Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The complexity of stochastic games
Information and Computation
The complexity of probabilistic verification
Journal of the ACM (JACM)
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Concurrent Omega-Regular Games
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Stochastic o-regular games
The complexity of Nash equilibria in infinite multiplayer games
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
The complexity of stochastic rabin and streett games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Complexity bounds for regular games
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Computing equilibria in two-player timed games via turn-based finite games
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Nash equilibria for reachability objectives in multi-player timed games
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Nash equilibrium in weighted concurrent timed games with reachability objectives
ICDCIT'12 Proceedings of the 8th international conference on Distributed Computing and Internet Technology
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We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with ω-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we single out several decidable restrictions of the problem. First, restricting the search space to stationary, or pure stationary, equilibria results in problems that are typically contained in PSPACE and NP, respectively. Second, we show that the existence of an equilibrium with a binary payoff (i.e. an equilibrium where each player either wins or loses with probability 1) is decidable. We also establish that the existence of a Nash equilibrium with a certain binary payoff entails the existence of an equilibrium with the same payoff in pure, finite-state strategies.