The major setting of "Battle Royal" by Ralph Ellison is the ballroom of the hotel where the narrator and his schoolmates go to participate in a boxing match. In the ballroom, a temporary boxing ring has been erected and there are seats around the ring. There are many white spectators in the crowd, and the atmosphere in the room is tense.
In other parts of the story, however, the action takes place in the narrator's home and in the realm of his dreams.
"Battle Royal," the first chapter of Invisible Man, is set in the American South in the late 1920's or early 1930's. This is critical because of the rampant racism that informed the lives of those living in the area at the time and which is a point of discussion of the book. In fact, the narrator, an African-American man, is eventually rendered invisible as a result of his skin color--a commentary on the erasure of black identity.
The first chapter is more specifically located in the main ballroom of a hotel, where the narrator has been brought by a group of white men in order to physically fight his fellow schoolmates. The boys are brought into a boxing ring, blindfolded, equipped with boxing gloves, and forced to beat each other up in a "battle royal" for the entertainment of the white audience. Believing that obedience is the way to achieve success as a young black man, the narrator acquiesces to the men's demands, sacrificing his individualism and dignity in order to participate in the bloody fight.
Thus, the setting ultimately plays a key role in allowing for the examination of racism, alienation, and individualism that are central to the novel.