In fact, there are over 63,000 book chapters, journal articles, conference reports (etc) on Google Scholar about that very topic. Scientists have
been studying it for years. Link to Google Scholar
Game theory is something that I love reading about. It's used in all kinds of human interaction research.
As to politicians wising up and using it, no. They will end up being an example in the "consequences" section of game theory articles. One thing
that the Republicans DID do was use a technique called "Framing" many years ago and continue to use that one. I don't think they plan it as well
as they used to. George Lakoff tried to teach Democrats to use that, but it was like herding cats.
Anyway, good idea and yes game theory has been used to analyze and predict results since about 1957: