Emergence of Power Law in a Market with Mixed Models

TL;DR

This paper demonstrates that mixing different asset exchange models among agents can produce wealth distributions with power law tails, explaining the emergence of Pareto-like wealth distributions.

Contribution

It introduces a novel approach where combining simple exchange models results in power law wealth distributions, aligning with empirical observations.

Findings

Power law tails emerge when agents follow different exchange models.

Mixing models leads to wealth condensation or exponential distributions.

Probabilistic mixing of models produces Pareto-like wealth distributions.

Abstract

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A yardsale(YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud(TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, {\it i.e.} there are some agents following TF model while rest follow YS model, it leads to distribution with power law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power law tail in wealth distribution if we allow the agents to follow either of the models with some probability.