In fact, people are starving at Katniss's District, 12, and there are people, like her father, dying from explosions while at work. How did the Capitol manage to have this game ongoing? The reasons are quite simple. One of them is power. Power to keep the society in "peace," power to rule, power to take anybody's life, power that grows fears. There is a reason for them to choose children at the age between 12 and 18 for the game. It is to show people the fact that they are so powerful, they can even make you gave up your own children. And the other fact that roots the strength of the Capitol in everyone's mind, is the Dark Days, when districts rises against the Capitol, but all ended up being defeated, and even with District 13 obliterated.
The other reason why the Hunger Games prevail is that people actually enjoy watching the game. Gale, one of the people who Katniss spent most of her time with before the game, mentions in the movie that, "What if everyone just stopped watching?. No one watches and they don't have the game. It's as simple as that." Yes, it is as simple as that. However, they will not stop watching. Because it is embarrassingly a part of human nature, and the Capitol is very good at making it amusing. Historically speaking, we did have a similar policy in our world in ancient times, such as the ancient empire of Rome, when the Roman Caesar made a strategy to please his people by feeding them plenty of food and a circus – the Colosseum, where people get amused by watching the fighters, so called Gladiators, fight and bleed. This policy which the Rome Caesar made use of, is an ancient formula of panem et circenses, the Latin word for "bread and circuses", and it is also where the name "Panem" came from. Just like its name, the nation of Panem actually obtains its "peace" by giving people entertainments more than enough, except for those from the lower-class district.