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The Max-Min Principle of Product Differentiation

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  • Nicholas Economides
  • Joel Steckel

Abstract

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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Bibliographic Info

Paper provided by Economics of Networks in its series Networks, Compatibility with number 94-16.

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Handle: RePEc:wop:ennenc:94-16

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  1. John R. Hauser, 1988. "Note—Competitive Price and Positioning Strategies," Marketing Science, INFORMS, vol. 7(1), pages 76-91.
  2. 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.
  3. Economides, Nicholas, 1984. "The principle of minimum differentiation revisited," European Economic Review, Elsevier, vol. 24(3), pages 345-368, April.
  4. 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).
  5. 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.
  6. 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.
  7. W.J. Lane, 1980. "Product Differentiation in a Market with Endogenous Sequential Entry," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 237-260, Spring.
  8. Economides, Nicholas, 1989. "Symmetric equilibrium existence and optimality in differentiated product markets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 178-194, February.
  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. 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.
  11. Neven, Damien, 1985. "Two Stage (Perfect) Equilibrium in Hotelling's Model," Journal of Industrial Economics, Wiley Blackwell, vol. 33(3), pages 317-25, March.
  12. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  13. 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.
  14. Economides, Nicholas, 1989. "Quality variations and maximal variety differentiation," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 21-29, February.
  15. John R. Hauser & Steven M. Shugan, 1983. "Defensive Marketing Strategies," Marketing Science, INFORMS, vol. 2(4), pages 319-360.
  16. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
  17. 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.
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Cited by:
  1. Andrea Mangani & Paolo Patelli, 2002. "The Max-Min Principle of Product Differentiation: An Experimental Analysis," LEM Papers Series 2002/05, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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