Wealth distribution in a System with Wealth-limited Interactions

TL;DR

This paper models wealth distribution in an economy by limiting interactions based on wealth similarity, successfully reproducing empirical Gibbsian and Pareto trends and their transition depending on interaction rules.

Contribution

It introduces a simple wealth-limited interaction model that explains the emergence of Gibbsian and Pareto wealth distributions and their transition points.

Findings

Wealth-limited interactions produce power law wealth distributions.

Transition from Gibbsian to Pareto distribution depends on the wealth-limiting parameter BETA.

Mutual and non-mutual interaction choices affect the transition point.

Abstract

We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher range, by simply limiting the an agents' interaction to only agents with nearly the same wealth. To do this, we introduce a parameter BETA that limits the range on the wealth of a partner with which an agent is allowed to interact. We show that this wealth-limited interaction is enough to distribute wealth in a purely power law trend. If the interaction is not wealth limited, the wealth distribution is expectedly Gibbsian. The value of BETA where the transition from a purely Gibbsian law to a purely power law distribution happens depends on whether the choice of interaction partner is mutual nor not. For a non-mutual choice, where the richer agent gets to decide, the transition happens at BETA=1.0. For a mutual choice, the transition is at BETA= 0.60. In order to generate a mixed Gibbs-Pareto distribution, we apply another wealth-based rule that depends on the parameter w_limit. An agent whose wealth is below w_limit can choose any partner to interact with, while an agent whose wealth is above w_limit is subject to the wealth-limited range in his choice of partner. A Gibbs-Pareto distribution appears if both these wealth-based rules are applied.