What is the theme or central idea of The Hunger Games?
The central idea of Suzanne Collins's trilogy The Hunger Games is that an individual has the ability to overcome the power of the tyrannical government. Another closely related theme central to the trilogy is that if an organization (in this case, the country) needs deception and falsehood to maintain itself, it will eventually fall apart.
All the action and various plot lines support these two ideas, directly or indirectly. The institution of the Hunger Games serves to keep the people of Panem in fear of the government and to prevent any thought of rebellion. The illusion of the victors securing a prosperous and worry-free life (well, almost worry-free -- they know that their children are not immune to becoming tributes) is shattered when these victors become the pawns of the Capitol. However, the Games themselves become the tool the rebels, led by the most unlikely person, the Head Gamemaker Plutarch Heavensbee, use to start the revolution. It is the poverty imposed by the Capitol on the Districts that leads Katniss to develop the skills to survive the Games and ultimately to become a central player in the rebellion.
The themes of romance in the trilogy are also tied to the main idea of government oppression and the individual's resistance. In Catching Fire, Katniss find herself in the position of having no choice but to marry Peeta if she wants to save her family. She reflects that normally in District 12 people have a freedom to choose who to marry, or not to marry at all, but she is denied the same right. Even though she eventually marries Peeta willingly, the circumstances that bring the couple together involve, in part, the deterioration of Katniss's relationship with Gale. This was brought about by their drastically different opinions on whether any innocent lives could be sacrificed in order to achieve victory. Ultimately, their friendship or any romantic interest is over when Katniss suspects that Gale was involved in a plot that resulted in Prim's death.
Finally, one more development that underscores the instability of totalitarian government of Panem is the existence of District 13. The citizens of Panem are told that it was destroyed as the consequence of the previous rebellion; in fact, not only it is still there, it also has been building up enough military power to take on the Capitol. When the Capitol agreed to leave District 13 alone (or risk being destroyed by its nuclear weapons) and lied to the rest of the country about the outcome, it compromised its own position. The flip side of the government's secret is that District 13 is enabled to be the hidden, underground (literally) center of the rebellion. The rumors of its existence empower some individuals to escape and seek refuge there. Even though Katniss originally witnesses only unsuccessful attempts, the start of the revolution leads to the inevitable exposure of District 13.
There are a number of themes in the book that could be argued as the main or central theme, but the constant theme of an individual working to overcome a corrupt system is one that stands out in my mind. Katniss constantly has to find ways to improve and strengthen herself in order to fight back against those who are running the games and ultimately the leaders responsible for the system in the first place.
Another possible theme is of course as simple as good versus evil, the innocent and hard-working people in the different districts having to fight against the decadent and lavishly living capital is another theme that comes up again and again.
This question has already been asked and answered here on eNotes: http://www.enotes.com/the-hunger-games/q-and-a/what-good-theme-hunger-games-152339
There are many themes found but the main theme is either one of Man vs. Society or survival of the fittest. In Man vs. Society Katniss wants to go against the Capitol but is unsure of what President Snow might do and while she retaliates, she has to ensure her family stays safe. As for survival of the fittest, the main idea of the Hunger Games is to have one victor which means survival of the fittest, no matter who's in your pact, in the end it turns out to be whoever is the fittest will be the victor.