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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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Author information

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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Editor information

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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