# On the origins of extreme wealth inequality in the Talent vs Luck Model

## TL;DR

This paper introduces a simplified Talent vs Luck model focusing solely on lucky events to explain the origins of extreme wealth inequality, supported by analytical approximations and numerical simulations.

## Contribution

It presents a simplified model that reproduces wealth inequality results and offers analytical insights into the role of lucky events in wealth distribution.

## Key findings

- Simplified model reproduces original wealth inequality results.
- Analytical approximations capture key mechanisms of wealth creation.
- Heterogeneous rates of capital increase from lucky events lead to complex wealth dynamics.

## Abstract

While wealth distribution in the world is highly skewed and heavy-tailed, human talent - as the majority of individual features - is normally distributed. In a recent computational study by Pluchino et al [Talent vs luck: The role of randomness in success and failure, Adv. Complex Syst. 21 (03-04) (2018) 1850014], it has been shown that the combined effects of both random external factors (lucky and unlucky events) and multiplicative dynamics in capital accumulation are able to clarify this apparent contradiction. We introduce here a simplified version (STvL) of the original Talent versus Luck (TvL) model, where only lucky events are present, and verify that its dynamical rules lead to the same very large wealth inequality as the original model. We also derive some analytical approximations aimed to capture the mechanism responsible for the creation of such wealth inequality from a Gaussian-distributed talent. Under these approximations, our analysis is able to reproduce quite well the results of the numerical simulations of the simplified model in special cases. On the other hand, it also shows that the complexity of the model lies in the fact that lucky events are transformed into an increase of capital with heterogeneous rates, which yields a non-trivial generalization of the role of multiplicative processes in generating wealth inequality, whose fully generic case is still not amenable to analytical computations.