Mr Erdogan may ultimately be swayed by a contest between two competing influences: the restraining power of NATO and the desire of Russia to sow discord among its rivals.
To play someone off someone else is to make those two people disagree, oppose each other. She played her parents off each other after their divorce to get what she wanted.
play someone off someone是指使两个人产生分歧,挑拨。在她的父母婚之后,她为了得到自己想要的,在两人之煽风点火。