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Nash Equilibrium in Duopoly with Products Defined by Two Characteristics

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  • Nicholas Economides

Abstract

This article analyzes the analogue of Hotelling's duopoly model when products are defined by two characteristics. Using the assumptions of the original model of Hotelling, we show that demand and profit functions are continuous for a wide class of utility functions. When the utility function is linear in the Euclidean distance in the space of characteristics, a noncooperative equilibrium in prices exists for all symmetric locations of firms. This is in contrast to the result in the one-characteristic model where a noncooperative equilibrium exists only when products are very different. The noncooperative equilibria are calculated and fully characterized. In contrast with the one-dimensional model of Hotelling, where equilibrium prices were constant irrespective of distance (of symmetric locations), here equilibrium prices tend to zero as the distance between products approaches zero.

Suggested Citation

  • 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.
  • Handle: RePEc:rje:randje:v:17:y:1986:i:autumn:p:431-439
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    Cited by:

    1. Elizalde, Javier, 2013. "Competition in multiple characteristics: An empirical test of location equilibrium," Regional Science and Urban Economics, Elsevier, vol. 43(6), pages 938-950.
    2. Funaki, Y. & Houba, H.E.D. & Motchenkova, E., 2012. "Market Power in Bilateral Oligopoly Markets with Nonexpendable Infrastructure," Discussion Paper 2012-041, Tilburg University, Tilburg Law and Economic Center.
    3. Torbenko, A., 2015. "Linear City Models: Overview and Typology," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 12-38.
    4. Ansari, A. & Economides, N. & Steckel, J., 1996. "The Max-Min-Min Principle of product Differentiation," Working Papers 96-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    5. Takatoshi Tabuchi, 2009. "Hotelling's Spatial Competition Reconsidered," CIRJE F-Series CIRJE-F-674, CIRJE, Faculty of Economics, University of Tokyo.
    6. Thill, Jean-Claude, 1997. "Multi-outlet firms, competition and market segmentation strategies," Regional Science and Urban Economics, Elsevier, vol. 27(1), pages 67-86, February.
    7. Veendorp, E. C. H. & Majeed, Anjum, 1995. "Differentiation in a two-dimensional market," Regional Science and Urban Economics, Elsevier, vol. 25(1), pages 75-83, February.
    8. Nicholas Economides & Joel Steckel, "undated". "The Max-Min Principle of Product Differentiation," Networks, Compatibility 94-16, Economics of Networks.
    9. 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.
    10. Garella, Paolo G. & Lambertini, Luca, 2014. "Bidimensional vertical differentiation," International Journal of Industrial Organization, Elsevier, vol. 32(C), pages 1-10.
    11. Braid, Ralph M., 1998. "Inventory costs and the optimal spacing of retail stores," Economics Letters, Elsevier, vol. 58(1), pages 127-131, January.

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