# oligopoly

Topics: Game theory, Nash equilibrium, Supply and demand Pages: 7 (1615 words) Published: September 30, 2013
﻿OLIGOPOLY

Oligopoly is a market with a few sellers. Fewness means in this market number of firms is such that one firm’s action affects the other firms in the market. Hence whenever any firm makes any decision regarding price etc, it has to take into account the behavioural response of the other. This main feature of oligopoly is called interdependence. This interdependence brings forth the need for strategic decision making. Strategic decision making involves conjectural variation. Conjectural variation implies one firm’s assumption about the response of other firms to its action. Suppose there are two firms A and B. Suppose A wants to produce more. In order to judge whether this decision of increasing production is gainful or not A has to conjecture how B will react to this decision. This is conjectural variation. The nature of the equilibrium changes with change in conjectural variation pattern.

In oligopoly firms have several decision variables. It can decide on quantity, price, quality of product, advertisement, investments, timing of entry in the market etc. Existence of so many decision variables gives rise to many models of oligopoly.

Two basic models of oligopoly are Cournot model and Bertrand model. Cournot model is based on two basic assumptions. 1. Firms compete with quantity, not the price. 2. Conjectural variation of the firms is zero i.e. firms assume when it changes quantity other firm will keep its output unchanged. In other words firm will derive its optimising strategy on the assumption of a given behaviour of the other firm. Bertrand model also assumes zero conjectural variation but it considers price competition, not quantity.

Cournot model
Earliest model of oligopoly is the Cournot model. To analyse this model we make the folowing assumptions. 1. There are two firms in the market.
2. Firms determine their output level and prices are determined in the market. 3. Conjectural variation of the firms is zero i.e. firms optimize, assuming constant output of the other. 4. Marginal cost of production is constant.

5. Demand in the market is represented by a linear demand curve of the form p = a – bq 6. Firms are profit maximizer.
Given these assumptions we can find out the best response functions of each firm, which traces the profit maximizing output levels of the firm corresponding to each output level of the other. In diagram this optimum output level can be plotted as the reaction curve of each seller. At the output levels where the two reaction curves intersect, we get the equilibrium. At this point two best response functions converge and therefore this equilibrium is Nash equilibrium- known as Cournot Nash equilibrium. The firms determine the output together and so it is a simultaneous move game.

Suppose the inverse market demand function is p = a – bq and cost functions are Ci = cqi. Marginal cost c is same for both firms. Then the  function of firm 1 and 2 are

Note that total output is

Firms calculate the following profit maximization conditions.

From the first equation we get the firm 1’s reaction function and from the second we get firm 2’s reaction function.

If we plot these two equations in q1 and q2 plane we get two reaction lines as follows.

q2

(a-c)/b

R1

(a-c)/2b

E
(a-c)/3b
R2

O (a-c)/3b (a-c)/2b (a-c)/b q1

R1 shows the best output level of firm 1 for any output of 2. So if firm 2 produces (a-c)/3b, firm 1 maximizes profit by producing (a-c)/3b. Similarly if firm 1 produces (a-c)/3b, firm 2maximizes profit by producing (a-c)/3b. Hence once (a-c)/3b output...