Extended Yard Sale model of wealth distribution on Erd\H{o}s-R\'enyi random networks

TL;DR

This paper extends the Yard Sale wealth distribution model to Erdős-Rényi networks, revealing that network structure influences wealth condensation patterns and phase transition behavior.

Contribution

It introduces a networked version of the Extended Yard Sale model and analyzes how Erdős-Rényi networks affect wealth distribution and phase transitions.

Findings

Networked model exhibits local wealth condensation.

Continuous phase transition persists in the networked case.

Network structure alters condensation from global to local.

Abstract

Excessive wealth concentration can undermine economic and social development. Random Asset Exchange (RAE) models provide valuable tools to investigate this phenomenon. Assuming that economic systems may operate optimally near the critical point of a continuous phase transition, the Extended Yard Sale (EYS) model introduced by Boghosian et al.~[Physica A 476, 15 (2017)] offers a compelling framework. This model captures the interplay between wealth redistribution and accumulation, exhibiting a continuous phase transition marked by a broad wealth distribution at criticality, separating a condensed phase -- where a microscopic fraction of agents holds a macroscopic share of total wealth -- from a distributed phase with a light-tailed wealth distribution. While the original EYS model assumes fully connected interactions, this work introduces and studies a networked variant where agents interact over Erd\H{o}s-R\'enyi random networks. The analysis combines Monte Carlo simulations with Quenched Mean Field and Mean Field approximations, exploring a variety of interaction and taxation schemes. A scaling analysis shows that, although the networked model also undergoes a continuous phase transition, it leads to local wealth condensation rather than the global condensation found in the fully connected case. These results deepen our understanding of wealth dynamics in structured populations and may help inform the development of more effective economic and social policies.