  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 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 to
vertex-ranked games, thus showing ExpTime-completeness of solving the former
games. Furthermore, 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

Computer Science and Game Theory