Wealth distribution on complex networks

TL;DR

This paper develops a theoretical framework to explain how the topology of complex networks influences wealth distribution in the Bouchaud--Mézard model, achieving good agreement with simulations across various network types.

Contribution

It introduces an analytical approach using adiabatic and independent assumptions to derive wealth distribution equations on complex networks, explaining previous numerical observations.

Findings

The theory matches simulation results for most network types.

Discrepancies occur in Watts--Strogatz networks with low rewiring rate.

The independent assumption breaks down in certain network configurations.

Abstract

We study the wealth distribution of the Bouchaud--M\'ezard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theorem, we derive equations that determine the probability distribution function. The results are compared to those of simulations for various networks. We find good agreement between our theory and the simulations, except the case of Watts--Strogatz networks with a low rewiring rate, due to the breakdown of independent assumption.