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Approximate Pure Nash Equilibria via Lovász Local Lemma

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Internet and Network Economics (WINE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5929))

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Abstract

In many types of games, mixed Nash equilibria is not a satisfying solution concept, as mixed actions are hard to interpret. However, pure Nash equilibria, which are more natural, may not exist in many games. In this paper we explore a class of graphical games, where each player has a set of possible decisions to make, and the decisions have bounded interaction with one another. In our class of games, we show that while pure Nash equilibria may not exist, there is always a pure approximate Nash equilibrium. We also show that such an approximate Nash equilibrium can be found in polynomial time. Our proof is based on the Lovász local lemma and Talagrand inequality, a proof technique that can be useful in showing similar existence results for pure (approximate) Nash equilibria also in other classes of games.

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Author information

Authors and Affiliations

  1. Cornell University,  

    Thành Nguyen & Éva Tardos

Authors
  1. Thành Nguyen
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  2. Éva Tardos
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Editor information

Editors and Affiliations

  1. Department of Information and Systems, Sapienza University of Rome, Via Ariosto 25, 00185, Roma, Italy

    Stefano Leonardi

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© 2009 Springer-Verlag Berlin Heidelberg

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Nguyen, T., Tardos, É. (2009). Approximate Pure Nash Equilibria via Lovász Local Lemma. In: Leonardi, S. (eds) Internet and Network Economics. WINE 2009. Lecture Notes in Computer Science, vol 5929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10841-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-10841-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10840-2

  • Online ISBN: 978-3-642-10841-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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