As I note in my comment to the OP, game theory is a big field with several essentially disconnected areas, and one can't really hope for a comprehensive introduction from a single text. I'll recommend two, but this still shouldn't be thought of as a complete introduction.

I learned what I know of non-cooperative game theory from "Game Theory" by Fudenberg and Tirole. The book is well-written if terse, and covers a wide range of topics with a great deal of rigor. I would caution you that the book is written more as a reference than a gentle introduction, but it is certainly self-contained and I was able to read the book with no previous knowledge of the theory. It is a bit dry, however.

As for combinatorial game theory, I'd recommend Berlekamp, Conway, and Guy's "Winning Ways for Your Mathematical Plays," depending on your temperament. The book's style is pretty tongue-in-cheek, and some of the mathematics is non-rigorous (though the details are easy to fill in). But it's an absolutely beautiful book.