Go has also provoked some interesting developments in Combinatorial Game Theory. Conway got started with "On Numbers and Games" (http://en.wikipedia.org/wiki/On_Numbers_and_Games) basically got started by analysing end-game situation in Go.

Note: Combinatorial Game Theory has almost no overlap with Game Theory. Interestingly Combinatorial Game Theory has some analogies in topology. You can for example give meaning to the temperature of a game.