To fight, contend, or compete with one (for something). Tom and I have vied with one another for top of the class since our freshman year.The embattled kingdom has been vying with three other nations for control over the region.It seems there's a new superstar in the racing world whom you'll have to vie with soon.
vie with
v.
To contend with someone to attain a goal, such as a victory in a contest: The champion sprinter will vie with the new young athlete in the final round of competition.