Purpose of the Battle Royales?

In the Battle Royale manga,novel or movie. Did they ever explain why they organised these things? Why did they do it in secret? I thought they did it to set an example for what happens to bad children. The hunger games broadcast their battles to strike fear. But what is the purpose of the the battles in battle royale? Why didn't they just execute the children in a public place?

This might have been explained...but I missed it.

Bump.

From the beginning of the novel (Meaning assuming there are no twists and such):

1. Yes, the government did it.
2. They didn't, it was publicised, everyone knew that one class would be a part of it, just not which. The main character (or one of them) recalled watching the last winner being interviewed on tv.
3. Uh, I don't think so.
4. There was a reason, but I really can't recall what it was. I read the beginning a while ago, and haven't picked it up in ages.
5. ^