Lions and Gazelle: Backward Induction

A magical savanna has an odd number $n$ of lions and one gazelle. The lions are hungry and want to eat the gazelle, but if a lion eats a gazelle (or another lion that has become a gazelle), it falls asleep and transforms into a gazelle itself -- making it vulnerable to being eaten by the remaining lions. Each lion is rational: it wants to eat if possible, but it values survival above all else. A lion will only eat if it can guarantee it won't be eaten afterward. How many gazelles are consumed when $n = 15$?