play somebody's game

play (someone's) game

To engage or participate in something according to the design, intentions, or conditions imposed by someone. I know the application process seems nonsensical and unintuitive, but you just have to play their game and do the paperwork the way they ask. I'll play your game for now, but if I find out you're not holding up your side of the bargain, I'm going to the police!
See also: game, play
Farlex Dictionary of Idioms.

play somebody’s ˈgame

,

play the same ˈgame (as somebody)

(also play somebody at their own ˈgame) use the same methods as a competitor, an opponent, an enemy, etc: Safeway started cutting their food prices, so Asda decided to play them at their own game by cutting prices even more.
See also: game, play
Farlex Partner Idioms Dictionary
See also:
  • play (someone's) game
  • play someone's game
  • make plain
  • keep (one) dangling
  • keep someone dangling
  • mean well
  • call (one's) shots
  • give pap with a hatchet
  • be sailing under false colors
  • be sailing under false colours