From Longman Dictionary of Contemporary Englishplay somebody off against somebody phrasal verbARGUEto encourage one person or group to compete or argue with another, in order to get some advantage for yourself The house seller may try to play one buyer off against another, to raise the price. → play→ See Verb table
Examples from the Corpus
play off against • Airlines usually negotiate privately with manufacturers, playing one off against another, of course.• The highly paid, like the corporations that employ them, are mobile, and can play one state off against another.• When mining companies and other investors rushed to Kinshasa to seek deals, he tried to play them off against each other.• The child may gravitate to the parent that is easier to manipulate or try to play one parent off against the other.• You need to present a united front and avoid taking sides or playing one child off against the other. 