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Utility function and location in the Hotelling game

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  • Takanori Ago

    (Senshu University)

Abstract

It is demonstrated herein that a slight expansion of the utility function in the duopolistic Hotelling game enables any symmetric location pair with respect to the center to be in equilibrium, which implies that any level of locational differentiation between the minimum Hotelling (Econ. J.39:41–57, 1929) and maximum D’Aspremont (Econom. 47:1145–1150, 1979) is obtained in one model. The location equilibrium is monotone with respect to the introduced parameter (k), while the equilibrium price and profits are not monotone (they are U-shaped). That is, the nearer the two firms are located, the higher their prices are set (with an upper limit) when k is sufficiently large. This counterintuitive phenomenon is interpreted as an example of strategic complementarity that is inherent in the Hotelling games.

Suggested Citation

  • Takanori Ago, 2023. "Utility function and location in the Hotelling game," Letters in Spatial and Resource Sciences, Springer, vol. 16(1), pages 1-9, December.
    • Handle: RePEc:spr:lsprsc:v:16:y:2023:i:1:d:10.1007_s12076-023-00344-w
    DOI: 10.1007/s12076-023-00344-w
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    References listed on IDEAS

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    1. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    2. L. Lambertini, 1993. "Equilibrium Locations in the Unconstrained Hotelling Game," Working Papers 155, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Tönu Puu, 2002. "Hotelling's "Ice cream dealers" with elastic demand," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 36(1), pages 1-17.
    4. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    5. Alain Egli, 2007. "Hotelling'S Beach With Linear And Quadratic Transportation Costs: Existence Of Pure Strategy Equilibria," Australian Economic Papers, Wiley Blackwell, vol. 46(1), pages 39-51, March.
    6. Dragone, Davide & Lambertini, Luca, 2020. "Equilibrium existence in the Hotelling model with convex production costs," Regional Science and Urban Economics, Elsevier, vol. 84(C).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Hotelling; Utility function; Location equilibrium; Price term;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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