Equal opportunities lead to maximum wealth inequality

TL;DR

This paper demonstrates through analytical modeling that equal opportunity alone cannot prevent maximum wealth inequality in fair markets, as wealth concentration emerges inherently from the system's dynamics.

Contribution

It generalizes previous models using master equation formalism to rigorously prove that equal expected returns lead to maximum wealth inequality.

Findings

Equal opportunity does not prevent wealth concentration.

Maximum inequality arises even with fair, unbiased markets.

Analytical proof using master equations confirms this phenomenon.

Abstract

If wealthier people have advantages in having higher returns than poor, inequality will unequivocally increase, but is equal opportunity enough to prevent it? According to several models in economics and econophysics, no. They all display wealth concentration as a peculiar feature of its dynamics, even though no individual can have repeating gains advantage. Here, generalizing these particular models, we present a rigorous analytical demonstration, using master equation formalism, that any fair market that gives each agent the same expected return conducts the system to maximum inequality.