Panem might have its share of problems, but vampires aren't one of them. So although the combat skills and courage of the titular heroine of Buffy the Vampire Slayer are not in question, this gauntlet isn't one for which she trained.
Sure, superhuman strength and intuition would make Buffy a tough girl to beat, but her good heart would do her in. Spectators would enjoy quite a show of martial arts and plucky one-liners, but when push came to stab - and without her closest allies - Buffy would take an honorable death.
Odds of Survival: Low.