King is in charge as far as we know. He rarely runs games. He encourages us to be loyal to our teams and backstab anyone else. It's something he rewards. However, he will step in on occasion to prevent rule breaking or tantrums by other Judges.
Queen runs games that are shallow and sexually oriented. Kissing games, dressing up in attractive clothing or stripping, cuddling. Things like that.
Surgeon can revive the dead and heal injuries outside games. Lepus has a pact with him in exchange for helping him out. If you lose his games, there's a penalty. He will take someone from your team to experiment on.
His daughter is Mirror. She started out like I described before. But now she is whole and malicious. Picking very purposely and knowingly at your issues. Her games are about us. She'll do thinks like...change your gender. Or the kind of person you are. Give you someone else's skills or powers.
Haunted's games are all tricks so far. Where she makes it seem like something bad will happen but that's not actually the case. Toys with emotions.
Shadow tends to do simple games. Telling truths or taking dares. Or playing a game where you guess who did what where.