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On the Communication Complexity of Approximate Nash Equilibria

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Algorithmic Game Theory (SAGT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7615))

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Abstract

We study the problem of computing approximate Nash equilibria, in a setting where players initially know their own payoffs but not the payoffs of other players. In order for a solution of reasonable quality to be found, some amount of communication needs to take place between the players. We are interested in algorithms where the communication is substantially less than the contents of a payoff matrix, for example logarithmic in the size of the matrix. At one extreme is the case where the players do not communicate at all; for this case (with 2 players having n×n matrices) ε-Nash equilibria can be computed for ε = 3/4, while there is a lower bound of slightly more than 1/2 on the lowest ε achievable. When the communication is polylogarithmic in n, we show how to obtain ε = 0.438. For one-way communication we show that ε = 1/2 is the exact answer.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, U.K.

    Paul W. Goldberg

  2. Department of Information and Computing Science, Utrecht University, P.O. Box 80089, 3508TB, Utrecht, The Netherlands

    Arnoud Pastink

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  1. Paul W. Goldberg
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  2. Arnoud Pastink
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Editors and Affiliations

  1. Department de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, ALBCOM, Jordi Girona 1-3, 08034, Barcelona,, Spain

    Maria Serna

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Goldberg, P.W., Pastink, A. (2012). On the Communication Complexity of Approximate Nash Equilibria. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_17

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  • DOI: https://doi.org/10.1007/978-3-642-33996-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33995-0

  • Online ISBN: 978-3-642-33996-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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