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Simple Stochastic Games and P-Matrix Generalized Linear Complementarity Problems

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Fundamentals of Computation Theory (FCT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3623))

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Abstract

We show that the problem of finding optimal strategies for both players in a simple stochastic game reduces to the generalized linear complementarity problem (GLCP) with a P-matrix, a well-studied problem whose hardness would imply NP = co–NP. This makes the rich GLCP theory and numerous existing algorithms available for simple stochastic games. As a special case, we get a reduction from binary simple stochastic games to the P-matrix linear complementarity problem (LCP).

The authors acknowledge support from the Swiss Science Foundation (SNF), Project No. 200021-100316/1.

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Authors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zürich, CH-8092, Zürich, Switzerland

    Bernd Gärtner & Leo Rüst

Authors
  1. Bernd Gärtner
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  2. Leo Rüst
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Editors and Affiliations

  1. Institut für Theoretische Informatik, Universität zu Lübeck, Germany

    Maciej Liśkiewicz

  2. Institut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Rüdiger Reischuk

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Gärtner, B., Rüst, L. (2005). Simple Stochastic Games and P-Matrix Generalized Linear Complementarity Problems. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_19

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  • DOI: https://doi.org/10.1007/11537311_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28193-1

  • Online ISBN: 978-3-540-31873-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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