The Collaborative International Dictionary of English v.0.48:

Competition \Com`pe*ti"tion\, n. [L. competition. See
   Compete.]
   The act of seeking, or endeavoring to gain, what another is
   endeavoring to gain at the same time; common strife for the
   same objects; strife for superiority; emulous contest;
   rivalry, as for approbation, for a prize, or as where two or
   more persons are engaged in the same business and each
   seeking patronage; -- followed by for before the object
   sought, and with before the person or thing competed with.
   [1913 Webster]

         Competition to the crown there is none, nor can be.
                                                  --Bacon.
   [1913 Webster]

         A portrait, with which one of Titian's could not come
         in competition.                          --Dryden.
   [1913 Webster]

         There is no competition but for the second place.
                                                  --Dryden.
   [1913 Webster]

         Where competition does not act at all there is complete
         monopoly.                                --A. T.
                                                  Hadley.

   Syn: Emulation; rivalry; rivalship; contest; struggle;
        contention; opposition; jealousy. See Emulation.
        [1913 Webster]

WordNet (r) 3.0 (2006):

competition
    n 1: a business relation in which two parties compete to gain
         customers; "business competition can be fiendish at times"
    2: an occasion on which a winner is selected from among two or
       more contestants [syn: contest, competition]
    3: the act of competing as for profit or a prize; "the teams
       were in fierce contention for first place" [syn:
       competition, contention, rivalry] [ant: cooperation]
    4: the contestant you hope to defeat; "he had respect for his
       rivals"; "he wanted to know what the competition was doing"
       [syn: rival, challenger, competitor, competition,
       contender]

Moby Thesaurus II by Grady Ward, 1.0:

51 Moby Thesaurus words for "competition":
   antagonism, antipathy, bad blood, championship, clashing,
   collision, competitor, concours, conflict, contention, contest,
   contrariety, contrariness, corrival, cross-purposes,
   cutthroat competition, disaccord, dissension, emulation, enmity,
   event, fractiousness, friction, game, gamesmanship, hostility,
   inimicalness, jockeying, lifemanship, match, meet, meeting,
   negativeness, noncooperation, obstinacy, one-upmanship, oppugnancy,
   perverseness, recalcitrance, refractoriness, rencontre, repugnance,
   rivalry, strife, striving, struggle, tournament, tug-of-war,
   uncooperativeness, vying, warfare