When managers of an oligopolist are trying to predict the decisions, reactions, and reactions to reactions of their competitors, they must assume that they are as intelligent and rational as themselves. In other market forms, firms largely ignore their competitors as price and market demand are given by a market determined equilibrium. For example, in a perfectly competitive market, the equilibrium price and quantity are determined by the intersection of the demand and supply curve for a good/service. In a monopoly the profit maximising equilibrium is where marginal cost equals marginal revenue. Where as in an oligopoly there is much more uncertainty as firms set their price and output at a level dependent on strategic considerations regarding the behaviour of its competitors.
The uncertainty in an oligopoly market can be modelled by conjectural variation. Also known as cross elasticity of demand between firms, conjectural variation is the measure of interdependence of firms. It captures the extent to which a firm reacts to a change in a strategic variable (such as: quantity, price or advertising) made by a competitor firm. It is essentially a form of game theory: “a mathematical attempt to capture behaviour in strategic situations, or games, in which an individual’s success in making choices depends on the choices of others.” ( (1991), Game theory: analysis of conflict, )
To demonstrate conjectural variation I will restrict our attention to a duopoly – a specific type of oligopoly where only two firms exist in one market. If a market is considered in which firms face the same market price, the inverse demand function can be shown as:
p = p(q) = p(qA + qB)
Consider total differential:
dp = dp * dqA + dp * dqB
dqA dqB
Divide through by dqA
dp = dp + dp * dqB
dqA dqA dqB dqA
This equation represents the overall effect of A’s output change on market price, as a sum of the direct (dp/dqA) and indirect effect (dp/dqB * dqB/dqA). The indirect effect being the change in B's output in reaction to A's change in output.
dqB/ dqA reflects the strategic uncertainty. It is known as A’s conjectural variation. A must therefore guess the variation in B’s output.
When A sets its output, it must therefore guess (conjecture) the change (variation) in B’s output. A similar expression for B exists, whereby dqA/ dqB is known as B’s conjectural variation.
Conjectural variation is used in many oligopoly models such as the Cournot model. The Cournot model, named after (1801-1877), was the first successful attempt to describe oligopoly equilibrium and is still used today. It was developed in the context of a natural spring where marginal costs equal zero (MC=0). It is based on a duolopoly, and has the following assumptions:
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Firms set output levels (qA, qB) and move simultaneously.
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Firms ignore their interdependence and believe dqB/ dqA = 0 and dqA/ dqB = 0, this is known as zero conjectural variations.
Zero conjectural variation is only true in the equilibrium.
“Consider a simple duopoly game, first analysed by Cournot (1838). We suppose that there are two firms who produce an identical good at zero cost. Each firm must decide how much output to produce without knowing the production decision of the other duolopolist. If the firms produce a total of x units of the good, the market price will be p(x); that is, p(x) is the inverse demand curve facing these two producers.” (Varian, H. (1992) Microeconomic Analysis. 3rd edition. New York: W. W. Norton & Company.)
In this model a reaction function is constructed for each firm, these show how much a firm will produce as a function of how much it thinks the other firm will produce. A’s reaction function tells us A’s profit-maximising output level given any output produced by B, whereas B’s reaction function tells us B’s profit-maximising output level given any output produced by A.
Equilibrium occurs at points qB* and qA*, which are consistent with both reaction functions. It is solved algebraically by solving both reaction functions simultaneously. A’s best response to qB* is qA*and B’s best response to qA* is qB*. This is known as the Cournot equilibrium. This equilibrium is an example of another equilibrium concept known as the Nash equilibrium, used in game theory. “Nash Equilibrium: Each firm is doing the best it can given what its competitors are doing.” (Pindyck, R and Rubinfeld, D. (2005) Microeconomics. 6th edition. New Jersey: Pearson Prentice Hall.)
If either firm is not on its best response curve, it changes its output to increase profit. Under the assumption of zero conjectural variation, as time passes, duopolists tend towards a market equilibrium level. This is due to each firm basing their supply decision upon the last known output by their competitor. As an example consider a new entrant into a market. Initially, the new entrant will maintain a low level of output in response to the original high level of output by the original firm. However as time passes, the increased supply due to the new entrant brings down prices and the initial monopoly producing firm is forced to decrease production. As a consequence the entrant will increase production. This continues until the two firms are in Cournot equilibrium.
As mentioned before, firms in oligopoly markets may co-operate and form cartels in order to maximise profits. This is known as collusion. The incentive to collude comes from the fact that oligopolies together produce more than the monopoly output. Due to the small number of firms in an oligopoly cartels are feasible. However secret collusion is tacit and illegal in many countries. If firms are found out they are fined. For example in August 2003 the OFT ruled that businesses had entered an anti competitive agreement to fix the price of top selling football shirts. Ten businesses were fined in total £18.6 million. This included Manchester United, The Football Association and JJB sports.
The incentive to collude can be shown in the Cournot model:
“The Cournot model analyses one possible way in which firms might interact in oligopolistic markets. However, as we have seen, while each firm maximises its own profit at the Cournot equilibrium (given its assumptions about the output choice of its rival) industry profit is not maximised. Output is greater, and price lower, than it would be if the industry were monopolised.” (Estrin, S., Laidler, D. and Dietrich, M. (2008) Macroeconomics. 5th edition. Harlow: Prentice Hall)
Therefore it can been seen that each firm could increase its profits by producing a lower output (moving in a south-westerly direction) as long as its rival co-operated and did the same. However if Cournot behaviour is assumed the firms will not react in this way. Firms must collude, and therefore set out an agreement, in order to maximise profits in this way. The agreement that firms come to must ensure that they cannot make each other worse off.
It is possible to construct a contract curve using the isoprofit curves and the reaction functions shown in the previous graph. Both firms want to increase profits by moving in a south-westerly direction on the graph. The contract curve is drawn as a locus of all the tangencies of the two isoprofit curves.
“The potential advantages of collusion will be exhausted and such movements cease, when they are unable to find another combination of outputs which would allow for an improvement in the profits of another. This is satisfied when the isoprofit curves are tangential.” (Estrin, S., Laidler, D. and Dietrich, M. (2008) Microeconomics. 5th edition. Harlow: Prentice Hall)
The collusive equilibrium will can lie at any of the available point on the contract curve dependant on the bargain determined between the two firms.
Although firms have a definite incentive to collude as they would earn more through a cartel, it is difficult to suggest that collusion is inevitable, given the strong financial motivation to cheat on an agreement. Oligopolist firms therefore often find themselves in a prisoner’s dilemma. “Prisoners dilemma: Game theory example in which two prisoners must decide separately whether to confess to a crime; if a prisoner confesses, he will receive a lighter sentence and his accomplice will receive a heavier one, but if neither confesses, sentences will be lighter than if both confess.” (Pindyck, R and Rubinfeld, D. (2005) Microeconomics. 6th edition. New Jersey: Pearson Prentice Hall.)
Oligopolists find themselves a similar situation to the prisoners in prisoner’s dilemma. They must decide whether to compete aggressively or passively with their competitors. Competing aggressively means they attempt to capture the larger share of the market compared to their competitor. However if both firms compete passively, limiting output and setting higher prices, higher profits will be made. Like in the prisoners, each firm has the ability to undercut its competitor, and each firm will know that its competitor has the same incentive. Hence although the outcome of co-operation may be desirable, the firms cannot trust each other as there is always the possibility of one of the firms lowering their prices to seize the majority of the market share.
As mentioned earlier it is illegal in most countries to agree to collude. Organisations such as the Competition Commission have been introduced to prevent collusive behaviour by investigating , markets and other enquiries related to regulated industries under in the . It is seen that by colluding, the consumer will lose out. Price is much higher, and production is less than in the Stackelberg and Cournot model. It is seen to be better to minimise the aggregate producer and consumer surplus, rather than to give the producer an advantage. On the other hand, the large quantity of legislation that restricts collusion would surely not exist if it was not for the strong likelihood of it happening.
Bibliography
(Estrin, S., Laidler, D. and Dietrich, M. (2008) Macroeconomics. 5th edition. Harlow: Prentice Hall)
(Friedman, F. (1977) Oligopolies and the Theory of Games. Netherlands: North-Holland Publishing Company)
( (1991), Game theory: analysis of conflict, )
(Pindyck, R and Rubinfeld, D. (2005) Microeconomics. 6th edition. New Jersey: Pearson Prentice Hall.)
(Varian, H. (1992) Microeconomic Analysis. 3rd edition. New York: W. W. Norton & Company.)
