On Pure Nash Equilibria in Stochastic Games

Ummels andWojtczak initiated the study of findingNash 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.