Context #1
Tony: Did you take my book?
Jack: What are you talking about? I didn't see any book.
Tony: Don't play dumb. I know you took it.
Context #2
Grace: So did you ask your boyfriend about that text he got from that girl Chrissy.
Amanda: Yeah, but he played dumb and said that she probably texted the wrong number.
Grace: So you think he was lying?
Amanda: Yeah, I could tell by the look on his face.
Meaning: "to play dumb" is used when someone pretends like they don't know something, when they really do know!