Video Game AI, Game Theory, and Abstract Algebra.

I have to do a project for my modern algebra class. The project guidlines are fairly open ended (as in we pick a topic and show as much as we want. The class has math ed majors in it aswell. So, the deliverable of the project can even be a lesson plan).

I picked the topic of game theory in hopes of connecting it somehow to AI in Starcraft or League of Legends or just in general how AI are designed for video games, but I am having trouble finding any topics/sites/papers relating AI and Algebra (except for things like a Tic-Tac-Toe AI).

Any help from the wards of the internet?