If I was any good at higher level math, I would have gone to medical school instead of law school. However, in the sense that law is a competition, game theory has some very interesting applications. Although I don't always rely on it, Wikipedia has a pretty good summation of how it came to be and some of the subsequent off shoots of the theory and how they apply.
In politics, especially lately, we seem to be operating under a Nash equilibrium in that neither side has any incentive to change their strategy. However, the probability of things remaining static forever is unlikely, due in part to the trembling hand perfect equilibrium where a player may make a "slip of the hand" and choose an unintended strategy.
The curious thing about this concept is if one of the players is clever enough to induce an opponent to make that step. While this is getting too deep for this blog, it is still nonetheless interesting.
Hmm, I wonder how I should play this?