Answer:

outstare

Answer	Crossword Clue
OUTSTARE	Blink later than, in a contest
OUTSTARE	Win a "no blinking" contest
OUTSTARE	Win an ogling match.

OUTSTARE	Put out of countenance, by gazing.
OUTSTARE	Look down.
OUTSTARE	Win an eye battle
OUTSTARE	Defeat in a don't-blink contest
OUTSTARE	Be victorious in a certain contest
OUTSTARE	Beat in an endurance contest