The protagonist of the short story "The Open Window" is Framton Nuttel. Framton is a man who visits the Sappleton family in the country in order to get some rest, as he suffers from a nervous condition. He is recommended to the family by his sister, who met the Sappletons in the past. 

The antagonist of the story is Vera. Vera is the 15 year-old niece of Mrs. Sappleton. She is a girl described as "self-possessed." This means that, even though she is young, she still has good control of her actions.  

The antagonist is the character or circumstance that acts against the protagonist as an adversary. Vera's character is the antagonist of Framton Nuttel because she tells him a fake story about her aunt's husband and two brothers, which worsens Framton's nervous condition to the point of sending him off running out of the house. 

Out of the characters, Framton would be dynamic because he changes: He goes from bad to worse. He had arrived in the house somewhat composed, and was sociable enough. He was able to carry a conversation with Vera, and kept control of himself until he saw, through the open window,  the supposed dead men arriving from their deadly hunting trip, which was Vera's fake story. 

This is when Framton cannot take it anymore and leaves the premises in horror. The rest of the characters would be static, or non-changing. 

The Open Window by Saki is a short story.  The main characters are:

Frampton Nuttel, the Protagonist, or the main character,  

Vera, Mrs. Sappleton's niece is the Antagonist or the character who provides the conflict in the story. They are the two main characters.  The supporting characters in the story include:

Mrs. Sappleton, her husband and brother, Ronnie,  who come home from hunting, with the dog.

Frampton Nuttel's sister who recommends that he go to the country to rest his rattled nerves. 

The protagonist of the story, the main character, is Framton Nuttel, a young man suffering from some kind of emotional problem who has come to the country to rest. The antagonist would be Vera, Mrs Sappleton's neice. After hearing of Nuttel's nervous condition, she invents a story about a window that's been left open in the room. She seems to have no qualms or guilt about scaring Nuttel so much he runs screeming out of the room. She make up an equally plausible story about why Nuttel left so quickly. The dynamic, round character is Nuttel, who at the beginning of the story is only moderately disturbed, but by the end of the story his sanity is gone and he has a nervous breakdown. As the ending of the story shows, Vera just keeps on making up "outlandish" stories.

Who is the protagonist and who is the antagonist in "The Open Window"?

The protagonist of the story "The Open Window" is Framton Nuttel. Framton is a stranger to the Sappleton family, which he goes to meet for the first time at their home in the country, in order to stay with them. He goes there in hopes to rest to get a cure for his nervous condition. His sister, who had visited the area and met the family years ago, had sent with him letters of introduction so that the Sappletons know who Framton is.

Since Nuttel needs to cure his current nerve condition, anything or anyone that attempts against that, or against Framton, would be considered his antagonist. The definition of "antagonist" is

1. a person who is opposed to, struggles against, or competes with another; opponent; adversary.

2. the adversary of the hero or protagonist of a drama or other literary work.

In this case, Nuttel's adversary, or antagonist, would be Mrs. Sappleton's niece, Vera. Vera is 15 years-old, described as "self-possessed", and the teller of the fictitious story about the deadly accident of Mrs. Sappleton's husband and her two young brothers.

Vera is his antagonist because she acted against Framton in full knowledge that her story would actually make his nerves even more delicate. Even though she was just being a mischievous teenager, she would still be considered his antagonist for this very reason.

Contrary to the antagonist, the protagonist of a story is the leading character. Framton is the leading character of "The Open Window" because he is at the center of the story, and because his main problem is also a big part of the plot.

Who is the protagonist and who is the antagonist in "The Open Window"?

This is a legiimate question but a hard one to answer. There are only three important characters in the story. It seems pretty obvious that Vera has to be the protagonist because she is the instigator of everything else that happens. If that is the case, then the antagonist has to be either Framton Nuttel or Mrs. Sappleton. For any story to be interesting, it has to be dramatic, and for any story to be dramatic, there has to be conflict. There does not appear to be any conflict at all between Framton and Vera, and therefore I suggest that the conflict has to be between Vera and her aunt.

I suggest that Mrs. Sappleton is the antagonist. She is trying to teach Vera to be a gracious hostess, and she has taken Framton's visit as an opportunity to let Vera practice her hostessing. Vera greets Framton as follows:

"My aunt will be down presently, Mr. Nuttel," said a very self-possessed young lady of fifteen; "in the meantime you must try and put up with me."

Vera must be an angry young lady. She resents being used by her aunt as a surrogate hostess. She does not want to grow up to be a woman like her giddy aunt. Vera resents being confined to the house because she is a female, while the three men go off to shoot birds and have a lark. She takes out her resentment on poor Framton Nuttel, who just happens to be in the wrong place at the wrong time and is neither the protagonist nor the antagonist. Framton might be said to be the "MacGuffin," the bone of contention between protagonist and antagonist.

Mrs. Sappleton wants Vera to play the gracious hostess and make Framton feel comfortable and welcome. Therefore, Vera does just the opposite and makes him feel so uncomfortable that he finally leaps up and runs out of the house in a panic. Her aunt wants a peaceful, quiet, civilized, stable, routine existence. Vera hides her true feelings but does her best to generate excitement, amusement, and uproar. She is using Framton to get back at her aunt for keeping her a prisoner and trying to mold her into another a female doormat like herself.

Vera is clever. First she finds out that Framton is a stranger in the region. She makes her story brief because she knows exactly how long she will have before her aunt appears; and she knows exactly, from boring experience, what her aunt will talk about when she does appear.

"Poor dear aunt, she has often told me how they went out, her husband with his white waterproof coat over his arm, and Ronnie, her youngest brother, singing 'Bertie, why do you bound?' as he always did to tease her, because it got on her nerves. Do you know, sometimes on still, quiet evenings like this, I almost get a creepy feeling that they will all walk in through that window - "

Bertie's singing probably got on Vera's nerves rather than on her aunt's. Vera has seen these scenes and heard her aunt's mindless drivel so many times that she is going a little crazy. She knows that the three hunters will shortly appear with the little spaniel and that Bertie will begin singing "I said, Bertie, why do you bound?" She knows her aunt will be looking forward to their return and talking about the only subject that ever gets talked about in this remote, benighted country household--the shooting of birds.

We can imagine that there is an ongoing contest between Vera and her aunt. Vera feels trapped, suffocated, tied to a Procrustean bed. She wins this little victory in her rebellion, but the reader feels that the contest will go on and on.