Gaussian Noise Effects on the Evolution of Wealth in a Closed System of n-Economies

TL;DR

This paper investigates how Gaussian noise influences wealth distribution dynamics in a closed system of n economies, showing it accelerates equilibrium and reduces variance compared to uniform noise.

Contribution

It demonstrates that Gaussian background noise significantly alters wealth evolution, leading to faster equilibrium and a more deterministic-like behavior in the model.

Findings

Gaussian noise reduces wealth distribution variance

Faster convergence to equilibrium under Gaussian noise

System resembles a deterministic model with Gaussian background

Abstract

Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between $n$ economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter $\epsilon$. We demonstrate, that within Gaussian noise, the variance of the resulting wealth distribution will significantly decrease, and the equilibrium state is reached faster than in the case of a uniform distributed $\epsilon$ parameter. Also, we show that the system with Gaussian noise strongly resembles a deterministic system which is solved by means of a Z-Transform based technique.