Transition from Exponential to Power Law Distributions in a Chaotic Market

TL;DR

This paper introduces a chaotic dynamics extension to gas-like market models, successfully reproducing exponential and power law money distributions and elucidating the transition between them, highlighting mechanisms behind economic inequality.

Contribution

It presents a novel chaotic gas-like model that overcomes previous limitations, explaining the transition from exponential to power law distributions in markets.

Findings

Chaotic dynamics reproduce real-world money distributions.

The model demonstrates a transition mechanism between distribution types.

It reveals the micro-level origins of economic inequality.

Abstract

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, non linear dynamics is introduced in the gas-like model in way that an effort to overcome these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents $(i,j)\Leftrightarrow(j,i)$. The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.