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Hotelling Games on Networks: Efficiency of Equilibria

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  • Gaëtan Fournier

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • 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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00983085.

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Date of creation: Apr 2014
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Handle: RePEc:hal:cesptp:halshs-00983085

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Keywords: Induced price of anarchy; induced price of stability; location games on networks; pure equilibria; large games;

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  1. Steffen Huck & Wieland M¸ller, 2002. "The East End, the West End, and King's Cross: on Clustering in the Four-Player Hotelling Game," Economic Inquiry, Western Economic Association International, Western Economic Association International, vol. 40(2), pages 231-240, April.
  2. Bester, Helmut & de Palma, Andre & Leininger, Wolfgang & Thomas, Jonathan & von Thadden, Ernst-Ludwig, 1996. "A Noncooperative Analysis of Hotelling's Location Game," Games and Economic Behavior, Elsevier, Elsevier, vol. 12(2), pages 165-186, February.
  3. Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1999. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/3319, ULB -- Universite Libre de Bruxelles.
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  6. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1145-50, September.
  7. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, Springer, vol. 36(3), pages 379-405, September.
  8. Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Strong equilibrium in cost sharing connection games," Games and Economic Behavior, Elsevier, Elsevier, vol. 67(1), pages 51-68, September.
  9. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  10. Eaton, B Curtis & Lipsey, Richard G, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 42(1), pages 27-49, January.
  11. Steffen Brenner, 2005. "Hotelling Games with Three, Four, and More Players," Journal of Regional Science, Wiley Blackwell, Wiley Blackwell, vol. 45(4), pages 851-864.
  12. Correa, Jose R. & Schulz, Andreas S. & Stier Moses, Nicolas E., 2003. "Selfish Routing in Capacitated Networks," Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management 4319-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  13. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 223-37, February.
  14. Correa, José R. & Schulz, Andreas S. & Stier-Moses, Nicolás E., 2008. "A geometric approach to the price of anarchy in nonatomic congestion games," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(2), pages 457-469, November.
  15. Martin J Osborne & Carolyn Pitchik, 1985. "Equilibrium in Hotelling's Model of Spatial Competition," Department of Economics Working Papers 1985-02, McMaster University.
  16. Knight, Vincent A. & Harper, Paul R., 2013. "Selfish routing in public services," European Journal of Operational Research, Elsevier, Elsevier, vol. 230(1), pages 122-132.
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