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Two Stage (Perfect) Equilibrium in Hotelling's Model

1985; Wiley; Volume: 33; Issue: 3 Linguagem: Inglês

10.2307/2098539

1467-6451

Damien Neven,

Business Strategy and Innovation

HOTELLING [I 929] suggests that his spatial competition model can be used to describe a wide range of differentiation problems. He points to the selection of product variety within an industry as a potential application. Most of the subsequent work in his tradition has taken the equivalence of the two problems for granted. In this note, we look more closely at this equivalence. We distinguish between two types of differentiated products according to the variety of preferences assumed with respect to those products. Building on this distinction, we recognize that the demand faced by a firm locating on Hotelling's line is analogous to the demand faced by a firm selecting a horizontally differentiated product. It should be emphasized, thus, that the equivalence between the geographical and the product selection problem is by no means general and relies on specific assumptions about consumers' preferences. Next, we formulate a small model, close to Hotelling's one in which firms select a horizontally differentiated product. Within this model, it will be shown that a pure strategy price equilibrium exists for every pair of products. This statement is to be contrasted with the results of d'Aspremont et al. [I979], who have shown that in the original Hotelling's setting an equilibrium fails to exist when firms are too close together. 1 In addition, we will examine the product selection problem faced by firms in a two-stage game: in the first stage, each firm selects a product; in the second stage, the firm defines a price for its product. We will seek the existence of a perfect equilibrium in this game. A perfect equilibrium in this context can be viewed as a Nash equilibrium in a game in which firms select a product, aware of the non-cooperative price equilibrium that will occur for each of their choices. It will be shown that contrary to Hotelling's principle, the two firms will maximise their differentiation (i.e. firms will locate at opposite ends of the market).