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
Competitive Markov decision processes
Competitive Markov decision processes
Concurrent Omega-Regular Games
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
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
Stochastic Games with Branching-Time Winning Objectives
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Theoretical Computer Science - Components and objects
On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
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
Rational behaviour and strategy construction in infinite multiplayer games
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical 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
The complexity of nash equilibria in limit-average games
CONCUR'11 Proceedings of the 22nd 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
| Hi-index | 0.00 |
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game $\mathcal G$, does there exist a pure-strategy Nash equilibrium of $\mathcal G$ where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably decidable variant of the problem is to restrict the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSpace respectively.