The Collaborative International Dictionary of English v.0.48:

Vie \Vie\ (v[imac]), v. i. [imp. & p. p. Vied (v[imac]d); p.
   pr. & vb. n. Vying (v[imac]"[i^]ng).] [OE. vien, shortened
   fr. envien, OF. envier to invite, to challenge, a word used
   in gambling, L. invitare to invite; of uncertain origin. Cf.
   Invite, Envie.]
   1. To stake a sum upon a hand of cards, as in the old game of
      gleek. See Revie. [Obs.]
      [1913 Webster]

   2. To strive for superiority; to contend; to use emulous
      effort, as in a race, contest, or competition.
      [1913 Webster]

            In a trading nation, the younger sons may be placed
            in such a way of life as . . . to vie with the best
            of their family.                      --Addison.
      [1913 Webster]

            While Waterloo with Cannae's carnage vies. --Byron.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Vying \Vy"ing\,
   a. & n. from Vie. -- Vy"ing*ly, adv.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

41 Moby Thesaurus words for "vying":
   antagonism, antipathy, bad blood, clashing, collision, competing,
   competition, competitive, conflict, contrariety, contrariness,
   cross-purposes, cutthroat, cutthroat competition, disaccord,
   dissension, emulation, emulous, enmity, fractiousness, friction,
   gamesmanship, hostility, in competition, in rivalry, inimicalness,
   jockeying, lifemanship, negativeness, noncooperation, obstinacy,
   one-upmanship, oppugnancy, perverseness, recalcitrance,
   refractoriness, repugnance, rival, rivaling, rivalry,
   uncooperativeness