  In the standard sequent presentations of Girard's Linear Logic (LL), there
are two "non-decreasing" rules, where the premises are not smaller than the
conclusion, namely the cut and the contraction rules. It is a universal concern
to eliminate the cut rule. We show that, using an admissible modification of
the tensor rule, contractions can be eliminated, and that cuts can be
simultaneously limited to a single initial occurrence. This view leads to a
consistent, but incomplete game model for LL with exponentials, which is
finitary, in the sense that each play is finite. The game is based on a set of
inference rules which does not enjoy cut elimination. Nevertheless, the cut
rule is valid in the model.
