Dynamics and equilibria under incremental horizontal differentiation on the Salop circle

Vermeulen, Ben and La Poutré, Han and de Kok, Ton (2012): Dynamics and equilibria under incremental horizontal differentiation on the Salop circle.

Abstract

We study product differentiation on a Salop circle when firms relocate incrementally due to bounded rationality. We prove that, under common assumptions on demand, firms relocate only when two or more firms target the same niche. In any other case, there is no incentive for any firm to relocate incrementally. We prove that all distributions in which firms are sufficiently far apart in product space are unstable Nash equilibria. We prove, in particular, that the classical equidistant distribution is an unstable Nash equilibrium that cannot emerge from another distribution. However, we show that if each firm is engaged in head-on rivalry with one other competitor, the industry converges to an ’equidistantesque’ equilibrium of clusters of rivals.

• Item Type: MPRA Paper
• Language: English
• Keywords: product differentiation; bounded rationality; Salop circle; equidistant equilibrium; maximum differentiation
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior > L22 - Firm Organization and Market Structure

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