  We investigate the effect of applying nonlinear redistributive taxes to the
yard-sale dynamics of assets. An amount of money is collected from each
individual (tax) and distributed back equally. We consider (i) a piecewise
linear tax, exempting those with wealth below a threshold $w_0$, and taxing the
excess wealth otherwise, and (ii) a power-law tax with exponent $\alpha>0$,
which allows embracing regressive, proportional and progressive rules. The
distribution of wealth obtained from numerical simulations of the agent-based
dynamics is compared with the solution of its associated Fokker-Planck equation
for the probability density function $P(w,t)$ of wealth $w$ at time $t$, in
good agreement. Based on these solutions, we analyze how the different rules
modify the distribution of wealth across the population, quantifying the level
of inequality through the Gini coefficient. We note that the introduction of an
exemption threshold does not always diminish inequality, depending on the
implementation details. Moreover, nonlinearity brings new stylized facts in the
distribution of wealth compared to the linear case, e.g., negative skewness,
bimodality, indicating stratification, or a flat shape meaning equality
populated wealth layers.
