Could you include a reference to alpha-beta pruning, since that is precisely what you're describing? Some readers may be more familiar with that subject domain and appreciate explicitly linking game theory to an established search algorithm.

I think you mean minimax. Alpha-beta pruning is the optimization to minimax that prunes branches as soon as any max (min) node evaluates lower (higher) than the highest (lowest) opposite-colored node evaluated so far among the grandparents' children.