Paper: arXiv 2310.16098

Authors: David W. Cohen, Bruce M. Boghosian

Abstract

We present analytical results for the Gini coefficient of economic inequality under the dynamics of a modified Yard-Sale Model of kinetic asset exchange. A variant of the Yard-Sale Model is introduced by modifying the underlying binary transaction of the classical system. It is shown that the Gini coefficient is monotone under the resulting dynamics but the approach to oligarchy, as measured by the Gini index, can be bounded by a first-order differential inequality used in conjunction with the differential Gronwall inequality. This result is in the spirit of entropy – entropy production inequalities for diffusive PDE. The asymptotics of the modified system, with a redistributive tax, are derived and shown to agree with the original, taxed Yard-Sale Model, which implies the modified system is as suitable for matching real wealth distributions. The Gini – Gini production inequality is shown to hold for a broader class of models.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides strong theoretical and mathematical derivations regarding inequality dynamics using Gronwall inequalities and kinetic exchange models. However, it lacks empirical backtesting or real-world data validation, remaining purely analytical.

Research Flowchart

  flowchart TD
    A[Research Goal: Bound approach to oligarchy in modified Yard-Sale Model] --> B[Data/Inputs: Wealth distributions & kinetic transaction rules]
    B --> C[Modify Binary Exchange Dynamics]
    C --> D[Analytical Derivation & Gronwall Inequality]
    D --> E[Incorporate Redistributive Tax Dynamics]
    E --> F[Key Outcome: Monotone Gini growth bounded via Gini-Gini production inequality]
    E --> G[Key Outcome: Taxed asymptotics match original model & real wealth data]