Compete

Com*pete" (?), v. i. [imp. & p. p. Competed; p. pr. & vb. n. Competing.] [L. completere, competitum; com- + petere to seek. See Petition.] To contend emulously; to seek or strive for the same thing, position, or reward for which another is striving; to contend in rivalry, as for a prize or in business; as, tradesmen compete with one another.

The rival statesmen, with eyes fixed on America, were all the while competing for European alliances.
Bancroft.