First thing people will roll on is who they are going to attack in the arena. After that is decided, then there will be a second dice roll to determine the results of the attack.
So this could lead to situations such as 4 players all attacking the same one other player. Don't get upset if you are ganged up on, it is just the luck of the dice.
So it'll need to be entirely the roll of the dice, without possible alliances or at least "non-aggression pacts" like the one suggested by BenKii? Granted, seems complicated enough to me to manage even so, strictly random, without needing to take anything else into account.
(Just saw the question and wondering whether it'd be pointless to answer.)