Game theory - self study

I've decided to flesh out my small comment into a (hopefully respectable) answer.

The book I read to learn Game Theory is called "The Compleat Strategyst", thanks to J.M. for pointing out that it is now a free download. This was one of the first books on Game Theory, and at this point is probably very dated, but it is a nice easy introduction and, since it is free, you may as well go through it. I read the whole book and did all the examples in a couple of weeks. I said before that Linear Algebra was a prerequisite, however after flipping through it again I see that they explain all the mechanics necessary within the book itself, so unless you are also interested in the theory behind it, you will be fine without any linear algebra background.

Since it sounds like you do want the theory (and almost any aspect of Game Theory beyond the introduction provided by that book will still require Linear Algebra) you may want to grab a Linear Algebra book. I'm partial to Axler's Linear Algebra Done Right, which is (in my opinion) sufficient for self-study.

The Wikipedia page on Game Theory lists many types of games. Aspects of the first five are covered at various lengths in "The Compleat Strategyst", these include:

• Cooperative or non-cooperative
• Symmetric and asymmetric
• Zero-sum and non-zero-sum
• Simultaneous and sequential
• Perfect information and imperfect information

The rest of the math you will need to know depends on what sort of games you're interested in exploring after that, and the math required is given away largely by the name:

• Combinatorial Game Theory will likely require combinatorics.
• Infinitely long games seem to be related to set theory.
• Both discrete and continuous games and many-player/population games would seem to require calculus (and perhaps differential equations).
• Stochastic outcomes are related to statistics.
• Metagames (also sometimes referred to as "reverse Game Theory") use some fairly sophisticated mathematics, so you'll probably need a good understanding of analysis and abstract algebra.

Also see this (somewhat duplicate) question for video lectures which will give you a better understanding of what game theory is before you shell out any money to buy anything.

Shameless Advertisement: Game Theory proposal on Area 51 that you should totally follow!

It definitely depends on the flavor of game theory you're interested in, but in my experience, no truly introductory text requires anything beyond simple algebra and logical reasoning. Once you get into something advanced, it requires in-depth knowledge of a specific subfield (say research on permutations), but that isn't something I would prepare for, assuming you can learn quickly. Rather, it seems mathematicians and social scientists often collaborate to solve these problems.

My Personal Recommendation: Wikipedia's entry on Game Theory and then also read about each game in the list of games and probably the entry on solution concepts.

No Math:
- Thinking Strategically
- The Evolution of Cooperation
- The Complexity of Cooperation
Minimal Notation
- Behavioral Game Theory
- The Theory of Learning in Games
(Technical) Textbooks
- An Introduction to Game Theory
- Algorithmic Game Theory
- Auction Theory
Reference Books:
- Combinatorial Auctions
- Handbook of Experimental Economics Results
- The Handbook of Experimental Economics
Journals
- Games and Economic Behavior

Reading recently-published papers is quite fun; they're usually sufficiently contained such that if you can read a paper (that is, read only its abstract, introduction, and conclusion), you can get a better idea of why concepts found in an undergraduate text are considered central.

You might find these lecture notes useful: Game Theory Lecture Notes by Levent Koçkesen.