Compete
Compete , intransitive verb
[Latin 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.