(n.) The act of rivaling, or the state of being a rival; a competition.

antagonism antipathy bad blood clashing collision competition competitiveness conflict contention contrariety contrariness controversy covetousness cross-purposes cutthroat competition disaccord discord dispute dissension emulation enmity enviousness envy feud fractiousness friction gamesmanship grudging grudgingness hostility inimicalness invidia invidiousness jealousy jockeying lifemanship negativeness noncooperation obstinacy one-upmanship oppugnancy perverseness recalcitrance refractoriness repugnance strife striving struggle tug-of-war uncooperativeness vying warfare