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

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  • Marco Menale
  • Giuseppe Toscani

Abstract

We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors. The macroscopic dynamics of their mean values follow a Lotka-Volterra system of ordinary differential equations. Unlike classical models of wealth and opinion formation, which tend to converge toward a steady-state profile, the oscillatory behavior of these densities only leads to the formation of local equilibria within the Fokker-Planck system. This makes tracking the evolution of most inequality measures challenging. However, an insightful perspective on the problem is obtained by using the coefficient of variation, a simple inequality measure closely linked to the Gini index. Numerical experiments confirm that, despite the system's oscillatory nature, inequality initially tends to decrease.

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  • Marco Menale & Giuseppe Toscani, 2025. "Measuring inequality in society-oriented Lotka--Volterra-type kinetic equations," Papers 2505.15526, arXiv.org.
    • Handle: RePEc:arx:papers:2505.15526
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    References listed on IDEAS

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