Trading leads to scale-free self-organization

TL;DR

This paper demonstrates that trading processes under simple assumptions naturally lead to a self-organized market exhibiting Pareto-like wealth distribution and scale-free return fluctuations.

Contribution

It reveals that trading dynamics alone can produce scale-free market behavior and wealth distribution without additional complex mechanisms.

Findings

Wealth distribution among market participants follows a Pareto law.

Return fluctuations exhibit scale-free, heavy-tailed behavior.

Market self-organization emerges from basic trading assumptions.

Abstract

Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of the distribution of returns of different financial assets have been confirmed in a series of works. The existence of a Pareto-like distribution of the wealth of market participants has been connected with the scale-free distribution of trading volumes and price-returns. The origin of the Pareto-like wealth distribution, however, remained obscure. Here we show that it is the process of trading itself that under two mild assumptions spontaneously leads to a self-organization of the market with a Pareto-like wealth distribution for the market participants and at the same time to a scale-free behavior of return fluctuations. These assumptions are (i) everybody trades proportional to his current capacity and (ii) supply and demand determine the relative value of the goods.