To manipulate two opposing sides of an argument, conflict, competition, etc., against one another for one's own benefit or advantage. My father and my uncle are engaged in a bitter business rivalry. If I can play them off against each other, I might be able to secure some sizeable investments for my own company. Janet has been playing Mary off against her boyfriend, Mike, so that Janet can date him herself. Don't you see? They've been playing us off against each other so that there's less competition for them to deal with.