three-cornered contest/fight
From Longman Dictionary of Contemporary Englishthree-cornered contest/fightthree-cornered contest/fightespecially British EnglishCOMPETITION a competition which involves three people or groups → three-corneredExamples from the Corpusthree-cornered contest/fight• Third, after a terrific three-cornered fight, were David Hoskins and David James.