Local Operators in Kinetic Wealth Distribution

TL;DR

This paper explores how local operators in kinetic wealth models influence the resulting wealth distributions, demonstrating their ability to generate various distributions including power-law tails and more egalitarian outcomes.

Contribution

It introduces the role of conservative local operators in wealth distribution models and shows how their parameters can produce diverse distribution types.

Findings

Local operators can generate all relevant wealth distributions.

Heterogeneous risk aversion is necessary for power-law tails.

Parameter tuning can lead to more egalitarian wealth distributions.

Abstract

The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering process. Here, we discuss the role of a class of conservative local operators, and we show that, depending on the values of their parameters, they can be used to generate all the relevant distributions. We also show numerically that in order to generate the power-law tail an heterogeneous risk aversion model is required. By changing the parameters of these operators one can also fine tune the resulting distributions in order to provide support for the emergence of a more egalitarian wealth distribution.