Play Dumb Meaning

(idiomatic) To pretend to be slow-witted or lacking in specific knowledge, usually in order to avoid responsibility or to gain some advantage.

Example: To pretend to be mute.
1904, Rex Ellingwood Beach, "The Mule Driver and the Garrulous Mute," in Pardners,
  I played dumb 'cause I knew if I talked at all, being simple and guileless, you all would twist me up and have the whole thing in a jiffy.
1966, "Milestones," Time, 1 Apr.,
  Died. Virginia Hill, 49, redheaded, free-spending playmate of the underworld . . . who later acted out a cameo role before the late Senator Estes Kefauver's Senate crime committee, playing dumb about the business dealings of her many racketeer friends.