Wealth concentration in systems with unbiased binary exchanges

TL;DR

This paper rigorously proves that in systems with unbiased binary wealth exchanges, the wealth distribution inevitably evolves towards perfect inequality with no mobility, highlighting fundamental limitations of such models.

Contribution

It provides a rigorous analytical proof that unbiased binary exchange models always lead to perfect inequality and zero mobility, clarifying their long-term behavior.

Findings

Unbiased binary exchanges lead to perfect wealth inequality.

Systems reach a state with zero mobility.

The model's dynamics are analytically characterized.

Abstract

Aiming to describe the wealth distribution evolution, several models consider an ensemble of interacting economic agents that exchange wealth in binary fashion. Intriguingly, models that consider an unbiased market, that gives to each agent the same chances to win in the game, are always out of equilibrium until the perfect inequality of the final state is attained. Here we present a rigorous analytical demonstration that any system driven by unbiased binary exchanges are doomed to drive the system to perfect inequality and zero mobility.