Tug of war was a game in which two parties or groups pulled on a rope until one side pulled the other over a line. Metaphorically, it referred to any long drawn-out fight over something.
In 2371, Seska and Neelix had a tug of war over a bag of mushrooms. (VOY: "State of Flux")
In 2372, Kathryn Janeway accused Q and Quinn of endangering USS Voyager with the Q Continuum's personal tug of war over Quinn's right to commit suicide. (VOY: "Death Wish")
In 2374, Chakotay described a tractor beam fight with the Hirogen as a tug of war which Voyager was losing as its beam power became depleted. (VOY: "Hunters")