Okay, technically chariot races were done in the circuses, and not so much in the arena, but come on. I like ponyplay too much to not utilize it at the mention of the word "arena". ^_^ I spend all day teaching horseback riding in arenas. So while I interpreted the prompt as some sort of gladiatorial thing, I also just had to bring in pony stuff at the word arena.
My interpretation of depicting polycule stuff is apparently just "playing with your mates." Which, yeah, that checks out.