beat (one) at (one's) own game
To defeat or triumph over someone by using their own strengths, techniques, or tactics to one's own advantage. He thinks that, because he's so much bigger than me, I won't want to fight with my fists, but I'm so quick that I'll be able to beat him at his own game. The senator keeps saying her policies are the will of the people, but if we can get an accurate poll of her constituency, we can beat her at her own game.
beat someone at his or her own game
Surpass someone in his or her own specialty or undertaking. For example, Jean knew that if she matched the new store's discount she would keep all her customers and beat the new competitors at their own game . The use of game for any kind of undertaking or scheme dates from the mid-1200s.