Answer and explanation:
I believe the most important conflict in "The Most Dangerous Game" is Man vs. Man - an external conflict played out between a protagonist and his/her antagonist. In this short story by Richard Connell, the main character - Rainsford - is a hunter who believes the world is devided into two classes: hunters and huntees. And he prides himself in thinking that he is lucky to belong to the strongest of those classes. He does not pity the animals he hunts.
However, as the story develops, Rainsford becomes the huntee. He accidently falls from a yatch and swims to an island belonging to General Zaroff. Just like Rainsford himself, Zaroff is a hunter who does not pity his preys. But he has gone beyond Rainsford, for he has begun to hunt men. Zaroff no longer saw animals as a challenge; they were just too easy to catch. Men, though, have the capacity to reason. Hunting them is more amusing than hunting a jaguar.
At first, Zaroff thinks he has found a colleague in Rainsford. He thinks they will begin to hunt together. Rainsford, however, does not live up to the general's expectations, since he considers what Zaroff does to be murder, not hunting. When he refuses to participate in it, Zaroff makes him his next game. That's when the conflict of Man vs. Man intensifies. Rainsford has to outsmart Zaroff. He is only given some clothes, food, and a hunting knife, while the general has a pistol and dogs. The forest itself is not much of a challenge; Rainsford is knowledgeable enough to use it to his favor. Still, the general is an outstanding tracker and finds him easily every time. In the end, Rainsford defeats Zaroff in his mansion, after hiding in his bedroom. They fight, but the general is no match for Rainford.