I want to self study game theory. Which math-related qualifications should I have? And can you recommend any books? Where do I have to begin?
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.