An oligopoly market is one that is dominated by a few large firms. Firms in an oligopoly selling similar but branded products, and thus advertising plays an important role in the market. Also, there are high barriers to entry, and thus the small number of firms in the market.
Interdependence of Oligopoly
Since there are only a few firms in the market, the decisions of one firm can significantly affect all the other firms. Thus, the firms are interdependent on each other, and in many cases they might want to collude.
Kinked Demand Theory (Non-collusive behavior)
If the firms do not collude, then for each individual firm, we will see a kinked demand curve. That is, at the current market price, the demand becomes elastic as price increases, and inelastic as price decreases.
Why? If a firm raises its price, then consumers are simply going to switch to the other firms. Thus, quantity will decrease drastically and the demand will be elastic. On the other hand, if a firm lowers its price, then all the other firms are going to follow suit. This, in the end, will mean that the firm doesn't get that much more quantity, and that the demand becomes sinelastic.
Of course, this is assuming that the firms are non-collusive, and that they do not cooperate with each other.
Cartels (collusion)
A lot of times, when firms pursue their own economic interest, they end off hurting each other. For example, a few firms might be constantly lowering their prices in order to gain more customers. However, in the end each firm is worse off: they haven't gained that many more customers (all other firms have done the same thing as it did), and prices are now a lot lower.
In situations like this, firms might decide to collude; they may decide to form an agreement to cooperate with each other. And one way to do this would be to form a cartel— to formally set an agreement to produce at a certain quantity and sell at a certain price. This in turn binds the firms into one, allowing them to become a monopoly and earn more profit.
However, a cartel is very difficult to maintain, for each firm has an incentive to cheat the system. For example, suppose the firms decide to limit the quantity of a product and sell it at a high price. Then by selling the product at a slightly lower price, a firm will gain a significantly larger profit. Thus, each firm wants to cheat.
