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

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, University of Salento, Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy

    Vittorio Bilò

  2. Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, 26500, Rio, Greece

    Ioannis Caragiannis

  3. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Angelo Fanelli

  4. Department of Informatics, University of L’Aquila, Via Vetoio, loc. Coppito, 67100, L’Aquila, Italy

    Gianpiero Monaco

  5. Mascotte Project, I3S (CNRS/UNSA) INRIA, Route des Lucioles 2004, 06902, Sophia Antipolis, France

    Gianpiero Monaco

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  1. Vittorio Bilò
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  2. Ioannis Caragiannis
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  3. Angelo Fanelli
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  4. Gianpiero Monaco
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Correspondence to Vittorio Bilò.

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A preliminary version of this paper appeared in Proceedings of the 3rd International Symposium on Algorithmic Game Theory (SAGT), LNCS 6386, Springer, pp. 90–101, 2010. This work was partially supported by the grant NRF-RF2009-08 “Algorithmic aspects of coalitional games” and the PRIN 2008 research project COGENT “Computational and game-theoretic aspects of uncoordinated networks” funded by the Italian Ministry of University and Research.

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Bilò, V., Caragiannis, I., Fanelli, A. et al. Improved Lower Bounds on the Price of Stability of Undirected Network Design Games. Theory Comput Syst 52, 668–686 (2013). https://doi.org/10.1007/s00224-012-9411-6

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  • DOI: https://doi.org/10.1007/s00224-012-9411-6

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