A family-network model for wealth distribution in societies

TL;DR

This paper introduces a family-network model that dynamically generates wealth distribution and network structure, successfully replicating empirical wealth distributions including Pareto tails and stable network topologies.

Contribution

The model uniquely combines network formation with wealth exchange dynamics, producing realistic wealth distributions and network structures without predefining the network topology.

Findings

Wealth distribution exhibits exponential behavior in low and medium wealth ranges.

Upper 5% of society follows a Pareto power-law tail with realistic indexes.

Generated networks converge to a Poissonian degree distribution.

Abstract

A model based on first-degree family relations network is used to describe the wealth distribution in societies. The network structure is not a-priori introduced in the model, it is generated in parallel with the wealth values through simple and realistic dynamical rules. The model has two main parameters, governing the wealth exchange in the network. Choosing their values realistically, leads to wealth distributions in good agreement with measured data. The cumulative wealth distribution function has an exponential behavior in the low and medium wealth limit, and shows the Pareto-like power-law tail for the upper 5% of the society. The obtained Pareto indexes are in good agreement with the measured ones. The generated family networks also converges to a statistically stable topology with a simple Poissonian degree distribution. On this family-network many interesting correlations are studied, and the main factors leading to wealth-diversification and the formation of the Pareto law are identified.