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A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

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Algorithmic Game Theory (SAGT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6386))

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Abstract

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, eliminating some of the difficulties involved in following the known indirect reduction.

A full version of this paper is available at http://arxiv.org/abs/1007.3886. Work supported in part by The Israel Science Foundation (grant No. 873/08).

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Authors and Affiliations

  1. Weizmann Institute of Science, PO Box 26, Rehovot, 76100, Israel

    Uriel Feige & Inbal Talgam-Cohen

Authors
  1. Uriel Feige
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  2. Inbal Talgam-Cohen
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Editors and Affiliations

  1. Lecturer, Department of Computer Science, University of Ioannina, Dourouti University Campus, 45110, Ioannina, Greece

    Spyros Kontogiannis

  2. Department of Informatics and Telecommunications Panepistimiopolis, Ilissia, Professor, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Elias Koutsoupias

  3. Computer Engineering and Informatics Department (CEID), University of Patras, 26500, Patras, Greece

    Paul G. Spirakis

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Feige, U., Talgam-Cohen, I. (2010). A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds) Algorithmic Game Theory. SAGT 2010. Lecture Notes in Computer Science, vol 6386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16170-4_13

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  • DOI: https://doi.org/10.1007/978-3-642-16170-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16169-8

  • Online ISBN: 978-3-642-16170-4

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