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Capacitated Network Design Games

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Algorithmic Game Theory (SAGT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7615))

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Abstract

We study a capacitated symmetric network design game, where each of n agents wishes to construct a path from a network’s source to its sink, and the cost of each edge is shared equally among its agents. The uncapacitated version of this problem has been introduced by Anshelevich et al. (2003) and has been extensively studied. We find that the consideration of edge capacities entails a significant effect on the quality of the obtained Nash equilibria (NE), under both the utilitarian and the egalitarian objective functions, as well as on the convergence rate to an equilibrium. The following results are established. First, we provide bounds for the price of anarchy (PoA) and the price of stability (PoS) measures with respect to the utilitarian (i.e., sum of costs) and egalitarian (i.e., maximum cost) objective functions. Our main result here is that, unlike the uncapacitated version, the network topology is a crucial factor in the quality of NE. Specifically, a network topology has a bounded PoA if and only if it is series-parallel (SP). Second, we show that the convergence rate of best-response dynamics (BRD) may be super linear (in the number of agents). This is in contrast to the uncapacitated version, where convergence is guaranteed within at most n iterations.

This work was partially supported by the Israel Science Foundation (grant number 1219/09), by the Leon Recanati Fund of the Jerusalem School of Business Administration, the Google Inter-university center for Electronic Markets and Auctions, and the People Programme (Marie Curie Actions) of the European Unions Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number 274919. The authors wish to thank Eli Ben-Sasson and Irit Dinur for helpful discussion.

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Authors and Affiliations

  1. Hebrew University of Jerusalem, Israel

    Michal Feldman & Tom Ron

  2. Harvard University, USA

    Michal Feldman

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  1. Michal Feldman
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  2. Tom Ron
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Editors and Affiliations

  1. Department de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, ALBCOM, Jordi Girona 1-3, 08034, Barcelona,, Spain

    Maria Serna

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Feldman, M., Ron, T. (2012). Capacitated Network Design Games. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-33996-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33995-0

  • Online ISBN: 978-3-642-33996-7

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