competition

n. rivalry, act of competing against another; contest

Competition is the rivalry of two or more parties over something. Competition occurs naturally between living organisms which coexist in an environment with limited resources. For example, animals compete over water supplies, food, and mates. In addition, humans compete for recognition, wealth and entertainment.
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n. competition, concurrence, contest, tournament, discord

(n.)
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.
  

Intra- or intermarket rivalry between businesses trying to obtain a larger piece of the same market share.