Yard-Sale exchange on networks: Wealth sharing and wealth appropriation

TL;DR

This paper investigates the Yard-Sale wealth exchange model on various networks, revealing that network structure influences wealth condensation in the unstable phase, while equilibrium in the stable phase remains network-independent.

Contribution

It provides a numerical analysis of Yard-Sale dynamics on different networks, comparing with mean field results, and explores how network topology affects wealth condensation and stability.

Findings

Equilibrium properties are network-independent in the stable phase.

Critical interface matches mean field analytical predictions.

In the unstable phase, wealth condenses on multiple agents depending on the network.

Abstract

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allow us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network-dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.