Effects of network topology on wealth distributions

TL;DR

This paper investigates how the structure of interaction networks influences wealth distribution patterns, revealing that heterogeneity and higher-order correlations in the network are crucial for reproducing the empirically observed mixed wealth distribution.

Contribution

It demonstrates that simple network properties are insufficient, and highlights the importance of network heterogeneity and correlations in shaping wealth distributions.

Findings

Homogeneous networks lead to log-normal or power-law wealth distributions.

Heterogeneous networks with variable link density reproduce mixed wealth distributions.

Higher-order network correlations influence wealth distribution patterns.

Abstract

We focus on the problem of how wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of log--normal and power--law behaviours. We then focus on the Bouchaud--M\'ezard model of wealth exchange, describing an economy of interacting agents connected through an exchange network. We report analytical and numerical results showing that the system self--organises towards a stationary state whose associated wealth distribution depends crucially on the underlying interaction network. In particular we show that if the network displays a homogeneous density of links, the wealth distribution displays either the log--normal or the power--law form. This means that the first--order topological properties alone (such as the scale--free property) are not enough to explain the emergence of the empirically observed \emph{mixed} form of the wealth distribution. In order to reproduce this nontrivial pattern, the network has to be heterogeneously divided into regions with variable density of links. We show new results detailing how this effect is related to the higher--order correlation properties of the underlying network. In particular, we analyse assortativity by degree and the pairwise wealth correlations, and discuss the effects that these properties have on each other.