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International Symposium on Algorithmic Game Theory

SAGT 2009: Algorithmic Game Theory pp 323–334Cite as

Nash Equilibria and the Price of Anarchy for Flows over Time

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5814))

Abstract

We study Nash equilibria in the context of flows over time. Many results on static routing games have been obtained over the last ten years. In flows over time (also called dynamic flows), flow travels through a network over time and, as a consequence, flow values on edges are time-dependent. This more realistic setting has not been tackled from the viewpoint of algorithmic game theory yet; but there is a rich literature on game theoretic aspects of flows over time in the traffic community.

We present a novel characterization of Nash equilibria for flows over time. It turns out that Nash flows over time can be seen as a concatenation of special static flows. The underlying flow over time model is the so-called deterministic queuing model that is very popular in road traffic simulation and related fields. Based upon this, we prove the first known results on the price of anarchy for flows over time.

This work is supported by DFG Research Center Matheon “Mathematics for key technologies” in Berlin.

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Authors and Affiliations

  1. TU Berlin, Inst. f. Mathematik, MA 5-2, Str. des 17. Juni 136, 10623, Berlin, Germany

    Ronald Koch & Martin Skutella

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  1. Ronald Koch
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  2. Martin Skutella
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Editors and Affiliations

  1. Department of Computer Science, University of Cyprus, 75 Kallipoleos Str., P.O. Box 20537, CY-1678, Nicosia, Cyprus

    Marios Mavronicolas

  2. Department of Computer Science and Engineering, European University Cyprus, 6 Diogenes Str., CY-1516, Nicosia, Cyprus

    Vicky G. Papadopoulou

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Koch, R., Skutella, M. (2009). Nash Equilibria and the Price of Anarchy for Flows over Time. In: Mavronicolas, M., Papadopoulou, V.G. (eds) Algorithmic Game Theory. SAGT 2009. Lecture Notes in Computer Science, vol 5814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04645-2_29

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  • DOI: https://doi.org/10.1007/978-3-642-04645-2_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04644-5

  • Online ISBN: 978-3-642-04645-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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