I think the best arena for mixed skills is Brazilian Vale Tudo. A Vale Tudo compitition is very simple. You win by knockout, submission, corner throwing in the towel, or doctor stoppage. The rules are you can't bite, fishhook, eyegouge, or put your hands or feet in your opponents shorts. There is a 30min time limit, no rounds, and the only protective gear is a cup and a mouthpiece.