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Parameterized Two-Player Nash Equilibrium

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Abstract

We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.

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Notes

  1. Note that N[I]=N(I)∪I denotes the closed neighborhood if I.

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Authors and Affiliations

  1. Max-Planck-Institute for Informatics, Saarbrücken, Germany

    Danny Hermelin & Magnus Wahlström

  2. Humboldt-Universität zu Berlin, Berlin, Germany

    Chien-Chung Huang

  3. Utrecht University, Utrecht, The Netherlands

    Stefan Kratsch

Authors
  1. Danny Hermelin
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  2. Chien-Chung Huang
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  3. Stefan Kratsch
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  4. Magnus Wahlström
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Corresponding author

Correspondence to Magnus Wahlström.

Additional information

The third author acknowledges support by the Netherlands Organisation for Scientific Research (NWO), project “KERNELS: Combinatorial Analysis of Data Reduction”.

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Hermelin, D., Huang, CC., Kratsch, S. et al. Parameterized Two-Player Nash Equilibrium. Algorithmica 65, 802–816 (2013). https://doi.org/10.1007/s00453-011-9609-z

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