what do the characters want, and what problems do they face?

Rainsford wants to find an animal to hunt that will challenge his hunting skills, since he is the greatest hunter.  Zaroff wants to hunt Rainsford because he thinks only man is a worthy opponent.  Zaroff already has hunted many men, most of whom do not survive even the smallest of hunts.  Ultimately the conflict is man vs man; however, in order to survive, there is also the conflict - for Rainsford especially - of man vs nature.