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The Missing Equilibria in Hotelling's Location Game

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  • Helmut Bester

Abstract

We study the location equilibrium in Hotelling's model of spatial competition. As d'Aspremont et al. (1979) have shown, with quadratic consumer transportation cost the two sellers will seek to move as far away from each other as possible. This generates a coordination problem which the literature typically ignores by restricting firm 1 to locate in the first half and firm 2 in the second half of market. We study the non-cooperative outcome in the absence of such a coordination device and find that the location game possesses an infinity of mixed strategy Nash equilibria. in these equilibria coordination failure invalidates the principle of 'maximum differentiation' and firms may even locate at the same point.

Suggested Citation

  • Helmut Bester, 1991. "The Missing Equilibria in Hotelling's Location Game," Discussion Papers 975, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:975
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    References listed on IDEAS

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    1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-640, May.
    2. Bester, Helmut, 1989. "Noncooperative Bargaining and Spatial Competition," Econometrica, Econometric Society, vol. 57(1), pages 97-113, January.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    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. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
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    Cited by:

    1. Derek K. Chan, 1999. "“Low†Balling†and Efficiency in a Two†Period Specialization Model of Auditing Competition," Contemporary Accounting Research, John Wiley & Sons, vol. 16(4), pages 609-642, December.

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    More about this item

    Keywords

    Spatialcompetition; Hotelling's location model; coordination games.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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