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Treewidth and Pure Nash Equilibria

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Parameterized and Exact Computation (IPEC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

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Abstract

We consider the complexity of w-PNE-GG, the problem of computing pure Nash equilibria in graphical games parameterized by the treewidth w of the underlying graph. It is well-known that the problem of computing pure Nash equilibria is NP-hard in general, but in polynomial time when restricted to games of bounded treewidth. We now prove that w-PNE-GG is W[1]-hard. Next we present a dynamic programming approach, which in contrast to previous algorithms that rely on reductions to other problems, directly attacks w-PNE-GG. We show that our algorithm is in FPT for games with strategy sets of bounded cardinality. Finally, we discuss the implications for solving games of O(logn) treewidth, the existence of polynomial kernels for w-PNE-GG, and constructing a sample or a maximum-payoff pure Nash equilibrium.

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zurich, 8092, Zurich, Switzerland

    Antonis Thomas

  2. Department of Information and Computing Sciences, Utrecht University, 3584 CC, Utrecht, The Netherlands

    Jan van Leeuwen

Authors
  1. Antonis Thomas
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  2. Jan van Leeuwen
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Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

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Thomas, A., van Leeuwen, J. (2013). Treewidth and Pure Nash Equilibria. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_29

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  • DOI: https://doi.org/10.1007/978-3-319-03898-8_29

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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