Suzanne Collins, the author of the novels, is known to be a huge fan of ancient Roman and Greek mythology. For example, from this interview:
Q: Thanks to a cruel futuristic government, 24 children are chosen by
lottery to compete in the annual Hunger Games—a fight to the death
that’s televised live. How did you come up with that idea?
A: It’s very much based on the myth of Theseus and the Minotaur, which
I read when I was eight years old. I was a huge fan of Greek and Roman
mythology. As punishment for displeasing Crete, Athens periodically
had to send seven youths and seven maidens to Crete, where they were
thrown into the labyrinth and devoured by the Minotaur, which is a
monster that’s half man and half bull. Even when I was a little kid,
the story took my breath away, because it was so cruel, and Crete was
so ruthless.
She discusses this in more detail in an interview with Scholastic:
Q: You weave action, adventure, mythology, sci-fi, romance, and
philosophy throughout The Hunger Games. What influenced the creation
of The Hunger Games?
A: A significant influence would have to be the
Greek myth of Theseus and the Minotaur. The myth tells how in
punishment for past deeds, Athens periodically had to send seven
youths and seven maidens to Crete, where they were thrown in the
Labyrinth and devoured by the monstrous Minotaur.
Even as a kid, I
could appreciate how ruthless this was. Crete was sending a very clear
message: “Mess with us and we’ll do something worse than kill you.
We’ll kill your children.” And the thing is, it was allowed; the
parents sat by powerless to stop it. Theseus, who was the son of the
king, volunteered to go. I guess in her own way, Katniss is a
futuristic Theseus.
In keeping with the classical roots, I send my
tributes into an updated version of the Roman gladiator games, which
entails a ruthless government forcing people to fight to the death as
popular entertainment. The world of Panem, particularly the Capitol,
is loaded with Roman references. Panem itself comes from the
expression “Panem et Circenses” which translates into “Bread and
Circuses.”
The audiences for both the Roman games and reality TV are
almost characters in themselves. They can respond with great
enthusiasm or play a role in your elimination.
As a final note, this interesting page at Shmoop discusses some of the allusions to Roman society, including:
- The name Panem (as discussed above)
- The arena and its similarity to the Colosseum
- Cinna - there were two Cinnas associated with Julius Caesar. One was a tyrant involved in his assassination, the other a poet murdered following the assassination after being mistakenly identified as the other Cinna.
- The large number of Roman names in the Capitol.
All of these references have obviously come from interviews with the author. The books don't provide any deeper reason for this and the movies certainly don't.
I would add that from an out of universe point of view, I think you've already described the link: "one could see the term "Capitol" and the actual Hunger Games as a kind of gladiator fights in relation to that". I think that's exactly what is at play here. The use of Roman symbolism throughout the Capitol only further emphasizes the strength and might of the Capitol over the weak, disjointed Districts.
