Parity decides whether the sheep survives

One sheep and $100$ tigers are left on an island that has unlimited grass. A tiger prefers eating the sheep to eating grass, but a tiger that eats the sheep is itself transformed into a sheep, and only one tiger can eat at a time. All tigers reason perfectly and value survival above everything. Will anyone eat the sheep?

No. Let $n$ be the number of tigers. If $n$ is odd the sheep is eaten, since the eater then faces $n-1$ (even) tigers and is safe; if $n$ is even, eating would leave an odd number of tigers who would eat the new sheep. This follows by induction from $n=1$, and $100$ is even.