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Location Games on Networks: Existence and Efficiency of Equilibria

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  • Gaëtan Fournier

    (Aix-Marseille School of Economics (AMSE), Groupement de recherche en économie quantitative d’Aix-Marseille (GREQAM), Aix-Marseille Université, 13001 Marseille, France)

  • Marco Scarsini

    (Dipartimento di Economia e Finanza, LUISS, 00197 Roma, Italy)

Abstract

We consider a game where a finite number of retailers choose a location, given that their potential consumers 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 borne 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 terms of the Price of Anarchy (i.e., the ratio of the worst equilibrium cost and the optimal cost) and the 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 bounded by two and one, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormoor:v:44:y:2019:i:1:p:212-235
    DOI: 10.1287/moor.2017.0921
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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.
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    Cited by:

    1. Gaëtan Fournier, 2019. "General distribution of consumers in pure Hotelling games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 33-59, March.
    2. 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.
    3. Omer Ben-Porat & Moshe Tennenholtz, 2019. "Multiunit Facility Location Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 865-889, August.

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