There are two conflicts that Rainsford has with himself throughout the story. The first one is that he finds it abhorrent to hunt human beings. He knows it is wrong,uncivilized, and cold-blooded murder. However,against his will, he is forced to take part in the game. In being hunted by another human being and in the mode of survival, he takes another human's life (Ivan). He climbed up the tree "excitedly" to see who had gotten killed. He really wanted it to be Zaroff and was disappointed.
Another example of this conflict comes at the end of the story. He, again, knows that it is wrong to kill another human being, but he knows that Zaroff will not allow him to leave the island. He has told Zaroff that he intends to let people know what is happening on the island. Zaroff says "in that case" and never finishes his sentence. When Rainsford wins the game, Zaroff congratulates him. But Rainsford says "I am still a beast at bay." This comment shows that he knows he has to fight to the death, and he challenges Zaroff and wins.
The third conflict is coping with the feeling of terror. It says that
"The Cossack was the cat; he was the mouse. It was then that he knew the full meaning of terror." (pg 10)
He has to survive and he has to push himself physically and mentally. He keeps telling himself not to lose his nerve and to think rationally. He hears the hounds coming after him and it says,
At daybreak, Rainsford, lying near the swamp, was awakened by a sound that made him know tha he had new things to learn about fear. ...It was the baying of the hounds."