An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange

Abstract

In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single individual. In this work, we prove that conjecture by demonstrating that the Gini coefficient, a measure of inequality commonly used by economists, is an $H$ function of both the Boltzmann and Fokker-Planck equations for the model.

10 pages, 1 figure, submitted to proceedings of the 23rd conference on the Discrete Simulation of Fluid Dynamics (DSFD 2014)

References in corpus (1)

• Fokker-Planck Description of Wealth Dynamics and the Origin of Pareto's Law

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• The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality
• The Growth of Oligarchy in a Yard-Sale Model of Asset Exchange: A Logistic Equation for Wealth Condensation
• Oligarchy as a Phase Transition: The effect of wealth-attained advantage in a Fokker-Planck description of asset exchange
• H-theorem at negative temperature: the random exchange model with bounds
• Derivation of wealth distributions from biased exchange of money
• Wealth Inequality in Agent-Based Economies: The Dominant Role of Social Protection over Growth
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• Limiting risk to reduce inequality: insights from the Yard-Sale model
• Unifying description of the damping regimes of a stochastic particle in a periodic potential
• Quantitative convergence guarantees for the mean-field dispersion process
• A Dynamical Equation for the Lorenz Curve: Dynamics of incomplete moments of probability distributions arising from Fokker-Planck equations
• Extended Yard Sale model of wealth distribution on Erdős-Rényi random networks
• A gradient flow perspective on McKean-Vlasov equations in econophysics