It is strongly implied, although not outright specified, that at the end of "The Most Dangerous Game," Rainsford recognizes that the only way to deal with General Zaroff is to attempt to beat him at his own game, of treating humans as if they were animals to be baited and used as prey.
Zaroff, thinking that Rainsford has escaped him as a quarry, goes home, thinking morosely about how he is going to have to replace his servant, Ivan, whom Rainsford has killed. He listens to opera and then goes to bed. He believes that Rainsford has been one of the most interesting beasts he has ever attempted to pursue. This opinion is borne out when, upon going to bed, he realizes that Rainsford is in his bedroom, waiting behind a curtain for him to arrive.
Zaroff tells Rainsford that he has won the game, but Rainsford parries, saying that actually he is still "a beast at bay," or still part of the game. He will not give up so easily, and he will not let Zaroff off the hook. Zaroff enjoys this and says that whichever of them gets the better of the other in their fight will sleep in the bed that night, while the other will be fed to the dogs.
Although there are no details of the fight, the fact that Rainsford is the one who ends up sleeping in the bed is a sure indication that he has bested Zaroff.