Strategies for training AI players on asymmetric games?

I'm familiar with things like self-play in training a player for games like Chess, Checkers, and many other games where move sets and goals are the same for both players - e.g. eliminate the other player's pieces, prevent the other player from moving (like in Amazons, for example), etc. But what about training a computer player for a game where one side has a different goal than the other? Thing like Maker-Breaker Games. I imagine I would want to train a strong Maker and then train a strong Breaker. So it seems like like an application of Reinforcement Learning and more like a Generative Adversarial Network.

Does anyone have any reading on these types of problems? Thanks.

Additionally, I'm looking to build a home computer with some funds I came into recently to help me train models (I can't depend on cloud services since the money is only available for a short time), and my budget is pretty big for a home system. Where should I go looking for something that is relatively quiet, usable, doesn't raise my electricity bill too high, and is still powerful enough to train models for years to come? I've looked into /r/buildapcforme but folks seem more focused on gaming over there. And I'm pretty hardware ignorant.