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The Max-Min-Min Principle of Product Differentiation

  • Asim Ansari

    (Graduate School of Business, Columbia University)

  • Nicholas Economides

    (Stern School of Business, New York University)

  • Joel Steckel

    (Stern School of Business, New York University)

We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importance on each product attribute; this is measured by a weight in the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. We seek subgame-perfect equilibria. We find that all such equilibria have maximal differentiation in one dimension only; in all other dimensions, they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of them, or all three.

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Paper provided by EconWPA in its series Industrial Organization with number 9702001.

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Length: 36 pages
Date of creation: 05 Feb 1997
Date of revision:
Handle: RePEc:wpa:wuwpio:9702001
Note: Type of Document - PDF/PostScript; prepared on IBM; to print on HP; pages: 36; figures: included at the end. forthcoming, Journal of Regional Science (1997)
Contact details of provider: Web page: http://econwpa.repec.org

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  1. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-50, September.
  2. Mark B. Vandenbosch & Charles B. Weinberg, 1995. "Product and Price Competition in a Two-Dimensional Vertical Differentiation Model," Marketing Science, INFORMS, vol. 14(2), pages 224-249.
  3. Neven, D. & Thisse, J-F., 1989. "On Quality And Variety Competition," CORE Discussion Papers 1989020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February.
  5. Tabuchi, Takatoshi, 1994. "Two-stage two-dimensional spatial competition between two firms," Regional Science and Urban Economics, Elsevier, vol. 24(2), pages 207-227, April.
  6. Neven, Damien, 1985. "Two Stage (Perfect) Equilibrium in Hotelling's Model," Journal of Industrial Economics, Wiley Blackwell, vol. 33(3), pages 317-25, March.
  7. John R. Hauser, 1988. "Note—Competitive Price and Positioning Strategies," Marketing Science, INFORMS, vol. 7(1), pages 76-91.
  8. Economides, Nicholas, 1993. "Quality variations in the circular model of variety-differentiated products," Regional Science and Urban Economics, Elsevier, vol. 23(2), pages 235-257, April.
  9. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
  10. K. Ravi Kumar & D. Sudharshan, 1988. "Defensive Marketing Strategies: An Equilibrium Analysis Based on Decoupled Response Function Models," Management Science, INFORMS, vol. 34(7), pages 805-815, July.
  11. Green, Paul E & Srinivasan, V, 1978. " Conjoint Analysis in Consumer Research: Issues and Outlook," Journal of Consumer Research, University of Chicago Press, vol. 5(2), pages 103-23, Se.
  12. Economides, Nicholas, 1984. "The principle of minimum differentiation revisited," European Economic Review, Elsevier, vol. 24(3), pages 345-368, April.
  13. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
  14. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  15. John R. Hauser & Steven M. Shugan, 2008. "Defensive Marketing Strategies," Marketing Science, INFORMS, vol. 27(1), pages 88-110, 01-02.
  16. Nicholas Economides, 1986. "Nash Equilibrium in Duopoly with Products Defined by Two Characteristics," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 431-439, Autumn.
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