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

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.