Source : Webster's Revised Unabridged Dictionary (1913)

Outstare \Out*stare"\, v. t.
   To excel or overcome in staring; to face down.

         I would outstare the sternest eyes that look. --Shak.

Source : WordNet®

outstare
     v : overcome or cause to waver or submit by (or as if by)
         staring; "He simply stared down his opponent" [syn: {stare
         down}, {outface}]