work both ends against the middle

Verb

play both sides against the middle (third-person singular simple present plays both sides against the middle, present participle playing both sides against the middle, simple past and past participle played both sides against the middle)

1. (idiomatic) To manipulate opponents or competitors in a manner which benefits the manipulator.
   • Some of the lesser Democrats, especially in the remoter reaches of the Bible country, have the same yearning, but they are not as numerous as the Republicans, all of whom have been greatly embarrassed by Dr. Hoover's laborious efforts to play both sides against the middle.1932, George Jean Nathan, Henry Louis Mencken, The American Mercury, page 383