Effects of introduction of new resources and fragmentation of existing resources on limiting wealth distribution in asset exchange models

TL;DR

This paper investigates how introducing new resources and fragmenting existing ones in asset exchange models affects wealth distribution, especially the emergence of power-law tails, without assuming conservation of wealth or agents.

Contribution

It explores wealth distribution in models with non-conservation of wealth and agents, highlighting conditions that lead to Pareto-like power-law tails.

Findings

Models with agent entry or fragmentation produce power-law wealth distributions.

Non-conservation of wealth or agents still results in Pareto tails.

Generalized asset exchange models can explain wealth distribution patterns.

Abstract

Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealth. Both these assumptions are unrealistic. In this paper, we study the limiting wealth distribution when one or both of these assumptions are not valid. Given the universality of the law, we have tried to study the wealth distribution from the asset exchange models point of view. We consider models in which a) new agents enter the market at constant rate b) richer agents fragment with higher probability introducing newer agents in the system c) both fragmentation and entry of new agents is taking place. While models a) and c) do not conserve total wealth or number of agents, model b) conserves total wealth. All these models lead to a power-law tail in the wealth distribution pointing to the possibility that more generalized asset exchange models could help us to explain emergence of power-law tail in wealth distribution.