In a monopoly, one firm holds the power to set prices. In an oligopoly, a few firms hold the power to set prices together. When only two firms hold the power to set prices in an industry, it is called a duopoly. A duopoly is a form of oligopoly.
When a firm is so prominent in an industry that it contains the power to determine supply and demand, it is considered to have a monopoly over that industry. The prefix "mono" comes from the Greek "monos," meaning "alone" or "one." The prefix "olig" is from the Greek "oligos," which means "a few." Therefore, an oligarchy is when the same power held by one company in a monopoly is shared by a few companies.
There are several different types of oligopolies. There are those in which the few companies are actually working together to control a market, those in which the companies are working separately but simultaneously and those where one company leads the others but does not have a distinct enough advantage to gain power over them.
In both monopolies and oligopolies, firms control markets in either one of two ways. They either control the supply of a product or service, thereby increasing demand, or they control the pricing, thereby controlling what consumers pay.