play someone/something off against someone/something
phrasal verb with play verb uk/pleɪ/ us/pleɪ/
（为渔利而）使相斗，挑拨离间
to encourage one person or group to compete or argue with another, hoping to gain some advantage from this situation
Management policy seemed to be to play one department off against another. 管理层的政策似乎在有意激起各部门之间的竞争。