Examples of Conflicts in "The Most Dangerous Game":
Man vs. Man: The hunt between Rainsford and General Zaroff, and the various hunts that Zaroff initiated with his prisoners.
Man vs. Nature: (1) Rainsford must deal with the swamp on the island while he eludes Zaroff. (2) The rocks that provide Ship-Trap Island its name entrap its survivors.
Man vs. Self: Rainsford mentally struggles with his doubts about his ability to elude Zaroff.
Man vs. Fate: (1) It could be considered an act of fate when Rainsford falls off the yacht. (2) Fate also comes into play when Rainsford arrives on the island inhabited by Zaroff--a hunter even more zealous than Rainsford.
"The Most Dangerous Game" is a compelling, exciting, widely-read short story, and the conflicts you list can be found with relative ease. To get you started, I'll give you some quotes to consider; you should be able to figure out what kind of conflict each quote shows.
Remember that a conflict is a struggle between two opposing forces, and there are two kinds of conflicts: internal and external.
"He struggled up to the surface and tried to cry out, but the wash from the speeding yacht slapped him in the face and the salt water in his open mouth made him gag and strangle. Desperately he struck out with strong strokes after the receding lights of the yacht."
"I will not lose my nerve. I will not."
"I'll cheerfully acknowledge myself defeated if I do not find you by midnight of the third day."
"Life is for the strong, to be lived by the strong, and, if needs be, taken by the strong."
Conflict is a basic concept that you have to understand as quickly as possible - the rest of literature revolves around it. By answering the following questions, you will identify the conflicts:
Man vs. man: who are the two main characters in the story? And what is the big "game" that they play with each other? This is a pretty big conflict.
Man vs. self: this is an internal conflict. Which of the characters must deal with a major decision? What is that decision about and what does he do?
Man vs. nature: as the "game" carries on, what problems arise with animals, with weather, with other things in nature that aren't necessarily controllable? These are man vs. nature conflicts.
Man vs. fate: this one is a little more philosophical. What is the outcome of the "game"? Man vs. fate is a question that asks: Was it the main character's fault that he ended up the way he did or was it out of his control the entire time? Who was responsible for the outcome, man or fate/destiny?