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Abstract: We introduce and discuss a nonlinear kinetic equation of Boltzmann type whichdescribes the evolution of wealth in a pure gambling process, where the entiresum of wealths of two agents is up for gambling, and randomly shared betweenthe agents. For this equation the analytical form of the steady states is foundfor various realizations of the random fraction of the sum which is shared tothe agents. Among others, Gibbs distribution appears as steady state in case ofa uniformly distributed random fraction, while Gamma distribution appears for arandom fraction which is Beta distributed. The case in which the gambling gameis only conservative-in-the-mean is shown to lead to an explicit heavy taileddistribution.



Author: Federico Bassetti, Giuseppe Toscani

Source: https://arxiv.org/







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