  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.
