Richard Connell's "The Most Dangerous Game" illustrates both internal conflict (man verses self) and external conflict (man verses man/nature, man verses supernatural is not present).
Man verses Self
When Rainsford first realizes the truth about the "game" he is playing, he becomes very frightened:
Then it was that Rainsford knew the full meaning of terror."I will not lose my nerve. I will not."
This understanding of fear and talking himself out of losing his nerve speaks to the internal conflict Rainsford feels. It is his own courage fighting his own fear.
Man verses Nature
Both Zaroff and Rainsford face the external conflict of man verses nature. Zaroff's supremacy over animals on earth is illustrated by his need to move onto something far more challenging.
"No animal had a chance with me any more...The weak of the world were put here to give the strong pleasure."
Although the quote refers to Zaroff's inability to find any animal that could reason, it illustrates his search of nature for a being which could. Zaroff had to move on from animals and take up the sport of hunting mankind.
Rainsford, on the other hand, is forced to face the jungles and Zaroff's hounds. Both elements of nature, he finds it necessary to kill the dogs (with the Burmese tiger pit) and put nature to his use (when climbing the trees for protection and making the traps).
Man verses Man
The greatest conflict of the story takes place between Zaroff and Rainsford. Zaroff, wanting to hunt an "animal" which can reason, has turned his attention to men. Rainsford, unfortunately, has literally washed up onto his island. Given Rainsford's renown as a hunter, Zaroff wishes to challenge him. Both men intend to kill the other in order to survive.
Evidence for the external conflict Man vs Nature Evidence (Zaroff):
Zaroff wanting to challenge nature by trying to hunt the man itself.
"I wanted the ideal animal to hunt," explained the general. "So I said, `What are the attributes of an ideal quarry?' And the answer was, of course, `It must have courage, cunning, and, above all, it must be able to reason."'
"But no animal can reason," objected Rainsford.
"My dear fellow," said the general, "there is one that can."
"But you can't mean--" gasped Rainsford.
"And why not?" -The Most Dangerous Game
Evidence for Rainsford Internal Conflict Evidence
Rainsford fights himself in his will to survive and to focus staying alive.
"Rainsford knew he could do one of two things. He could stay where he was and wait. That was suicide. He could flee. That was postponing the inevitable. For a moment he stood there, thinking. An idea that held a wild chance came to him, and, tightening his belt, he headed away from the swamp. " - The Most Dangerous Game
Evidence for External Conlict Man vs Man
•Zaroff v.Rainsford while hunting each other, both are hunting each other for their lives. Both are using their hunting tricks to try to kill each other. They are doing everything because they are in surivial mode right now, and will do anything to fight for their lives.
"They would be on him any minute now. His mind worked frantically. He thought of a native trick he had learned in Uganda. He slid down the tree. He caught hold of a springy young sapling and to it he fastened his hunting knife, with the blade pointing down the trail; with a bit of wild grapevine he tied back the sapling. Then he ran for his life. The hounds raised their voices as they hit the fresh scent. Rainsford knew now how an animal at bay feels.
He had to stop to get his breath. The baying of the hounds stopped abruptly, and Rainsford's heart stopped too. They must have reached the knife. " - The Most Dangerous Game