  Many-body perturbation theory is often formulated in terms of an expansion in
the dressed instead of the bare Green's function, and in the screened instead
of the bare Coulomb interaction. However, screening can be calculated on
different levels of approximation, and it is important to define what is the
most appropriate choice. We explore this question by studying a
zero-dimensional model (so called 'one-point model') that retains the structure
of the full equations. We study both linear and non-linear response
approximations to the screening. We find that an expansion in terms of the
screening in the random phase approximation is the most promising way for an
application in real systems. Moreover, by making use of the nonperturbative
features of the Kadanoff-Baym equation for the one-body Green's function, we
obtain an approximate solution in our model that is very promising, although
its applicability to real systems has still to be explored.
