The Ring Design Game with Fair Cost Allocation

[Extended Abstract]
  • Angelo Fanelli
  • Dariusz Leniowski
  • Gianpiero Monaco
  • Piotr Sankowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)


In this paper we study the network design game when the underlying network is a ring. In a network design game we have a set of players, each of them aims at connecting nodes in a network by installing links and sharing the cost of the installation equally with other users. The ring design game is the special case in which the potential links of the network form a ring. It is well known that in a ring design game the price of anarchy may be as large as the number of players. Our aim is to show that, despite the worst case, the ring design game always possesses good equilibria. In particular, we prove that the price of stability of the ring design game is at most 3/2, and such bound is tight. We believe that our results might be useful for the analysis of more involved topologies of graphs, e.g., planar graphs.


Nash Equilibrium Planar Graph Design Game Congestion Game Undirected Network 
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  1. 1.
    Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38(4), 1602–1623 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bilò, V., Caragiannis, I., Fanelli, A., Monaco, G.: Improved Lower Bounds on the Price of Stability of Undirected Network Design Game. In: Theory of Computing Systems (to appear), doi:10.1007/s00224-012-9411-6Google Scholar
  3. 3.
    Chen, H.-L., Roughgarden, T.: Network design with weighted players. Theory of Computing Systems 45, 302–324 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Christodoulou, G., Chung, C., Ligett, K., Pyrga, E., van Stee, R.: On the Price of Stability for Undirected Network Design. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 86–97. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Fiat, A., Kaplan, H., Levy, M., Olonetsky, S., Shabo, R.: On the Price of Stability for Designing Undirected Networks with Fair Cost Allocations. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part I. LNCS, vol. 4051, pp. 608–618. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Rosenthal, R.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Angelo Fanelli
    • 1
  • Dariusz Leniowski
    • 2
  • Gianpiero Monaco
    • 2
    • 3
  • Piotr Sankowski
    • 2
    • 4
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  2. 2.Institute of InformaticsUniversity of WarsawPoland
  3. 3.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversity of L’AquilaItaly
  4. 4.Department of Computer and System ScienceSapienza University of RomePoland

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