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]