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Learning objectives

This chapter covers the following topics:

n interdependence and the analysis of price and output determination in oligopoly

n the Cournot, Chamberlin and Stackelberg models of output determination in duopoly

n the Bertrand and Edgeworth models of price determination in duopoly

n the models of the kinked demand curve and price leadership

n game theory and the analysis of decision making in oligopoly

Key terms

4.1 Introduction

Oligopoly theory rests on recognition of the importance of the number of firms in the industry, and the nature of the product. These two characteristics are closely related. An industry is defined by the nature of the product it supplies. Firms pro-ducing highly differentiated products may not even see themselves as being in direct competition with others. The more homogeneous the products of different firms, however, the greater the awareness of competitors. In all oligopolistic markets, a few sellers account for a substantial proportion of total sales. The fewness of the firms is the chief identifying characteristic of an oligopoly.

As a result of the fewness of firms within a clearly defined industry, producing a fairly homogeneous product or service, the central problem of oligopoly focuses on the recognition of the firms’ mutual dependence or interdependence. Interdependence means a firm is aware that its own actions affect the actions of its rivals, and vice versa. Profit maximization and survival in an oligopoly depends on how effectively each firm operates in this situation of interdependence.

For Sartre, hell is dependence on others . . . In every room of Sartre’s hell, each person wants something he cannot get except from certain others, who refuse. People sometimes avoid frustration; sometimes, in real life, the others consent. But people are always dependent on others and so they are always vulnerable.

(Schick, 1997, pp. 82–3) This chapter begins in Section 4.2 with a general discussion of the key issues of interdependence, conjectural variation, independent action and collusion in oligopoly. Subsequently, the structure of the chapter reflects the development of theories of independent action in oligopoly, as they have tackled the central issue of interdependence. In Section 4.3, we examine Cournot’s original model of output determination in a duopoly, based on a simple assumption that two firms take their output decisions sequentially, each in the expectation that its rival will not sub-sequently react. Other models that recognize the importance of interdependence include Chamberlin’s model of joint profit maximization, in which ‘mutual depend-ence was recognized’. Although this recognition involved some broad theorizing, the process was invaluable in the sense that it asked the right questions concerning short- and long-run reactions, time-lags, imperfect knowledge, irrational conduct, and so on. Stackelberg’s leader–follower model builds in an assumption that one firm learns to anticipate its rivals’ reactions to its own decisions, and exploits this foresight to increase its own profit at its rivals’ expense.

The Cournot, Chamberlin and Stackelberg models focus mainly on the firms’ out-put decisions in duopoly or oligopoly. In Section 4.4, we examine the complementary models developed by Bertrand and Edgeworth, which focus on price-setting. The Bertrand model provides a theoretical justification for the idea that intense price competition might occur in markets with few firms producing a similar or identical product. The Edgeworth model focuses on the possibility that oligopolistic markets 116 Chapter 4 n Oligopoly: non-collusive models

might be permanently unstable, with no long-run equilibrium price or output level ever being achieved.

Another attempt to introduce a greater degree of reality into oligopoly theory is Sweezy’s kinked demand curve model, examined in Section 4.5. Although challenged on empirical grounds, this model rests on the core assumption that firms’ behaviour is determined by expectations as to what actions rivals are most likely to take. In this respect, it represents a major contribution to the development of more realistic models of oligopoly. This section also considers models of price leadership in oligo-poly, in which one firm takes decisions on price and the others simply follow the lead of the price-setting firm.

Finally, Section 4.6 focuses on game theory. Game theory is the study of decision making in situations of conflict. It has many applications throughout the social, behavioural and physical sciences; and accordingly, its remit is much wider than just economics. Nevertheless, its focus on uncertainty, interdependence, conflict and strategy makes it ideally suited to the analysis of decision making in oligopoly.

Game theory shows how situations can arise in which firms take decisions that may appear rational from each firm’s individual perspective, but which lead to outcomes that are sub-optimal when assessed according to criteria reflecting the collective interest of all the firms combined. Theoretically, in many respects game theory is the strongest of all the approaches examined in Chapter 4 as regards its treatment of the key issue of interdependence.

4.2 Interdependence, conjectural variation, independent action and collusion

At the beginning of the twentieth century, classical microeconomic analysis focused on the models of perfect competition and pure monopoly in its attempt to describe the behaviour of firms. While no one pretended what was being presented was an exact copy of real business behaviour, it was felt the two extremes sufficiently defined a spectrum on which reality could be conveniently located. It almost seemed what was being argued was that defining the colours white and black would somehow enable other colours, such as yellow and purple, to be described simply by mixing white and black together in the correct proportions. It soon became apparent, however, that these two models were unable to explain many aspects of business conduct in the real world, such as product differentiation, advertising, price wars, parallel pricing, and tacit and explicit collusion. An additional theory was required to deal with the vast area of industry structure that lies between the two polar cases of perfect competition and monopoly. This middle ground, known as imperfect competition, can be subdivided into two: monopolistic competition, occupying the analytical space closest to perfect competition; and oligopoly, taking up the remain-ing large portion of the spectrum.

The term ‘oligopoly’ is derived from the Greek oligoi meaning a few and poleo to sell. Chamberlin (1957) describes how this term first came into use. He claims to have been the modern-day originator in 1929, when he named one of his articles

‘Duopoly and oligopoly’. Unfortunately F.W. Taussig, the editor of the Quarterly 4.2 Interdependence, conjectural variation, independent action and collusion 117

Journal of Economics, thought the word was monstrous and crossed it out. The amended title was ‘Duopoly and value where sellers are few’. When Chamberlin published his book Monopolistic Competition in 1933, he included the original term.

However, Chamberlin notes the same term also appears in Thomas More’s Utopia, first printed in 1516.

Interdependence provides the main challenge for the analysis of oligopoly. Oligo-polists are outward turning, and there is an element of circularity in the analysis of their behaviour. Each firm’s optimal behaviour depends on its assumptions about its rivals’ likely reactions, and even on its assumptions about its rivals’ assumptions.

‘I’ (an oligopolist) cannot define my best policies unless I know what ‘You’

(my rival) are going to do; by the same token, however, you cannot define your best move unless you know what I will do.

(Asch, 1969, p. 54) Faced with this situation of interdependence, the firms must make some guesses or conjectures as to the likely actions of rivals. Each firm must determine its price or output, while making assumptions about its rivals’ likely reactions to its own actions. The term conjectural variation refers to the assumptions a firm makes about the reactions it expects from its rivals in response to its own actions.

It is often suggested that the solution to the oligopoly problem is one of two extremes: either pure independent action, or pure collusion, in which all scope for independent action is extinguished. The possibility of collusion arises when two or more rival firms recognize their interdependence, creating the potential for bargain-ing to take place between the firms, with a view to formulatbargain-ing some plan of joint action. Bargaining could take the form of explicit negotiations, or it could be clouded in tacit behaviour where the firms reveal their own positions and react to their rivals’

positions through various recognized moves and counter-moves. If bargaining does take place in some form, an agreement on the coordination of activity is a likely outcome. Again, any agreement reached could be either explicit, or tacit.

However, in some ways this dichotomy between pure independent action and pure collusion is at odds with reality. Both independent action and collusion are a matter of degree, and while examples may be found that conform to the polar cases, the great majority of cases fall somewhere between these two extremes. The typical oligopoly contains elements of both independence and collusion. For the purpose of identifying various stages along the spectrum of oligopolistic behaviour, it is useful to define the limits as clearly as possible.

Pure independent action implies a firm reaches a unilateral decision on a course of action, without any prior contact with its rivals. However, even this definition could produce outcomes similar to those achieved through collusion, if the firm were subsequently to revise its decisions in the light of its rivals’ reactions. Therefore the definition is somewhat incomplete. We must add that we expect the firm to assume its rivals will not react. This implies pure independent action can only exist either in a state of unnatural ignorance, or in an atomistic market where the actions of one firm are too insignificant to have any effect on its rivals.

Pure collusion exists where an agreement or an undertaking is reached regarding the levels of output or price. Bain (1959, p. 272) defined collusion in its purest form 118 Chapter 4 n Oligopoly: non-collusive models

as consisting of the following features: all sellers in the industry are covered by the agreement; the agreement is specific and enforceable; the agreement clearly states the price to be charged and outputs to be allocated to each member; there is a formula governing the distribution of benefits to the members of the agreement; and all members rigidly adhere to the terms of the agreement. In fact, Bain’s suggestion is really a prescription for a successful cartel. Under pure collusion the firms agree to operate collectively as if they were a single monopolist. All independent action, including the striving for individual benefit, is constrained.

We now describe several types of behaviour that fall between these two extremes of pure independent action and pure collusion. Such behaviour has attracted a diverse array of labels, and no universally agreed terminology exists. For example, the terms ‘imperfect collusion’, ‘unorganized oligopoly’ and ‘interdependent con-duct with no agreement’ have all been used by economists to describe similar forms of behaviour.

Machlup (1952a, pp. 504 –11) describes four types of conduct under the general heading of ‘uncoordinated oligopoly’.

n The first model is ‘fighting oligopoly’. Some reasons why firms might slide into economic warfare include the existence of surplus stocks or limited storage facilities, which lead to near-ruinous price wars. Arguably, this type of behavi-our was seen in the global petroleum industry in the mid-1980s. On the whole, economists tend to restrict themselves to analyses of rational behaviour, termed vigorous price competition, and ignore other, more extreme forms of conduct.

Firms that wish to hurt others, firms that harbour resentments or firms that simply enjoy a fight are difficult to accommodate within the standard methodology.

n The second model is ‘hyper-competitive oligopoly’. Typically, a significant num-ber of firms sell a fairly homogeneous product in an imperfect market. Market imperfection is due to lack of precise knowledge as to future prices, sales, changes in quality, and so on. Decisions are often taken on the basis of speculation or rumour. Although conscious of rivals, the typical firm is not inhibited by their presence as it strives for increased market share, believing rival firms to be as aggressive as itself. Individuality and non-conformity tend to preclude cooperation.

Buyers are price-conscious, and are quick to play off one seller against another.

Although this model approaches perfect competition, interdependence sharpens the potential gains and losses. This form of competition might be regarded as

‘demoralized, unhealthy and chaotic’ (Machlup 1952a, p. 508).

n The third model is ‘chain oligopoly’. In a relatively competitive industry, some firms find themselves effectively competing among smaller subsets of firms, perhaps distinguished by small qualitative differences in product character-istics. Linkages between these subsets create interdependence. For example, L competes directly with K and M; M competes directly with L and N; and so on.

Each firm operates within an oligopolistic sub-group, but the sub-groups overlap.

Any increase in the total number of firms tends to reduce interdependence.

Should any sub-group attempt to exploit its position through collusion, it would soon be swamped by entrants, because the boundaries between sub-groups are fluid. Behaviour therefore tends to be relatively competitive.

4.2 Interdependence, conjectural variation, independent action and collusion 119

n The fourth model is ‘guessing-game oligopoly’. A small group of firms might normally be expected to collude, were it not for the presence of a few stubborn characters who refuse to play ball. Therefore the firms have to operate independ-ently, and try to guess the likely reactions of their rivals to their own decisions.

In practice, however, these guesses are not too difficult, as certain behavioural conventions evolve and firms develop the tendency to play safe, by adhering to these conventions. This reduces the degree of uncertainty and the level of guesswork that is required.

The dichotomy between pure independent action and pure collusion identified above encounters one obvious contradiction: that once sellers recognize their inter-dependence, no truly independent action can occur. Each seller takes into account the likely reactions of its rivals. Therefore the amplitude of price and output changes is dampened by consideration of potential rivalrous reaction. Coordinated or parallel behaviour is more likely the greater the degree of interdependence, and the greater the degree of uncertainty. Indeed, movement towards some form of collusion is often motivated fundamentally by a desire to reduce uncertainty. Accordingly, some economists (Machlup 1952a, p. 439) see all oligopolies as collusive to some extent.

Unfortunately for policy makers or regulators, this may imply there is no non-collusive standard of comparison against which to assess the implications of collusion for competition or consumer welfare (Asch and Seneca, 1976).

In contrast, Bain (1959, p. 208) argues that in a number of scenarios, interdepen-dent sellers can still operate indepeninterdepen-dently. With ‘implicit bargaining’, for example, every announced change in price or output represents an implicit invitation to one’s rivals to react in an acceptable manner. If acceptable behaviour results, there is a weak form of tacit collusion. However, this is not tacit collusion in the generally understood sense, since there is no regular action or uniformity of behaviour. Bain also discusses the case where interdependent firms exchange information on matters such as price, sales, or future plans, but then fix their output levels and prices inde-pendently. However, no obvious distinction is made between what does and what does not constitute independent action. Can a firm truly be said to act independently if it has to rely on information from its rivals before it can make its own decisions?

Nevertheless, despite this ambiguity, the structure of Chapters 4 and 5 of this book adheres to the conventional dichotomy between independent action and collusion under oligopoly. The remaining sections of Chapter 4 discuss theories of oligopoly that focus primarily on independent decision making. Then Chapter 5 examines theories of collusion.

4.3 Models of output determination in duopoly