Dynamics and equilibria under incremental horizontal differentiation on the Salop circle

Ben Vermeulen, Han La Poutré and Ton de Kok

MPRA Paper from University Library of Munich, Germany

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.

Keywords: product differentiation; bounded rationality; Salop circle; equidistant equilibrium; maximum differentiation (search for similar items in EconPapers)
JEL-codes: C73 L13 L22 (search for similar items in EconPapers)
Date: 2012-04
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