A contest.
"The two runners went head to head in a fierce vie for first place."
To fight for superiority; to contend; to compete eagerly so as to gain something.
"The two rival bakeries vie for the title of best shop in town by offering increasingly elaborate free samples."
In plain English: To vie means to compete with someone else for something you both want.
"The two companies vie for market share in the new technology sector."
Usage: Vie is often confused with the similar-sounding word "view," but they have completely different meanings and spellings. Use vie when describing a competition or struggle, not when referring to looking at something.
The word vie is a shortened version of envy, derived from dropping its initial sound. It originally carried the same meaning as its longer relative before evolving to specifically mean competing for something.