Study of a Market Model with Conservative Exchanges on Complex Networks

TL;DR

This paper investigates how complex network structures influence conservative wealth exchange models, revealing the persistence of a poverty line and correlations between node degree and wealth, with implications for inequality.

Contribution

It extends previous exchange models by analyzing the effects of complex network topologies like Erdős-Rényi and scale-free networks on wealth distribution and inequality.

Findings

Poverty line with finite wealth persists across network types.

Spatial correlations between node degree and wealth are significant.

Network topology affects the Gini coefficient and inequality measures.

Abstract

Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum wealth or poverty line. On the other hand, the wealth distribution exhibited an exponential shape as a function of the square of the wealth. These results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme. In the present paper we study the effect of distributing the agents on a complex network. We have considered archetypical complex networks: Erd\"{o}s-R\'enyi random networks and scale-free networks. The presence of a poverty line with finite wealth is preserved but spatial correlations are important, particularly between the degree of the node and the wealth. We present a detailed study of the correlations, as well as the changes in the Gini coefficient, that measures the inequality, as a function of the type and average degree of the considered networks.