  In this paper, we study turn-based quantitative multiplayer non zero-sum
games played on finite graphs with both reachability and safety objectives. In
this framework a player with a reachability objective aims at reaching his own
goal as soon as possible, whereas a player with a safety objective aims at
avoiding his bad set or, if impossible, delaying its visit as long as possible.
We prove the existence of Nash equilibria with finite memory in quantitative
multiplayer reachability/safety games. Moreover, we prove the existence of
finite-memory secure equilibria for quantitative two-player reachability games.
