I have been watching http://academicearth.org/lectures/introduction-to-game-theory and I think I figured out a way to phrase what we are trying to do in our revaluation. The concept I was referring to is called dominant/dominated strategy. A strategy strictly dominates another strategy if, in all cases, regardless of another's actions, there is a better payoff. What we should do to break the dilemma, then, is to create a pure, perfectly dominant strategy. A perfectly dominant strategy would be one that, regardless of the situation, dominates all other strategies. To create this we need to change our payoff to be one that is outside of another's control, thus making others' actions irrelevant. This can be done by the promotion of the feeling of self-pride, pride in having done the action knowing the consequences. The outcome of the action is irrelevant (even if it hurts another, but this will be discussed later). What matters is that we shape our payoff to be the pride that comes with acting, not with the consequence. Cheats!
The problem with this idea, like Alex mentioned, is that it leaves no place for ethics. It's effective as a cold war strategy, and it's the reason John Nash was so enormously well-received, despite his paranoid schizophrenia. It's the idea of purity, the idea of an infinitely superior position, a position so superior that it will never be demoted by another seeking superiority.
You can't "break the dilemma" once and for all because you can never make the payoff entirely outside of the other's control. The actions of the other are always relevant. This is what ethics means. It's not a popular viewpoint, but I think that a new symptomatology of things like paranoid schizophrenia and autism could show a relationship between these disorders and ethics. For instance, autism is characterized by a 'lack of theory of mind,' an abiding disregard for the viewpoint of the other, or an ignorance of such a viewpoint. Simon Baron-Cohen published a fascinating paper arguing that autism is much more likely to occur in children of mathematicians and scientists than in children of those who work in other areas.
I digress, but I hope you see my point. I'm sure there are even mathematicians who have used formulas to argue against Nash's theory, but they don't get much funding because the government wants ways to win wars, and as a way to annihilate other people, game theory works quite well. That doesn't mean it should be eliminated or that it's wrong. You can't annihilate annihilation. But you have to move outside of it as well.