The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange: A Logistic Equation for Wealth Condensation

TL;DR

This paper introduces an analytical model showing how wealth condensation in a Yard-Sale Model with wealth-attained advantage follows a logistic growth pattern over time, revealing the dynamics of wealth concentration.

Contribution

It provides the first analytic time-dependent solution for wealth condensation in a Yard-Sale Model with continuous wealth-attained advantage bias.

Findings

Wealth condensation obeys a logistic equation over time.

Phase transition to wealth coexistence is characterized as second-order.

Analytic results clarify the dynamics of wealth accumulation.

Abstract

The addition of wealth-attained advantage (WAA) to the Yard-Sale Model (YSM) of asset exchange has been demonstrated to induce wealth condensation. In a model of WAA for which the bias is a continuous function of the wealth difference of the transacting agents, the condensation was shown to arise from a second-order phase transition to a coexistence regime. In this paper, we present the first analytic time-dependent results for this model, by showing that the condensed wealth obeys a logistic equation in time.