There is this widely-held theory that big companies can use their size to out-compete small companies by engaging in predatory pricing. They use size and profitability in other (usually monopolized) markets to outlast a smaller, specialized competitor in a niche market by writing off the losses in this small market which the competitor cannot afford to.
Back in reality, it turns out that companies that try to maintain a monopoly in this manner (predatory pricing) have a hard time making money using this tactic. It costs them more to maintain their monopoly than they can ever recoup through higher prices. Let's say that they lower their prices by ten cents for a year, and drive somebody out of the business. In order to make back that money, they need to raise their prices by ten cents over their original monopoly price. But the party that they put out of business went into business precisely because they saw a way to suck off excess profits by competing with the monopoly. Now the market price is ten cents higher, and the profits are even more attractive to a new entrant. So somebody else goes into the business, and the monopoly can't even go back to their old price. They have to go back to the old "lose ten cents per" price, because that's what's necessary to drive the competition out of business.
Predatory pricing doesn't work according to the standard theory.
Update 5/17: Adam writes to point out another problem with the theory. When the price gets lowered by the "predator", that increases demand, so the company has to sell more. When they raise prices again, that reduces the demand and makes it harder to recoup their loss.
Update 8/7: Cathal writes to say that predatory pricing can work under certain market conditions if you also know something your competitor does not (asymmetric information).