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On the Hardness and Existence of Quasi-Strict Equilibria

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Algorithmic Game Theory (SAGT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4997))

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Abstract

This paper investigates the computational properties of quasi-strict equilibrium, an attractive equilibrium refinement proposed by Harsanyi, which was recently shown to always exist in bimatrix games. We prove that deciding the existence of a quasi-strict equilibrium in games with more than two players is NP-complete. We further show that, in contrast to Nash equilibrium, the support of quasi-strict equilibrium in zero-sum games is unique and propose a linear program to compute quasi-strict equilibria in these games. Finally, we prove that every symmetric multi-player game where each player has two actions at his disposal contains an efficiently computable quasi-strict equilibrium which may itself be asymmetric.

This material is based upon work supported by the Deutsche Forschungsgemeinschaft under grant BR 2312/3-2.

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Authors and Affiliations

  1. Institut für Informatik, Universität München, 80538, München, Germany

    Felix Brandt & Felix Fischer

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  1. Felix Brandt
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  2. Felix Fischer
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Editors and Affiliations

  1. Institut für Informatik, Universität Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Burkhard Monien  & Ulf-Peter Schroeder  & 

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Brandt, F., Fischer, F. (2008). On the Hardness and Existence of Quasi-Strict Equilibria. In: Monien, B., Schroeder, UP. (eds) Algorithmic Game Theory. SAGT 2008. Lecture Notes in Computer Science, vol 4997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79309-0_26

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  • DOI: https://doi.org/10.1007/978-3-540-79309-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79308-3

  • Online ISBN: 978-3-540-79309-0

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