Duke It Out Meaning

(idiomatic) To argue heavily or at length.

Example: To fight, especially with the fists.
  A large crowd came to watch the boxers duke it out.
  The candidates duked it out on the proposal for hours.
2007, New York Times [1] 29 January
  Like pharmaceutical companies that sue generic drug makers over their patents or technology companies that duke it out over who owns the right to microchip designs, Levi’s says it is trying to protect its most valuable asset, its trademarks.