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The Price of Anarchy for Polynomial Social Cost

Authors: Martin Gairing, Thomas Lücking, Marios Mavronicolas, and Burkhard Monien

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract

In this work, we consider an interesting variant of the well-studied KP model [KP99] for selfish routing that reflects some influence from the much older Wardrop [War52]. In the new model, user traffics are still unsplittable, while social cost is now the expectation of the sum, over all links, of a certain polynomial evaluated at the total latency incurred by all users choosing the link; we call it polynomial social cost. The polynomials that we consider have non-negative coefficients. We are interested in evaluating Nash equilibria in this model, and we use the Price of Anarchy as our evaluation measure. We prove the Fully Mixed Nash Equilibrium Conjecture for identical users and two links, and establish an approximate version of the conjecture for arbitrary many links. Moreover, we give upper bounds on the Price of Anarchy.

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Martin Gairing, Thomas Lücking, Marios Mavronicolas, and Burkhard Monien. The Price of Anarchy for Polynomial Social Cost. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{gairing_et_al:DagSemProc.05011.19,
  author =	{Gairing, Martin and L\"{u}cking, Thomas and Mavronicolas, Marios and Monien, Burkhard},
  title =	{{The Price of Anarchy for Polynomial Social Cost}},
  booktitle =	{Computing and Markets},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.19},
  URN =		{urn:nbn:de:0030-drops-2005},
  doi =		{10.4230/DagSemProc.05011.19},
  annote =	{Keywords: selfish routing , KP-model , price of anarchy , fully mixed Nash Equilibrium}
}

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The Price of Anarchy for Polynomial Social Cost

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