Moments of the steady-state wealth distribution in a Boltzmann-type kinetic model of gambling for arbitrary exchange distributions

Abstract

We formulate a scheme that enables the recursive calculation of the moments of the steady-state wealth distribution in the Bassetti-Toscani kinetic model of gambling for arbitrary exchange distributions. We verify the obtained expression for the exact moments by comparing the first five moments (n = 0; 1; 2; 3; 4) corresponding to Bassetti and Toscani's symmetric beta exchange distribution. We also demonstrate the utility of the scheme by, for the first time, obtaining moments of the steady-state wealth distribution corresponding to exchange distribution that can be written as a sum of generalized beta distributions.