a state in which two people, companies, etc. are competing for the same thing rivalry (with somebody/something) (for something) a fierce rivalry for world supremacy rivalry (between A and B) (for something) There is a certain amount of friendly rivalry between the teams. political rivalries sibling rivalry (= between brothers and sisters)Extra examples rivalry between the army and the police rivalry for the party leadership rivalry over who is to head the delegation rivalry with foreign companies the bitter rivalry that existed between them the fiercest rivalry in professional sports the increasing rivalry among competitors in the industry Her parents had been very aware of the problems of sibling rivalry before the younger child was born. The coup attempt sharpened old political rivalries. They are locked in a fierce rivalry for world supremacy.