One over the other or one over another?

Hi. Please help. I think that I am right in that we can use the word "between" (which I think is a preposition) instead of the word (also I think is a preposition) "among" for cases which there more than two things involved if each one is distinguishable individually (I hope what I wrote correctly reflects what I wanted to say, and also it is correct - not sure for both, though). Then which phrase should we use to reference it at a later time (for example, as in the case below), one over the other or one over another?

(made-up sentences)

eg,

This game is going to be a close match-up between China, Japan and Korea.

... You shouldn't favor one over the other (or one over another?).