There are several definitions of competition, and many misconceptions about what "competition" is, so it is very important to dialog about the issue of competition and cooperation within the context of an appropriate definition. Without agreement on semantics, the discussion will degrade because of the fallacy of equivocation.
It is important that we start with definitions within the sport context. The renown sport sociologist Jay Coakley (1994) defines competition as, "a social process that occurs when rewards are given to people on the basis of how their performances compare with the performances of others doing the same task or participating in the same event" (p. 78). In turn, cooperation is defined by Coakley as, "a social process through which performance is evaluated and rewarded in terms of the collective achievements of a group of people working together to reach a particular goal" (p. 79). Sport psychologists Weinberg and Gould (2007) infer from this definition that the success of one forces the failure of another in competition. This is consistent with how educational psychologist Kohn (1986) defines competition in his arugment against competition. According to Kohn, competition has "mutually exclusive goal attainment."
And, for more general definitions we will look to Dictionary.com's many definitions of "competition" and "cooperation." Note that the ecology definition of competition is what many people focus on when arguing competition's support of Darwin's ideas of survival of the fittest. While "winning" in competition is one way to survive, I posit that "fitness" is also supported by cooperation and used quite often by organisms as a means of survival and growth, especially by humans. Furthermore, competition is not in direct opposition of cooperation in many cases.
As a final note, the term "sport" is not synonymous with "competition." Also, competition requires another person (or organism) to compete against. In other words, a man cannot compete against himself. Likewise, a person cannot compete against the elements, such as the wind or a golf course.
References
Kohn, A. (1986). No contest: The case against competition. Boston: Houghton Mifflin.
Coakley, J. (1994). Sports in society: Issues & controversies (4th ed.). Mirror/Mosbey College.
Competition. (n.d.). Dictionary.com unabridged. Retrieved November 18, 2009, from Dictionary.com website: http://dictionary.reference.com/browse/competition
Cooperation. (n.d.). Dictionary.com unabridged. Retrieved November 18, 2009, from Dictionary.com website: http://dictionary.reference.com/browse/cooperation
Weinberg, R. S., & Gould, D. (2007). Foundations of sport and exercise psychology (4th ed.). Champaign, IL: Human Kinetics.