to pressure someone to capitulate, back down, or yield by staring. Don't try to stare me down. I have nerves of steel. I tried to stare down my opponent, but it didn't work.
Cause someone to waver or give in by or as if by being stared at. For example, Insisting on a better room, he stared down the manager until he got it. This expression alludes to staring at someone without being the first to blink or lower one's gaze. [Mid-1800s]
To intimidate someone or cause someone to submit by staring: I was able to stare down the lion, and it turned and ran away. If your enemies try to stare you down, just smile back at them.