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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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  • 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. Tore Nilssen & Lars Sørgard, 1998. "Time Schedule and Program Profile: TV News in Norway and Denmark," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 7(2), pages 209-235, June.
    2. 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.
    3. Yukihiko Funaki & Harold Houba & Evgenia Motchenkova, 2020. "Market power in bilateral oligopoly markets with non-expandable infrastructures," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 525-546, June.
    4. María Isabel Berenguer Maldonado & Santiago Carbó Valverde & Miguel Ángel Fortes Escalona, 2005. "Cournot Competition In A Two‐Dimensional Circular City," Manchester School, University of Manchester, vol. 73(1), pages 40-49, January.
    5. Torbenko, A., 2015. "Linear City Models: Overview and Typology," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 12-38.
    6. 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.
    7. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    8. Takatoshi Tabuchi, 2009. "Hotelling's Spatial Competition Reconsidered," CIRJE F-Series CIRJE-F-674, CIRJE, Faculty of Economics, University of Tokyo.
    9. Stefan Roth, 1999. "Möglichkeiten und Grenzen ökonomischer Positionierungsmodelle," Schmalenbach Journal of Business Research, Springer, vol. 51(3), pages 243-266, March.
    10. 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.
    11. Wenxuan Shan & Qianqian Yan & Chao Chen & Mengjie Zhang & Baozhen Yao & Xuemei Fu, 2019. "Optimization of competitive facility location for chain stores," Annals of Operations Research, Springer, vol. 273(1), pages 187-205, February.
    12. Stefano Colombo & Noriaki Matsushima, 2020. "Competition Between Offline and Online Retailers with Heterogeneous Customers," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 57(3), pages 647-664, November.
    13. 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.
    14. Nicholas Economides & Joel Steckel, "undated". "The Max-Min Principle of Product Differentiation," Networks, Compatibility 94-16, Economics of Networks.
    15. 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.
    16. Garella, Paolo G. & Lambertini, Luca, 2014. "Bidimensional vertical differentiation," International Journal of Industrial Organization, Elsevier, vol. 32(C), pages 1-10.
    17. Stanislav Stoykov & Ivan Kostov, 2023. "Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior," Games, MDPI, vol. 14(2), pages 1-25, March.
    18. Heidrun C. Hoppe & Ulrich Lehmann-Grube, 2000. "Spatial Competition in Credit Markets," CSEF Working Papers 32, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    19. Braid, Ralph M., 1998. "Inventory costs and the optimal spacing of retail stores," Economics Letters, Elsevier, vol. 58(1), pages 127-131, January.
    20. Basaure, Arturo & Vesselkov, Alexandr & Töyli, Juuso, 2020. "Internet of things (IoT) platform competition: Consumer switching versus provider multihoming," Technovation, Elsevier, vol. 90.
    21. Basaure, Arturo & Vesselkov, Alexandr, 2018. "Internet of things (IoT) platform competition: consumer switching versus provider multihoming," 22nd ITS Biennial Conference, Seoul 2018. Beyond the boundaries: Challenges for business, policy and society 190352, International Telecommunications Society (ITS).

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