Disclaimer: I've never read/seen the Hunger Games, and it's been ages since I saw Rollerball or Running Man...

In the Hunger Games, aren't the districts competing against each other? Perhaps the elite plan on the competitive nature of humanity to win out against any force that might try to unite them. Combine that with the anger one district would feel against another if their competitor - who is their only chance at getting more food - is killed. That just makes you dislike the other guys more. As long as all the lower people are fighting amongst themselves, the elite figure they'll be okay. I'd imagine it's not a perfect system, but it sounds like the world they live in doesn't leave them much of a choice.