In his treatise “Human Action”, Mises devotes a short chapter (5 pages) to explaining what competition is, and what competition is not. He combats the misunderstanding of markets that is at the root of Antitrust legislation and interventions to break up “monopolies.” The fact that monopolies exist is not a problem as long as new competitors have the opportunity to pitch their ideas to the consumers without legal barriers. The consumer decides how successful an entrepreneur will be based on how well the entrepreneur serves the customers. As Mises puts it, a poet may have a monopoly on his own rhymes, but that doesn’t mean he can command the market for them.
You can read Mises’ excellent chapter on competition here on Liberty Fund’s Online Library of Liberty.