Read John Nash's Equilibrium. It is the origin of the theory you are asking about, and as somebody who did consider being a Sub Captain for fear of nuclear war with superpowers, you probably should already be familiar with it even if you don't understand the contents of the movie <i>A Beautiful Mind</i>.
I'll summarize its brinkmanship:
Good wins most if not all of the time.
Bad only wins rarely.
If Bad wins, Good always overcomes, until the long run is over and new actors enter the stage for new brinkmanship.
The outcome is the status quo due to rationality and a convex tradeoff between risk and reward. When bad wins, good overcomes because of rationality and the supposed force known as equilibria, therefore bad never wins and only tries to influence good. Both sides do nothing.
Mathematically it will take at least years before you figure this out, because it took me that long after I read it to understand why it deserved a Nobel Prize.
In my Game Theory class as a Sophomore at Centre College, I did win this game with $265. Only after did I realize that the prisoner's dilemma is brinkmanship, leaving me with a solid understanding of how the United States will rule this world nearly ad infinitum.