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Dynamics and equilibria under incremental horizontal differentiation on the Salop circle

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  • Vermeulen, Ben
  • La Poutré, Han
  • de Kok, Ton
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    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.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 51449.

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    Date of creation: Apr 2012
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    Handle: RePEc:pra:mprapa:51449

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    Keywords: product differentiation; bounded rationality; Salop circle; equidistant equilibrium; maximum differentiation;

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    15. Gupta, Barnali & Lai, Fu-Chuan & Pal, Debashis & Sarkar, Jyotirmoy & Yu, Chia-Ming, 2004. "Where to locate in a circular city?," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 759-782, June.
    16. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages S251-78, October.
    17. Tyagi, Rajeev K, 1999. "Pricing Patterns as Outcomes of Product Positions," The Journal of Business, University of Chicago Press, vol. 72(1), pages 135-57, January.
    18. Pal, Debashis, 1998. "Does Cournot competition yield spatial agglomeration?," Economics Letters, Elsevier, vol. 60(1), pages 49-53, July.
    19. Chia-Ming Yu, 2007. "Price and quantity competition yield the same location equilibria in a circular market-super-," Papers in Regional Science, Wiley Blackwell, vol. 86(4), pages 643-655, November.
    20. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
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