I remember a Radiolab episode a while back about ultra-long distance cycling -- a 3000-mile long race. According to the story, one of the competitors began hallucinating that zombies were chasing him. His support team thought about that, and said, "Yes! They're gaining on you! You've got to keep going to keep away from them!"
He didn't win the race -- I don't remember if he even finished -- but the hallucination kept him much more competitive for much longer.