On Pure Nash Equilibria in Stochastic Games

  • Ankush Das
  • Shankara Narayanan Krishna
  • Lakshmi Manasa
  • Ashutosh Trivedi
  • Dominik Wojtczak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ankush Das
    • 1
  • Shankara Narayanan Krishna
    • 1
  • Lakshmi Manasa
    • 1
  • Ashutosh Trivedi
    • 1
  • Dominik Wojtczak
    • 2
  1. 1.Department of Computer Science and EngineeringIIT BombayMumbaiIndia
  2. 2.Department of Computer ScienceThe University of LiverpoolLiverpoolUK

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