Problem: Barton Fink is a 1991 American period film written, produced, directed and edited by the Coen brothers. Set in 1941, it stars John Turturro in the title role as a young New York City playwright who is hired to write scripts for a film studio in Hollywood, and John Goodman as Charlie, the insurance salesman who lives next door at the run-down Hotel Earle. The Coens wrote the screenplay for Barton Fink in three weeks while experiencing difficulty during the writing of Miller's Crossing. They began filming the former soon after Miller's Crossing was finished.

In 1989, filmmakers Joel and Ethan Coen began writing the script for a film eventually released as Miller's Crossing. The many threads of the story became complicated, and after four months they found themselves lost in the process. Although biographers and critics later referred to it as writer's block, the Coen brothers rejected this description. "It's not really the case that we were suffering from writer's block," Joel said in a 1991 interview, "but our working speed had slowed, and we were eager to get a certain distance from Miller's Crossing." They went from Los Angeles to New York and began work on a different project. In three weeks, the Coens wrote a script with a title role written specifically for actor John Turturro, with whom they'd been working on Miller's Crossing. The new film, Barton Fink, was set in a large, seemingly-abandoned hotel. This setting, which they named the Hotel Earle, was a driving force behind the story and mood of the new project. While filming their 1984 film Blood Simple in Austin, Texas, the Coens had seen a hotel which made a significant impression: "We thought, 'Wow, Motel Hell.' You know, being condemned to live in the weirdest hotel in the world." The writing process for Barton Fink was smooth, they said, suggesting that the relief of being away from Miller's Crossing may have been a catalyst. They also felt satisfied with the overall shape of the story, which helped them move quickly through the composition. "Certain films come entirely in one's head; we just sort of burped out Barton Fink." While writing, the Coens created a second leading role with another actor in mind: John Goodman, who had appeared in their 1987 comedy Raising Arizona. His new character, Charlie, was Barton's next-door neighbor in the cavernous hotel. Even before writing, the Coens knew how the story would end, and wrote Charlie's final speech at the start of the writing process. The script served its diversionary purpose, and the Coens put it aside: "Barton Fink sort of washed out our brain and we were able to go back and finish Miller's Crossing." Once production of the first film was finished, the Coens began to recruit staff to film Barton Fink. Turturro looked forward to playing the lead role, and spent a month with the Coens in Los Angeles to coordinate views on the project: "I felt I could bring something more human to Barton. Joel and Ethan allowed me a certain contribution. I tried to go a little further than they expected." As they designed detailed storyboards for Barton Fink, the Coens began looking for a new cinematographer, since their associate Barry Sonnenfeld - who had filmed their first three films - was occupied with his own directorial debut, The Addams Family. The Coens had been impressed with the work of English cinematographer Roger Deakins, particularly the interior scenes of the 1988 film Stormy Monday. After screening other films he had worked on (including Sid and Nancy and Pascali's Island), they sent a script to Deakins and invited him to join the project. His agent advised against working with the Coens, but Deakins met with them at a cafe in Notting Hill and they soon began working together on Barton Fink.

who wrote the script?

Answer with quotes: the Coens wrote a script with a title role written specifically for actor John Turturro,

Problem: Thompson was born in Sheffield, Alabama, on August 19, 1942, the son of Ruth Inez (nee Bradley) and Fletcher Session Thompson (born Lauderdale County, Alabama, August 26, 1919, died Lawrenceburg, Tennessee, May 27, 1990), who was an automobile salesman. Thompson had English and distant Dutch ancestry. He attended public school in Lawrenceburg, graduating from Lawrence County High School, where he played high-school football. Thereafter, he worked days in the local post office, and nights at the Murray bicycle assembly plant.

Marie Ragghianti's case became the subject of a book, Marie, written by Peter Maas and published in 1983. The film rights were purchased by director Roger Donaldson, who, after traveling to Nashville to speak with the people involved with the original case, asked Thompson if he wanted to play himself. The resulting film, Marie, was Thompson's first acting role and was released in 1985. Roger Donaldson then cast Thompson in the part of CIA director in the 1987 film No Way Out. In 1990, he was cast as Ed Trudeau, the head of Dulles Airport, in the action sequel Die Hard 2, as Rear Admiral Painter in The Hunt for Red October, and as Big John, the President of NASCAR, in the movie Days of Thunder (patterned on Big Bill France). Thompson went on to appear in many films and television shows. A 1994 New York Times profile wrote, "When Hollywood directors need someone who can personify governmental power, they often turn to [Thompson]." He portrayed a fictional President of the United States in Last Best Chance, as well as two historical presidents: Ulysses S. Grant in Bury My Heart at Wounded Knee (2007) and the voice of Andrew Jackson in Rachel and Andrew Jackson: A Love Story (both produced for TV). In the final months of his U.S. Senate term in 2002, Thompson joined the cast of the long-running NBC television series Law & Order, playing conservative District Attorney Arthur Branch for the next five years. Thompson began filming during the August 2002 Senate recess. He made occasional appearances in the same role on other TV shows, such as Law & Order: Special Victims Unit, Law & Order: Criminal Intent, and the pilot episode of Conviction. On May 30, 2007, he asked to be released from the role, potentially in preparation for a presidential bid. Due to concerns about the equal-time rule, reruns featuring the Branch character were not shown on NBC while Thompson was a potential or actual presidential candidate, but TNT episodes were unaffected. In May 2007, he took a break from acting to run for the Republican nomination for president in the 2008 election, winning 11 delegates before dropping out of the race in January 2008. In 2009, he returned to acting with a guest appearance on the ABC television series Life on Mars and in the movie Alleged, about the Scopes Trial.

Did Thompson immediately agree to play himself?

Answer with quotes:
The resulting film, Marie, was Thompson's first acting role and was released in 1985.