Work

Measuring inequality in society-oriented Lotka–Volterra-type kinetic equations

Year: 2025

Type: article

Abstract: We propose a method for quantifying inequality within a system of coupled Fokker–Planck-type equations, which model the evolution of probability densities for two populations interacting pairwise by economic motivations. The macroscopic dynamics of their mean values follows a Lotka–Volterra system of ordinary differential equations. Therefore, unlike classical models of wealth distribution, which converge toward a steady equilibrium profile, the oscillatory behavior of the mean values only leads to the formation, within the Fokker–Planck system, of time-dependent quasi-equilibria. This makes measuring the evolution in time of inequality in the system challenging. An insightful perspective on the problem is commonly gained through the Gini index. However, the coefficient of variation offers an alternative, mathematically convenient inequality measure that retains the essential characteristics of the Gini index. Numerical experiments confirm that, despite the system’s oscillatory nature, inequality initially tends to decrease.

Source: Physica A Statistical Mechanics and its Applications

DOI: 10.1016/j.physa.2025.131023

Authors: M. Menale, G. Toscani

Institutions: University of Naples Federico II, University of Pavia, Istituto di Matematica Applicata e Tecnologie Informatiche

Language: English

Topic: Complex Systems and Time Series Analysis

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", National Board for Higher Mathematics, Center for Neuroscience Research, Gruppo Nazionale per la Fisica Matematica