The Prisoners Dilemma and the Ability of Firms to Collude

The Prisoners Dilemma and the Ability of Firms to Collude

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The Prisoners Dilemma and the Ability of Firms to Collude

An oligopoly is a market consisting of a few large interdependent firms who are usually always trying to second-guess each other's behaviour. There is a high degree of interdependence between each firm in the industry meaning individual firms must take into account the effects of their actions on their rivals, and the course of action that will follow as a result on behalf of the rival firm which will also have consequences. The market as we will see is also allocatively inefficient as price is above marginal cost. There are barriers to entry and exit in an oligopoly meaning that potential new firms will have huge costs if they try to enter the industry and sometimes firms collude in order to prevent new firms from becoming any threat. For example if a new firm tries to enter the industry the cartel can quite easily reduce its prices in the short run so as to remove the new firm. An example of a heavy barrier to entry for new firms is the cost of National or even International advertising. As a result of the firms being interdependent, there are various varieties of collusion in oligopolies to try and create some stable space for the firms to operate in. There are three kinds of collusion:

· cartel (contractual)
· covert
· tacit

Cartels usually exist where there are agreements between incumbent firms with prices so that they can share what would be monopoly supernormal profits between them, acting as a monopoly. Firms will get together to decide to restrict the output and raise the price, for example OPEC (Organisation for Petroleum Exporting Countries). In the UK legally binding agreements in cartels are against the restrictive practices legislation and are therefore illegal. Some cartels last longer than others do as some cartels may break contracts. Some examples of cartels include Rowntrees, Cadbury's, the concrete industry with three firms (Rugby, Blue Circle and United).

An example of covert collusion would be the cement industry, which was found guilty of rigging contracts and was fined eight million pounds.

Tacit collusion is forming implicit contracts as if they are colluding; for example the soap powders industry. In this type of market rather than competing using prices, non-price competition occurs. Examples of non-price competition are special offers, advertising and quality of service, all of which are to establish their own brand loyalty and maintain a high concentration ratio of the market.

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Figure 1. shows an oligopolistic firm operating in such a way where it produces where marginal cost is equal to marginal revenue so as to profit maximise. The equilibrium is at price P* and quantity Q*. It produces at this quantity because of the firm were to increase its output by an extra unit, marginal cost would exceed marginal revenue and therefore the firm would make a loss. If the firm were to decrease the quantity produced then the firm would still be able to produce more until point D where the firm can no longer make any more profit. Therefore the oligopoly's supernormal profits would be ABCD which in a cartel would be shared equally.

The firms work out the market price by a process called "cost plus pricing". Firms will take the average cost of production, plus a profit mark up of a certain percentage and this will be the price. So, if demand increases quantity does not change much, so prices remain quite stable. Oligopolies will compete to increase demand by advertising and market shares.

Fig 1.

The main theories of oligopolistic competition are prisoner's dilemma
(Axel Rod) and game theory, which involve a compromise between the firms to charge one price for all their products throughout the industry, so as to share all profits. Therefore supernormal profits will exist in an oligopoly if the collusion between the firms is sustainable. This is where prisoner's dilemma comes in which is an explanation of why price wars exist in oligopolies, which seem to be mutually self-destructive and in the long run eventually the firms realise to start tacitly colluding to reduce uncertainty.

Prisoner's Dilemma Theory: Table 1.

Best solution for both firms.

Keep price Cut price Outcome in £million
P and G Keep price (2,2) (-20,18) for (P+G,Unilever)
Cut price (18,-20) (-10,-10)
Worst Solution for both firms.

Therefore looking above at Table 2, which shows the theory of prisoner's dilemma, it is clear that the two firms should collude. If Unilever keep their price constant then profits will be £2m or a possibility of £18m, so Unilever will decide to cut their prices so as to make more profit. P and G as a result of this price cut is faced with either making a loss of £20m or £10m if they cut their prices, so it cuts its prices also. In other words price-cutting is the dominant strategy. Consequently they are led to a price cut even though it is not actually in their interests to do it.

Therefore the two firms are both better off collectively keeping a tacit price deal (even though there are no supernormal profits). However there is a temptation to think that if they cut their prices unilaterally they will be able to grab the whole market for themselves and drive the other firm out of the industry.

Fig 3.

Price Stability.

It is believed that each firm in an oligopoly knows that if they cut their prices the other firms will also lower their prices. However the firm also knows that if it were to raise its prices the other firms would do nothing. In which case demand is elastic and must face what is known as a kinked demand curve. Figure 3 shows a pessimistic firm, who reckons that if they put their prices up they will disrupt the tacit collusion. If prices are put down then other firms in the industry will follow suit leading to a price war and the average revenue curve will be down (AR down). The diagram also shows the marginal revenue curves (MR up and MR down). Initially the firm is at point A at profit maximisation where marginal revenue is equal to marginal cost (where the curves intersect) producing at q* with price P*. Supposing now that marginal costs now increase, as a result the firm will now produce at point B, which absorbs the costs increase. Therefore collusion is now implicit so there are no more price fluctuations. So according to this model there will be a sustainable price due to sticky prices and tacit collusion.

In conclusion the uncertainty that exists in oligopoly industries, plus the high costs of the non-price competition policies I have explained earlier can lead to collusive behaviour by firms. These firms will come to some sort of an agreement either by fixing a stable price or by establishing quotas for each firm (restricting output) so as to profit maximise. Prisoner's dilemma explains that there are four possible outcomes, depending on many factors, which show the high degree of interdependence I talked about earlier. By this I mean that whatever one firm decides to do it will have an effect on the other rival firm, and also that there will be a reaction which will affect the first firm and leads to what are known as price wars. Price wars are linked with protecting or increasing market share as oppose to profit maximisation. They normally occur after a cartel has been broken or after a long period of stable prices. Examples of Price Wars are in the newspaper industry and with mobile phone companies, both constantly reducing their prices.

Collusion is obviously more likely to succeed when there is some method of making sure that the other firm or firms stick to the original agreement whether it is sticking to a certain price or whether it is sticking to the original quota. Therefore if there are fewer firms in the cartel, it is more likely that each firm will be able to observe each others behaviour and to share information. If the production costs of each firm are almost the same from the beginning, it should mean that the firms should share similar profits, so that the incentive to cheat is less because it is clear the other firm is not making more. oligopoly industry where there are high barriers to entry and exit. This is because if there are no new firms joining the industry, all the incumbents are not threatened by potential rivals giving a greater feel of security. Therefore the firm maintains a high concentration ratio of that industry and this feeling of security may in fact be enough to not feel they have to cheat. There are even some firms whose goals are more geared to the size of the company rather than profit maximisation. For example some managerial salaries are linked to the size of the company and it is highly unlikely for a large company to go into liquidation.

However collusion is unlikely to succeed for many reasons. Firstly there is a great incentive to secretly undercut so as to gain greater profit and market share. Also some firms may think that their quotas are not large enough. This is often the reason why cartels are broken, as a result of overproduction by one firm, at a time when the industry relies on quantity restrictions in order to maintain price stability. It is also common for cartels to be broken during a recession where tension errupts among firms in the cartel due to falling demand and profits. Another reason a cartel might not work is disagreements amongst members of the cartel, which could not be repaired. An example where this occurred is OPEC (the Organisation of Petroleum Exporting Countries) where some of its members produced more than the arranged quotas. Finally the prisoner's dilemma game suggests that all collusive agreements are bound to collapse because it is still in the best interest of each firm to break whatever agreement to receive high short run supernormal profits. There is also a theory called "travel trade" where initially a firm will form a cartel, then compete drastically until it is bankrupt. New firms will join in and the stages repeat!


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Applied Economics edited by Brian Atkinson, Frank Livesey and Bob Milward
Economics Third Edition by John Sloman
Principles Lecture notes by Jonathan Haskel + seminar notes
H.Varian Intermediate Microeconomics, Norton, 1998.
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