Suzanne Collins cited Roman gladiatorial games and Greek mythology as a prime inspiration for the series, especially the myth of Theseus.
In the Theseus myth, the city of Athens had once organized a sporting event which was won by the son of the king of Minos. Out of jealousy, the Athenians had killed the son, which in turn caused a war between the two cities that was won by Minos. As punishment for the murder of his son, the king of Minos ordered that Athens send seven boys and seven girls every few years (accounts vary) to Minos, who would be placed in the labyrinth below Minos to serve as food for the Minotaur. Theseus finally lifted the penalty by killing the Minotaur. This theme of forcing a conquered enemy to sacrifice several of its younglings in penance is indeed the core element of the book.
The idea of fighters battling amongst one another in an enclosed arena is one of the most common hallmarks of Roman society. Yet there are more elements from Roman culture that seem to have influenced 'The Hunger Games'. The name of the fictional country Panem is a direct reference to the Roman strategy of panem et circenses, or 'bread and games'; many Roman rulers found that they could get away with any abuse of power, as long as they appeased the public with food (bread) and entertainment (games). The Panem government does quite the same, keeping the Capitol citizens satisfied with lavish luxuries and shallow entertainment, at the expense of their subjugated enemies (the citizens of the outlying districts).
The name 'tribute' for the candidates who are to compete with each other in the Hunger Games is aptly chosen. When the Romans conquered other territories during their invasions, they often granted its people considerable self-control under Roman rule, in return for tribute, which was a form of submission taxes consisting of money, goods, and sometimes even soldiers to serve in the Roman army. The tributes in 'The Hunger Games' are also extorted from the districts after having been subjugated by the Capitol; they are presented to the public in typical Roman fashion, i.e. in chariots during a triumph parade.
Other elements include the Cornucopia, better known as the Horn of Plenty, which is a symbol of abundance in classic mythology; character names such as Seneca (Roman philosopher), Cinna (Roman politician and opponent of the imperial dictatorship), Cato, Claudius and Caesar (Roman statesmen).