Local operators in kinetic wealth distribution

The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering process. Here, we discuss the role of a class of conservative local operators, and we show that, depending on the values of their parameters, they can be used to generate all the relevant distributions. We also show numerically that in order to generate the power-law tail, an heterogeneous risk aversion model is required. By changing the parameters of these operators, one can also fine tune the resulting distributions in order to provide support for the emergence of a more egalitarian wealth distribution.