Edgeworth Model:

To analyse the Edgeworth solution of  oligopoly let us consider two profit maximising firms A and B, selling a homogeneous product and having identical cost function with marginal cost (MC) equals to zero. We also assume that they face a linear market demand curve. In the following figure, DA represents the market demand faced by firm A and DB represents that of firm B.   

Unlike Bertrand, Edgeworth assumes that none of the duopolists can produce an output as large as the competitive market's.

Suppose firm A is the first one to enter the market. Equating MR and MC, it decides to produce OE at price OP₁.Now suppose B enters the market and sets price slightly below OP₁ and thus captures all of A's customers. But then B can cater to the market demand only up to OD, hence amount left to be sold by firm A is AC (= DB, by construction).  Firm A rather than accept the reduction in revenue decides to reduce the price slightly below that of B's. As a result, A can now capture all of B's customers.  However, once again, A can sell only up to OC. This process would go on until price falls to OP₂, and each of the duopolist produce the maximum possible output.

However, the price OP₂ is not stable because one of the firms can raise it's price and thereby it's revenue as well as profit (because MC = 0). For instance, A will try to raise price assuming B will maintain it if OP₂. A has no fears of loosing customers to B, because B is producing it's maximum possible output so that rest of the market is to be catered to by A only. Now B would also reconsider that a price rise from OP₂ would not result in a loss of sales. Therefore, it would raise price almost up to OP₁. A would respond by reducing price and the same process ensues once again as before. We see that price would fluctuate between OP₁ and OP₂ and there would be no stable price equilibrium.