Oligopoly theories

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Is there a satisfactory theory that describes behaviour of oligopolies discuss?

No there is no satisfactory theory that describes behavior of oligopoly. First used by English humanist Sir Thomas More (1478-1535) in Utopia (1516), and later developed by the French economist Antoine Augustin Cournot (1801-1877), oligopoly theory is characterized by a few suppliers producing a heavily differentiated good (differentiated through advertising, marketing and so on).
The problem of interdependence has thwarted economists' attempts to develop a good theory of oligopoly. When there are only a few sellers, each recognizes that his decisions affect others who may react to what he does.
This problem of interdependence can be shown in terms of game theory in a situation that is identical to the prisoners' dilemma. The table below shows the pricing options of the only two gas stations in an isolated town. The payoffs in the center are profits. If both stations charge high prices, the joint profits are maximized. But then each has a temptation to cut prices to get to a more favorable corner. If one of them gives in to this temptation, it may start a gas price war as the other firm must retaliate. They then end in the least favorable position of lowest joint profits. We could expand the table to show what would happen if they cut prices even further, to $.80, and we would see that this cut would make them both still worse off. Gas price wars do break out occasionally, but they usually do not last long. Rather quickly, the firms realize the futility of the fight, and will try to return to the original position.
There may be no equilibrium solution in a situation of this sort. Rather, there may be a period of collusion in which firms agree (though it may be an unspoken agreement) to keep prices high. Then, the collusion may disintegrate as firms begin cheating and finally a new period of collusion may begin. Whether sellers collude or compete will depend on many factors that can be difficult to measure and put into a theory, such as the number of sellers, their personalities, whether they have equal or unequal shares of the market, whether their costs are the same, the ease of cheating and of detecting cheating, and whether the sellers can compete on nonprice bases such as service and quality.
A thorough examination of the possibilities of oligopolistic strategies and how well they fit observed behavior of real-world oligopolies is a large and controversial subject that is beyond the scope of these readings. The important point concerning economic efficiency is that if oligopolists perceive their demand curves as downward-sloping (that is, if they take into account that the amount they produce will have a significant effect on the price they can charge), their marginal revenue curves will lie below their demand curves and they will restrict output relative to what an industry of price takers would. Thus, there ...