Why are children used in The Hunger Games?

Answer 1

If you've actually read the whole book, you know why. It exists because the Districts of Panem revolted at one point against the Capitol since they weren't being treated fairly. When they lost, the Capitol forced them to send their children as tributes for the Hunger Games to remind them not to revolt.

Answer 2

The Hunger Games exist to stop people rebelling. They use children because children are defenceless and it is the Capitol's way of saying "look what we can do to your children."

On the other hand, the use of children killing each other is one of many reasons the uprising begins.