I would probably organize it like a big game of infection tag. You start with one or a few people who are tagged, but each person who's found becomes tagged as

I would probably organize it like a big game of infection tag. You start with one or a few people who are tagged, but each person who's found becomes tagged as well, and becomes a searcher. When you find somebody, you scan a QR code on their phone (or on a race bib that everybody pins to their clothes). A trivial database on your phone tells you who was found last, how many are left, etc.