Saki's short story, entitled "The Open Window," presents several conflicts.
The first one is probably man (or the individual) vs society. Mr. Nuttel has come from the city to rest because of a nervous disorder. We can infer that this is caused primarily due to city life has he has left the city to rest in the country. We might venture to infer that man vs self is also represented in Nuttel's case as he struggles to deal with a specific aspect of his personal health, which he seems unable to control on his own. Man vs man is also present, as Mr. Nuttel has come under some sincere criticism from his sister who does not want him to bury himself alone in the country. A letter of introduction from his sister has brought him to this home. There is also man vs man as he is set up at the hands of the clever Vera who creates such a believable story. And while it is not accurate, for a time he believes he is facing the supernatural—the "ghosts" of Vera's uncle and cousins (and this would be man vs the supernatural).
Vera, who is staying with her aunt and and uncle, and has little other company beyond them and her two cousins (who she probably has nothing to in common with given their age and gender), is most likely bored. It is hard to say where exactly this conflict rests: however, Vera's inability to find a more productive and kinder form of entertainment would probably introduce the conflict of man vs. self. She uses Mr. Nuttel to amuse herself, and this is man vs man.
Ironically, though there are several examples of different kinds of conflict, the mood of the story is not filled with the tension often found in a story with so much conflict, although these conflicts do introduce a sense of mystery and fear, as well as excitement—in the reader.