We present a numerical study of several inequality measures across two kinetic wealth-exchange models with extreme inequality features (namely the Banerjee model, and the Chakraborti or yard-sale model) and two earthquake simulating models (namely the Chakrabarti-Stinchcombe two-fractal overlap model and the nonlinear dynamical Burridge-Knopoff model). For each model we compute numerically the Lorenz function for the respective models' wealth, overlap magnitude or avalanche distributions. We then estimate the variations of Gini ($g$), Pietra ($p$), and Kolkata ($k$) indices in these models with systematic variations of saving propensity (for the two wealth-exchange models), with systematic variations of generation or block numbers (for the two earthquake simulating models). We find that for appropriate values of the respective model parameters, the inequality indices $g$ and $k$ in corresponding the distributions (of “wealth” or “avalanche”) show quantitatively similar behavior, namely $g=k\simeq 0.86$, which was identified earlier to correspond to the precursor point of criticality in self-organized critical models ($k=0.80$ corresponds to that for Pareto's 80-20 law). The values of $p/(2k-1)$ in all these (wealth exchange and earthquake) models remain a little above unity, as was predicted theoretically. These observations for the inequality indices $g, k$, and $p$ across the socioeconomic and geophysical models indicate the presence of unifying subtle features in the statistics of such disparate dynamical systems.

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• Complex systems
• Econophysics
• Geophysics
• Physics & society