Facets of the Fully Mixed Nash Equilibrium Conjecture

  • Rainer Feldmann
  • Marios Mavronicolas
  • Andreas Pieris
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4997)


In this work, we continue the study of the many facets of the Fully Mixed Nash Equilibrium Conjecture, henceforth abbreviated as the FMNE Conjecture, in selfish routing for the special case of n identical users over two (identical) parallel links. We introduce a new measure of Social Cost, defined to be the expectation of the square of the maximum congestion on a link; we call it Quadratic Maximum Social Cost. A Nash equilibrium (NE) is a stable state where no user can improve her (expected) latency by switching her mixed strategy; a worst-case NE is one that maximizes Quadratic Maximum Social Cost. In the fully mixed NE, all mixed strategies achieve full support.

Formulated within this framework is yet another facet of the FMNE Conjecture, which states that the fully mixed Nash equilibrium is the worst-case NE. We present an extensive proof of the FMNE Conjecture; the proof employs a mixture of combinatorial arguments and analytical estimations. Some of these analytical estimations are derived through some new bounds on generalized medians of the binomial distribution [22] we obtain, which are of independent interest.


Nash Equilibrium Binomial Distribution Mixed Strategy Pure Strategy Combinatorial Argument 
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 2008

Authors and Affiliations

  • Rainer Feldmann
    • 1
  • Marios Mavronicolas
    • 2
  • Andreas Pieris
    • 3
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Department of Computer Science, University of Cyprus, Nicosia CY-1678, Cyprus, Currently visiting Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, 33102 PaderbornGermany
  3. 3.Computing LaboratoryUniversity of OxfordOxfordUnited Kingdom

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