An H Theorem for Boltzmann's Equation for the Yard-Sale Model of Asset Exchange The Gini Coefficient as an H Functional

作者：Boghosian Bruce M^*; Johnson Merek; Marcq Jeremy A

来源：Journal of Statistical Physics, 2015, 161(6): 1339-1350.

DOI：10.1007/s10955-015-1316-8

• Boltzmann equation
• Asset exchange model
• Yard-Sale model
• H theorem
• Gini coefficient
• Pareto distribution

In recent work (Boghosian, Phys Rev E 89:042804-042825, 2014; Boghosian, Int J Mod Phys 25:1441008-1441015, 2014), 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.

• 出版日期2015-12