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In an oligopolistic market, a certain good or service is provided by a small number of sellers (for example, if in your town there are only two or three available providers of internet, you've got an oligopoly there; or if there are 10, but 3 of them control over 90% of the market share, that's still an oligopoly).
Since there are only a small number of participants, they are likely to be very aware of each other (compare the situation of having one competitor to having 100 of them). If the market is unregulated, they are likely to negociate among each other and employ restrictive trade practices, for example form a cartel and agree to maintain prices as a certain level; or divide the market among each other (much more doable with a small number of competitors than with a large number). If they do this, the situation becomes very similar to having a monopoly- they can maximize their profit by producing fewer goods and selling them at higher prices than would be the case for perfect competition. (A good example you can look at is how the OPEC controls the international price of oil). Since this is suboptimal for consummers, many states have anti-cartel laws.
According to J. Perloff (Microeconomics Theory & Applications with Calculus. page 445. Pearson 2008), oligopolies are price settersrather than price takers; unlike in a perfect competition situation. However, unlike in a monopoly situation, the prices you can set depend on what your competitor does (if they drop prices and you don't, they are going to accaparate your consumers). In an oligopoly, each firm is so large that its actions affect market conditions: market prices are characterised by interdependence.
Game theory can be used to understand how oligopolies function: economist Joseph Louis Francois Bertrand (1822-1900) offers such a model: say I have a firm, and you have a firm, we're producing the same homogenous product and we're the only providers on the market. I choose to sell at price PA and you sell at price PB. Assuming products are perfect substitutes, sales will be split evenly and equilibrum is reached when PA=PB=MC (the marginal cost of producing an unit of the good).
(How it works: say it costs me 2$ to produce 1 Product; and I sell it for 3$; you sell it for 2.50$, so everyone buys from you and I run a loss; so I lower my price, then you lower your price to keep up with me and so on, until we both end-up selling at 2$, make no profit but run no loss. If I'd start selling at less than the MC I'd run losses rather than stagnating).
The model depends on the assumption that consumers want to buy from the lowest priced firm, which, in turn, depends on the assumption that the only possible difference between the products is their price; which doesn't really happen in real life. Branding, marketing, visibility, product differentiation, search and transport costs may make the difference. Therefore, in oligopolistic markets, you are likely to see a lot of non-price competition: through advertising, loyalty schemes, product differentiation etc.
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