Examples of American firms that are currently part of an oligopoly market include media companies like Walt Disney and Comcast, tech companies like Apple and Microsoft, and airlines like Delta and United.
Now let's think about why these firms are classified as part of oligopolies. An oligopoly market happens when competing companies actually come together to coordinate their efforts, raise prices, restrict other competitors, and increase their profits. Note, however, that companies don't always coordinate or collude directly. Most of the time, they do not, because the government frowns on that sort of thing. Still, though, where there is only a small number of competitors in an industry, informal agreements can quickly pop up to protect the group of companies and increase the group's control of the market.
Let's look at the oligopoly of airline companies as an example. Delta, United, American, and Southwest together corner almost sixty-five percent of domestic airline travel market. These airlines tend to hover their prices right around the same rates. Their flight offerings, features, and fees are similar, as they share the market and tend not to undercut each other. They probably don't directly coordinate, but when one sets a rate, fee, or requirement, the others follow suit to keep things even.