Actually, the other Links are never computer-controlled. You control all of them at once on 1-player! It's pretty cool. You can also use a simple button-press to choose an individual Link. However, it is required to have GBAs for multi-player, because they not only work as a controller but are used to see things inside of houses and in caves, that way it's like a competition and they won't see what you see. It's also used for text when talking to people.
It's a good game alone, and pretty long. Though when you play with friends, it's even better. I recommend it.