I've seen some people say game theory disproves economics? What exactly is it?
That is illogical, as game theory is part of economics, along with a couple others.
More: http://levine.sscnet.ucla.edu/general/whatis.htm (http://levine.sscnet.ucla.edu/general/whatis.htm)
Yeah, economics pretty much IS game theory on a large scale.
The idea of game theory--and this makes it different from pretty much every other science except economics--is that it takes into consideration how human beings will react.
Example: You and a friend are given numbers. All each of you know about the other person's number is that it's one away from yours, either one above or one below (and that they're positive integers). Your number is 2. So at this point, you don't know if your friend's number is 1 or 3.
Your friend is then asked if he knows what your number is. He says he does not. This is where game theory comes in: if he'd had the number 1, he would have known immediately that your number is 2. But since he doesn't, then you know his number is 3.