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General distribution of consumers in pure Hotelling games

Author

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  • Gaëtan Fournier

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

A pure Hotelling game is a spatial competition between a finite number of players who simultaneously select a location in order to attract as many consumers as possible. In this paper, we study the case of a general distribution of consumers on a network generated by a metric graph. Because players do not compete on price, the continuum of consumers shop at the closest player's location. If the number of sellers is large enough, we prove the existence of an approximate equilibrium in pure strategies, and we construct it.

Suggested Citation

  • Gaëtan Fournier, 2019. "General distribution of consumers in pure Hotelling games," Post-Print hal-01994400, HAL.
    • Handle: RePEc:hal:journl:hal-01994400
    DOI: 10.1007/s00182-018-0648-4
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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," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 27-49.
    2. Matías Núñez & Marco Scarsini, 2017. "Large Spatial Competition," Springer Optimization and Its Applications, in: Lina Mallozzi & Egidio D'Amato & Panos M. Pardalos (ed.), Spatial Interaction Models, pages 225-246, Springer.
    3. Hans Peters & Marc Schröder & Dries Vermeulen, 2018. "Hotelling’s location model with negative network externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 811-837, September.
    4. 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.
    5. 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.
    6. Neven, Damien J., 1986. "On Hotelling's competition with non-uniform customer distributions," Economics Letters, Elsevier, vol. 21(2), pages 121-126.
    7. Montes-Rojas, Gabriel, 2015. "Spatial competition and the location on firms with non uniformly distributed costumers," Revista de Economía Política de Buenos Aires, Universidad de Buenos Aires. Facultad de Ciencias Económicas., issue 14, pages 83-107, December.
    8. Gaëtan Fournier & Marco Scarsini, 2019. "Location Games on Networks: Existence and Efficiency of Equilibria," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 212-235, February.
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    Cited by:

    1. Hans Peters & Marc Schröder & Dries Vermeulen, 2018. "Hotelling’s location model with negative network externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 811-837, September.
    2. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    3. Gaetan Fournier & Karine Van Der Straeten & Jorgen Weibull, 2020. "Spatial competition with unit-demand functions," Papers 2001.11422, arXiv.org.
    4. Dodge Cahan & Hongjia H. Chen & Louis Christie & Arkadii Slinko, 2021. "Spatial competition on 2-dimensional markets and networks when consumers don’t always go to the closest firm," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 945-970, December.

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    More about this item

    Keywords

    Hotelling games; Location games on networks; Pure equilibria; Approximate Nash equilibria; Large 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
    • R30 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - General

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