There aren't any really explicit shout outs in The Hunger Games, but we know from interviews that Suzanne Collins was inspired, in part, by the ancient Roman Empire. Below are a few connections we see. Can you spot any others?
Panem: Suzanne Collins has said that Panem is supposed to be like ancient Rome: "Panem itself comes from the Latin expression 'Panem et Circenses' which translates into 'Bread and Circuses'" (source). This term refers to the techniques used by the Roman Empire to keep the masses happy and docile (read more here).
The Hunger Games and the Arena: With our Roman history glasses on, we can't help but see the Hunger Games arena as very similar to the Colosseum in Rome, where gladiators would fight to the death for the entertainment of the citizens of the Empire's capitol.
Cinna: There are two guys named "Cinna" who are closely tied to Julius Caesar. One was a politician involved in the assassination plot against Julius Caesar (whom many thought to be a tyrant). The other was a poet who was murdered following the assassination of Caesar, having been mistaken for the other Cinna. (BTW, both of these Cinnas appear in Shakespeare's Julius Caesar.) So what might this say about Cinna the stylist? He's certainly an artist, kind of like Cinna the poet. Does his name indicate that he might also be a rebel, plotting against the oppressive Panem?
Names from Roman history: There are a bunch of names in The Hunger Games that pop up frequently in the history of ancient Rome, particularly during the time of Julius Caesar (not to mention in Shakespeare's Julius Caesar). These include Cato, Portia, Octavia, and Flavia. You might even be familiar with some of them from HBO's Rome. These Roman generally go with characters who are from the Capitol or the wealthy districts.