Improved Lower Bounds on the Price of Stability of Undirected Network Design Games

  • Vittorio Bilò
  • Ioannis Caragiannis
  • Angelo Fanelli
  • Gianpiero Monaco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6386)


Bounding the price of stability of undirected network design games with fair cost allocation is a challenging open problem in the Algorithmic Game Theory research agenda. Even though the generalization of such games in directed networks is well understood in terms of the price of stability (it is exactly H n , the n-th harmonic number, for games with n players), far less is known for network design games in undirected networks. The upper bound carries over to this case as well while the best known lower bound is 42/23 ≈ 1.826. For more restricted but interesting variants of such games such as broadcast and multicast games, sublogarithmic upper bounds are known while the best known lower bound is 12/7 ≈ 1.714. In the current paper, we improve the lower bounds as follows. We break the psychological barrier of 2 by showing that the price of stability of undirected network design games is at least 348/155 ≈ 2.245. Our proof uses a recursive construction of a network design game with a simple gadget as the main building block. For broadcast and multicast games, we present new lower bounds of 20/11 ≈ 1.818 and 1.862, respectively.


Nash Equilibrium Direct Edge Multicast Tree Congestion Game Undirected Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Albers, S.: On the value of coordination in network design. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 294–303 (2008)Google Scholar
  2. 2.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 311–322. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Chen, H.-L., Roughgarden, T.: Network design with weighted players. Theory of Computing Systems 45, 302–324 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Christodoulou, G., Koutsoupias, E.: The price of anarchy and stability of correlated equilibria of linear congestion games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    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.) Approximation and Online Algorithms. LNCS, vol. 5893, pp. 86–97. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    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. LNCS, vol. 4051, pp. 608–618. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Li, J.: An O(logn/loglogn) upper bound on the price of stability for undirected Shapley network design games. Information Processing Letters 109(15), 876–878 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Papadimitriou, C.H.: Algorithms, games and the internet. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC), pp. 749–753 (2001)Google Scholar
  11. 11.
    Rosenthal, R.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vittorio Bilò
    • 1
  • Ioannis Caragiannis
    • 2
  • Angelo Fanelli
    • 3
  • Gianpiero Monaco
    • 4
  1. 1.Department of MathematicsUniversity of SalentoLecceItaly
  2. 2.RACTI & Department of Computer Engineering and InformaticsUniversity of PatrasGreece
  3. 3.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  4. 4.Mascotte Project, I3S (CNRS/UNSA) INRIASophia AntipolisFrance

Personalised recommendations