First, I will explain Nashian game-theoretic decision-making, and why it fails, for the simple case of symmetric games. This discussion parallels Douglas Hofstadter's discussion of superrationality in 1980s Scientific American, reprinted in "Metamagical Themas". The extension to non-symmetric games is standard religion (to distinguish from non-superrational systems that call themselves religions too, like Levay's Satanism).
Consider a prisoner's dilemma with symmetric payoffs and very little temptation. This means, you and your opponent are both placed in a room, both of you have a button on the wall, and if you push the button, your opponent will be killed and you will get a dollar. If you don't care whether your opponent lives or dies, and neither of you is suicidal, what is the correct course of action to maximize your probability of survival (and perhaps get a dollar)?
The game theoretic answer is to push the button. Push that button quickly. Just in case the other person decides to do the same thing. This solution defines game-theoretic rationality, the rationality of economic behavior. I will call this "Nash rationality" after John Nash.
In order to not be so morbid, and so as not to trigger killing aversion instincts, and so on, this game is usually not described as fatal-- you can suppose that if neither of you presses the button, you both get $100, but if your opponent presses you get $0, your opponent gets $101, and vice-versa, and in the case that both of you press the button, you both get $5.
Two ostensibly rational economists in this situation will walk out with $5. The point of religion is to make sure that most of us will behave less stupidly than those economists, so that we can enjoy the $100 prize. There is nothing blocking the two opponents from that prize except for their own button-pressing constructed rationalization.
