An oligopoly is, by definition, "a state of limited competition, in which a market is shared by a small number of producers or sellers." An important thing to keep in mind when thinking about oligopolies is that the firms maintain their position by creating and maintaining massive barriers to entry. A prime example of a current oligopoly is the cable television/internet market. Typically a region is dominated by a small number of firms who have maintained their position via high barriers to entry (the significant capital costs associated with entering the marketplace are for all intents and purposes insurmountable).
In a market with few firms, there really only are two choices regarding competitive strategy; they can either collude or they can compete.
There are benefits and drawbacks to each decision. For collusion, the primary drawback is that collusion is illegal. More specifically, explicit collusion is illegal. Oligopolies typically operate under the auspices of implicit collusion. Implicit collusion is defined as "seemingly independent, but parallel, actions among competing firms in an industry." The delineation between implicit and explicit collusion is the lack of an explicit agreement between firms. The primary benefit to collusion is that the firms are able to control the marketplace much like a monopolist. This allows them significant leverage over both the consumer and the government and also likely leads to high profitability.
For competition, the primary drawback is that firms are not maximizing their profitability given the market structure. The firms are likely to compete on price, which will eat into their respective margins. The primary benefit of competition is that through competition, there likely will be a winner. There are a number of dimensions that firms can compete on: price, quality, service, and so on. As a result, competition in oligopolies significantly benefits both the consumer and the most innovative or well-run firm within the oligopoly.