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The Complexity of Nash Equilibria in Limit-Average Games

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CONCUR 2011 – Concurrency Theory (CONCUR 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6901))

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Abstract

We study the computational complexity of Nash equilibria in concurrent games with limit-average objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a Nash equilibrium in pure strategies is decidable, even if we put a constraint on the payoff of the equilibrium. Our undecidability result holds even for a restricted class of concurrent games, where nonzero rewards occur only on terminal states. Moreover, we show that the constrained existence problem is undecidable not only for concurrent games but for turn-based games with the same restriction on rewards. Finally, we prove that the constrained existence problem for Nash equilibria in (pure or randomised) stationary strategies is decidable and analyse its complexity.

This work was supported by ESF RNP “Games for Design and Verification” (GAMES), the French project ANR-06-SETI-003 (DOTS) and EPSRC grant EP/G050112/1.

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Author information

Authors and Affiliations

  1. LSV, CNRS & ENS Cachan, France

    Michael Ummels

  2. University of Liverpool, UK

    Dominik Wojtczak

  3. Computing Laboratory, Oxford University, UK

    Dominik Wojtczak

Authors
  1. Michael Ummels
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  2. Dominik Wojtczak
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Editor information

Editors and Affiliations

  1. Software Modeling and Verification, RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Joost-Pieter Katoen

  2. Fakultät für Ingenieurwesen, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen,, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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Ummels, M., Wojtczak, D. (2011). The Complexity of Nash Equilibria in Limit-Average Games. In: Katoen, JP., König, B. (eds) CONCUR 2011 – Concurrency Theory. CONCUR 2011. Lecture Notes in Computer Science, vol 6901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23217-6_32

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  • DOI: https://doi.org/10.1007/978-3-642-23217-6_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23216-9

  • Online ISBN: 978-3-642-23217-6

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