OLIGOPOLY:

An oligopoly is a market structure where few large firms control the entire relevant market. The good that the firms produce are largely similar, thought not necessarily identical.  

How does a firm in an oligopoly make P and Q decisions?

Rule1: Regardless of the market-structure that a firm is placed in, any firm will definitely do a Marginal Analysis, and produce a Q that sets MR=MC.

Rule 2: A. What is different for an oligopoly firm is the fact that because of it's sheer size, any one firm has a great chance of influencing the consumers in it's favor (or against it), because of the firm's action. By virtue of all firms being rational enough to imagine what other firms might do, it is unique that any one firm's actions yield consequences not just because of what it did, BUT also because of what others did too! This (Unwanted) INTER-DEPENDENCE, is a distinct feature of an oligopoly. 

Rule 2: B. Because every existing firm must NOW consider not just what it can do, but also what other firms can do, any one firm must have a strategy in place. Strategy is a plan of action, for all possible scenarios. (Thus in incorporating interdependence and uncertainty to some extent, we can already appreciate that OLIGOPOLY is a more realistic market type, in comparison to perfectly competitive market).

How does an oligopoly use strategy?

Assume 2 firms, of equal size (and thus equal technology etc) and somewhat similar products (example: Coke and Pepsi).

Based on whether the firms charge low price (=$1) or high price (=$2), there are four possible scenarios:

Scenario A (Both opt for Low P): Let us start with the scenario where they both, independently reached a price of $1 as a price at which each of them just about covers all opportunity costs, leaving 0 economic profit for each of them.

Let us assume that demand curve for cola drinks tells us that at a price of $1, 100 people demand a drink. Thus when both Coke and Pepsi charge $1 each they will be splitting the market----(50, 50).

Thus Total Revenue for Coke = Price*Quantity = $1*50 = $50

and Total Revenue for Pepsi = Price*Quantity = $1*50 = $50

Scenario B (Coke opts for Low P, Pepsi opts for High P):: When Coke charges $1, but Pepsi charges $2, clearly no one buys Pepsi, and thus Coke ends up with the entire market. 

Thus Q = (100, 0)

Thus Total Revenue for Coke = Price*Quantity = $1*100 = $100

and Total Revenue for Pepsi = Price*Quantity = $2*0 = $0

Scenario C (Coke opts for High P, Pepsi opts for Low P): When Coke charges $2, but Pepsi charges $1, clearly no one buys Coke, and thus Pepsi ends up with the entire market. 

Thus Q = (0, 100)

Thus Total Revenue for Coke = Price*Quantity = $2*0 = $0

and Total Revenue for Pepsi = Price*Quantity = $1*100 = $100

Scenario D (Both opt for High P):: When both Coke and Pepsi charge $2, two things will happen to the quantity of cola drinks demanded: first at a P = $2, the total Q demanded will be less than 100. Let us assume that the demand curve tells us that at a P=$2, Q demanded is 60. Second thing that happens to Q is, that with both firms charging the same (high) price, the market will be again split. 

This time Q = (30,30)

Thus Total Revenue for Coke = Price*Quantity = $2*30 = $60

and Total Revenue for Pepsi = Price*Quantity = $2*30 = $60

What will the firm do?

In Scenario B: Coke makes $100, while Pepsi makes $0. Obviously coke likes this scenario the most. But the problem is that this outcome for Coke is contingent on Pepsi choosing a High price. But if Pepsi knows that charging a high price when competitor charges low price results in 0 profit, clearly Pepsi will NOT charge a high P, and thus Pepsi will charge L also. And both firms will be back to Scenario A.

In Scenario C: Pepsi makes $100, while Coke makes $0. Obviously Pepsi likes this scenario the most. But the problem is that this outcome for Pepsi is contingent on Coke choosing a High price. But if Coke knows that charging a high price when competitor charges low price results in 0 profit, clearly Coke will NOT charge a high P, and thus Coke will charge L also. And both firms will be back to Scenario A.

In Scenario A: Both firms make $50 each, even when they know they could both have made $60 or $100. This is almost like both firms were in a perfectly competitive scenario, and competing on price. 

In Scenario D: Both firms make $60 each. However this is an unstable situation because every firm has an incentive to lower the P and completely snatch the entire market from the other firm UNLESS the firms could enter into an agreement, to charge high P only. Such an agreement called collusion for Price (or Q )fixing is called a cartel, and is illegal.

**So unless the firms can enter into an (illegal) agreement to collude, the equilibrium solution for this market will be both firms charging LOW prices.