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The Complexity of Approximate Nash Equilibrium in Congestion Games with Negative Delays

  • Frédéric Magniez
  • Michel de Rougemont
  • Miklos Santha
  • Xavier Zeitoun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

Abstract

We extend the study of the complexity of computing an ε-approximate Nash equilibrium in symmetric congestion games from the case of positive delay functions to delays of arbitrary sign. Our results show that with this extension the complexity has a richer structure, and it depends on the exact nature of the signs allowed. We first prove that in symmetric games with increasing delay functions and with α-bounded jump the ε-Nash dynamic converges in polynomial time when all delays are negative, similarly to the case of positive delays. We are able to extend this result to monotone delay functions. We then establish a hardness result for symmetric games with increasing delay functions and with α-bounded jump when the delays can be both positive and negative: in that case computing an ε-approximate Nash equilibrium becomes PLS-complete, even if each delay function is of constant sign or of constant absolute value.

Keywords

Nash Equilibrium Polynomial Time Pure Strategy Hardness Result Delay 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 2011

Authors and Affiliations

  • Frédéric Magniez
    • 1
  • Michel de Rougemont
    • 1
    • 2
  • Miklos Santha
    • 1
    • 3
  • Xavier Zeitoun
    • 1
    • 4
  1. 1.LIAFAUniv. Paris Diderot, CNRSParisFrance
  2. 2.Univ. Paris 2ParisFrance
  3. 3.Centre for Quantum TechnologiesNational University of SingaporeSingapore
  4. 4.Univ. Paris SudOrsayFrance

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