The Origins of Extreme wealth inequality in the Talent versus luck Model
We introduce a simplified version (STvL) of the 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. On the other hand, it also shows that the complexity of the model lies in the stochastic transformation of lucky events into an increase of capital, so that, when the talent heterogeneity of the population increases, the task of finding a formal analytical relationship between the distributions of capital, talent and luck in either the TvL or the STvL models becomes very hard.