If you want to understand the contributions of Nobel laureates Schelling and Aumann, you can read a summary of several posts from Bill Polley. There are parts of game theory in many subfields in economics -- in my own area, fiscal and monetary policy coordination and government-union interactions are well described with game theoretic notions. But does it get us to the real work of economics, to provide for explanation and prediction?

I'm a little more optimistic of game theory than many of those in Bill's post. Remember, the story of free-market economics is that institutions form that allow us to expand the circle of potential transactors. People find ways to "do business" with others in a way that is cooperative. Cooperative games are a neat way to illustrate how the circle expands. Will it generate "testable hypotheses"? I don't know, but it can give us some powerful metaphors.