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The Max-Min Principle of Product Differentiation

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  • Nicholas Economides
  • Asim Ansari
  • 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 New York University, Leonard N. Stern School of Business, Department of Economics in its series Working Papers with number 94-16.

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Date of creation: 1994
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Handle: RePEc:ste:nystbu:94-16

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Postal: New York University, Leonard N. Stern School of Business, Department of Economics, 44 West 4th Street, New York, NY 10012-1126
Phone: (212) 998-0860
Fax: (212) 995-4218
Web page: http://w4.stern.nyu.edu/economics/
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References

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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. John R. Hauser & Steven M. Shugan, 1983. "Defensive Marketing Strategies," Marketing Science, INFORMS, vol. 2(4), pages 319-360.
  3. Economides, Nicholas, 1989. "Quality variations and maximal variety differentiation," Regional Science and Urban Economics, Elsevier, vol. 19(1), pages 21-29, February.
  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. 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.
  6. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation for Research in Economics, Yale University.
  7. Economides, Nicholas, 1984. "The principle of minimum differentiation revisited," European Economic Review, Elsevier, vol. 24(3), pages 345-368, April.
  8. 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.
  9. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
  10. 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.
  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. 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).
  13. Neven, Damien, 1985. "Two Stage (Perfect) Equilibrium in Hotelling's Model," Journal of Industrial Economics, Wiley Blackwell, vol. 33(3), pages 317-25, March.
  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. 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.
  16. d'ASPREMONT, Claude & GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "On Hotelling's "Stability in competition"," CORE Discussion Papers RP -385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. 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.
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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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