On Pure Nash Equilibria in Stochastic Games
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.
KeywordsStochastic games Nash equilibrium Pure strategy Finite-state strategy
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