Dic: vie (as a verb)

V-RECIP

If one person or thing is vying with another for something, the people or things are competing for it. [FORMAL]

• California is vying with other states to capture a piece of the growing communications market.
• Four rescue plans are vying to save the zoo.
• In hospitals, business plans vie with patients for doctors' attention.
• The two are vying for the support of New York voters.
• = compete

.... Cobuild

To strive for victory or superiority; contend. See Synonyms at rival.

Short for Middle English envien, from Old French envier, from Latin invtre, to invite, give occasion for; seeinvite.

... American Heritage, http://www.thefreedictionary.com/vie