The original prisoner’s dilemma story involves two criminals who are arrested after com-mitting a serious crime. The police have no proof of their involvement except for a minor infraction. The prosecutor offers them a deal whereby the one who implicates the other escapes all punishment and the other gets a heavy prison sentence. If both implicate the other, both end up in prison for a long time. The dominant strategy is for each criminal to implicate the other. Consequently they both end up getting relatively heavy prison sentences. When the game is repeated, however, co-operation can be sustained implicitly through dynamic strategies. In his classic book, The Evolution of Co-operation, University of Michigan political scientist Robert Axelrod studied empirically and experimentally the strategies that lead players involved in prisoner’s dilemma situations to co-operative outcomes. His starting point was an unexpected experimental result. When experts were asked to submit strategies for repeated prisoner’s dilemma games and these strategies were matched with each other in a computer tournament, tit-for-tat, the simplest strategy, won. This was a strategy under which each player started by co-operating, and then did to the other player what that player had done to him previously. Axelrod’s analysis of the data found tit-for-tat had four prop-erties making a strategy successful. A successful strategy should be nice: confronted with a co-operative player, it should reciprocate. It should also be provocable: faced with an uncalled defection, it should respond. It should be forgiving: after responding to a defec-tion, it should go back to co-operation. And it should be easy to understand: other players Case study 4.3
4.7 Summary
The fewness of the firms is the chief defining characteristic of oligopoly. The central problem of oligopoly focuses on the recognition of the firms’ interdependence when they are few in number. Interdependence implies each firm is aware its actions affect the actions of its rivals. There are as many different models of oligopoly as there are assumptions about how firms behave when faced with this situation of inter-dependence. It is often suggested that the solution to the oligopoly problem is one of two extremes: either pure independent action, or pure collusion where all scope for independent action is extinguished. In reality both independent action and collusion
4.7 Summary 157
should be able to anticipate the consequences of their actions. Axelrod presents a surprising example of the usefulness of a variant of this strategy: First World War trench warfare. Here is a summary of his account.
The historical situation in the quiet sectors along the Western Front was a (repeated) prisoner’s dilemma. At any time, the choices of two small units facing each other are to shoot to kill or deliberately to shoot to avoid causing damage. For both sides, weakening the enemy is important because it promotes survival. Therefore, in the short run it is better to do damage now, whether the enemy is shooting back or not. What made trench warfare so different from most other combat was that the same small units faced each other in immobile sectors for extended periods of time. This changed the game from a one-move prisoner’s dilemma in which defection is the dominant choice, to an iterated prisoner’s dilemma in which conditional strategies are possible. The result accorded with the theory’s predictions: with sustained interaction, the stable outcome could be mutual co-operation based upon reciprocity [emphasis added]. In particular, both sides followed strategies that would not be the first to defect, but that would be provoked if the other defected. As the lines stabilized, non-aggression between the troops emerged spontaneously in many places along the front.
The earliest instances may have been associated with meals served at the same times on both sides of no-man’s land. An eyewitness noted that: ‘In one section the hour of 8 to 9 a.m.
was regarded as consecrated to private business, and certain places indicated by a flag were regarded as out of bounds by the snipers on both sides.’ In the summer of 1915 [a soldier noted that] ‘It would be child’s play to shell the road behind the enemy’s trenches, crowded as it must be with ration wagons and water carts, into a bloodstained wilderness but on the whole there is silence. After all, if you prevent your enemy from drawing his rations, his remedy is simple: he will prevent you from drawing yours.’ The strategies were provocable.
During the periods of mutual restraint, the enemy soldiers took pains to show each other they could indeed retaliate if necessary. For example, German snipers showed their prowess to the British by aiming at spots on the walls of cottages and firing until they had cut a hole.
Source: Extracted from Robert Axelrod (1984) The Evolution of Co-operation. © The Financial Times Limited, 18 October 1999. Reprinted with permission.
are matters of degree, and the great majority of cases fall somewhere between these two extremes. However, Chapters 4 and 5 are structured in accordance with this traditional dichotomy. Chapter 4 has dealt mainly with models of independent action; in Chapter 5, the emphasis shifts towards collusion.
The Cournot duopoly model is the earliest theory of output determination in oligo-poly. Cournot assumes the firms maximize their own profit subject to the constraint that the other firm’s output is fixed at its current level; or equivalently, both firms select their outputs so as to maximize profit subject to a zero conjectural variation assumption. Zero conjectural variation is equivalent to the behavioural assumption that leads to what is known in game theory terminology as a Nash equilibrium.
Under this assumption, the Cournot duopolists achieve a market equilibrium that lies somewhere between the polar cases of monopoly and perfect competition.
Other possible solutions to the model of output determination under duopoly include Chamberlin’s model of joint profit maximization; Stackelberg’s leader–follower model; and Stackelberg disequilibrium, in which both firms simultaneously behave aggressively, leading to overproduction and a price war.
In the Bertrand and Edgeworth models of price determination under duopoly, there is a zero conjectural variation assumption with respect to price. Both firms maximize their own profit subject to the constraint that the other firm’s price is fixed at its current level. In Bertrand’s model, the firms’ output levels are unconstrained.
Edgeworth considers the implications of a production capacity constraint. These models recognize the possibility that oligopolistic markets may deliver outcomes such as intense price competition (Bertrand) or perpetual instability with no deter-minate market equilibrium (Edgeworth). In contrast, the kinked demand curve model suggests price under oligopoly may become ‘sticky’; while models of price leadership suggest that one way for oligopolists to deal with their situation of inter-dependence is to delegate responsibility for price-setting to a single dominant firm or price leader.
Game theory is an approach to decision making in which two or more decision makers or players face choices between a number of possible courses of action or actions at any stage of the game. The property of interdependence is the key defining characteristic of a game. Although game theory has many applications throughout the social and physical sciences, it is the treatment of interdependence that makes game theory relevant to an understanding of decision making in oligopoly. Game theory shows how situations can arise in which players take decisions that appear rational from an individual perspective, but lead to outcomes that appear sub-optimal when assessed according to criteria reflecting the players’ collective interest.
However, games do not always generate unique solutions, since strategic decisions and outcomes are dependent on sociological and psychological as well as economic behavioural patterns and conventions. For this reason, game theory is often better at explaining observed patterns of behaviour after the event than it is at predicting behaviour in advance.
It should be apparent from Chapter 4 that oligopoly can generate many possible outcomes. It seems that almost anything can happen in oligopoly, from outright collusion to bitter price wars. As a result some economists (for example, Rothschild, 1947) have suggested that oligopoly theory is indeterminate. The consensus, how-ever, is still largely in favour of developing better theory and better models.
158 Chapter 4 n Oligopoly: non-collusive models
Discussion questions 159 But it would be misleading to conclude that we cannot develop theories which predict oligopolistic conduct and performance with tolerable precision. A more constructive interpretation is this: to make workable predictions we need a theory much richer than the received theories of pure competition and pure monopoly, including variables irrelevant to those polar cases. In our quest for a realistic oligopoly theory we must acquire Professor Mason’s ‘ticket of admission to institutional economics’, at the same time retaining the more sharply honed tools with which economic theorists have traditionally worked.
(Scherer, 1980, p. 152) Nevertheless, it is still the case that we have no clear and unambiguous solution to the central issue of interdependence. Firms and individuals may react in many different ways, and this is reflected in the large number of models examined in this chapter. It is the presence of the rival firms in oligopoly that creates uncertainty, which in turn makes oligopoly theory so difficult and challenging.
Discussion questions
1. Explain the relevance of the concepts of interdependence, conjectural variation, independent action and collusion to our understanding of oligopoly.
2. What types of conduct are associated with Machlup’s notion of uncoordinated oligopoly?
3. Does Cournot’s original duopoly model have any relevance to our understanding of price and output determination under oligopoly?
4. Explain the role played by the assumption of zero conjectural variation in the derivation of the Cournot–Nash equilibrium.
5. Compare and contrast the Cournot, Chamberlin, Stackelberg and Edgeworth models of price and output determination for a duopoly.
6. Suggest examples from the real world that approximate to each of the classical theories of oligopoly.
7. With reference to each of the examples quoted in Case study 4.1, identify product or cost characteristics that may have contributed to the tendency for competition to be manifested in the form of a price war.
8. Quote real world examples of oligopolistic firms that have benefited from a first-mover advantage.
9. With reference to Sweezy’s model of the kinked demand curve, explain the reasons why we might expect price to be unresponsive to small variations in cost in the case of oligopoly.
What are the main limitations of the kinked demand curve model?
10. Explain the distinction between dominant and barometric price leadership. How are price leaders chosen?
160 Chapter 4 n Oligopoly: non-collusive models
11. Explain the relationship between Cournot’s solution to the problem of output determination in duopoly, and the game theory concept of the Nash equilibrium.
12. Explain what is meant by the term mixed strategy. Under what circumstances is it advisable for the players in a non-cooperative game to adopt mixed strategies?
13. In repeated games, it is often assumed that rivals are more likely to cooperate with one another than to compete. Under what conditions might competition be likely to break out in a repeated game?
14. With reference to Case study 4.2, which theoretical model of oligopoly best explains the behaviour of the leading firms in the UK’s market for digital television services?
15. With reference to Case study 4.3, outline the contribution of the model of the prisoner’s dilemma to our understanding of strategic behaviour.
Further reading
Asch, P. and Seneca, J. (1976) Is collusion profitable? Review of Economics and Statisitics, 58, 1–10.
Hall, R.L. and Hitch, C.J. (1939) Price theory and business behaviour, Oxford Economic Papers, 2, 12 – 45.
Haskel, J. and Scaramozzino, P. (1997) Do other firms matter in oligopolies? Journal of Industrial Economics, 45, 27– 45.
Kashyap, A. (1995) Sticky prices: new evidence from retail catalogues, Quarterly Journal of Economics, 110, 245 –74.
Machlup, F. (1952a) The Economics of Sellers’ Competition. Baltimore, MD: Johns Hopkins University Press.
Robinson, J. (1969) The Economics of Imperfect Competition, 2nd edn. London: Macmillan.
Roth, A.E. (1991) Game theory as a part of empirical economics, Economic Journal, 101, 107–14.
Stigler, G.J. (1978) The literature of economics: the case of the kinked oligopoly demand curve, Economic Inquiry, 16, 185 –204. Reprinted as Reading 10 in Wagner, L. (ed.) Readings in Applied Microeconomics.
Oxford: Oxford University Press (1981).
5.1 Introduction
Collusion between firms attracts much attention from the public, the press and govern-ment. One manifestation of collusion is price-fixing, which is easily recognized as having adverse consequences for consumer welfare.