  In earlier work, we derived a nonlinear, nonlocal Fokker-Planck equation for
the Yard-Sale Model of asset exchange. In the absence of redistribution, we
showed that the Gini coefficient is a Lyapunov functional for this model,
tending to one in the time-asymptotic limit, corresponding to maximal
inequality. When a one-parameter model of redistribution is introduced, we
showed that the model admits a steady state similar to Pareto's Law.
  In this work, we analyze the form of this distribution in greater detail,
both analytically and numerically. We find that, while Pareto's Law is
approximately valid for low redistribution, it gives way to something like
Gibrat's Law at higher redistribution. We also prove that, while this Pareto or
Gibrat behavior persists over many orders of magnitude, it ultimately gives way
to gaussian decay at extremely large wealth.
  Following the work of Moukarzel et al., we introduce a bias in favor of the
wealthier agent. We derive the corresponding modification to the Fokker-Planck
equation, and we show this leads to wealth condensation when the bias exceeds a
critical value. Earlier work took the bias to be a discontinuous function of
the wealth differential between the two transacting agents, and reported a
first-order phase transition to absolute oligarchy. By contrast, in this work
we take the bias to be a continuous function of the wealth differential, and
consequently we observe a second-order phase transition with a region of
coexistence between the oligarch and a distribution of non-oligarchs.
  We additionally show that the onset of wealth condensation has a reciprocal
effect on the character of the non-oligarchical part of the distribution.
Specifically, we show that the above-mentioned gaussian decay at extremely
large wealth is valid both above and below criticality, but degenerates to
exponential decay precisely at criticality.
