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International Workshop on Combinatorial Algorithms

IWOCA 2010: Combinatorial Algorithms pp 121–124Cite as

Single Parameter FPT-Algorithms for Non-trivial Games

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6460))

Abstract

We know that k -Uniform Nash is W[2]-Complete when we consider imitation symmetric win-lose games (with k as the parameter) even when we have two players. However, this paper provides positive results regarding Nash equilibria. We show that consideration of sparse games or limitations of the support result in fixed-parameter algorithms with respect to one parameter only for the k -Uniform Nash problem. That is, we show that a sample uniform Nash equilibrium in r-sparse imitation symmetric win-lose games is not as hard because it can be found in FPT time (i.e polynomial in the size of the game, but maybe exponential in r). Moreover, we show that, although NP-Complete, the problem of Best Nash Equilibrium is also fix-parameter tractable.

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Authors and Affiliations

  1. School of ICT, Griffith University, Queensland, Australia, 4111

    Vladimir Estivill-Castro & Mahdi Parsa

Authors
  1. Vladimir Estivill-Castro
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  2. Mahdi Parsa
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of London, King’s College, The Strand, WC2R 2LS, London, UK

    Costas S. Iliopoulos

  2. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    William F. Smyth

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© 2011 Springer-Verlag Berlin Heidelberg

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Estivill-Castro, V., Parsa, M. (2011). Single Parameter FPT-Algorithms for Non-trivial Games. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_13

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  • DOI: https://doi.org/10.1007/978-3-642-19222-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19221-0

  • Online ISBN: 978-3-642-19222-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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