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Selfish Routing in Non-cooperative Networks: A Survey

  • Conference paper
Book cover Mathematical Foundations of Computer Science 2003 (MFCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2747))

Abstract

We study the problem of n users selfishly routing traffics through a shared network. Users route their traffics by choosing a path from their source to their destination of the traffic with the aim of minimizing their private latency. In such an environment Nash equilibria represent stable states of the system: no user can improve its private latency by unilaterally changing its strategy.

In the first model the network consists only of a single source and a single destination which are connected by m parallel links. Traffics are unsplittable. Users may route their traffics according to a probability distribution over the links. The social optimum minimizes the maximum load of a link. In the second model the network is arbitrary, but traffics are splittable among several paths leading from their source to their destination. The goal is to minimize the sum of the edge latencies.

Many interesting problems arise in such environments: A first one is the problem of analyzing the loss of efficiency due to the lack of central regulation, expressed in terms of the coordination ratio. A second problem is the Nashification problem, i.e. the problem of converting any given non-equilibrium routing into a Nash equilibrium without increasing the social cost. The Fully Mixed Nash Equilibrium Conjecture (FMNE Conjecture) states that a Nash equilibrium, in which every user routes along every possible edge with probability greater than zero, is a worst Nash equilibrium with respect to social cost. A third problem is to exactly specify the sub-models in which the FMNE Conjecture is valid. The well-known Braess’s Paradox shows that there exist networks, such that strict sub-networks perform better when users are selfish. A natural question is the following network design problem: Given a network, which edges should be removed to obtain the best possible Nash equilibrium.

We present complexity results for various problems in this setting, upper and lower bounds for the coordination ratio, and algorithms solving the problem of Nashification. We survey results on the validity of the FMNE Conjecture in the model of unsplittable flows, and for the model of splittable flows we survey results for the network design problem.

Partly supported by the DFG-SFB 376 and by the IST Program of the EU under contract numbers IST-1999-14186 (ALCOM-FT), and IST-2001-33116 (FLAGS).

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Authors and Affiliations

  1. Department of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    R. Feldmann, M. Gairing, Thomas Lücking, Burkhard Monien & Manuel Rode

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  1. R. Feldmann
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  2. M. Gairing
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  3. Thomas Lücking
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  4. Burkhard Monien
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  5. Manuel Rode
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Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Branislav Rovan

  2. Charles University, Prague, Czech Republic

    Peter Vojtáš

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Feldmann, R., Gairing, M., Lücking, T., Monien, B., Rode, M. (2003). Selfish Routing in Non-cooperative Networks: A Survey. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-45138-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40671-6

  • Online ISBN: 978-3-540-45138-9

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