Thiel's monopoly comments seem to provoke a lot of confusion; they make more sense if you replace the word "monopoly" with "a position in the market such that customers are willing to pay significantly more for what you sell than for their best available alternative." Some examples:

* Apple is able to charge a premium on iPhones relative to the best non-Apple alternatives because a lot of people are willing to pay it. (Do they have a monopoly on smartphones? Definitely not; there are loads of companies selling good phones. But they have a monopoly on their smartphones.)

* Fast food joints are forced into heated low-margin competition with each other because they're pretty interchangeable. If McDonald's starts charging too much, people will just shrug and buy basically the same food from Burger King.

* Classic monopolies are extreme cases. At one point if you wanted telephone service in the US you either paid whatever AT&T was charging or you didn't get telephone service.

When people hear Thiel's comments they tend to think of classic monopolies, but most of the examples he gives are of companies that have plenty of competitors -- and a durable advantage that they can use to maintain decent profits margins without customers jumping ship.