If there's a limit to the precision to which one can compare slices of pizza, any algorithm that can meet or beat that precision can be successful.
But the game gets more interesting if the perceptions of the players are subject to influence! Say player A can choose to buy a pitcher of beer for player B, or cause him to travel at relativistic speeds with respect to the pizza . . .
i'm not sure the protocol is a good answer, the assumption bothers me.