Just thought I'd reproduce most of a comment I made on the Storygames forums because I've deliberately buried the lede in the mechanics, and for comments should make it more obvious what I'm doing even if the players aren't always meant to find out.
The core of Hunger Games is about both how people crack but keep going under horrible pressure, and about finding humanity in the midst of truly awful situations. <em>Panem</em> is intended to do that when played with everyone as Tributes (team play is a much more superficial game and intended in part to bury the intended game that much deeper).
If I've got things right (and I know it'll take fine tuning), the driver to the game is stress. Stress, people breaking down, and how they are pushed and how they crack under pressure. The stress track is meant to look relatively mild and in practice to really break the characters down - but in the opening session they should be used to being able to spend stress almost freely. I might need more teeth behind the pressure valves, but that's where that hook is. Breaking them down (note that the only stat that doesn't take a hit on one is Strong, which is incredibly valuable in the arena but almost useless outside).
The finding humanity in the midst of horrible things has two drivers. First no Tribute can win on their own. That's part of the purpose behind the Pack, and the District 2 Tribute rules. You need allies. Allies in the midst of that, who could cut your throat in your sleep, when the explicit rules say that only one can win. Second, I'm trying to point the game that way by what the Tributes can't do. Tributes explicitly have no access to the "Read another person" move until a long time into the game. There is quite literally no mechanical way for one Tribute to know they can trust another. You have to roleplay it out. (The only exception being the 7-9 Aid Other: Expose yourself to truth). Finally, with two surviving PCs, the Hunger Games end with a cross between Prisoner's Dilemma and chicken.
So we have a game that looks like a PvP game that you can not win by playing pure PvP - so you need to trust another person but have no mechanical ability to do so. Your only possible choice if you are playing to win is to roleplay it out. The humanity. The trust in the midst of the horrible situation. And either the trust to the last, each being willing to die for the other, or the final betrayal.