A History of Game Theory - Vol. 1

By Mary Ann Dimand; Robert W. Dimand | Go to book overview
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3

STRATEGIC INTERDEPENDENCE

Cournot’s heirs and asymmetry

Cournot’s model of duopoly, discussed in the preceding chapter, opened up a new channel of enquiry in economics: the modelling of firm behaviour in situations of strategic interdependence in which there is more than one firm, but not so many that each is powerless. More immediate criticisms of Cournot’s model and dynamic variants are discussed above. This chapter focuses on richer models in which the symmetry of the Cournot model is abandoned, from either the producer’s or the consumer’s side.

For one firm to move before others, or for a firm to have a different cost function or influence on the market, alters the game considerably. In the first section below, the model of price leadership and Stackelberg’s examination of leadership in a market are discussed, as well as the ‘kinked demand curve’ model of Paul Sweezy, and Hall and Hitch.

Where different firms’ products are perceived as differing from the consumer’s standpoint, even a small number of firms in a market are no longer symmetric because their products are no longer perfect substitutes. Hotelling’s, Chamberlin’s and Robinson’s models in which firms interact strategically by setting not only price or quantity, but product characteristics, are analysed from a game-theoretic perspective in the second section.


PRODUCER ASYMMETRY

The work discussed in this section expanded on Cournot’s duopoly model by examining the results of various forms of asymmetry in producers’ power, whether due to size or to priority.

Zeuthen and Stackelberg, whose work on asymmetric market power was pivotal, both agreed and disagreed on the existence and uniqueness of equilibrium. Zeuthen, writing at a time when a belief in the indeterminacy of equilibrium under duopoly was general, felt that equilibrium is determinate under most rules of the game and that the economist’s task is to work out which rules obtain, or are ‘probable’:

The case of ‘monopolistic competition’, i.e. the instance in which several

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