In an oligopolistic structure, only a few large companies control most of the market. Rather than competing with one another, they use their collective market power to operate as a sort of legal monopoly. They collaborate on pricing so one company doesn't undercut the other. They make it extremely difficult for a new firm to enter the market (by collectively out-competing smaller firms and setting up regulations to keep new firms out). As a result, oligopolies can make tremendous amounts of profit by dominating the market.
