  We give a new characterization of flat affine manifolds in terms of an action
of the Lie algebra of classical infinitesimal affine transformations on the
bundle of linear frames. We characterize flat affine symplectic Lie groups
using symplectic \'etale affine representations and as a consequence of this,
we show that a flat affine symplectic Lie group with bi-invariant symplectic
connection contains a nontrivial one parameter subgroup formed by central
translations. We give two methods for constructing flat affine symplectic Lie
groups, thus obtaining all those having bi-invariant symplectic connections. We
get nontrivial examples of simply connected flat affine symplectic Lie groups
in every even dimension.
