Are the main characters in "The Most Dangerous Game" static or dynamic?
I'm not sure that I would agree that Rainsford is a dynamic character. "The Most Dangerous Game" is an action story rather than a psychological one, and its plot dynamic revolves around who will kill whom rather than any moral dilemmas or psychological epiphanies.
Both Rainsford and Zaroff are hunters and both see no problem in preying on animals, as they see other living beings only as trophies to be mounted on their walls. Both are also soldiers by training and thus have made careers out of killing human beings. Although Zaroff is the more extreme villain, in a sense he is the logical conclusion to the activities in which they both have engaged, they are not really that different. Although the younger Rainsford has not yet started hunting people, and still has a conventional horror of doing so, the end of the story opens up the possibility that he will become the next Zaroff. We don't really see Rainsford developing empathy (plotting to save the other prisoners) or anything beyond a desire for personal survival.
The two main characters in Richard Connell's "The Most Dangerous Game" are both world-class hunters--Rainsford and General Zaroff. Characters can be either static (remaining relatively unchanged) or dynamic (undergoing change) throughout the course of a story. In this case, there is one of each--Zaroff is static and Rainsford is dynamic.
The General is the same at the end of the selection as he is at the beginning: sophisticated, cultured, cruel, sadistic, and self-absorbed. Rainsford, though, does experience a change both in circumstances and in thinking throughout the course of the story. Initially he was insensitive to the feelings of the hunted, uncaring about anything but his own pleasure in hunting. Once the great reversal happens and Rainsford becomes the hunted, his perspective on everything changes. That is a perfect description of a dynamic character--someone for whom everything changes.