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Nash Equilibria in Discrete Routing Games with Convex Latency Functions

  • Martin Gairing
  • Thomas Lücking
  • Marios Mavronicolas
  • Burkhard Monien
  • Manuel Rode
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

We study Nash equilibria in a discrete routing game that combines features of the two most famous models for non-cooperative routing, the KP model [16] and the Wardrop model [27]. In our model, users share parallel links. A user strategy can be any probability distribution over the set of links. Each user tries to minimize its expected latency, where the latency on a link is described by an arbitrary non-decreasing, convex function. The social cost is defined as the sum of the users’ expected latencies. To the best of our knowledge, this is the first time that mixed Nash equilibria for routing games have been studied in combination with non-linear latency functions.

As our main result, we show that for identical users the social cost of any Nash equilibrium is bounded by the social cost of the fully mixed Nash equilibrium. A Nash equilibrium is called fully mixed if each user chooses each link with non-zero probability. We present a complete characterization of the instances for which a fully mixed Nash equilibrium exists, and prove that (in case of its existence) it is unique. Moreover, we give bounds on the coordination ratio and show that several results for the Wardrop model can be carried over to our discrete model.

Keywords

Nash Equilibrium Social Cost Mixed Strategy Pure Strategy Latency Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Martin Gairing
    • 1
  • Thomas Lücking
    • 1
  • Marios Mavronicolas
    • 2
  • Burkhard Monien
    • 1
  • Manuel Rode
    • 1
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Department of Computer ScienceUniversity of CyprusNicosiaCyprus

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