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**1 - 3**of**3**### Duopoly in the Hotelling Model of Horizontal Differentiation ∗

"... The Hotelling model with finite consumer reservation price is, in its various forms, perhaps the canonical model of horizontal product differentiation. Yet the following key aspects of this model are little understood: (i) the existence of asymmetric price equilibria when consumers have unit demands ..."

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The Hotelling model with finite consumer reservation price is, in its various forms, perhaps the canonical model of horizontal product differentiation. Yet the following key aspects of this model are little understood: (i) the existence of asymmetric price equilibria when consumers have unit demands and (ii) for a very broad set of model specifications, the non-monotonicity of price as a function of consumers ’ transportation cost, i.e., the degree of product differentiation in the market. We provide a complete characterization of the asymmetric equilibria, show that they exist for a comparatively “wide ” range of markets, and argue that their existence is robust to various extensions of the prototype model. Introducing elasticity into consumer demands suppresses the kink in the firms ’ demand functions and ensures the uniqueness (and symmetry) of the price equilibrium. However, the key perverse comparative static of the symmetric kinked equilibrium, decreasing price as a function of transport cost, survives relaxation of the unit-demand assumption. Indeed the symmetric kinked equilibrium of the unit-demand case is a special case of a general but largely unexplored set of equilibria in the Hotelling model we call weak duopoly. Weak-duopoly equilibria exist for intermediate values of transportation cost for a very broad class of consumer demands.

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"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."

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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.

### Horizontal differentiation and price competition with sequential entry∗

, 2003

"... We study a class of differentiation games à la Hotelling. Two firms choose a price and a location in the consumers ’ space. The leader first chooses both variables, and the follower observes them before playing. It is shown that in such games, any equilibrium has the property that the follower alway ..."

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We study a class of differentiation games à la Hotelling. Two firms choose a price and a location in the consumers ’ space. The leader first chooses both variables, and the follower observes them before playing. It is shown that in such games, any equilibrium has the property that the follower always gets a greater profit (in the absence of entry barrier). An equilibrium is shown to always exist and we qualify the equilibria with respect to the willingness to pay for the family of products. Some extensions are looked at. In particular, we investigate the effect of entry barriers on the strategies of the leader. Key words: horizontal differentiation; price commitment; catalog competition; sequential moves.