If I have to pick one story that most influenced 'The Hunger Games,' it would be the Greek myth of Theseus, which I read when I was about 8 years old. In punishment for past deeds, Athens periodically had to send seven youths and seven maidens to a labyrinth. In the maze was this Minotaur, and it would eat them.
If your parent is deployed and you are that young, you spend the whole time wondering where they are and waiting for them to come home. As time passes and the absence is longer and longer, you become more and more concerned - but you don't really have the words to express your concern. There's only this continued absence.
One of the reasons it's important for me to write about war is I really think that the concept of war, the specifics of war, the nature of war, the ethical ambiguities of war, are introduced too late to children. I think they can hear them, understand them, know about them, at a much younger age without being scared to death by the stories.