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International Conference on Theory and Applications of Models of Computation

TAMC 2015: Theory and Applications of Models of Computation pp 359–371Cite as

On Pure Nash Equilibria in Stochastic Games

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9076)

Abstract

Ummels and Wojtczak initiated the study of finding Nash equilibria in simple stochastic multi-player games satisfying specific bounds. They showed that deciding the existence of pure-strategy Nash equilibria (pureNE) where a fixed player wins almost surely is undecidable for games with \(9\) players. They also showed that the problem remains undecidable for the finite-strategy Nash equilibrium (finNE) with \(14\) players. In this paper we improve their undecidability results by showing that pureNE and finNE problems remain undecidable for \(5\) or more players.

Keywords

  • Stochastic games
  • Nash equilibrium
  • Pure strategy
  • Finite-state strategy

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Fig. 1.

Notes

  1. 1.

    The \(i\)th element of vector \(\bar{x}\) corresponds to the payoff of player \(i\).

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, IIT Bombay, Mumbai, India

    Ankush Das, Shankara Narayanan Krishna, Lakshmi Manasa & Ashutosh Trivedi

  2. Department of Computer Science, The University of Liverpool, Liverpool, UK

    Dominik Wojtczak

Authors
  1. Ankush Das
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  2. Shankara Narayanan Krishna
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  3. Lakshmi Manasa
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  4. Ashutosh Trivedi
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  5. Dominik Wojtczak
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Corresponding author

Correspondence to Lakshmi Manasa .

Editor information

Editors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    Rahul Jain

  2. National University of Singapore, Singapore, Singapore

    Sanjay Jain

  3. National University of Singapore, Singapore, Singapore

    Frank Stephan

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Das, A., Krishna, S.N., Manasa, L., Trivedi, A., Wojtczak, D. (2015). On Pure Nash Equilibria in Stochastic Games. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_31

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  • DOI: https://doi.org/10.1007/978-3-319-17142-5_31

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