  We introduce quantitative reductions, a novel technique for structuring the
space of quantitative games and solving them that does not rely on a reduction
to qualitative games. We show that such reductions exhibit the same desirable
properties as their qualitative counterparts and that they additionally retain
the optimality of solutions. Moreover, we introduce vertex-ranked games as a
general-purpose target for quantitative reductions and show how to solve them.
In such games, the value of a play is determined only by a qualitative winning
condition and a ranking of the vertices.
  We provide quantitative reductions of quantitative request-response games and
of quantitative Muller games to vertex-ranked games, thus showing
EXPTIME-completeness of solving the former two kinds of games. In addition, we
exhibit the usefulness and flexibility of vertex-ranked games by showing how to
use such games to compute fault-resilient strategies for safety specifications.
This work lays the foundation for a general study of fault-resilient strategies
for more complex winning conditions.
