GALE: If no one watches, then they don't have a game. It's as simple as that.
Like our world, reality television holds enormous power in Panem. Everyone watches the annual Games. And, having decided that TV's a useful tool for controlling the population, the Capitol now needs to play by television's rules if they hope to hold on to power.
SNOW: This is how we remember our past. This is how we safeguard our future.
This is what we call an excuse. He's citing heritage and tradition and all that jazz as the reason for the Games. In reality, it's just a raw exercise of power: we're killing your kids because we can. That should keep y'all in line if you're ever thinking of another uprising.
EFFIE: I think it's one of the wonderful things about this opportunity, that even though you're here and even though it's just for a little while, you get to enjoy all of this.
This is an expression of power that, frankly, isn't much better than throwing them into an arena and killing them. The nice things on the train just remind them of how little they have. The Capitol is happy to let them enjoy it for a few days instead of using those resources to make life better for people at home. As part of the power structure herself, Effie can't even see how ridiculous her words sound to Katniss and Peeta.
CAESAR: Now see that? I love that. Two young people holding their hands up, saying, I'm proud I come from District 12. We will not be overlooked. I love that!
Caesar trivializes any power or pride that Katniss and Peeta might be expressing, saying essentially, isn't it just so darn cute how these two dirt-poor and soon-to-be-dead kids want to be acknowledged? In order to survive, Katniss and Peeta totally pretend to buy in to the charade.
HAYMITCH: Tomorrow they'll bring you in one by one and evaluate you. This is important, because higher ratings will mean sponsors. This is the time to show them everything. There'll be a bow. Make sure you use it. Peeta, you make sure to show your strength. They'll start with District 1, so the two of you will go last. I don't know how else to put this. Make sure they remember you.
Katniss and Peeta are going to get sized up like pieces of meat and assigned numbers that may make a difference between life and death. Any slight degree of power they have comes from their ability to impress the judges.
SNOW: Hope. It is the only thing stronger than fear. A little hope is effective. A lot of hope is dangerous. A spark is fine, as long as it's contained.
SNOW: So, contain it.
Snow's power clearly isn't absolute. Things can get out of hand, at least from his perspective, and that means he needs to make sure none of the citizens of Panem see any serious chance to regain power.
PEETA: I just don't want them to change me.
At the end of the day, that's what power boils down to, doesn't it? Being able to change someone who doesn't want to be changed, whether it's shooting them in the head or forcing them to kill. Peeta's only control over his life is to be true to himself somehow.
HAYMITCH: Don't kill her. You'll just create a martyr.
SENECA: Well, it seems we've already got one.
HAYMITCH: I hear these rumors out of District 11. This could get away from you.
SENECA: What do you want?
HAYMITCH: You have a lot of anger out there. I know you know how to handle a mob. You've done it before. If you can't scare them, give them something to root for.
SENECA: Such as?
HAYMITCH: Young love.
Haymitch is smart. He seems to be giving Seneca some advice about how to keep from losing his control over the masses, but he's really trying to help Katniss and Peeta survive. We can see why he was a Hunger Games winner. He knows how to play the power game.
SNOW: So you like an underdog?
SENECA: Everyone likes an underdog.
SNOW: I don't. Have you been out there? 10? 11? 12?
SENECA: Not personally. No.
SNOW: Well, I have. There are lots of underdogs. Lots of coal, too. Grow crops, minerals, things we need. There are lots of underdogs. And I think if you could see them you would not root for them either. I like you. Be careful.
Here's the Marxist class struggle. The poor Districts supply the elites with what they need to survive, while they themselves are starving. Snow knows the risks in trying to keep poor people down.
HAYMITCH: They don't take these things lightly. When they ask, you say you couldn't help yourself. You were so in love with this boy that the thought of not being with him was unthinkable. You'd rather die than not be with him. You understand?
Haymitch is letting them know that even though they've survived the Games, they're still under the Capitol's control. Katniss has to convince the Capitol that she wasn't rebelling—she was just in love. Otherwise, she'd be too big a threat.