Bouchaud-M\'ezard model on a random network

TL;DR

This paper analyzes the Bouchaud-Mézard model on a random network, deriving an analytical wealth distribution and identifying conditions for wealth condensation, with results validated through simulations.

Contribution

It provides an analytical solution for the stationary wealth distribution in the BM model on a random network, extending previous mean-field results.

Findings

Wealth condensation occurs at higher interaction strength than mean-field predictions.

Analytical results agree well with numerical simulations.

The model explains Pareto's law in a networked economy.

Abstract

We studied the Bouchaud-M\'ezard(BM) model, which was introduced to explain Pareto's law in a real economy, on a random network. Using "adiabatic and independent" assumptions, we analytically obtained the stationary probability distribution function of wealth. The results shows that wealth-condensation, indicated by the divergence of the variance of wealth, occurs at a larger $J$ than that obtained by the mean-field theory, where $J$ represents the strength of interaction between agents. We compared our results with numerical simulation results and found that they were in good agreement.