play both ends against the middle

play both ends against the middle (gain an advantage by setting opposing parties or interests against one another; maneuver opposing groups in order to benefit oneself) — играть на чужих разногласиях; использовать чужие разногласия в своих целях; настраивать одного против другого, используя разогласия; сталкивать лбами; ~ подыгрывать и нашим, и вашим

Example 1: Some children are adept at manipulating their parents, playing both ends against the middle.(The American Heritage)

Example 2: You know, he's a supreme confidence man, a real good con man, and I think he was playing both ends against the middle, and we later became certain of that because many of his calls were intercepted, calls to the Iranians were intercepted and analyzed by our intelligence people, and we realized how duplicitous he was.

see also
[play one off against another]
[run with the hare and hunt with the hounds]
[и нашим и вашим]