compete

from The American Heritage® Dictionary of the English Language, 5th Edition.

• intransitive verb To strive against another or others to attain a goal, such as an advantage or victory. synonym: rival.

from The Century Dictionary.

• To seek or strive for the same thing as another; enter into competition or rivalry; vie: with for before the thing sought and with before the person or thing rivaled.
• In political economics, to engage in rivalry in the sale or purchase of a commodity or service; also, figuratively, of a commodity or service, to be open to choice as against some other commodity or service. Thus iron is said to compete with stone in the construction of buildings; water routes compete with railways in the handling of traffic.

from the GNU version of the Collaborative International Dictionary of English.

• intransitive verb 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• verb 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.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• verb compete for something; engage in a contest; measure oneself against others