What kinds of literature could be assigned as companions with The Hunger Games?"The Lottery" by Shirley Jackson is one I have. What others could...

If you are looking for short stories or other examples of
literature to help you, I think that you want to find works that play with the theme of
how the individual responds to a bizarre world.  Ursula Leguin's "The Ones Who Walk Away
from Omelas" is an excellent example of this idea.  It is something that can get the
reader to think about how bizarre the world of Omelas is and what parallels can be seen
in our world today.  Another similar example of such a story would be Bradbury's "The
Veldt."  In Collins' work, children are set to be the hunted.  Bradbury's short story
flips this in articulating what happens when the parents are the hunted?  Exploring this
inversion of power, contrasting it to Collins' work, and examining how violence is used
by those in the position of power would all be interesting ideas to emerge.  Lowry's
book, The Giver, is another great example of the bizarre nature of
a world where the protagonist has to make a choice as to whether they will instill the
idea of justice in a world that lacks it.  I think that these might be good starting
points for you.