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Hotelling Games on Networks: Efficiency of Equilibria

  • Gaëtan Fournier

    ()

    (Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Marco Scarsini

    ()

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

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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  1. Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1985. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/1759, ULB -- Universite Libre de Bruxelles.
  2. Huck, S. & Müller, W. & Vriend, N.J., 2002. "The East End, the West End and King's Cross : On clustering in the four-player Hotelling game," Other publications TiSEM 1e3e12cd-ae62-49dc-8f43-1, Tilburg University, School of Economics and Management.
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  4. Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Strong equilibrium in cost sharing connection games," Games and Economic Behavior, Elsevier, vol. 67(1), pages 51-68, September.
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  8. Martin J Osborne & Carolyn Pitchik, 1985. "Equilibrium in Hotelling's Model of Spatial Competition," Department of Economics Working Papers 1985-02, McMaster University.
  9. 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, vol. 12(2), pages 165-186, February.
  10. 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, vol. 64(2), pages 457-469, November.
  11. Steffen Brenner, 2005. "Hotelling Games with Three, Four, and More Players," Journal of Regional Science, Wiley Blackwell, vol. 45(4), pages 851-864.
  12. Hervé Moulin, 2010. "Auctioning or assigning an object: some remarkable VCG mechanisms," Social Choice and Welfare, Springer, vol. 34(2), pages 193-216, February.
  13. 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, vol. 42(1), pages 27-49, January.
  14. Aoyagi, Masaki & Okabe, Atsuyuki, 1993. "Spatial competition of firms in a two-dimensional bounded market," Regional Science and Urban Economics, Elsevier, vol. 23(2), pages 259-289, April.
  15. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
  16. 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 223-37, February.
  17. Correa, Jose R. & Schulz, Andreas S. & Stier Moses, Nicolas E., 2003. "Selfish Routing in Capacitated Networks," Working papers 4319-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
  18. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, vol. 36(3), pages 379-405, September.
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