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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.

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Bibliographic Info

Article provided by The RAND Corporation in its journal RAND Journal of Economics.

Volume (Year): 17 (1986)
Issue (Month): 3 (Autumn)
Pages: 431-439

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Handle: RePEc:rje:randje:v:17:y:1986:i:autumn:p:431-439

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Cited by:
  1. Veendorp, E. C. H. & Majeed, Anjum, 1995. "Differentiation in a two-dimensional market," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 25(1), pages 75-83, February.
  2. Paolo Giorgio GARELLA & Luca LAMBERTINI, 2010. "Bidimensional vertical differentiation," Departmental Working Papers, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano 2010-04, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  3. Ansari, A. & Economides, N. & Steckel, J., 1996. "The Max-Min-Min Principle of product Differentiation," Working Papers, New York University, Leonard N. Stern School of Business, Department of Economics 96-10, New York University, Leonard N. Stern School of Business, Department of Economics.
  4. Takatoshi Tabuchi, 2009. "Hotelling's Spatial Competition Reconsidered," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-674, CIRJE, Faculty of Economics, University of Tokyo.
  5. Andrea Mangani & Paolo Patelli, 2002. "The Max-Min Principle of Product Differentiation: An Experimental Analysis," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 2002/05, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  6. Nicholas Economides & Asim Ansari & Joel Steckel, 1994. "The Max-Min Principle of Product Differentiation," Working Papers, New York University, Leonard N. Stern School of Business, Department of Economics 94-16, New York University, Leonard N. Stern School of Business, Department of Economics.
  7. Elizalde, Javier, 2013. "Competition in multiple characteristics: An empirical test of location equilibrium," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 43(6), pages 938-950.
  8. Braid, Ralph M., 1998. "Inventory costs and the optimal spacing of retail stores," Economics Letters, Elsevier, Elsevier, vol. 58(1), pages 127-131, January.
  9. Thill, Jean-Claude, 1997. "Multi-outlet firms, competition and market segmentation strategies," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 27(1), pages 67-86, February.

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