Important point.

Let's assume that your utility function (which is identical to theirs) simply weights and adds your payoff and theirs; that is, if you get X and they get Y, your function is U(X,Y) = aX+bY. In that case, working backwards from the utilities in the table, and subject to the constraint that a+b=1, here are the payoffs:

a/b=2: (you care twice as much about yourself)
(3,3) (-5,10)
(10,-5) (1,1)

a/b=3:
(3,3) (-2.5,7.5)
(7.5,-2.5) (1,1)

a=b:
Impossible. With both people being unselfish utilitarians, the utilities can never differ based on the same outcome.

b=0: (selfish)
The table as given in the post

I think the most important result is the case a=b: the dilemma makes no sense at all if the players weight both payoffs equally, because you can never produce asymmetrical utilities.

EDIT: My newbishness is showing. How do I format this better? Is it HTML?