Exponential wealth distribution in a random market. A rigorous explanation

TL;DR

This paper provides a rigorous analytical explanation for the emergence of exponential wealth distribution in gas-like economic models, which previously was observed only through simulations.

Contribution

It offers the first rigorous proof explaining why exponential wealth distributions appear as the equilibrium in certain economic gas-like models.

Findings

Exponential wealth distribution emerges as the asymptotic regime.

The analytical explanation confirms simulation results.

The model's equilibrium is rigorously characterized.

Abstract

In simulations of some economic gas-like models, the asymptotic regime shows an exponential wealth distribution, independently of the initial wealth distribution given to the system. The appearance of this statistical equilibrium for this type of gas-like models is explained in a rigorous analytical way.