Which Is the Worst-Case Nash Equilibrium?

  • Thomas Lücking
  • Marios Mavronicolas
  • Burkhard Monien
  • Manuel Rode
  • Paul Spirakis
  • Imrich Vrto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


A Nash equilibrium of a routing network represents a stable state of the network where no user finds it beneficial to unilaterally deviate from its routing strategy. In this work, we investigate the structure of such equilibria within the context of a certain game that models selfish routing for a set of n users each shipping its traffic over a network consisting of m parallel links. In particular, we are interested in identifying the worst-case Nash equilibrium – the one that maximizes social cost. Worst-case Nash equilibria were first introduced and studied in the pioneering work of Koutsoupias and Papadimitriou [9].

More specifically, we continue the study of the Conjecture of the Fully Mixed Nash Equilibrium, henceforth abbreviated as FMNE Conjecture, which asserts that the fully mixed Nash equilibrium, when existing, is the worst-case Nash equilibrium. (In the fully mixed Nash equilibrium, the mixed strategy of each user assigns (strictly) positive probability to every link.) We report substantial progress towards identifying the validity, methodologies to establish, and limitations of, the FMNE Conjecture.


Nash Equilibrium Social Cost Pure Strategy Link Capacity Cost Matrix 
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 2003

Authors and Affiliations

  • Thomas Lücking
    • 1
  • Marios Mavronicolas
    • 2
  • Burkhard Monien
    • 1
  • Manuel Rode
    • 1
  • Paul Spirakis
    • 3
    • 4
  • Imrich Vrto
    • 5
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Department of Computer ScienceUniversity of CyprusNicosiaCyprus
  3. 3.Computer Technology InstitutePatrasGreece
  4. 4.Department of Computer Engineering and InformaticsUniversity of Patras, RionPatrasGreece
  5. 5.Institute of MathematicsSlovak Academy of SciencesDúbravskaá 9Slovak Republic

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