three-way contest; triangular battle
Used for a competition or conflict involving three parties, such as in politics, sports, or games. The kanji 鼎 refers to a three-legged vessel, symbolizing three-way balance or rivalry.
The next election looks set to be a three-way contest between the ruling party and the two main opposition parties.
This game takes the form of a triangular battle among three factions.
鼎立 is the noun meaning 'triangular position' or 'three-cornered rivalry'; 鼎立戦 adds 戦 (battle/contest) to explicitly denote a contest.
From 鼎 (かなえ, a three-legged metal vessel) + 立 (standing) + 戦 (battle/contest). The image of three legs standing in balance gives the sense of a three-way rivalry.