical mechanics framework.