Theory of Computing Systems

, Volume 52, Issue 4, pp 668–686 | Cite as

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

  • Vittorio Bilò
  • Ioannis Caragiannis
  • Angelo Fanelli
  • Gianpiero Monaco


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 Unique Nash Equilibrium Broadcast Tree 
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.



We would like to thank George Christodoulou and Martin Hoefer for helpful discussions at early stages of this work.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vittorio Bilò
    • 1
  • Ioannis Caragiannis
    • 2
  • Angelo Fanelli
    • 3
  • Gianpiero Monaco
    • 4
    • 5
  1. 1.Department of MathematicsUniversity of SalentoLecceItaly
  2. 2.Research Academic Computer Technology Institute & Department of Computer Engineering and InformaticsUniversity of PatrasRioGreece
  3. 3.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  4. 4.Department of InformaticsUniversity of L’AquilaL’AquilaItaly
  5. 5.Mascotte ProjectI3S (CNRS/UNSA) INRIASophia AntipolisFrance

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