One thing that struck me throughout is the recurring theme that Katniss can't receive gifts, especially gifts of sacrifice, without feeling that she owes them. She always incurs debt with every gift. Haymitch even capitalizes on this during the games to get her to do what he wants her to do.
This is exactly how we feel when we receive a Christmas present and haven't gotten one for them. We feel we owe them. We feel like we're in their debt. And that we must repay them.
Works righteousness is in all of us. And when we engage in it, we ourselves step into the the Hunger Games arena. We're fighting to live. We don't want to die. And so the game makes us who we are. We aren't allowed then to get out of the games on our own terms (like Peeta wanted to). We must play the game. And that game forms us. It changes us. It kills us. For there can be only one Victor of that game: He who only is righteous, Jesus Christ our Lord.
With that, HERE is a great article that confirmed my initial suspicion and took it to far greater depth and insight.