Widening Disparity and its Suppression in a Stochastic Replicator Model

TL;DR

This paper investigates winner-take-all phenomena in stochastic replicator models, showing how disparity widens over time and how nonlinear load like taxation can stabilize the distribution.

Contribution

It introduces a stochastic replicator model with fluctuating growth rates and demonstrates how nonlinear load suppresses disparity widening, providing insights into competitive systems.

Findings

Disparity widens indefinitely in the model without intervention.

A lognormal distribution describes the nonstationary evolution.

Nonlinear load leads to a stationary distribution, suppressing disparity.

Abstract

Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all elements are statistically equivalent. A lognormal distribution describes well the nonstationary time evolution. If a nonlinear load corresponding to progressive taxation is introduced, a stationary distribution is obtained and disparity widening is suppressed.