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The East End, the West End, and King's Cross: On Clustering in the Four-Player Hotelling Game

Author

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  • Steffen Huck

    (Royal Holloway College, University of London)

  • Wieland Müller

    (Humboldt University Berlin)

  • Nicolaas J. Vriend

    () (Queen Mary and Westfield College, University of London)

Abstract

We study experimentally a standard four-player Hotelling game, with a uniform density of consumers and inelastic demand. The pure strategy Nash equilibrium configuration consists of two firms located at one quarter of the ``linear city'', and the other two at three quarters. We do not observe convergence to such an equilibrium. In our experimental data we find three clusters. Besides the direct proximity of the two equilibrium locations this concerns the focal mid-point. Moreover, we observe that whereas this mid-point appears to become more notable over time, other focal points fade away. We explain how these observations are related to best-response dynamics, and to the fact that the players rely on best-responses in particular when they are close to the equilibrium configuration.

Suggested Citation

  • Steffen Huck & Wieland Müller & Nicolaas J. Vriend, 2000. "The East End, the West End, and King's Cross: On Clustering in the Four-Player Hotelling Game," Working Papers 409, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp409
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    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp409.pdf
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    References listed on IDEAS

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    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," Review of Economic Studies, Oxford University Press, vol. 42(1), pages 27-49.
    2. Brown Kruse, Jamie & Schenk, David J., 2000. "Location, cooperation and communication: An experimental examination," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 59-80, January.
    3. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    4. Shaked, A, 1982. "Existence and Computation of Mixed Strategy Nash Equilibrium for 3-Firms Location Problem," Journal of Industrial Economics, Wiley Blackwell, vol. 31(1-2), pages 93-96, September.
    5. Collins, Richard & Sherstyuk, Katerina, 2000. "Spatial Competition with Three Firms: An Experimental Study," Economic Inquiry, Western Economic Association International, vol. 38(1), pages 73-94, January.
    6. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    7. Osborne, Martin J & Pitchik, Carolyn, 1986. "The Nature of Equilibrium in a Location Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 223-237, February.
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    Citations

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    Cited by:

    1. Nikolas Tsakas & Dimitrios Xefteris, 2017. "Electoral Competition with Third Party Entry in the Lab," University of Cyprus Working Papers in Economics 09-2017, University of Cyprus Department of Economics.
    2. Orzen, Henrik & Sefton, Martin, 2008. "An experiment on spatial price competition," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 716-729, May.
    3. Aurélie Bonein & Stéphane Turolla, 2017. "Spatial competition with demand uncertainty: A laboratory experiment," Working Papers SMART - LERECO 17-12, INRA UMR SMART-LERECO.
    4. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00983085, HAL.
    5. Lisa R. Anderson & Beth A. Freeborn & Jessica Holmes & Mark Jeffreys & Dan Lass & Jack Soper, 2006. "Location, Location, Location! A Classroom Demonstration of the Hotelling Model," Working Papers 44, Department of Economics, College of William and Mary, revised 05 Feb 2007.
    6. Wilfred Amaldoss & Woochoel Shin, 2011. "Competing for Low-End Markets," Marketing Science, INFORMS, vol. 30(5), pages 776-788, September.
    7. Barreda-Tarrazona, Iván & García-Gallego, Aurora & Georgantzís, Nikolaos & Andaluz-Funcia, Joaquín & Gil-Sanz, Agustín, 2011. "An experiment on spatial competition with endogenous pricing," International Journal of Industrial Organization, Elsevier, vol. 29(1), pages 74-83, January.
    8. Camacho-Cuena, Eva & Garcia-Gallego, Aurora & Georgantzis, Nikolaos & Sabater-Grande, Gerardo, 2005. "Buyer-seller interaction in experimental spatial markets," Regional Science and Urban Economics, Elsevier, vol. 35(2), pages 89-108, March.
    9. Christian Ewerhart, 2014. "Mixed equilibrium in a pure location game: the case of n ≥ 4 firms," ECON - Working Papers 168, Department of Economics - University of Zurich.

    More about this item

    Keywords

    Location model; Nonconvergence; Focal point; Best-response dynamics;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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