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Linear Complementarity and P-Matrices for Stochastic Games

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Perspectives of Systems Informatics (PSI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4378))

Abstract

We define the first nontrivial polynomially recognizable subclass of P-matrix Generalized Linear Complementarity Problems (GLCPs) with a subexponential pivot rule. No such classes/rules were previously known. We show that a subclass of Shapley turn-based stochastic games, subsuming Condon’s simple stochastic games, is reducible to the new class of GLCPs. Based on this we suggest the new strongly subexponential combinatorial algorithms for these games.

Supported by the Grant IG2003-2 067 from the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) and the Swedish Research Council (VR) grants “Infinite Games: Algorithms and Complexity” and “Interior-Point Methods for Infinite Games”.

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Authors and Affiliations

  1. IDSIA, Lugano, Switzerland and TU Wien, Austria

    Ola Svensson & Sergei Vorobyov

Authors
  1. Ola Svensson
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  2. Sergei Vorobyov
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Irina Virbitskaite Andrei Voronkov

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Svensson, O., Vorobyov, S. (2007). Linear Complementarity and P-Matrices for Stochastic Games. In: Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2006. Lecture Notes in Computer Science, vol 4378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70881-0_35

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  • DOI: https://doi.org/10.1007/978-3-540-70881-0_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70880-3

  • Online ISBN: 978-3-540-70881-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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