Concentration Effects in a Kinetic Model with Wealth and Knowledge Exchanges

Using a kinetic equation of Boltzmann type, we describe the effect of mutual knowledge and wealth exchanges in a closed community where all the interactions inside the population are binary. Some numerical experiments demonstrating, among other things, concentration or clustering effects, are presented. Moreover, asymptotic studies are performed, in particular in two cases: the full quasi-invariant model, for which a limit nonlinear Fokker–Planck equation is derived, and a quasi-invariant knowledge model, for which a numerical convergence rate study is led.