Yes, all of that is laid out in the preamble at the beginning of the movie. But when we join the story, most of the districts have bought into the patriotism and honor themes that the rich district has wrapped around the games. They have bought into the system, and that is the problem to be solved. Hope resides in the people of the poorest district since they have the least stake in the system. Their participation is mainly the result of compulsion by the state and economic desparation. This makes them ripe for rebellion if they can only gain consciousness of their own strength and the tenuous nature of the exploiter class’s hold on power.
I thought only two of the districts did that. The rest were just trying to survive, and showed considerable disdain for the procedure. They were compelled to do so at the threat of death. There was no mass celebration when the names were picked in 12, just silence.