In short, real-world examples of "cooperation" are often not as selfless as, say, volunteering to donate blood or anonymously sending cash to a charity. Instead, real-world cooperation is often enforced by a group of peers, using a combination of economic, legal and social incentives to reward those who act with the group and to impose costs on those outside the group. Those who are quick to believe that cooperation should be automatically equated with virtue should take a step back and consider both what each specific cooperative behavior is intended to achieve and how it is enforced among those within the group who might have preferred not to cooperate in a certain situation.
In contrast, competition within a market context actually happens as a series of genuinely cooperative decisions, every time a buyer and seller come together in a mutually agreed-upon and voluntarily made transaction. This idea of cooperation within the market is at the heart of what the philosopher Robert Nozick referred to in his 1974 work, Anarchy, State, and Utopia, as "capitalist acts between consenting adults."
This is from "The Blurry Line between Competition and Cooperation," Econlib Feature article for February, released moments ago. The author is a first-time author for this site: Timothy Taylor, managing editor of the American Economic Association's Journal of Economic Perspectives.
This would make a good reading for microeconomics courses in which professors want to get across the nature of competition. Read the whole thing.