Most retailers do choose their own markup. Ironically, Apple got sued for working with book publishers where the book publishers set the price and Apple chose the markup.
However, the book publishers wanted this arrangement because Amazon was selling ebooks at a loss devaluing the hardcover and paperback books.
https://www.cnet.com/news/just-as-critics-feared-fortnite-fo...
Edit:
Most retailers do choose their own markup. Ironically, Apple got sued for working with book publishers where the book publishers set the price and Apple chose the markup.
However, the book publishers wanted this arrangement because Amazon was selling ebooks at a loss devaluing the hardcover and paperback books.