The Computational Complexity of Weak Saddles

  • Felix Brandt
  • Markus Brill
  • Felix Fischer
  • Jan Hoffmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5814)

Abstract

We continue the recently initiated study of the computational aspects of weak saddles, an ordinal set-valued solution concept proposed by Shapley. Brandt et al. gave a polynomial-time algorithm for computing weak saddles in a subclass of matrix games, and showed that certain problems associated with weak saddles of bimatrix games are NP-complete. The important question of whether weak saddles can be found efficiently was left open. We answer this question in the negative by showing that finding weak saddles of bimatrix games is NP-hard, under polynomial-time Turing reductions. We moreover prove that recognizing weak saddles is coNP-complete, and that deciding whether a given action is contained in some weak saddle is hard for parallel access to NP and thus not even in NP unless the polynomial hierarchy collapses. Our hardness results are finally shown to carry over to a natural weakening of weak saddles.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Felix Brandt
    • 1
  • Markus Brill
    • 1
  • Felix Fischer
    • 1
  • Jan Hoffmann
    • 1
  1. 1.Institut für InformatikLudwig-Maximilians-Universität MünchenMünchenGermany

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