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Hotelling Games on Networks: Efficiency of Equilibria

Author

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  • Gaëtan Fournier

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Marco Scarsini

    () (Engineering and System Design Pillar - Singapore University of Technology and Design)

Abstract

We consider a Hotelling game where a finite number of retailers choose a location, given that their potential customers are distributed on a network. Retailers do not compete on price but only on location, therefore each consumer shops at the closest store. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost bore by the consumers with the cost that could be achieved if the retailers followed the dictate of a benevolent planner. We perform this comparison in term of the induced price of anarchy, i.e., the ratio of the worst equilibrium cost and the optimal cost, and the induced price of stability, i.e., the ratio of the best equilibrium cost and the optimal cost. We show that, asymptotically in the number of retailers, these ratios are two and one, respectively.

Suggested Citation

  • Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00983085, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00983085
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00983085
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Matías Núñez & Marco Scarsini, 2016. "Competing over a finite number of locations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 125-136, October.
    2. Lapatinas, Athanasios & Garas, Antonios, 2016. "The role of networks in firms’ multi-characteristics competition and market-share inequality," MPRA Paper 68959, University Library of Munich, Germany.
    3. Peters H.J.M. & Schröder M.J.W. & Vermeulen A.J., 2015. "Waiting in the queue on Hotelling’s Main Street," Research Memorandum 040, Maastricht University, Graduate School of Business and Economics (GSBE).
    4. Antonios Garas & Athanasios Lapatinas, 2016. "The role of consumer networks in firms' multi-characteristics competition and market-share inequality," Papers 1601.05660, arXiv.org, revised Aug 2017.

    More about this item

    Keywords

    Induced price of anarchy; induced price of stability; location games on networks; pure equilibria; large games; Prix de l'anarchie induit; prix de la stabilité induit; jeu de location sur un réseau; équilibre pur;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • R30 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - General
    • R39 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - Other

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