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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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Correspondence to Lakshmi Manasa .

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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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