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We study the problem of transfers in a population structured by a continuousvariable corresponding to the quantity being transferred. The model is ofBoltzmann type with kernels corresponding to the specific rules of the transferprocess. We focus our interest on the well-posedness of the Cauchy problem inthe space of measures and $L^1$. We characterize transfer kernels that give acontinuous semiflow in the space of measures and $L^1$. We construct someexamples of kernels that may be particularly interesting in economicapplications. Our model considers blind money transfers between individuals.The two models are the ``Robin Hood model'', where the richest individualunconditionally gives a fraction of their wealth to the poorest when a transferoccurs, and the other extreme, the ``Sheriff of Nottingham model'', where therichest unconditionally takes a fraction of the poorest's wealth. Between thesetwo extreme cases is a continuum of intermediate models obtained byinterpolating the kernels. We illustrate those models with numericalsimulations and show that any small fraction of the ``Sheriff of Nottingham''in the transfer rules leads to a segregated population with extremely poor andextremely rich individuals after some time. Although our study is motivated byeconomic applications, we believe that this study is a first step towards abetter understanding of many transfer phenomena occurring in the life sciences.

Robin Hood model versus Sheriff of Nottingham model: transfers in population dynamics