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.]
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   2. To strive for superiority; to contend; to use emulous
      effort, as in a race, contest, or competition.
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            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.
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            While Waterloo with Cannae's carnage vies. --Byron.
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The Collaborative International Dictionary of English v.0.48:

Vie \Vie\, v. t.
   1. To stake; to wager. [Obs.] --B. Jonson.
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   2. To do or produce in emulation, competition, or rivalry; to
      put in competition; to bandy. [Obs.]
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            She hung about my neck; and kiss on kiss
            She vied so fast.                     --Shak.
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            Nor was he set over us to vie wisdom with his
            Parliament, but to be guided by them. --Milton.
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            And vying malice with my gentleness,
            Pick quarrels with their only happiness. --Herbert.
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The Collaborative International Dictionary of English v.0.48:

Vie \Vie\, n.
   A contest for superiority; competition; rivalry; strife;
   also, a challenge; a wager. [Obs.]
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         We 'll all to church together instantly,
         And then a vie for boys.                 --J. Fletcher.
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WordNet (r) 3.0 (2006):

vie
    v 1: compete for something; engage in a contest; measure oneself
         against others [syn: compete, vie, contend]

Moby Thesaurus II by Grady Ward, 1.0:

62 Moby Thesaurus words for "vie":
   admit of comparison, antagonize, battle, be commensurable,
   be comparable, beat against, beat up against, breast the wave,
   buck, buffet, buffet the waves, challenge, challenge comparison,
   close with, combat, come up to, compare, compare to, compare with,
   compete, compete with, contend, contend against, contend for,
   contest, cope, counter, emulate, equal, fight, fight against,
   fight for, grapple with, jockey, join battle with, labor against,
   match, match up with, measure up to, meet, militate against,
   not compare with, offer resistance, outvie, parallel, pit, reluct,
   reluctate, resemble, rival, stack up with, stem the tide,
   stickle for, stipulate for, strive against, strive for,
   struggle against, struggle for, take on, test one another, vie for,
   vie with