"The Most Dangerous Game" is largely a story that emphasizes man versus man and man versus nature conflicts, though there are elements of a man versus self conflict within Rainsford.
Rainsford's conflict with nature occurs early on, when the ship begins to sink. Not only does the water threaten him, but the dark of night makes it harder for him to see where he's going or what's happening:
Rainsford sprang up and moved quickly to the rail, mystified. He strained his eyes in the direction from which the reports had come, but it was like trying to see through a blanket. He leaped upon the rail and balanced himself there, to get greater elevation; his pipe, striking a rope, was knocked from his mouth. He lunged for it; a short, hoarse cry came from his lips as he realized he had reached too far and had lost his balance. The cry was pinched off short as the blood-warm waters of the Caribbean Sea dosed over his head.
This is the first time the mighty hunter Rainsford is rendered vulnerable by powers out of his control.
By and large, most of the conflict is between people. The moment Rainsford first encounters another person on Shiptrap Island is immediately fraught with mortal danger:
The first thing Rainsford's eyes discerned was the largest man Rainsford had ever seen—a gigantic creature, solidly made and black bearded to the waist. In his hand the man held a long-barreled revolver, and he was pointing it straight at Rainsford's heart.
The servant Ivan prefigures the more potent threat represented by Zaroff. When Zaroff first appears, Rainsford regards him as handsome and aristocratic in appearance, but within moments, he shows his "red lips and pointed teeth," foreshadowing his brutality and thirst for violence.
While much of the conflict between Zaroff and Rainsford is physical, earlier on, the two clash over philosophies of hunting. Zaroff has no qualms killing humans he considers lower than himself (which appears to include almost everyone), while Rainsford still has moral scruples, even if he does enjoy the thrill of the hunt:
"Thank you, I'm a hunter, not a murderer."
"Dear me," said the general, quite unruffled, "again that unpleasant word. But I think I can show you that your scruples are quite ill founded."
"Life is for the strong, to be lived by the strong, and, if needs be, taken by the strong. The weak of the world were put here to give the strong pleasure. I am strong. Why should I not use my gift? If I wish to hunt, why should I not? I hunt the scum of the earth: sailors from tramp ships—lassars, blacks, Chinese, whites, mongrels—a thoroughbred horse or hound is worth more than a score of them."
"But they are men," said Rainsford hotly.
"Precisely," said the general. "That is why I use them. It gives me pleasure. They can reason, after a fashion. So they are dangerous."
This goes to show that the conflict between these two men is as psychological as it is physical.
Lastly, while man versus self is not prominent, it does appear in Rainsford's own fears of losing his life. The sound of the general's laughter in particular chills him:
He stood there, rubbing his injured shoulder, and Rainsford, with fear again gripping his heart, heard the general's mocking laugh ring through the jungle.
Eventually, Rainsford overcomes all three of these obstacles: his hunting prowess allows him to survive the elements and Zaroff, but his own courage allows him to overcome inner anxieties about his ability to survive.