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Hotelling Games on Networks: Efficiency of Equilibria

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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

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  • Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Documents de travail du Centre d'Economie de la Sorbonne 14033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:14033
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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. 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.
    3. 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.
    4. Garas, Antonios & Lapatinas, Athanasios, 2017. "The role of consumer networks in firmsÂ’ multi-characteristics competition and market share inequality," Structural Change and Economic Dynamics, Elsevier, vol. 43(C), pages 76-86, December.
    5. 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).

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    More about this item

    Keywords

    Induced price of anarchy; induced price of stability; location games on networks; pure equilibria; large games;
    All these keywords.

    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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