Shakespeare in the Hunger Games?

Yes, I'm reading them.  Technically, listening on audio book.  I like to know what the latest pop culture things are all about.  Just don't ask me about 50 Shades of Grey...

Anyway, I discovered (and I don't think it's a spoiler) that the bad guy's first name is Coriolanus.  Really?  That caught my attention quickly.  I wondered why for awhile, but could not immediately make the connection.

Then I learned that a girl who has her tongue cut out is named Lavinia.  Aw come on!  That can't be coincidence.

Of course, there's an obvious connection to Roman history running through the games (not even counting the whole bread and circuses, gladiatorial thing).  Once I started looking I realized that other characters are named Cinna ("I am Cinna the Poet!  I am Cinna the Poet!!"), Octavia...heck there's even a Caesar.

So does anybody know whether the author had any Shakespeare thoughts in mind with these stories?  I'm guessing that perhaps she had enough passing familiarity with Shakespeare that she was able to pull names at will, and just used them as she saw fit.  The Lavinia thing probably isn't a coincidence, I suspect that when she was seeking a Roman name for her girl with no tongue, Lavinia was the obvious choice for anybody who knows who that is.