Combinatorial Game Theory Prerequisites

Question

I am planning to self-study Combinatorial Game Theory.

I have gathered some useful references from here.

Reference for combinatorial game theory.

I plan to make a study about a local combinatorial game here in our country.

Unfortunately, the school I am in does not offer any Combinatorial Game Theory course.

What do you think are the prerequisites before studying this subject?

I still have some electives to choose for the next semester and I'm thinking of choosing subjects which are somewhat related and useful in studying Combinatorial Game Theory.

Any ideas? Thank you!

Answer 1

I'm reading the first volume of Winning Ways for Your Mathematical Plays and see that it's listed on the recommendations thread. It doesn't have any prerequisites except for some basic set theory (used to formalize the concept of a combinatorial game). It does require some mathematical maturity such as familiarity with proofs; also, concepts like surreal numbers or move values can be quite abstract, and the book doesn't hand-hold you.

I believe this should be similar for other books because the field of CGT doesn't have very much formal prerequisites, but it's also not a field that a beginning student of mathematics is expected to learn first or early.

If you want an online course, I've heard good things about Games Without Chance by Dr Tom Morley on Coursera.

Answer 2

Winning Ways is great, but it focuses largely on impartial games. Nevertheless, that book and impartial games are the foundation of the field.

The link you provided is quite good. I found Fraenkel's Combinatorial games: Selected bibliography with a succinct Gourmet Introduction, although I had to correspond with him directly to get an understanding of why there's no precise definition of "combinatorial game" (the field is ever expanding, and in some sense, the definition is a function of games that can be analyzed with the intent of solving, like Poker in recent years.)

I've found Thomas Ferguson's work to be quite helpful. He has a page with links to his papers: Game Theory, Second Edition, 2014

But the paper that helped me the most in understanding the basic concepts was Erik Demaine's Playing Games with Algorithms: Algorithmic Combinatorial Game Theory