1
general::
Phrase(s): stare someone down
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.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
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]
American Heritage Idioms